diff --git a/.buildinfo b/.buildinfo new file mode 100644 index 000000000..88f95a6a3 --- /dev/null +++ b/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 96b7fc1f3c86e90a33bf3a8de5afed24 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/_sources/create_new_backend.rst.txt b/_sources/create_new_backend.rst.txt new file mode 100644 index 000000000..128328664 --- /dev/null +++ b/_sources/create_new_backend.rst.txt @@ -0,0 +1,499 @@ +.. + Copyright 2020 Intel Corporation + +.. _create_backend_wrappers: + +Integrating a Third-party Library to oneAPI Math Kernel Library (oneMKL) Interfaces +==================================================================================== + +This step-by-step tutorial provides examples for enabling new third-party libraries in oneMKL. + +oneMKL has a header-based implementation of the interface layer (``include`` directory) and a source-based implementation of the backend layer for each third-party library (``src`` directory). To enable a third-party library, you must update both parts of oneMKL and integrate the new third-party library to the oneMKL build and test systems. + +`1. Create Header Files`_ + +`2. Integrate Header Files`_ + +`3. Create Wrappers`_ + +`4. Integrate Wrappers To the Build System`_ + +`5. Update the Test System`_ + +.. _generate_header_files: + +1. Create Header Files +---------------------- + +For each new backend library, you should create the following two header files: + +* Header file with a declaration of entry points to the new third-party library wrappers +* Compiler-time dispatching interface (see `oneMKL Usage Models <../README.md#supported-usage-models>`_) for new third-party libraries + +**Header File Example**: command to generate the header file with a declaration of BLAS entry points in the oneapi::mkl::newlib namespace + +.. code-block:: bash + + python scripts/generate_backend_api.py include/oneapi/mkl/blas.hpp \ # Base header file + include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Output header file + oneapi::mkl::newlib # Wrappers namespace + +Code snippet of the generated header file ``include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp`` + +.. code-block:: cpp + + namespace oneapi { + namespace mkl { + namespace newlib { + + void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer &x, std::int64_t incx, + cl::sycl::buffer &result); + + + +**Compile-time Dispatching Interface Example**: command to generate the compile-time dispatching interface template instantiations for ``newlib`` and supported device ``newdevice`` + +.. code-block:: bash + + python scripts/generate_ct_instant.py include/oneapi/mkl/blas/detail/blas_ct_templates.hpp \ # Base header file + include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp \ # Output header file + include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Header file with declaration of entry points to wrappers + newlib \ # Library name + newdevice \ # Backend name + oneapi::mkl::newlib # Wrappers namespace + +Code snippet of the generated header file ``include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp`` + +.. code-block:: cpp + + namespace oneapi { + namespace mkl { + namespace blas { + + template <> + void asum(cl::sycl::queue &queue, std::int64_t n, + cl::sycl::buffer &x, std::int64_t incx, + cl::sycl::buffer &result) { + asum_precondition(queue, n, x, incx, result); + oneapi::mkl::newlib::asum(queue, n, x, incx, result); + asum_postcondition(queue, n, x, incx, result); + } + + +.. _integrate_header_files: + +2. Integrate Header Files +------------------------- + +Below you can see structure of oneMKL top-level include directory: + +:: + + include/ + oneapi/ + mkl/ + mkl.hpp -> oneMKL spec APIs + types.hpp -> oneMKL spec types + blas.hpp -> oneMKL BLAS APIs w/ pre-check/dispatching/post-check + detail/ -> implementation specific header files + exceptions.hpp -> oneMKL exception classes + backends.hpp -> list of oneMKL backends + backends_table.hpp -> table of backend libraries for each domain and device + get_device_id.hpp -> function to query device information from queue for Run-time dispatching + blas/ + predicates.hpp -> oneMKL BLAS pre-check post-check + detail/ -> BLAS domain specific implementation details + blas_loader.hpp -> oneMKL Run-time BLAS API + blas_ct_templates.hpp -> oneMKL Compile-time BLAS API general templates + cublas/ + blas_ct.hpp -> oneMKL Compile-time BLAS API template instantiations for + onemkl_blas_cublas.hpp -> backend wrappers library API + mklcpu/ + blas_ct.hpp -> oneMKL Compile-time BLAS API template instantiations for + onemkl_blas_mklcpu.hpp -> backend wrappers library API + / + / + + +To integrate the new third-party library to a oneMKL header-based part, following files from this structure should be updated: + +* ``include/oneapi/mkl/detail/backends.hpp``: add the new backend + + **Example**: add the ``newbackend`` backend + + .. code-block:: diff + + enum class backend { mklcpu, + + newbackend, + + + .. code-block:: diff + + static backendmap backend_map = { { backend::mklcpu, "mklcpu" }, + + { backend::newbackend, "newbackend" }, + +* ``include/oneapi/mkl/detail/backends_table.hpp``: add new backend library for supported domain(s) and device(s) + + **Example**: enable ``newlib`` for ``blas`` domain and ``newdevice`` device + + .. code-block:: diff + + enum class device : uint16_t { x86cpu, + ... + + newdevice + }; + + static std::map>> libraries = { + { domain::blas, + { { device::x86cpu, + { + #ifdef ENABLE_MKLCPU_BACKEND + LIB_NAME("blas_mklcpu") + #endif + } }, + + { device::newdevice, + + { + + #ifdef ENABLE_NEWLIB_BACKEND + + LIB_NAME("blas_newlib") + + #endif + + } }, + +* ``include/oneapi/mkl/detail/get_device_id.hpp``: add new device detection mechanism for Run-time dispatching + + **Example**: enable ``newdevice`` if the queue is targeted for the Host + + .. code-block:: diff + + inline oneapi::mkl::device get_device_id(cl::sycl::queue &queue) { + oneapi::mkl::device device_id; + + if (queue.is_host()) + + device_id=device::newdevice; + +* ``include/oneapi/mkl/blas.hpp``: include the generated header file for the compile-time dispatching interface (see `oneMKL Usage Models <../README.md#supported-usage-models>`_) + + **Example**: add ``include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp`` generated at the `1. Create Header Files`_ step + + .. code-block:: diff + + #include "oneapi/mkl/blas/detail/mklcpu/blas_ct.hpp" + #include "oneapi/mkl/blas/detail/mklgpu/blas_ct.hpp" + + #include "oneapi/mkl/blas/detail/newlib/blas_ct.hpp" + + +The new files generated at the `1. Create Header Files`_ step result in the following updated structure of the BLAS domain header files. + +.. code-block:: diff + + include/ + oneapi/ + mkl/ + blas.hpp -> oneMKL BLAS APIs w/ pre-check/dispatching/post-check + blas/ + predicates.hpp -> oneMKL BLAS pre-check post-check + detail/ -> BLAS domain specific implementation details + blas_loader.hpp -> oneMKL Run-time BLAS API + blas_ct_templates.hpp -> oneMKL Compile-time BLAS API general templates + cublas/ + blas_ct.hpp -> oneMKL Compile-time BLAS API template instantiations for + onemkl_blas_cublas.hpp -> backend wrappers library API + mklcpu/ + blas_ct.hpp -> oneMKL Compile-time BLAS API template instantiations for + onemkl_blas_mklcpu.hpp -> backend wrappers library API + + newlib/ + + blas_ct.hpp -> oneMKL Compile-time BLAS API template instantiations for + + onemkl_blas_newlib.hpp -> backend wrappers library API + / + / + +.. _generate_wrappers_and_cmake: + +3. Create Wrappers +------------------ +Wrappers convert Data Parallel C++ (DPC++) input data types to third-party library data types and call corresponding implementation from the third-party library. Wrappers for each third-party library are built to separate oneMKL backend libraries. The ``libonemkl.so`` dispatcher library loads the wrappers at run-time if you are using the interface for run-time dispatching, or you will link with them directly in case you are using the interface for compile-time dispatching (for more information see `oneMKL Usage Models <../README.md#supported-usage-models>`_). + +All wrappers and dispatcher library implementations are in the ``src`` directory: + +:: + + src/ + include/ + function_table_initializer.hpp -> general loader implementation w/ global libraries table + blas/ + function_table.hpp -> loaded BLAS functions declaration + blas_loader.cpp -> BLAS wrappers for loader + backends/ + cublas/ -> cuBLAS wrappers + mklcpu/ -> Intel oneMKL CPU wrappers + mklgpu/ -> Intel oneMKL GPU wrappers + / + / + +Each backend library should contain a table of all functions from the chosen domain. + +``scripts/generate_wrappers.py`` can help to generate wrappers with the "Not implemented" exception for all functions based on the provided header file. + +You can modify wrappers generated with this script to enable third-party library functionality. + +**Example**: generate wrappers for ``newlib`` based on the header files generated and integrated previously, and enable only one ``asum`` function + +The command below generates two new files: + +* ``src/blas/backends/newlib/newlib_wrappers.cpp`` - DPC++ wrappers for all functions from ``include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp`` +* ``src/blas/backends/newlib/newlib_wrappers_table_dyn.cpp`` - structure of symbols for run-time dispatcher (in the same location as wrappers), suffix ``_dyn`` indicates that this file is required for dynamic library only. + +.. code-block:: bash + + python scripts/generate_wrappers.py include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Base header file + src/blas/function_table.hpp \ # Declaration for structure of symbols + src/blas/backends/newlib/newlib_wrappers.cpp \ # Output wrappers + newlib # Library name + +You can then modify ``src/blas/backends/newlib/newlib_wrappers.cpp`` to enable the C function ``newlib_sasum`` from the third-party library ``libnewlib.so``. + +To enable this function: + +* Include the header file ``newlib.h`` with the ``newlib_sasum`` function declaration +* Convert all DPC++ parameters to proper C types: use the ``get_access`` method for input and output DPC++ buffers to get row pointers +* Submit the DPC++ kernel with a C function call to ``newlib`` as ``single_task`` + +The following code snippet is updated for ``src/blas/backends/newlib/newlib_wrappers.cpp``: + +.. code-block:: diff + + #include + + #include "oneapi/mkl/types.hpp" + + #include "oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp" + + + + #include "newlib.h" + + namespace oneapi { + namespace mkl { + namespace newlib { + + void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer &x, std::int64_t incx, + cl::sycl::buffer &result) { + - throw std::runtime_error("Not implemented for newlib"); + + queue.submit([&](cl::sycl::handler &cgh) { + + auto accessor_x = x.get_access(cgh); + + auto accessor_result = result.get_access(cgh); + + cgh.single_task([=]() { + + accessor_result[0] = ::newlib_sasum((const int)n, accessor_x.get_pointer(), (const int)incx); + + }); + + }); + } + + void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer &x, std::int64_t incx, + cl::sycl::buffer &result) { + throw std::runtime_error("Not implemented for newlib"); + } + +Updated structure of the ``src`` folder with the ``newlib`` wrappers: + +.. code-block:: diff + + src/ + blas/ + loader.hpp -> general loader implementation w/ global libraries table + function_table.hpp -> loaded BLAS functions declaration + blas_loader.cpp -> BLAS wrappers for loader + backends/ + cublas/ -> cuBLAS wrappers + mklcpu/ -> Intel oneMKL CPU wrappers + mklgpu/ -> Intel oneMKL GPU wrappers + + newlib/ + + newlib.h + + newlib_wrappers.cpp + + newlib_wrappers_table_dyn.cpp + / + / + +.. _integrate_backend_to_build_system: + +4. Integrate Wrappers to the Build System +----------------------------------------- +Here is the list of files that should be created/updated to integrate the new wrappers for the third-party library to the oneMKL build system: + +* Add the new option ``ENABLE_XXX_BACKEND`` for the new third-party library to the top of the ``CMakeList.txt`` file. + + **Example**: changes for ``newlib`` in the top of the ``CMakeList.txt`` file + + .. code-block:: diff + + option(ENABLE_MKLCPU_BACKEND "" ON) + option(ENABLE_MKLGPU_BACKEND "" ON) + + option(ENABLE_NEWLIB_BACKEND "" ON) + +* Add the new directory (``src//backends/``) with the wrappers for the new third-party library under the ``ENABLE_XXX_BACKEND`` condition to the ``src//backends/CMakeList.txt`` file. + + **Example**: changes for ``newlib`` in ``src/blas/backends/CMakeLists.txt`` + + .. code-block:: diff + + if(ENABLE_MKLCPU_BACKEND) + add_subdirectory(mklcpu) + endif() + + + + if(ENABLE_NEWLIB_BACKEND) + + add_subdirectory(newlib) + + endif() + +* Create the ``cmake/FindXXX.cmake`` cmake config file to find the new third-party library and its dependencies. + + **Example**: new config file ``cmake/FindNEWLIB.cmake`` for ``newlib`` + + .. code-block:: cmake + + include_guard() + # Find library by name in NEWLIB_ROOT cmake variable or environment variable NEWLIBROOT + find_library(NEWLIB_LIBRARY NAMES newlib + HINTS ${NEWLIB_ROOT} $ENV{NEWLIBROOT} + PATH_SUFFIXES "lib") + # Make sure that the library was found + include(FindPackageHandleStandardArgs) + find_package_handle_standard_args(NEWLIB REQUIRED_VARS NEWLIB_LIBRARY) + # Set cmake target for the library + add_library(ONEMKL::NEWLIB::NEWLIB UNKNOWN IMPORTED) + set_target_properties(ONEMKL::NEWLIB::NEWLIB PROPERTIES + IMPORTED_LOCATION ${NEWLIB_LIBRARY}) + +* Create the ``src//backends//CMakeList.txt`` cmake config file to specify how to build the backend layer for the new third-party library. + + ``scripts/generate_cmake.py`` can help to generate the initial ``src//backends//CMakeList.txt`` config file automatically for all files in the directory. + Note: all source files with the ``_dyn`` suffix are added to build if the target is a dynamic library only. + + **Example**: command to generate the cmake config file for the ``src/blas/backends/newlib`` directory + + .. code-block:: bash + + python scripts/generate_cmake.py src/blas/backends/newlib \ # Full path to the directory + newlib # Library name + + You should manually update the generated config file with information about the new ``cmake/FindXXX.cmake`` file and instructions about how to link with the third-party library. + + **Example**: update the generated ``src/blas/backends/newlib/CMakeLists.txt`` file + + .. code-block:: diff + + # Add third-party library + - # find_package(XXX REQUIRED) + + find_package(NEWLIB REQUIRED) + + .. code-block:: diff + + target_link_libraries(${LIB_OBJ} + PUBLIC ONEMKL::SYCL::SYCL + - # Add third-party library to link with here + + PUBLIC ONEMKL::NEWLIB::NEWLIB + ) + +Now you can build the backend library for ``newlib`` to make sure the third-party library integration was completed successfully (for more information, see `Build with cmake <../README.md#building-with-cmake>`_) + +.. code-block:: bash + + cd build/ + cmake .. -DNEWLIB_ROOT= \ + -DENABLE_MKLCPU_BACKEND=OFF \ + -DENABLE_MKLGPU_BACKEND=OFF \ + -DENABLE_NEWLIB_BACKEND=ON \ # Enable new third-party library backend + -DBUILD_FUNCTIONAL_TESTS=OFF # At this step we want build only + cmake --build . -j4 + +.. _integrate_backend_to_test_system: + +5. Update the Test System +------------------------- + +Update the following files to enable the new third-party library for unit tests: + +* ``src/config.hpp.in``: add a cmake option for the new third-party library so this macro can be propagated to unit tests + + **Example**: add ``ENABLE_NEWLIB_BACKEND`` + + .. code-block:: diff + + #cmakedefine ENABLE_MKLCPU_BACKEND + + #cmakedefine ENABLE_NEWLIB_BACKEND + +* ``tests/unit_tests/CMakeLists.txt``: add instructions about how to link tests with the new backend library + + **Example**: add the ``newlib`` backend library + + .. code-block:: diff + + if(ENABLE_MKLCPU_BACKEND) + add_dependencies(test_main_ct onemkl_blas_mklcpu) + if(BUILD_SHARED_LIBS) + list(APPEND ONEMKL_LIBRARIES onemkl_blas_mklcpu) + else() + list(APPEND ONEMKL_LIBRARIES -foffload-static-lib=${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libonemkl_blas_mklcpu.a) + find_package(MKL REQUIRED) + list(APPEND ONEMKL_LIBRARIES ${MKL_LINK_C}) + endif() + endif() + + + + if(ENABLE_NEWLIB_BACKEND) + + add_dependencies(test_main_ct onemkl_blas_newlib) + + if(BUILD_SHARED_LIBS) + + list(APPEND ONEMKL_LIBRARIES onemkl_blas_newlib) + + else() + + list(APPEND ONEMKL_LIBRARIES -foffload-static-lib=${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libonemkl_blas_newlib.a) + + find_package(NEWLIB REQUIRED) + + list(APPEND ONEMKL_LIBRARIES ONEMKL::NEWLIB::NEWLIB) + + endif() + + endif() + +* ``tests/unit_tests/include/test_helper.hpp``: add the helper function for the compile-time dispatching interface with the new backend, and specify the device for which it should be called + + **Example**: add the helper function for the ``newlib`` compile-time dispatching interface with ``newdevice`` if it is the Host + + .. code-block:: diff + + #ifdef ENABLE_MKLGPU_BACKEND + #define TEST_RUN_INTELGPU(q, func, args) \ + func args + #else + #define TEST_RUN_INTELGPU(q, func, args) + #endif + + + + #ifdef ENABLE_NEWLIB_BACKEND + + #define TEST_RUN_NEWDEVICE(q, func, args) \ + + func args + + #else + + #define TEST_RUN_NEWDEVICE(q, func, args) + + #endif + + .. code-block:: diff + + #define TEST_RUN_CT(q, func, args) \ + do { \ + + if (q.is_host()) \ + + TEST_RUN_NEWDEVICE(q, func, args); \ + + +* ``tests/unit_tests/main_test.cpp``: add the targeted device to the vector of devices to test + + **Example**: add the targeted device CPU for ``newlib`` + + .. code-block:: diff + + } + } + + + + #ifdef ENABLE_NEWLIB_BACKEND + + devices.push_back(cl::sycl::device(cl::sycl::host_selector())); + + #endif + +Now you can build and run functional testing for enabled third-party libraries (for more information see `Build with cmake <../README.md#building-with-cmake>`_). + +.. code-block:: bash + + cd build/ + cmake .. -DNEWLIB_ROOT= \ + -DENABLE_MKLCPU_BACKEND=OFF \ + -DENABLE_MKLGPU_BACKEND=OFF \ + -DENABLE_NEWLIB_BACKEND=ON \ + -DBUILD_FUNCTIONAL_TESTS=ON + cmake --build . -j4 + ctest diff --git a/_sources/domains/blas/asum.rst.txt b/_sources/domains/blas/asum.rst.txt new file mode 100644 index 000000000..7ccb31694 --- /dev/null +++ b/_sources/domains/blas/asum.rst.txt @@ -0,0 +1,158 @@ +.. _onemkl_blas_asum: + +asum +==== + +Computes the sum of magnitudes of the vector elements. + +.. _onemkl_blas_asum_description: + +.. rubric:: Description + +The ``asum`` routine computes the sum of the magnitudes of elements of a +real vector, or the sum of magnitudes of the real and imaginary parts +of elements of a complex vector: + +.. math:: + + result = \sum_{i=1}^{n}(|Re(x_i)| + |Im(x_i)|) + +where ``x`` is a vector with ``n`` elements. + +``asum`` supports the following precisions for data: + + .. list-table:: + :header-rows: 1 + + * - T + - T_res + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_asum_buffer: + +asum (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void asum(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void asum(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the scalar result is stored (the sum of magnitudes of + the real and imaginary parts of all elements of the vector). + + +.. _onemkl_blas_asum_usm: + +asum (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event asum(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event asum(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to input vector ``x``. The array holding the vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to the output matrix where the scalar result is stored + (the sum of magnitudes of the real and imaginary parts of all + elements of the vector). + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/axpy.rst.txt b/_sources/domains/blas/axpy.rst.txt new file mode 100644 index 000000000..9921f6e89 --- /dev/null +++ b/_sources/domains/blas/axpy.rst.txt @@ -0,0 +1,184 @@ +.. _onemkl_blas_axpy: + +axpy +==== + +Computes a vector-scalar product and adds the result to a vector. + +.. _onemkl_blas_axpy_description: + +.. rubric:: Description + +The ``axpy`` routines compute a scalar-vector product and add the result +to a vector: + +.. math:: + + y \leftarrow alpha * x + y + +where: + +``x`` and ``y`` are vectors of ``n`` elements, + +``alpha`` is a scalar. + +``axpy`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_axpy_buffer: + +axpy (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void axpy(sycl::queue &queue, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void axpy(sycl::queue &queue, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + alpha + Specifies the scalar alpha. + + x + Buffer holding input vector ``x``. The buffer must be of size at least + (1 + (``n`` – 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at least + (1 + (``n`` – 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_axpy_usm: + +axpy (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event axpy(sycl::queue &queue, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event axpy(sycl::queue &queue, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + alpha + Specifies the scalar alpha. + + x + Pointer to the input vector ``x``. The array holding the vector + ``x`` must be of size at least (1 + (``n`` – 1)*abs(``incx``)). See + :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to the input vector ``y``. The array holding the vector + ``y`` must be of size at least (1 + (``n`` – 1)*abs(``incy``)). See + :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/axpy_batch.rst.txt b/_sources/domains/blas/axpy_batch.rst.txt new file mode 100644 index 000000000..d3dc9e642 --- /dev/null +++ b/_sources/domains/blas/axpy_batch.rst.txt @@ -0,0 +1,247 @@ +.. _onemkl_blas_axpy_batch: + +axpy_batch +========== + +Computes a group of ``axpy`` operations. + +.. _onemkl_blas_axpy_batch_description: + +.. rubric:: Description + +The ``axpy_batch`` routines are batched versions of :ref:`onemkl_blas_axpy`, performing +multiple ``axpy`` operations in a single call. Each ``axpy`` +operation adds a scalar-vector product to a vector. + +``axpy_batch`` supports the following precisions for data. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_axpy_batch_usm: + +axpy_batch (USM Version) +------------------------ + +.. rubric:: Description + +The USM version of ``axpy_batch`` supports the group API and strided API. + +The group API operation is defined as +:: + + idx = 0 + for i = 0 … group_count – 1 + for j = 0 … group_size – 1 + X and Y are vectors in x[idx] and y[idx] + Y := alpha[i] * X + Y + idx := idx + 1 + end for + end for + +The strided API operation is defined as +:: + + for i = 0 … batch_size – 1 + X and Y are vectors at offset i * stridex, i * stridey in x and y + Y := alpha * X + Y + end for + +where: + +``alpha`` is scalar, + +``X`` and ``Y`` are vectors. + +For group API, ``x`` and ``y`` arrays contain the pointers for all the input vectors. +The total number of vectors in ``x`` and ``y`` are given by: + +.. math:: + + total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i] + +For strided API, ``x`` and ``y`` arrays contain all the input vectors. +The total number of vectors in ``x`` and ``y`` are given by the ``batch_size`` parameter. + +**Group API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event axpy_batch(sycl::queue &queue, + std::int64_t *n, + T *alpha, + const T **x, + std::int64_t *incx, + T **y, + std::int64_t *incy, + std::int64_t group_count, + std::int64_t *group_size, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event axpy_batch(sycl::queue &queue, + std::int64_t *n, + T *alpha, + const T **x, + std::int64_t *incx, + T **y, + std::int64_t *incy, + std::int64_t group_count, + std::int64_t *group_size, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Array of ``group_count`` integers. ``n[i]`` specifies the number of elements in vectors ``X`` and ``Y`` for every vector in group ``i``. + + alpha + Array of ``group_count`` scalar elements. ``alpha[i]`` specifies the scaling factor for vector ``X`` in group ``i``. + + x + Array of pointers to input vectors ``X`` with size ``total_batch_count``. + The size of array allocated for the ``X`` vector of the group ``i`` must be at least (1 + (``n[i]`` – 1)*abs(``incx[i]``))``. + See :ref:`matrix-storage` for more details. + + incx + Array of ``group_count`` integers. ``incx[i]`` specifies the stride of vector ``X`` in group ``i``. + + y + Array of pointers to input/output vectors ``Y`` with size ``total_batch_count``. + The size of array allocated for the ``Y`` vector of the group ``i`` must be at least (1 + (``n[i]`` – 1)*abs(``incy[i]``))``. + See :ref:`matrix-storage` for more details. + + incy + Array of ``group_count`` integers. ``incy[i]`` specifies the stride of vector ``Y`` in group ``i``. + + group_count + Number of groups. Must be at least 0. + + group_size + Array of ``group_count`` integers. ``group_size[i]`` specifies the number of ``axpy`` operations in group ``i``. + Each element in ``group_size`` must be at least 0. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Array of pointers holding the ``Y`` vectors, overwritten by ``total_batch_count`` ``axpy`` operations of the form + ``alpha`` * ``X`` + ``Y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + +**Strided API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event axpy_batch(sycl::queue &queue, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + std::int64_t stridex, + T *y, + std::int64_t incy, + std::int64_t stridey, + std::int64_t batch_size, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event axpy_batch(sycl::queue &queue, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + std::int64_t stridex, + T *y, + std::int64_t incy, + std::int64_t stridey, + std::int64_t batch_size, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in ``X`` and ``Y``. + + alpha + Specifies the scalar ``alpha``. + + x + Pointer to input vectors ``X`` with size ``stridex`` * ``batch_size``. + + incx + Stride of vector ``X``. + + stridex + Stride between different ``X`` vectors. + + y + Pointer to input/output vectors ``Y`` with size ``stridey`` * ``batch_size``. + + incy + Stride of vector ``Y``. + + stridey + Stride between different ``Y`` vectors. + + batch_size + Specifies the number of ``axpy`` operations to perform. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Output vectors, overwritten by ``batch_size`` ``axpy`` operations of the form + ``alpha`` * ``X`` + ``Y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:**:ref:`blas-like-extensions` diff --git a/_sources/domains/blas/blas-level-1-routines.rst.txt b/_sources/domains/blas/blas-level-1-routines.rst.txt new file mode 100644 index 000000000..c96c2d54c --- /dev/null +++ b/_sources/domains/blas/blas-level-1-routines.rst.txt @@ -0,0 +1,76 @@ +.. _blas-level-1-routines: + +BLAS Level 1 Routines +===================== + + +.. container:: + + + BLAS Level 1 includes routines which perform + vector-vector operations as described in the following table. + + + .. container:: tablenoborder + + + .. list-table:: + :header-rows: 1 + + * - Routines + - Description + * - :ref:`onemkl_blas_asum` + - Sum of vector magnitudes + * - :ref:`onemkl_blas_axpy` + - Scalar-vector product + * - :ref:`onemkl_blas_copy` + - Copy vector + * - :ref:`onemkl_blas_dot` + - Dot product + * - :ref:`onemkl_blas_sdsdot` + - Dot product with double precision + * - :ref:`onemkl_blas_dotc` + - Dot product conjugated + * - :ref:`onemkl_blas_dotu` + - Dot product unconjugated + * - :ref:`onemkl_blas_nrm2` + - Vector 2-norm (Euclidean norm) + * - :ref:`onemkl_blas_rot` + - Plane rotation of points + * - :ref:`onemkl_blas_rotg` + - Generate Givens rotation of points + * - :ref:`onemkl_blas_rotm` + - Modified Givens plane rotation of points + * - :ref:`onemkl_blas_rotmg` + - Generate modified Givens plane rotation of points + * - :ref:`onemkl_blas_scal` + - Vector-scalar product + * - :ref:`onemkl_blas_swap` + - Vector-vector swap + * - :ref:`onemkl_blas_iamax` + - Index of the maximum absolute value element of a vector + * - :ref:`onemkl_blas_iamin` + - Index of the minimum absolute value element of a vector + +.. toctree:: + :hidden: + + asum + axpy + copy + dot + sdsdot + dotc + dotu + nrm2 + rot + rotg + rotm + rotmg + scal + swap + iamax + iamin + + +**Parent topic:** :ref:`onemkl_blas` diff --git a/_sources/domains/blas/blas-level-2-routines.rst.txt b/_sources/domains/blas/blas-level-2-routines.rst.txt new file mode 100644 index 000000000..427acbc9b --- /dev/null +++ b/_sources/domains/blas/blas-level-2-routines.rst.txt @@ -0,0 +1,105 @@ +.. _blas-level-2-routines: + +BLAS Level 2 Routines +===================== + + +.. container:: + + + BLAS Level 2 includes routines which perform + matrix-vector operations as described in the following table. + + + .. container:: tablenoborder + + + .. list-table:: + :header-rows: 1 + + * - Routines + - Description + * - :ref:`onemkl_blas_gbmv` + - Matrix-vector product using a general band matrix + * - :ref:`onemkl_blas_gemv` + - Matrix-vector product using a general matrix + * - :ref:`onemkl_blas_ger` + - Rank-1 update of a general matrix + * - :ref:`onemkl_blas_gerc` + - Rank-1 update of a conjugated general matrix + * - :ref:`onemkl_blas_geru` + - Rank-1 update of a general matrix, unconjugated + * - :ref:`onemkl_blas_hbmv` + - Matrix-vector product using a Hermitian band matrix + * - :ref:`onemkl_blas_hemv` + - Matrix-vector product using a Hermitian matrix + * - :ref:`onemkl_blas_her` + - Rank-1 update of a Hermitian matrix + * - :ref:`onemkl_blas_her2` + - Rank-2 update of a Hermitian matrix + * - :ref:`onemkl_blas_hpmv` + - Matrix-vector product using a Hermitian packed matrix + * - :ref:`onemkl_blas_hpr` + - Rank-1 update of a Hermitian packed matrix + * - :ref:`onemkl_blas_hpr2` + - Rank-2 update of a Hermitian packed matrix + * - :ref:`onemkl_blas_sbmv` + - Matrix-vector product using symmetric band matrix + * - :ref:`onemkl_blas_spmv` + - Matrix-vector product using a symmetric packed matrix + * - :ref:`onemkl_blas_spr` + - Rank-1 update of a symmetric packed matrix + * - :ref:`onemkl_blas_spr2` + - Rank-2 update of a symmetric packed matrix + * - :ref:`onemkl_blas_symv` + - Matrix-vector product using a symmetric matrix + * - :ref:`onemkl_blas_syr` + - Rank-1 update of a symmetric matrix + * - :ref:`onemkl_blas_syr2` + - Rank-2 update of a symmetric matrix + * - :ref:`onemkl_blas_tbmv` + - Matrix-vector product using a triangular band matrix + * - :ref:`onemkl_blas_tbsv` + - Solution of a linear system of equations with a triangular band matrix + * - :ref:`onemkl_blas_tpmv` + - Matrix-vector product using a triangular packed matrix + * - :ref:`onemkl_blas_tpsv` + - Solution of a linear system of equations with a triangular packed matrix + * - :ref:`onemkl_blas_trmv` + - Matrix-vector product using a triangular matrix + * - :ref:`onemkl_blas_trsv` + - Solution of a linear system of equations with a triangular matrix + + + + +.. toctree:: + :hidden: + + gbmv + gemv + ger + gerc + geru + hbmv + hemv + her + her2 + hpmv + hpr + hpr2 + sbmv + spmv + spr + spr2 + symv + syr + syr2 + tbmv + tbsv + tpmv + tpsv + trmv + trsv + +**Parent topic:** :ref:`onemkl_blas` diff --git a/_sources/domains/blas/blas-level-3-routines.rst.txt b/_sources/domains/blas/blas-level-3-routines.rst.txt new file mode 100644 index 000000000..bb7f3f4d6 --- /dev/null +++ b/_sources/domains/blas/blas-level-3-routines.rst.txt @@ -0,0 +1,55 @@ +.. _blas-level-3-routines: + +BLAS Level 3 Routines +===================== + + +.. container:: + + BLAS Level 3 includes routines which perform + matrix-matrix operations as described in the following table. + + + .. container:: tablenoborder + + + .. list-table:: + :header-rows: 1 + + * - Routines + - Description + * - :ref:`onemkl_blas_gemm` + - Computes a matrix-matrix product with general matrices. + * - :ref:`onemkl_blas_hemm` + - Computes a matrix-matrix product where one input matrix is Hermitian and one is general. + * - :ref:`onemkl_blas_herk` + - Performs a Hermitian rank-k update. + * - :ref:`onemkl_blas_her2k` + - Performs a Hermitian rank-2k update. + * - :ref:`onemkl_blas_symm` + - Computes a matrix-matrix product where one input matrix is symmetric and one matrix is general. + * - :ref:`onemkl_blas_syrk` + - Performs a symmetric rank-k update. + * - :ref:`onemkl_blas_syr2k` + - Performs a symmetric rank-2k update. + * - :ref:`onemkl_blas_trmm` + - Computes a matrix-matrix product where one input matrix is triangular and one input matrix is general. + * - :ref:`onemkl_blas_trsm` + - Solves a triangular matrix equation (forward or backward solve). + + + +.. toctree:: + :hidden: + + gemm + hemm + herk + her2k + symm + syrk + syr2k + trmm + trsm + +**Parent topic:** :ref:`onemkl_blas` diff --git a/_sources/domains/blas/blas-like-extensions.rst.txt b/_sources/domains/blas/blas-like-extensions.rst.txt new file mode 100644 index 000000000..6f7c72003 --- /dev/null +++ b/_sources/domains/blas/blas-like-extensions.rst.txt @@ -0,0 +1,50 @@ +.. _blas-like-extensions: + +BLAS-like Extensions +==================== + + +.. container:: + + + oneAPI Math Kernel Library DPC++ provides additional routines to + extend the functionality of the BLAS routines. These include routines + to compute many independent vector-vector and matrix-matrix operations. + + The following table lists the BLAS-like extensions with their descriptions. + + + .. container:: tablenoborder + + + .. list-table:: + :header-rows: 1 + + * - Routines + - Description + * - :ref:`onemkl_blas_axpy_batch` + - Computes groups of vector-scalar products added to a vector. + * - :ref:`onemkl_blas_gemm_batch` + - Computes groups of matrix-matrix products with general matrices. + * - :ref:`onemkl_blas_trsm_batch` + - Solves a triangular matrix equation for a group of matrices. + * - :ref:`onemkl_blas_gemmt` + - Computes a matrix-matrix product with general matrices, but updates + only the upper or lower triangular part of the result matrix. + * - :ref:`onemkl_blas_gemm_bias` + - Computes a matrix-matrix product using general integer matrices with bias + + + + + +.. toctree:: + :hidden: + + axpy_batch + gemm_batch + trsm_batch + gemmt + gemm_bias + +**Parent topic:** :ref:`onemkl_blas` diff --git a/_sources/domains/blas/blas.rst.txt b/_sources/domains/blas/blas.rst.txt new file mode 100644 index 000000000..e37dbecc2 --- /dev/null +++ b/_sources/domains/blas/blas.rst.txt @@ -0,0 +1,15 @@ +.. _onemkl_blas: + +BLAS Routines ++++++++++++++ + +oneMKL provides DPC++ interfaces to the Basic Linear Algebra Subprograms (BLAS) routines (Level1, Level2, Level3), as well as several BLAS-like extension routines. + +.. toctree:: + :maxdepth: 1 + + blas-level-1-routines.rst + blas-level-2-routines.rst + blas-level-3-routines.rst + blas-like-extensions.rst + diff --git a/_sources/domains/blas/copy.rst.txt b/_sources/domains/blas/copy.rst.txt new file mode 100644 index 000000000..939b3ef6f --- /dev/null +++ b/_sources/domains/blas/copy.rst.txt @@ -0,0 +1,159 @@ +.. _onemkl_blas_copy: + +copy +==== + +Copies a vector to another vector. + +.. _onemkl_blas_copy_description: + +.. rubric:: Description + +The ``copy`` routines copy one vector to another: + +.. math:: + + y \leftarrow x + +where ``x`` and ``y`` are vectors of n elements. + +``copy`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + + +.. _onemkl_blas_copy_buffer: + +copy (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void copy(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void copy(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at least + (1 + (``n`` – 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_copy_usm: + +copy (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event copy(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event copy(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to the input vector ``x``. The array holding the vector + ``x`` must be of size at least (1 + (``n`` – 1)*abs(``incx``)). See + :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/dot.rst.txt b/_sources/domains/blas/dot.rst.txt new file mode 100644 index 000000000..e2a8b4723 --- /dev/null +++ b/_sources/domains/blas/dot.rst.txt @@ -0,0 +1,182 @@ +.. _onemkl_blas_dot: + +dot +=== + +Computes the dot product of two real vectors. + +.. _onemkl_blas_dot_description: + +.. rubric:: Description + +The ``dot`` routines perform a dot product between two vectors: + +.. math:: + + result = \sum_{i=1}^{n}X_iY_i + +``dot`` supports the following precisions for data. + + .. list-table:: + :header-rows: 1 + + * - T + - T_res + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``float`` + - ``double`` + +.. container:: Note + + .. rubric:: Note + :class: NoteTipHead + + For the mixed precision version (inputs are float while result is + double), the dot product is computed with double precision. + +.. _onemkl_blas_dot_buffer: + +dot (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void dot(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void dot(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + x + Buffer holding input vector ``x``. The buffer must be of size at least + (1 + (``n`` – 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at least + (1 + (``n`` – 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the result (a scalar) will be stored. + + +.. _onemkl_blas_dot_usm: + +dot (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event dot(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T_res *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event dot(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T_res *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + x + Pointer to the input vector ``x``. The array holding the vector ``x`` + must be of size at least (1 + (``n`` – 1)*abs(``incx``)). See + :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to the input vector ``y``. The array holding the vector ``y`` + must be of size at least (1 + (``n`` – 1)*abs(``incy``)). See + :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to where the result (a scalar) will be stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/dotc.rst.txt b/_sources/domains/blas/dotc.rst.txt new file mode 100644 index 000000000..c776c03a5 --- /dev/null +++ b/_sources/domains/blas/dotc.rst.txt @@ -0,0 +1,170 @@ +.. _onemkl_blas_dotc: + +dotc +==== + +Computes the dot product of two complex vectors, conjugating the first vector. + +.. _onemkl_blas_dotc_description: + +.. rubric:: Description + +The ``dotc`` routines perform a dot product between two complex +vectors, conjugating the first of them: + +.. math:: + + result = \sum_{i=1}^{n}\overline{X_i}Y_i + +``dotc`` supports the following precisions for data. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_dotc_buffer: + +dotc (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void dotc(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void dotc(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + The number of elements in vectors ``x`` and ``y``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + The stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details.. + + incy + The stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + result + The buffer where the result (a scalar) is stored. + + +.. _onemkl_blas_dotc_usm: + +dotc (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void dotc(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void dotc(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + The number of elements in vectors ``x`` and ``y``. + + x + Pointer to input vector ``x``. The array holding the input + vector ``x`` must be of size at least (1 + (``n`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + The stride of vector ``x``. + + y + Pointer to input vector ``y``. The array holding the input + vector ``y`` must be of size at least (1 + (``n`` - + 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details.. + + incy + The stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + The pointer to where the result (a scalar) is stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/dotu.rst.txt b/_sources/domains/blas/dotu.rst.txt new file mode 100644 index 000000000..ff3503973 --- /dev/null +++ b/_sources/domains/blas/dotu.rst.txt @@ -0,0 +1,170 @@ +.. _onemkl_blas_dotu: + +dotu +==== + +Computes the dot product of two complex vectors. + +.. _onemkl_blas_dotu_description: + +.. rubric:: Description + +The ``dotu`` routines perform a dot product between two complex vectors: + +.. math:: + + result = \sum_{i=1}^{n}X_iY_i + +``dotu`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_dotu_buffer: + +dotu (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void dotu(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void dotu(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the result (a scalar) is stored. + + +.. _onemkl_blas_dotu_usm: + +dotu (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event dotu(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event dotu(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + x + Pointer to the input vector ``x``. The array holding input + vector ``x`` must be of size at least (1 + (``n`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input vector ``y``. The array holding input vector + ``y`` must be of size at least (1 + (``n`` - 1)*abs(``incy``)). + See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to where the result (a scalar) is stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/gbmv.rst.txt b/_sources/domains/blas/gbmv.rst.txt new file mode 100644 index 000000000..fbc52e864 --- /dev/null +++ b/_sources/domains/blas/gbmv.rst.txt @@ -0,0 +1,285 @@ +.. _onemkl_blas_gbmv: + +gbmv +==== + +Computes a matrix-vector product with a general band matrix. + +.. _onemkl_blas_gbmv_description: + +.. rubric:: Description + +The ``gbmv`` routines compute a scalar-matrix-vector product and add +the result to a scalar-vector product, with a general band matrix. +The operation is defined as + +.. math:: + + y \leftarrow alpha*op(A)*x + beta*y + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``m``-by-``n`` matrix with ``kl`` sub-diagonals and +``ku`` super-diagonals, + +``x`` and ``y`` are vectors. + +``gbmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_gbmv_buffer: + +gbmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gbmv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + std::int64_t kl, + std::int64_t ku, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gbmv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + std::int64_t kl, + std::int64_t ku, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. + See + :ref:`onemkl_datatypes` for more + details. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + kl + Number of sub-diagonals of the matrix ``A``. Must be at least + zero. + + ku + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least ``lda``\ \*\ ``n`` + if column major layout is used or at least ``lda``\ \*\ ``m`` + if row major layout is used. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``kl`` + + ``ku`` + 1), and positive. + + x + Buffer holding input vector ``x``. The length ``len`` of vector + ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` is + transposed. The buffer must be of size at least (1 + (``len`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The length ``len`` of + vector ``y`` is ``m``, if ``A`` is not transposed, and ``n`` if + ``A`` is transposed. The buffer must be of size at least (1 + + (``len`` - 1)*abs(``incy``)) where ``len`` is this length. See + :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_gbmv_usm: + +gbmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gbmv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + std::int64_t kl, + std::int64_t ku, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gbmv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + std::int64_t kl, + std::int64_t ku, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See + :ref:`onemkl_datatypes` for + more details. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + kl + Number of sub-diagonals of the matrix ``A``. Must be at least + zero. + + ku + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n`` if column + major layout is used or at least ``lda``\ \*\ ``m`` if row + major layout is used. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``kl`` + + ``ku`` + 1), and positive. + + x + Pointer to input vector ``x``. The length ``len`` of vector + ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` + is transposed. The array holding input vector ``x`` must be of + size at least (1 + (``len`` - 1)*abs(``incx``)). See + :ref:`matrix-storage` for more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The length ``len`` of + vector ``y`` is ``m``, if ``A`` is not transposed, and ``n`` if + ``A`` is transposed. The array holding input/output vector + ``y`` must be of size at least (1 + (``len`` - + 1)*abs(``incy``)) where ``len`` is this length. + See :ref:`matrix-storage` for more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/gemm.rst.txt b/_sources/domains/blas/gemm.rst.txt new file mode 100644 index 000000000..f8265f1ce --- /dev/null +++ b/_sources/domains/blas/gemm.rst.txt @@ -0,0 +1,451 @@ +.. _onemkl_blas_gemm: + +gemm +==== + +Computes a matrix-matrix product with general matrices. + +.. _onemkl_blas_gemm_description: + +.. rubric:: Description + +The ``gemm`` routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, with general matrices. The +operation is defined as: + +.. math:: + + C \leftarrow alpha*op(A)*op(B) + beta*C + +where: + +op(``X``) is one of op(``X``) = ``X``, or op(``X``) = ``X``\ :sup:`T`, or +op(``X``) = ``X``\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A``, ``B`` and ``C`` are matrices, + +``op(A)`` is an ``m``-by-``k`` matrix, + +``op(B)`` is a ``k``-by-``n`` matrix, + +``C`` is an ``m``-by-``n`` matrix. + +``gemm`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - Ts + - Ta + - Tb + - Tc + * - ``float`` + - ``half`` + - ``half`` + - ``float`` + * - ``half`` + - ``half`` + - ``half`` + - ``half`` + * - ``float`` + - ``float`` + - ``float`` + - ``float`` + * - ``double`` + - ``double`` + - ``double`` + - ``double`` + * - ``std::complex`` + - ``std::complex`` + - ``std::complex`` + - ``std::complex`` + * - ``std::complex`` + - ``std::complex`` + - ``std::complex`` + - ``std::complex`` + +.. _onemkl_blas_gemm_buffer: + +gemm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gemm(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + Ts beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gemm(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + Ts beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Specifies the form of op(``A``), the transposition operation + applied to ``A``. + + transb + Specifies the form of op(``B``), the transposition operation + applied to ``B``. + + m + Specifies the number of rows of the matrix op(``A``) and of the + matrix ``C``. The value of m must be at least zero. + + n + Specifies the number of columns of the matrix op(``B``) and the + number of columns of the matrix ``C``. The value of n must be at + least zero. + + k + Specifies the number of columns of the matrix op(``A``) and the + number of rows of the matrix op(``B``). The value of k must be at + least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + The buffer holding the input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m`` + * - Row major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k`` + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``m``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``m``. + + b + The buffer holding the input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n`` + + See :ref:`matrix-storage` for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + The buffer holding the input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + +.. container:: section + + .. rubric:: Output Parameters + + c + The buffer, which is overwritten by + ``alpha``\ \*\ op(``A``)*op(``B``) + ``beta``\ \*\ ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized before + calling ``gemm``. + + +.. _onemkl_blas_gemm_usm: + +gemm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gemm(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + const Ta *a, + std::int64_t lda, + const Tb *b, + std::int64_t ldb, + Ts beta, + Tc *c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gemm(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + const Ta *a, + std::int64_t lda, + const Tb *b, + std::int64_t ldb, + Ts beta, + Tc *c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Specifies the form of op(``A``), the transposition operation + applied to ``A``. + + + transb + Specifies the form of op(``B``), the transposition operation + applied to ``B``. + + + m + Specifies the number of rows of the matrix op(``A``) and of the + matrix ``C``. The value of m must be at least zero. + + + n + Specifies the number of columns of the matrix op(``B``) and the + number of columns of the matrix ``C``. The value of n must be + at least zero. + + + k + Specifies the number of columns of the matrix op(``A``) and the + number of rows of the matrix op(``B``). The value of k must be + at least zero. + + + alpha + Scaling factor for the matrix-matrix product. + + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m`` + * - Row major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k`` + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``m``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``m``. + + b + Pointer to input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n`` + + See :ref:`matrix-storage` for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + The pointer to input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by + ``alpha``\ \*\ op(``A``)*op(``B``) + ``beta``\ \*\ ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling ``gemm``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/gemm_batch.rst.txt b/_sources/domains/blas/gemm_batch.rst.txt new file mode 100644 index 000000000..8c146bb66 --- /dev/null +++ b/_sources/domains/blas/gemm_batch.rst.txt @@ -0,0 +1,607 @@ +.. _onemkl_blas_gemm_batch: + +gemm_batch +========== + +Computes a group of ``gemm`` operations. + +.. _onemkl_blas_gemm_batch_description: + +.. rubric:: Description + +The ``gemm_batch`` routines are batched versions of :ref:`onemkl_blas_gemm`, performing +multiple ``gemm`` operations in a single call. Each ``gemm`` +operation perform a matrix-matrix product with general matrices. + +``gemm_batch`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_gemm_batch_buffer: + +gemm_batch (Buffer Version) +--------------------------- + +.. rubric:: Description + +The buffer version of ``gemm_batch`` supports only the strided API. + +The strided API operation is defined as: +:: + + for i = 0 … batch_size – 1 + A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c. + C := alpha * op(A) * op(B) + beta * C + end for + +where: + +op(X) is one of op(X) = X, or op(X) = X\ :sup:`T`, or op(X) = X\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A``, ``B``, and ``C`` are matrices, + +op(``A``) is ``m`` x ``k``, op(``B``) is +``k`` x ``n``, and ``C`` is ``m`` x ``n``. + +The ``a``, ``b`` and ``c`` buffers contain all the input matrices. The stride +between matrices is given by the stride parameter. The total number +of matrices in ``a``, ``b`` and ``c`` buffers is given by the ``batch_size`` parameter. + +**Strided API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gemm_batch(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + std::int64_t stridea, + sycl::buffer &b, + std::int64_t ldb, + std::int64_t strideb, + T beta, + sycl::buffer &c, + std::int64_t ldc, + std::int64_t stridec, + std::int64_t batch_size) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gemm_batch(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + std::int64_t stridea, + sycl::buffer &b, + std::int64_t ldb, + std::int64_t strideb, + T beta, + sycl::buffer &c, + std::int64_t ldc, + std::int64_t stridec, + std::int64_t batch_size) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Specifies op(``A``) the transposition operation applied to the + matrices ``A``. See :ref:`onemkl_datatypes` for more details. + + transb + Specifies op(``B``) the transposition operation applied to the + matrices ``B``. See :ref:`onemkl_datatypes` for more details. + + m + Number of rows of op(``A``) and ``C``. Must be at least zero. + + + n + Number of columns of op(``B``) and ``C``. Must be at least zero. + + + k + Number of columns of op(``A``) and rows of op(``B``). Must be at + least zero. + + alpha + Scaling factor for the matrix-matrix products. + + a + Buffer holding the input matrices ``A`` with size ``stridea`` * ``batch_size``. + + lda + The leading dimension of the matrices ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``m``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``m``. + + stridea + Stride between different ``A`` matrices. + + b + Buffer holding the input matrices ``B`` with size ``strideb`` * ``batch_size``. + + ldb + The leading dimension of the matrices``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + strideb + Stride between different ``B`` matrices. + + beta + Scaling factor for the matrices ``C``. + + c + Buffer holding input/output matrices ``C`` with size ``stridec`` * ``batch_size``. + + ldc + The leading dimension of the mattrices ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + stridec + Stride between different ``C`` matrices. Must be at least + ``ldc`` * ``n``. + + batch_size + Specifies the number of matrix multiply operations to perform. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by ``batch_size`` matrix multiply + operations of the form ``alpha`` * op(``A``)*op(``B``) + ``beta`` * ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized before + calling ``gemm_batch``. + + + +.. _onemkl_blas_gemm_batch_usm: + +gemm_batch (USM Version) +--------------------------- + +.. rubric:: Description + +The USM version of ``gemm_batch`` supports the group API and strided API. + +The group API operation is defined as: +:: + + idx = 0 + for i = 0 … group_count – 1 + for j = 0 … group_size – 1 + A, B, and C are matrices in a[idx], b[idx] and c[idx] + C := alpha[i] * op(A) * op(B) + beta[i] * C + idx = idx + 1 + end for + end for + +The strided API operation is defined as +:: + + for i = 0 … batch_size – 1 + A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c. + C := alpha * op(A) * op(B) + beta * C + end for + +where: + +op(X) is one of op(X) = X, or op(X) = X\ :sup:`T`, or op(X) = X\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A``, ``B``, and ``C`` are matrices, + +op(``A``) is ``m`` x ``k``, op(``B``) is ``k`` x ``n``, and ``C`` is ``m`` x ``n``. + + +For group API, ``a``, ``b`` and ``c`` arrays contain the pointers for all the input matrices. +The total number of matrices in ``a``, ``b`` and ``c`` are given by: + +.. math:: + + total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i] + +For strided API, ``a``, ``b``, ``c`` arrays contain all the input matrices. The total number of matrices +in ``a``, ``b`` and ``c`` are given by the ``batch_size`` parameter. + +**Group API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gemm_batch(sycl::queue &queue, + onemkl::transpose *transa, + onemkl::transpose *transb, + std::int64_t *m, + std::int64_t *n, + std::int64_t *k, + T *alpha, + const T **a, + std::int64_t *lda, + const T **b, + std::int64_t *ldb, + T *beta, + T **c, + std::int64_t *ldc, + std::int64_t group_count, + std::int64_t *group_size, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gemm_batch(sycl::queue &queue, + onemkl::transpose *transa, + onemkl::transpose *transb, + std::int64_t *m, + std::int64_t *n, + std::int64_t *k, + T *alpha, + const T **a, + std::int64_t *lda, + const T **b, + std::int64_t *ldb, + T *beta, + T **c, + std::int64_t *ldc, + std::int64_t group_count, + std::int64_t *group_size, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Array of ``group_count`` ``onemkl::transpose`` values. ``transa[i]`` specifies the form of op(``A``) used in + the matrix multiplication in group ``i``. See :ref:`onemkl_datatypes` for more details. + + transb + Array of ``group_count`` ``onemkl::transpose`` values. ``transb[i]`` specifies the form of op(``B``) used in + the matrix multiplication in group ``i``. See :ref:`onemkl_datatypes` for more details. + + m + Array of ``group_count`` integers. ``m[i]`` specifies the + number of rows of op(``A``) and ``C`` for every matrix in group ``i``. All entries must be at least zero. + + n + Array of ``group_count`` integers. ``n[i]`` specifies the + number of columns of op(``B``) and ``C`` for every matrix in group ``i``. All entries must be at least zero. + + k + Array of ``group_count`` integers. ``k[i]`` specifies the + number of columns of op(``A``) and rows of op(``B``) for every matrix in group ``i``. All entries must be at + least zero. + + alpha + Array of ``group_count`` scalar elements. ``alpha[i]`` specifies the scaling factor for every matrix-matrix + product in group ``i``. + + a + Array of pointers to input matrices ``A`` with size ``total_batch_count``. + + See :ref:`matrix-storage` for more details. + + lda + Array of ``group_count`` integers. ``lda[i]`` specifies the + leading dimension of ``A`` for every matrix in group ``i``. All + entries must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda[i]`` must be at least ``m[i]``. + - ``lda[i]`` must be at least ``k[i]``. + * - Row major + - ``lda[i]`` must be at least ``k[i]``. + - ``lda[i]`` must be at least ``m[i]``. + + b + Array of pointers to input matrices ``B`` with size ``total_batch_count``. + + See :ref:`matrix-storage` for more details. + + ldb + + Array of ``group_count`` integers. ``ldb[i]`` specifies the + leading dimension of ``B`` for every matrix in group ``i``. All + entries must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb[i]`` must be at least ``k[i]``. + - ``ldb[i]`` must be at least ``n[i]``. + * - Row major + - ``ldb[i]`` must be at least ``n[i]``. + - ``ldb[i]`` must be at least ``k[i]``. + + beta + Array of ``group_count`` scalar elements. ``beta[i]`` specifies the scaling factor for matrix ``C`` + for every matrix in group ``i``. + + c + Array of pointers to input/output matrices ``C`` with size ``total_batch_count``. + + See :ref:`matrix-storage` for more details. + + ldc + Array of ``group_count`` integers. ``ldc[i]`` specifies the + leading dimension of ``C`` for every matrix in group ``i``. All + entries must be positive and ``ldc[i]`` must be at least + ``m[i]`` if column major layout is used to store matrices or at + least ``n[i]`` if row major layout is used to store matrices. + + group_count + Specifies the number of groups. Must be at least 0. + + group_size + Array of ``group_count`` integers. ``group_size[i]`` specifies the + number of matrix multiply products in group ``i``. All entries must be at least 0. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Overwritten by the ``m[i]``-by-``n[i]`` matrix calculated by + (``alpha[i]`` * op(``A``)*op(``B``) + ``beta[i]`` * ``C``) for group ``i``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling ``gemm_batch``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + +**Strided API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gemm_batch(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + std::int64_t stridea, + const T *b, + std::int64_t ldb, + std::int64_t strideb, + T beta, + T *c, + std::int64_t ldc, + std::int64_t stridec, + std::int64_t batch_size, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gemm_batch(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t m, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + std::int64_t stridea, + const T *b, + std::int64_t ldb, + std::int64_t strideb, + T beta, + T *c, + std::int64_t ldc, + std::int64_t stridec, + std::int64_t batch_size, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Specifies op(``A``) the transposition operation applied to the + matrices ``A``. See :ref:`onemkl_datatypes` for more details. + + transb + Specifies op(``B``) the transposition operation applied to the + matrices ``B``. See :ref:`onemkl_datatypes` for more details. + + m + Number of rows of op(``A``) and ``C``. Must be at least zero. + + n + Number of columns of op(``B``) and ``C``. Must be at least zero. + + k + Number of columns of op(``A``) and rows of op(``B``). Must be at + least zero. + + alpha + Scaling factor for the matrix-matrix products. + + a + Pointer to input matrices ``A`` with size ``stridea`` * ``batch_size``. + + lda + The leading dimension of the matrices ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``m``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``m``. + + stridea + Stride between different ``A`` matrices. + + b + Pointer to input matrices ``B`` with size ``strideb`` * ``batch_size``. + + ldb + The leading dimension of the matrices``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + strideb + Stride between different ``B`` matrices. + + beta + Scaling factor for the matrices ``C``. + + c + Pointer to input/output matrices ``C`` with size ``stridec`` * ``batch_size``. + + ldc + The leading dimension of the mattrices ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + stridec + Stride between different ``C`` matrices. + + batch_size + Specifies the number of matrix multiply operations to perform. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output matrices, overwritten by ``batch_size`` matrix multiply + operations of the form ``alpha`` * op(``A``)*op(``B``) + ``beta`` * ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized before + calling ``gemm_batch``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-like-extensions` diff --git a/_sources/domains/blas/gemm_bias.rst.txt b/_sources/domains/blas/gemm_bias.rst.txt new file mode 100644 index 000000000..e027006c5 --- /dev/null +++ b/_sources/domains/blas/gemm_bias.rst.txt @@ -0,0 +1,271 @@ +.. _onemkl_blas_gemm_bias: + +gemm_bias +========= + +Computes a matrix-matrix product using general integer matrices with bias. + +.. _onemkl_blas_gemm_bias_description: + +.. rubric:: Description + +The gemm_bias routines compute a scalar-matrix-matrix product and +add the result to a scalar-matrix product, using general integer matrices with biases/offsets. +The operation is defined as: + +.. math:: + + \scriptstyle C \leftarrow alpha*(op(A) - A\_offset)*(op(B) - B\_offset) + beta*C + C\_offset + +where: + +op(``X``) is one of op(``X``) = ``X``, or op(``X``) = ``X``\ :sup:`T`, or +op(``X``) = ``X``\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A_offset`` is an ``m``-by-``k`` matrix with every element equal to the value ao, + +``B_offset`` is a ``k``-by-``n`` matrix with every element equal to the value bo, + +``C_offset`` is an ``m``-by-``n`` matrix defined by the +co buffer as described below, + +``A``, ``B``, and ``C`` are matrices, + +op(``A``) is ``m`` x ``k``, op(``B``) is ``k`` x ``n``, and +``C`` is ``m`` x ``n``. + +``gemm_bias`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - Ts + - Ta + - Tb + - Tc + * - ``float`` + - ``std::int8_t`` + - ``std::uint8_t`` + - ``std::int32_t`` + +.. _onemkl_blas_gemm_bias_buffer: + +gemm_bias (Buffer Version) +-------------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gemm_bias(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + onemkl::offset offset_type, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + sycl::buffer &a, + std::int64_t lda, + Ta ao, + sycl::buffer &b, + std::int64_t ldb, + Tb bo, + Ts beta, + sycl::buffer &c, + std::int64_t ldc, + sycl::buffer &co) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gemm_bias(sycl::queue &queue, + onemkl::transpose transa, + onemkl::transpose transb, + onemkl::offset offset_type, + std::int64_t m, + std::int64_t n, + std::int64_t k, + Ts alpha, + sycl::buffer &a, + std::int64_t lda, + Ta ao, + sycl::buffer &b, + std::int64_t ldb, + Tb bo, + Ts beta, + sycl::buffer &c, + std::int64_t ldc, + sycl::buffer &co) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + transa + Specifies op(``A``), the transposition operation applied to + ``A``. See + :ref:`onemkl_datatypes` for + more details. + + transb + Specifies op(``B``), the transposition operation applied to + ``B``. See + :ref:`onemkl_datatypes` for + more details. + + offset_type + Specifies the form of ``C_offset`` used in the matrix + multiplication. See + :ref:`onemkl_datatypes` for + more details. + + m + Number of rows of op(``A``) and ``C``. Must be at least zero. + + n + Number of columns of op(``B``) and ``C``. Must be at least + zero. + + k + Number of columns of op(``A``) and rows of op(``B``). Must be + at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + The buffer holding the input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m`` + * - Row major + - ``A`` is an ``m``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``m``. + - ``A`` is an ``k``-by-``m`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k`` + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``m``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``m``. + + ao + Specifies the scalar offset value for matrix ``A``. + + b + Buffer holding the input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n`` + + See :ref:`matrix-storage` for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + bo + Specifies the scalar offset value for matrix ``B``. + + beta + Scaling factor for matrix ``C``. + + c + Buffer holding the input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . + See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + co + Buffer holding the offset values for matrix ``C``. + + If ``offset_type`` = ``offset::fix``, the ``co`` array must have + size at least 1. + + + If ``offset_type`` = ``offset::col``, the ``co`` array must have + size at least ``max(1,m)``. + + + If ``offset_type`` = ``offset::row``, the ``co`` array must have + size at least ``max(1,n)``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by ``alpha`` * (op(``A``) - + ``A_offset``)*(op(``B``) - ``B_offset``) + ``beta`` * ``C`` + ``C_offset``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling ``gemm_bias``. + + + **Parent topic:** :ref:`blas-like-extensions` diff --git a/_sources/domains/blas/gemmt.rst.txt b/_sources/domains/blas/gemmt.rst.txt new file mode 100644 index 000000000..308ef0ed2 --- /dev/null +++ b/_sources/domains/blas/gemmt.rst.txt @@ -0,0 +1,418 @@ +.. _onemkl_blas_gemmt: + +gemmt +===== + +Computes a matrix-matrix product with general matrices, but updates +only the upper or lower triangular part of the result matrix. + +.. _onemkl_blas_gemmt_description: + +.. rubric:: Description + +The gemmt routines compute a scalar-matrix-matrix product and add +the result to the upper or lower part of a scalar-matrix product, +with general matrices. The operation is defined as: + +.. math:: + + C \leftarrow alpha*op(A)*op(B) + beta*C + +where: + +op(``X``) is one of op(``X``) = ``X``, or op(``X``) = ``X``\ :sup:`T`, or +op(``X``) = ``X``\ :sup:`H`, + +``alpha`` and ``beta`` are scalars + +``A``, ``B``, and ``C`` are matrices + +op(``A``) is ``n`` x ``k``, op(``B``) is ``k`` x ``n``, and +``C`` is ``n`` x ``n``. + +``gemmt`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_gemmt_buffer: + +gemmt (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gemmt(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gemmt(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``C``\ ’s data is stored in its upper or + lower triangle. See :ref:`onemkl_datatypes` for more details. + + transa + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + transb + Specifies op(``B``), the transposition operation applied to + ``B``. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows of op(``A``), columns of op(``B``), and + columns and rows of\ ``C``. Must be at least zero. + + k + Number of columns of op(``A``) and rows of op(``B``). Must be + at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Buffer holding the input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Buffer holding the input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + + See :ref:`matrix-storage` for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + Buffer holding the input/output matrix ``C``. Must have size at + least ``ldc`` \* ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least + ``m``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by the upper or lower triangular + part of ``alpha`` * op(``A``)*op(``B``) + ``beta`` * ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling gemmt. + + +.. _onemkl_blas_gemmt_usm: + +gemmt (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gemmt(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gemmt(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::transpose transb, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``C``\ ’s data is stored in its upper or + lower triangle. See + :ref:`onemkl_datatypes` for + more details. + + transa + Specifies op(``A``), the transposition operation applied to + ``A``. See + :ref:`onemkl_datatypes` for + more details. + + transb + Specifies op(``B``), the transposition operation applied to + ``B``. See + :ref:`onemkl_datatypes` for + more details. + + n + Number of columns of op(``A``), columns of op(``B``), and + columns of\ ``C``. Must be at least zero. + + k + Number of columns of op(``A``) and rows of op(``B``). Must be + at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k`` + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``A`` not transposed + - ``A`` transposed + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Pointer to input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n`` + + See :ref:`matrix-storage` for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``B`` not transposed + - ``B`` transposed + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + Pointer to input/output matrix ``C``. Must have size at least + ``ldc`` \* ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least + ``m``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by the upper or lower + triangular part of ``alpha`` * op(``A``)*op(``B``) + ``beta`` * ``C``. + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling gemmt. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-like-extensions` diff --git a/_sources/domains/blas/gemv.rst.txt b/_sources/domains/blas/gemv.rst.txt new file mode 100644 index 000000000..367a7eef0 --- /dev/null +++ b/_sources/domains/blas/gemv.rst.txt @@ -0,0 +1,261 @@ +.. _onemkl_blas_gemv: + +gemv +==== + +Computes a matrix-vector product using a general matrix. + +.. _onemkl_blas_gemv_description: + +.. rubric:: Description + +The ``gemv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a general matrix. The +operation is defined as: + +.. math:: + + y \leftarrow alpha*op(A)*x + beta*y + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``m``-by-``n`` matrix, and ``x``, ``y`` are vectors. + +``gemv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_gemv_buffer: + +gemv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gemv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gemv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + trans + Specifies ``op(A)``, the transposition operation applied to ``A``. + + m + Specifies the number of rows of the matrix ``A``. The value of + ``m`` must be at least zero. + + n + Specifies the number of columns of the matrix ``A``. The value of + ``n`` must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + The buffer holding the input matrix ``A``. Must have a size of at + least ``lda``\ \*\ ``n`` if column major layout is used or at + least ``lda``\ \*\ ``m`` if row major layout is used. See + :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + + x + Buffer holding input vector ``x``. The length ``len`` of vector + ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` is + transposed. The buffer must be of size at least (1 + (``len`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for more details. + + incx + The stride of vector ``x``. + + beta + The scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The length ``len`` of + vector ``y`` is ``m``, if ``A`` is not transposed, and ``n`` if + ``A`` is transposed. The buffer must be of size at least (1 + + (``len`` - 1)*abs(``incy``)) where ``len`` is this length. See + :ref:`matrix-storage` for more details. + + incy + The stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + The buffer holding updated vector ``y``. + + +.. _onemkl_blas_gemv_usm: + +gemv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gemv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gemv(sycl::queue &queue, + onemkl::transpose trans, + std::int64_t m, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + trans + Specifies ``op(A)``, the transposition operation applied to + ``A``. See + :ref:`onemkl_datatypes` for + more details. + + m + Specifies the number of rows of the matrix ``A``. The value of + ``m`` must be at least zero. + + n + Specifies the number of columns of the matrix ``A``. The value + of ``n`` must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + The pointer to the input matrix ``A``. Must have a size of at + least ``lda``\ \*\ ``n`` if column major layout is used or at + least ``lda``\ \*\ ``m`` if row major layout is used. See + :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + + x + Pointer to the input vector ``x``. The length ``len`` of vector + ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` + is transposed. The array holding vector ``x`` must be of size + at least (1 + (``len`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + The stride of vector ``x``. + + beta + The scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The length ``len`` of + vector ``y`` is ``m``, if ``A`` is not transposed, and ``n`` if + ``A`` is transposed. The array holding input/output vector + ``y`` must be of size at least (1 + (``len`` - + 1)*abs(``incy``)) where ``len`` is this length. See :ref:`matrix-storage` for + more details. + + incy + The stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + The pointer to updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/ger.rst.txt b/_sources/domains/blas/ger.rst.txt new file mode 100644 index 000000000..334362bca --- /dev/null +++ b/_sources/domains/blas/ger.rst.txt @@ -0,0 +1,226 @@ +.. _onemkl_blas_ger: + +ger +=== + +Computes a rank-1 update of a general matrix. + +.. _onemkl_blas_ger_description: + +.. rubric:: Description + +The ``ger`` routines compute a scalar-vector-vector product and add the +result to a general matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*y^T + A + +where: + +``alpha`` is scalar, + +``A`` is an ``m``-by-``n`` matrix, + +``x`` is a vector of length ``m``, + +``y`` is a vector of length ``n``. + +``ger`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_ger_buffer: + +ger (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void ger(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void ger(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``m`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n`` if column major layout is used or at least ``lda``\ \*\ ``m`` + if row major layout is used. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated matrix ``A``. + + +.. _onemkl_blas_ger_usm: + +ger (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event ger(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event ger(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``m`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n`` if column major layout is used or at least ``lda``\ \*\ ``m`` + if row major layout is used. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated matrix ``A``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/gerc.rst.txt b/_sources/domains/blas/gerc.rst.txt new file mode 100644 index 000000000..20c3e2174 --- /dev/null +++ b/_sources/domains/blas/gerc.rst.txt @@ -0,0 +1,227 @@ +.. _onemkl_blas_gerc: + +gerc +==== + +Computes a rank-1 update (conjugated) of a general complex matrix. + +.. _onemkl_blas_gerc_description: + +.. rubric:: Description + +The ``gerc`` routines compute a scalar-vector-vector product and add the +result to a general matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*y^H + A + + +where: + +``alpha`` is a scalar, + +``A`` is an ``m``-by-``n`` matrix, + +``x`` is a vector of length ``m``, + +``y`` is vector of length ``n``. + +``gerc`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_gerc_buffer: + +gerc (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void gerc(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void gerc(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``m`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n`` if column major layout is used or at least ``lda``\ \*\ ``m`` + if row major layout is used. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated matrix ``A``. + + +.. _onemkl_blas_gerc_usm: + +gerc (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event gerc(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event gerc(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to the input vector ``x``. The array holding input + vector ``x`` must be of size at least (1 + (``m`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to the input/output vector ``y``. The array holding the + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A``\ must have size at least ``lda``\ \*\ ``n`` if column + major layout is used or at least ``lda``\ \*\ ``m`` if row + major layout is used. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated matrix ``A``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/geru.rst.txt b/_sources/domains/blas/geru.rst.txt new file mode 100644 index 000000000..a04907116 --- /dev/null +++ b/_sources/domains/blas/geru.rst.txt @@ -0,0 +1,227 @@ +.. _onemkl_blas_geru: + +geru +==== + +Computes a rank-1 update (unconjugated) of a general complex matrix. + +.. _onemkl_blas_geru_description: + +.. rubric:: Description + +The ``geru`` routines routines compute a scalar-vector-vector product and +add the result to a general matrix. The operation is defined as + +.. math:: + + A \leftarrow alpha*x*y^T + A + +where: + +``alpha`` is a scalar, + +``A`` is an ``m``-by-``n`` matrix, + +``x`` is a vector of length ``m``, + +``y`` is a vector of length ``n``. + +``geru`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_geru_buffer: + +geru (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void geru(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void geru(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``m`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n`` if column major layout is used or at least ``lda``\ \*\ ``m`` + if row major layout is used. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at least + ``m`` if column major layout is used or at least ``n`` if row + major layout is used. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated matrix ``A``. + + +.. _onemkl_blas_geru_usm: + +geru (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event geru(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event geru(sycl::queue &queue, + std::int64_t m, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + m + Number of rows of ``A``. Must be at least zero. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to the input vector ``x``. The array holding input + vector ``x`` must be of size at least (1 + (``m`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n`` if column + major layout is used or at least ``lda``\ \*\ ``m`` if row + major layout is used. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be positive and at + least ``m`` if column major layout is used or at least ``n`` + if row major layout is used. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated matrix ``A``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/hbmv.rst.txt b/_sources/domains/blas/hbmv.rst.txt new file mode 100644 index 000000000..8b1e73c4e --- /dev/null +++ b/_sources/domains/blas/hbmv.rst.txt @@ -0,0 +1,245 @@ +.. _onemkl_blas_hbmv: + +hbmv +==== + +Computes a matrix-vector product using a Hermitian band matrix. + +.. _onemkl_blas_hbmv_description: + +.. rubric:: Description + +The ``hbmv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian band matrix. The +operation is defined as + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` Hermitian band matrix, with ``k`` +super-diagonals, + +``x`` and ``y`` are vectors of length ``n``. + +``hbmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hbmv_buffer: + +hbmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + 1), + and positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``m`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_hbmv_usm: + +hbmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to the input matrix ``A``. The array holding input + matrix ``A`` must have size at least ``lda``\ \*\ ``n``. See + :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + + 1), and positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``m`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/hemm.rst.txt b/_sources/domains/blas/hemm.rst.txt new file mode 100644 index 000000000..35a7bbc2d --- /dev/null +++ b/_sources/domains/blas/hemm.rst.txt @@ -0,0 +1,315 @@ +.. _onemkl_blas_hemm: + +hemm +==== + +Computes a matrix-matrix product where one input matrix is Hermitian +and one is general. + +.. _onemkl_blas_hemm_description: + +.. rubric:: Description + +The ``hemm`` routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, where one of the matrices in the +multiplication is Hermitian. The argument ``left_right`` determines +if the Hermitian matrix, ``A``, is on the left of the multiplication +(``left_right`` = ``side::left``) or on the right (``left_right`` = +``side::right``). Depending on ``left_right``, the operation is +defined as: + +.. math:: + + C \leftarrow alpha*A*B + beta*C + +or + +.. math:: + + C \leftarrow alpha*B*A + beta*C + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is a Hermitian matrix, either ``m``-by-``m`` or ``n``-by-``n`` +matrices, + +``B`` and ``C`` are ``m``-by-``n`` matrices. + +``hemm`` supports the following precisions: + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hemm_buffer: + +hemm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hemm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hemm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the multiplication + (``side::left``) or on the right side (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of the matrix ``B`` and ``C``. + + The value of ``m`` must be at least zero. + + n + Specifies the number of columns of the matrix ``B`` and ``C``. + + The value of ``n`` must be at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``A`` is on the left of the multiplication, + or ``lda``\ \*\ ``n`` if ``A`` is on the right. See :ref:`matrix-storage` + for more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if ``A`` is on + the left of the multiplication, or at least ``n`` if ``A`` is on + the right. Must be positive. + + b + Buffer holding input matrix ``B``. Must have size at least + ``ldb``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldb``\ \*\ ``m`` if row + major layout is used to store matrices. See :ref:`matrix-storage` for + more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + beta + Scaling factor for matrix ``C``. + + c + The buffer holding the input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by ``alpha``\ \*\ ``A``\ \*\ ``B`` + + ``beta``\ \*\ ``C`` (``left_right`` = ``side::left``) or + ``alpha``\ \*\ ``B``\ \*\ ``A`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::right``). + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized before + calling ``hemm``. + + + +.. _onemkl_blas_hemm_usm: + +hemm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hemm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hemm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the + multiplication (``side::left``) or on the right side + (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of the matrix ``B`` and ``C``. + + The value of ``m`` must be at least zero. + + n + Specifies the number of columns of the matrix ``B`` and ``C``. + + The value of ``n`` must be at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Pointer to input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``A`` is on the left of the + multiplication, or ``lda``\ \*\ ``n`` if ``A`` is on the right. + See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if ``A`` is + on the left of the multiplication, or at least ``n`` if ``A`` + is on the right. Must be positive. + + b + Pointer to input matrix ``B``. Must have size at least + ``ldb``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldb``\ \*\ ``m`` if row + major layout is used to store matrices. See :ref:`matrix-storage` for + more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + beta + Scaling factor for matrix ``C``. + + c + The pointer to input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by + ``alpha``\ \*\ ``A``\ \*\ ``B`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::left``) or + ``alpha``\ \*\ ``B``\ \*\ ``A`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::right``). + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling ``hemm``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/hemv.rst.txt b/_sources/domains/blas/hemv.rst.txt new file mode 100644 index 000000000..073c83874 --- /dev/null +++ b/_sources/domains/blas/hemv.rst.txt @@ -0,0 +1,232 @@ +.. _onemkl_blas_hemv: + +hemv +==== + +Computes a matrix-vector product using a Hermitian matrix. + +.. _onemkl_blas_hemv_description: + +.. rubric:: Description + +The ``hemv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian matrix. The +operation is defined as + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` Hermitian matrix, + +``x`` and ``y`` are vectors of length ``n``. + +``hemv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hemv_buffer: + +hemv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hemv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hemv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether *A* is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``m``, and + positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + + +.. _onemkl_blas_hemv_usm: + +hemv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hemv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hemv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether *A* is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``m``, and + positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/her.rst.txt b/_sources/domains/blas/her.rst.txt new file mode 100644 index 000000000..dbbb36713 --- /dev/null +++ b/_sources/domains/blas/her.rst.txt @@ -0,0 +1,205 @@ +.. _onemkl_blas_her: + +her +=== + +Computes a rank-1 update of a Hermitian matrix. + +.. _onemkl_blas_her_description: + +.. rubric:: Description + +The ``her`` routines compute a scalar-vector-vector product and add the +result to a Hermitian matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*x^H + A + +where: + +``alpha`` is scalar, + +``A`` is an ``n``-by-``n`` Hermitian matrix, + +``x`` is a vector of length ``n``. + +``her`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_her_buffer: + +her (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void her(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void her(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \= ``upper`` or the updated + lower triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \ =\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + + +.. _onemkl_blas_her_usm: + +her (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event her(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event her(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether *A* is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper`` or the updated + lower triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/her2.rst.txt b/_sources/domains/blas/her2.rst.txt new file mode 100644 index 000000000..5c4543f01 --- /dev/null +++ b/_sources/domains/blas/her2.rst.txt @@ -0,0 +1,231 @@ +.. _onemkl_blas_her2: + +her2 +==== + +Computes a rank-2 update of a Hermitian matrix. + +.. _onemkl_blas_her2_description: + +.. rubric:: Description + +The ``her2`` routines compute two scalar-vector-vector products and add +them to a Hermitian matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A + +where: + +``alpha`` is a scalar, + +``A`` is an ``n``-by-``n`` Hermitian matrix, + +``x`` and ``y`` are vectors or length ``n``. + +``her2`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_her2_buffer: + +her2 (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void her2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void her2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated + lower triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + + + +.. _onemkl_blas_her2_usm: + +her2 (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event her2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event her2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated + lower triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/her2k.rst.txt b/_sources/domains/blas/her2k.rst.txt new file mode 100644 index 000000000..d3f02f957 --- /dev/null +++ b/_sources/domains/blas/her2k.rst.txt @@ -0,0 +1,397 @@ +.. _onemkl_blas_her2k: + +her2k +===== + +Performs a Hermitian rank-2k update. + +.. _onemkl_blas_her2k_description: + +.. rubric:: Description + +The ``her2k`` routines perform a rank-2k update of an ``n`` x ``n`` +Hermitian matrix ``C`` by general matrices ``A`` and ``B``. + +If ``trans`` = ``transpose::nontrans``, the operation is defined as: + +.. math:: + + C \leftarrow alpha*A*B^H + conjg(alpha)*B*A^H + beta*C + +where ``A`` is ``n`` x ``k`` and ``B`` is ``k`` x ``n``. + +If ``trans`` = ``transpose::conjtrans``, the operation is defined as: + +.. math:: + + C \leftarrow alpha*B*A^H + conjg(alpha)*A*B^H + beta*C + +where ``A`` is ``k`` x ``n`` and ``B`` is ``n`` x ``k``. + +In both cases: + +``alpha`` is a complex scalar and ``beta`` is a real scalar. + +``C`` is a Hermitian matrix and ``A`` , ``B`` are general matrices. + +The inner dimension of both matrix multiplications is ``k``. + +``her2k`` supports the following precisions: + + .. list-table:: + :header-rows: 1 + + * - T + - T_real + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_her2k_buffer: + +her2k (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void her2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T_real beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void her2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T_real beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies the operation to apply, as described above. Supported + operations are ``transpose::nontrans`` and + ``transpose::conjtrans``. + + n + The number of rows and columns in ``C``. The value of ``n`` must + be at least zero. + + k + The inner dimension of matrix multiplications. The value of ``k`` + must be at least equal to zero. + + alpha + Complex scaling factor for the rank-2k update. + + a + Buffer holding input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for + more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Buffer holding input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + + See :ref:`matrix-storage` + for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Real scaling factor for matrix ``C``. + + c + Buffer holding input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least ``n``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by the updated ``C`` matrix. + + +.. _onemkl_blas_her2k_usm: + +her2k (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event her2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T_real beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event her2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T_real beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies the operation to apply, as described above. Supported + operations are ``transpose::nontrans`` and + ``transpose::conjtrans``. + + n + The number of rows and columns in ``C``. The value of ``n`` + must be at least zero. + + k + The inner dimension of matrix multiplications. The value of + ``k`` must be at least equal to zero. + + alpha + Complex scaling factor for the rank-2k update. + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Pointer to input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + + See :ref:`matrix-storage` for + more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Real scaling factor for matrix ``C``. + + c + Pointer to input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least + ``n``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by the updated ``C`` + matrix. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/herk.rst.txt b/_sources/domains/blas/herk.rst.txt new file mode 100644 index 000000000..32c306ee9 --- /dev/null +++ b/_sources/domains/blas/herk.rst.txt @@ -0,0 +1,309 @@ +.. _onemkl_blas_herk: + +herk +==== + +Performs a Hermitian rank-k update. + +.. _onemkl_blas_herk_description: + +.. rubric:: Description + +The ``herk`` routines compute a rank-k update of a Hermitian matrix +``C`` by a general matrix ``A``. The operation is defined as: + +.. math:: + + C \leftarrow alpha*op(A)*op(A)^H + beta*C + +where: + +op(``X``) is one of op(``X``) = ``X`` or op(``X``) = ``X``\ :sup:`H`, + +``alpha`` and ``beta`` are real scalars, + +``C`` is a Hermitian matrix and ``A`` is a general matrix. + +Here op(``A``) is ``n`` x ``k``, and ``C`` is ``n`` x ``n``. + +``herk`` supports the following precisions: + + .. list-table:: + :header-rows: 1 + + * - T + - T_real + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_herk_buffer: + +herk (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void herk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T_real alpha, + sycl::buffer &a, + std::int64_t lda, + T_real beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void herk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T_real alpha, + sycl::buffer &a, + std::int64_t lda, + T_real beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See + :ref:`onemkl_datatypes` for more + details. Supported operations are ``transpose::nontrans`` and + ``transpose::conjtrans``. + + n + The number of rows and columns in ``C``.The value of ``n`` must be + at least zero. + + k + Number of columns in op(``A``). + + The value of ``k`` must be at least zero. + + alpha + Real scaling factor for the rank-k update. + + a + Buffer holding input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for + more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + beta + Real scaling factor for matrix ``C``. + + c + Buffer holding input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least ``n``. + +.. container:: section + + .. rubric:: Output Parameters + + c + The output buffer, overwritten by + ``alpha``\ \*op(``A``)*op(``A``)\ :sup:`T` + ``beta``\ \*\ ``C``. + The imaginary parts of the diagonal elements are set to zero. + + + +.. _onemkl_blas_herk_usm: + +herk (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event herk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T_real alpha, + const T* a, + std::int64_t lda, + T_real beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event herk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T_real alpha, + const T* a, + std::int64_t lda, + T_real beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. Supported operations are ``transpose::nontrans`` + and ``transpose::conjtrans``. + + n + The number of rows and columns in ``C``.The value of ``n`` must + be at least zero. + + k + Number of columns in op(``A``). + + The value of ``k`` must be at least zero. + + alpha + Real scaling factor for the rank-k update. + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + beta + Real scaling factor for matrix ``C``. + + c + Pointer to input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least + ``n``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by + ``alpha``\ \*op(``A``)*op(``A``)\ :sup:`T` + + ``beta``\ \*\ ``C``. The imaginary parts of the diagonal + elements are set to zero. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/hpmv.rst.txt b/_sources/domains/blas/hpmv.rst.txt new file mode 100644 index 000000000..fa9153216 --- /dev/null +++ b/_sources/domains/blas/hpmv.rst.txt @@ -0,0 +1,228 @@ +.. _onemkl_blas_hpmv: + +hpmv +==== + +Computes a matrix-vector product using a Hermitian packed matrix. + +.. _onemkl_blas_hpmv_description: + +.. rubric:: Description + +The ``hpmv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian packed matrix. +The operation is defined as + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` Hermitian matrix supplied in packed form, + +``x`` and ``y`` are vectors of length ``n``. + +``hpmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hpmv_buffer: + +hpmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``\ +1))/2. See :ref:`matrix-storage` for + more details. + + The imaginary parts of the diagonal elements need not be set and + are assumed to be zero. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + + +.. _onemkl_blas_hpmv_usm: + +hpmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``\ +1))/2. See + :ref:`matrix-storage` for + more details. + + The imaginary parts of the diagonal elements need not be set + and are assumed to be zero. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/hpr.rst.txt b/_sources/domains/blas/hpr.rst.txt new file mode 100644 index 000000000..d0f25916e --- /dev/null +++ b/_sources/domains/blas/hpr.rst.txt @@ -0,0 +1,201 @@ +.. _onemkl_blas_hpr: + +hpr +=== + +Computes a rank-1 update of a Hermitian packed matrix. + +.. _onemkl_blas_hpr_description: + +.. rubric:: Description + +The ``hpr`` routines compute a scalar-vector-vector product and add the +result to a Hermitian packed matrix. The operation is defined as + +.. math:: + + A \leftarrow alpha*x*x^H + A + +where: + +``alpha`` is scalar, + +``A`` is an ``n``-by-``n`` Hermitian matrix, supplied in packed form, + +``x`` is a vector of length ``n``. + +``hpr`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hpr_buffer: + +hpr (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hpr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hpr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for + more details. + + The imaginary part of the diagonal elements need not be set and + are assumed to be zero. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + + +.. _onemkl_blas_hpr_usm: + +hpr (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hpr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hpr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``-1))/2. See + :ref:`matrix-storage` for + more details. + + The imaginary part of the diagonal elements need not be set and + are assumed to be zero. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/hpr2.rst.txt b/_sources/domains/blas/hpr2.rst.txt new file mode 100644 index 000000000..3ec58cc46 --- /dev/null +++ b/_sources/domains/blas/hpr2.rst.txt @@ -0,0 +1,226 @@ +.. _onemkl_blas_hpr2: + +hpr2 +==== + +Performs a rank-2 update of a Hermitian packed matrix. + +.. _onemkl_blas_hpr2_description: + +.. rubric:: Description + +The ``hpr2`` routines compute two scalar-vector-vector products and add +them to a Hermitian packed matrix. The operation is defined as + +.. math:: + + A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A + +where: + +``alpha`` is a scalar, + +``A`` is an ``n``-by-``n`` Hermitian matrix, supplied in packed form, + +``x`` and ``y`` are vectors of length ``n``. + +``hpr2`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_hpr2_buffer: + +hpr2 (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void hpr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void hpr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for + more details. + + The imaginary parts of the diagonal elements need not be set and + are assumed to be zero. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + + + +.. _onemkl_blas_hpr2_usm: + +hpr2 (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event hpr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event hpr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``-1))/2. See + :ref:`matrix-storage` for + more details. + + The imaginary parts of the diagonal elements need not be set + and are assumed to be zero. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the Hermitian + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the Hermitian matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + The imaginary parts of the diagonal elements are set to zero. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/iamax.rst.txt b/_sources/domains/blas/iamax.rst.txt new file mode 100644 index 000000000..a1823a442 --- /dev/null +++ b/_sources/domains/blas/iamax.rst.txt @@ -0,0 +1,167 @@ +.. _onemkl_blas_iamax: + +iamax +===== + +Finds the index of the element with the largest absolute value in a vector. + +.. _onemkl_blas_iamax_description: + +.. rubric:: Description + +The ``iamax`` routines return an index ``i`` such that ``x[i]`` +has the maximum absolute value of all elements in vector ``x`` (real +variants), or such that (\|Re(``x[i]``)\| + \|Im(``x[i]``)\|) is maximal +(complex variants). + +If either ``n`` or ``incx`` are not positive, the routine returns +``0``. + +If more than one vector element is found with the same largest +absolute value, the index of the first one encountered is returned. + +If the vector contains ``NaN`` values, then the routine returns the +index of the first ``NaN``. + +``iamax`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std:complex`` + +.. container:: Note + + .. rubric:: Note + :class: NoteTipHead + + The index is zero-based. + +.. _onemkl_blas_iamax_buffer: + +iamax (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void iamax(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void iamax(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + The number of elements in vector ``x``. + + x + The buffer that holds the input vector ``x``. The buffer must be + of size at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` + for more details. + + incx + The stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + result + The buffer where the zero-based index ``i`` of the maximal element + is stored. + + +.. _onemkl_blas_iamax_usm: + +iamax (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event iamax(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event iamax(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + The number of elements in vector ``x``. + + x + The pointer to the input vector ``x``. The array holding the + input vector ``x`` must be of size at least (1 + (``n`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + The stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + The pointer to where the zero-based index ``i`` of the maximal + element is stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/iamin.rst.txt b/_sources/domains/blas/iamin.rst.txt new file mode 100644 index 000000000..94dbcf55f --- /dev/null +++ b/_sources/domains/blas/iamin.rst.txt @@ -0,0 +1,160 @@ +.. _onemkl_blas_iamin: + +iamin +===== + +Finds the index of the element with the smallest absolute value. + +.. _onemkl_blas_iamin_description: + +.. rubric:: Description + +The ``iamin`` routines return an index ``i`` such that ``x[i]`` has +the minimum absolute value of all elements in vector ``x`` (real +variants), or such that (\|Re(``x[i]``)\| + \|Im(``x[i]``)\|) is minimal +(complex variants). + +If either ``n`` or ``incx`` are not positive, the routine returns +``0``. + +If more than one vector element is found with the same smallest +absolute value, the index of the first one encountered is returned. + +If the vector contains ``NaN`` values, then the routine returns the +index of the first ``NaN``. + +``iamin`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. container:: Note + + .. rubric:: Note + :class: NoteTipHead + + The index is zero-based. + +.. _onemkl_blas_iamin_buffer: + +iamin (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void iamin(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void iamin(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector x. + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the zero-based index ``i`` of the minimum element + will be stored. + + +.. _onemkl_blas_iamin_usm: + +iamin (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event iamin(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event iamin(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + The pointer to input vector ``x``. The array holding input + vector ``x`` must be of size at least (1 + (``n`` - + 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector x. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to where the zero-based index ``i`` of the minimum + element will be stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/nrm2.rst.txt b/_sources/domains/blas/nrm2.rst.txt new file mode 100644 index 000000000..31ec6330c --- /dev/null +++ b/_sources/domains/blas/nrm2.rst.txt @@ -0,0 +1,158 @@ +.. _onemkl_blas_nrm2: + +nrm2 +==== + +Computes the Euclidean norm of a vector. + +.. _onemkl_blas_nrm2_description: + +.. rubric:: Description + +The ``nrm2`` routines computes Euclidean norm of a vector + +.. math:: + + result = \| x\| + +where: + +``x`` is a vector of ``n`` elements. + +``nrm2`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + - T_res + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_nrm2_buffer: + +nrm2 (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void nrm2(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void nrm2(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the Euclidean norm of the vector ``x`` will be + stored. + + +.. _onemkl_blas_nrm2_usm: + +nrm2 (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event nrm2(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event nrm2(sycl::queue &queue, + std::int64_t n, + const T *x, + std::int64_t incx, + T_res *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to where the Euclidean norm of the vector ``x`` will be + stored. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/rot.rst.txt b/_sources/domains/blas/rot.rst.txt new file mode 100644 index 000000000..78f089402 --- /dev/null +++ b/_sources/domains/blas/rot.rst.txt @@ -0,0 +1,208 @@ +.. _onemkl_blas_rot: + +rot +=== + +Performs rotation of points in the plane. + +.. _onemkl_blas_rot_description: + +.. rubric:: Description + +Given two vectors ``x`` and ``y`` of ``n`` elements, the ``rot`` routines +compute four scalar-vector products and update the input vectors with +the sum of two of these scalar-vector products as follow: + +.. math:: + + \left[\begin{array}{c} + x\\y + \end{array}\right] + \leftarrow + \left[\begin{array}{c} + \phantom{-}c*x + s*y\\ + -s*x + c*y + \end{array}\right] + +``rot`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + - T_scalar + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_rot_buffer: + +rot (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void rot(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + T_scalar c, + T_scalar s) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void rot(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + T_scalar c, + T_scalar s) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + c + Scaling factor. + + s + Scaling factor. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding updated buffer ``x``. + + y + Buffer holding updated buffer ``y``. + + + +.. _onemkl_blas_rot_usm: + +rot (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event rot(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + T_scalar c, + T_scalar s, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event rot(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + T_scalar c, + T_scalar s, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input vector ``y``. The array holding input vector + ``y`` must be of size at least (1 + (``n`` - 1)*abs(``incy``)). + See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + c + Scaling factor. + + s + Scaling factor. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated matrix ``x``. + + y + Pointer to the updated matrix ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/rotg.rst.txt b/_sources/domains/blas/rotg.rst.txt new file mode 100644 index 000000000..e5700ae7d --- /dev/null +++ b/_sources/domains/blas/rotg.rst.txt @@ -0,0 +1,175 @@ +.. _onemkl_blas_rotg: + +rotg +==== + +Computes the parameters for a Givens rotation. + +.. _onemkl_blas_rotg_description: + +.. rubric:: Description + +Given the Cartesian coordinates ``(a, b)`` of a point, the ``rotg`` +routines return the parameters ``c``, ``s``, ``r``, and ``z`` +associated with the Givens rotation. The parameters ``c`` and ``s`` +define a unitary matrix such that: + +.. math:: + + \begin{bmatrix}c & s \\ -s & c\end{bmatrix}. + \begin{bmatrix}a \\ b\end{bmatrix} + =\begin{bmatrix}r \\ 0\end{bmatrix} + +The parameter ``z`` is defined such that if \|\ ``a``\ \| > +\|\ ``b``\ \|, ``z`` is ``s``; otherwise if ``c`` is not 0 ``z`` is +1/``c``; otherwise ``z`` is 1. + +``rotg`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + - T_res + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_rotg_buffer: + +rotg (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void rotg(sycl::queue &queue, + sycl::buffer &a, + sycl::buffer &b, + sycl::buffer &c, + sycl::buffer &s) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void rotg(sycl::queue &queue, + sycl::buffer &a, + sycl::buffer &b, + sycl::buffer &c, + sycl::buffer &s) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed + + a + Buffer holding the ``x``-coordinate of the point. + + b + Buffer holding the ``y``-coordinate of the point. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the parameter ``r`` associated with the Givens + rotation. + + b + Buffer holding the parameter ``z`` associated with the Givens + rotation. + + c + Buffer holding the parameter ``c`` associated with the Givens + rotation. + + s + Buffer holding the parameter ``s`` associated with the Givens + rotation. + + +.. _onemkl_blas_rotg_usm: + +rotg (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event rotg(sycl::queue &queue, + T *a, + T *b, + T_real *c, + T *s, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event rotg(sycl::queue &queue, + T *a, + T *b, + T_real *c, + T *s, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed + + a + Pointer to the ``x``-coordinate of the point. + + b + Pointer to the ``y``-coordinate of the point. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the parameter ``r`` associated with the Givens + rotation. + + b + Pointer to the parameter ``z`` associated with the Givens + rotation. + + c + Pointer to the parameter ``c`` associated with the Givens + rotation. + + s + Pointer to the parameter ``s`` associated with the Givens + rotation. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/rotm.rst.txt b/_sources/domains/blas/rotm.rst.txt new file mode 100644 index 000000000..f64097dbc --- /dev/null +++ b/_sources/domains/blas/rotm.rst.txt @@ -0,0 +1,266 @@ +.. _onemkl_blas_rotm: + +rotm +==== + +Performs modified Givens rotation of points in the plane. + +.. _onemkl_blas_rotm_description: + +.. rubric:: Description + +Given two vectors ``x`` and ``y``, each vector element of these +vectors is replaced as follows: + +.. math:: + + \begin{bmatrix}x_i \\ y_i\end{bmatrix}= + H + \begin{bmatrix}x_i \\ y_i\end{bmatrix} + +for ``i`` from 1 to ``n``, where ``H`` is a modified Givens +transformation matrix. + +``rotm`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_rotm_buffer: + +rotm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void rotm(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer ¶m) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void rotm(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer ¶m) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + param + Buffer holding an array of size 5. + + The elements of the ``param`` array are: + + ``param[0]`` contains a switch, ``flag``. The other array elements + ``param[1-4]`` contain the components of the modified Givens + transformation matrix ``H``: + h\ :sub:`11`, h\ :sub:`21`, h\ :sub:`12`, and + h\ :sub:`22`, respectively. + + Depending on the values of ``flag``, the components of ``H`` + are set as follows: + + | ``flag = -1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix} + + | ``flag = 0.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix} + + | ``flag = 1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix} + + | ``flag = -2.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix} + + In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 + are assumed based on the value of ``flag`` and are not required to + be set in the ``param`` vector. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding updated buffer ``x``. + + y + Buffer holding updated buffer ``y``. + + + +.. _onemkl_blas_rotm_usm: + +rotm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event rotm(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + T *param, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event rotm(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + T *param, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to the input vector ``x``. The array holding the vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + yparam + Pointer to the input vector ``y``. The array holding the vector + ``y`` must be of size at least (1 + (``n`` - 1)*abs(``incy``)). + See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + param + Buffer holding an array of size 5. + + The elements of the ``param`` array are: + + ``param[0]`` contains a switch, ``flag``. The other array elements + ``param[1-4]`` contain the components of the modified Givens + transformation matrix ``H``: + h\ :sub:`11`, h\ :sub:`21`, h\ :sub:`12`, and + h\ :sub:`22`, respectively. + + Depending on the values of ``flag``, the components of ``H`` + are set as follows: + + | ``flag = -1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix} + + | ``flag = 0.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix} + + | ``flag = 1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix} + + | ``flag = -2.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix} + + In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 + are assumed based on the value of ``flag`` and are not required to + be set in the ``param`` vector. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated array ``x``. + + y + Pointer to the updated array ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/rotmg.rst.txt b/_sources/domains/blas/rotmg.rst.txt new file mode 100644 index 000000000..402ea0394 --- /dev/null +++ b/_sources/domains/blas/rotmg.rst.txt @@ -0,0 +1,257 @@ +.. _onemkl_blas_rotmg: + +rotmg +===== + +Computes the parameters for a modified Givens rotation. + +.. _onemkl_blas_rotmg_description: + +.. rubric:: Description + +Given Cartesian coordinates (``x1``, ``y1``) of an +input vector, the ``rotmg`` routines compute the components of a modified +Givens transformation matrix ``H`` that zeros the ``y``-component of +the resulting vector: + +.. math:: + + \begin{bmatrix}x1 \\ 0\end{bmatrix}= + H + \begin{bmatrix}x1\sqrt{d1} \\ y1\sqrt{d2}\end{bmatrix} + +``rotmg`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_rotmg_buffer: + +rotmg (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void rotmg(sycl::queue &queue, + sycl::buffer &d1, + sycl::buffer &d2, + sycl::buffer &x1, + sycl::buffer &y1, + sycl::buffer ¶m) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void rotmg(sycl::queue &queue, + sycl::buffer &d1, + sycl::buffer &d2, + sycl::buffer &x1, + sycl::buffer &y1, + sycl::buffer ¶m) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + d1 + Buffer holding the scaling factor for the ``x``-coordinate of the + input vector. + + d2 + Buffer holding the scaling factor for the ``y``-coordinate of the + input vector. + + x1 + Buffer holding the ``x``-coordinate of the input vector. + + y1 + Scalar specifying the ``y``-coordinate of the input vector. + +.. container:: section + + .. rubric:: Output Parameters + + d1 + Buffer holding the first diagonal element of the updated matrix. + + d2 + Buffer holding the second diagonal element of the updated matrix. + + x1 + Buffer holding the ``x``-coordinate of the rotated vector before + scaling + + param + Buffer holding an array of size 5. + + The elements of the ``param`` array are: + + ``param[0]`` contains a switch, ``flag``. The other array elements + ``param[1-4]`` contain the components of the modified Givens + transformation matrix ``H``: + h\ :sub:`11`, h\ :sub:`21`, h\ :sub:`12`, and + h\ :sub:`22`, respectively. + + Depending on the values of ``flag``, the components of ``H`` are + set as follows: + + | ``flag = -1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix} + + | ``flag = 0.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix} + + | ``flag = 1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix} + + | ``flag = -2.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix} + + In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 + are assumed based on the value of ``flag`` and are not required to + be set in the ``param`` vector. + + + +.. _onemkl_blas_rotmg_usm: + +rotmg (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event rotmg(sycl::queue &queue, + T *d1, + T *d2, + T *x1, + T *y1, + T *param, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event rotmg(sycl::queue &queue, + T *d1, + T *d2, + T *x1, + T *y1, + T *param, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + d1 + Pointer to the scaling factor for the ``x``-coordinate of the + input vector. + + d2 + Pointer to the scaling factor for the ``y``-coordinate of the + input vector. + + x1 + Pointer to the ``x``-coordinate of the input vector. + + y1 + Scalar specifying the ``y``-coordinate of the input vector. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + d1 + Pointer to the first diagonal element of the updated matrix. + + d2 + Pointer to the second diagonal element of the updated matrix. + + x1 + Pointer to the ``x``-coordinate of the rotated vector before + scaling + + param + Buffer holding an array of size 5. + + The elements of the ``param`` array are: + + ``param[0]`` contains a switch, ``flag``. The other array elements + ``param[1-4]`` contain the components of the modified Givens + transformation matrix ``H``: + h\ :sub:`11`, h\ :sub:`21`, h\ :sub:`12`, and + h\ :sub:`22`, respectively. + + Depending on the values of ``flag``, the components of ``H`` + are set as follows: + + | ``flag = -1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix} + + | ``flag = 0.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix} + + | ``flag = 1.0``: + + .. math:: + + H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix} + + | ``flag = -2.0``: + + .. math:: + + H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix} + + In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 + are assumed based on the value of ``flag`` and are not required to + be set in the ``param`` vector. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/sbmv.rst.txt b/_sources/domains/blas/sbmv.rst.txt new file mode 100644 index 000000000..34528c2a8 --- /dev/null +++ b/_sources/domains/blas/sbmv.rst.txt @@ -0,0 +1,244 @@ +.. _onemkl_blas_sbmv: + +sbmv +==== + +Computes a matrix-vector product with a symmetric band matrix. + +.. _onemkl_blas_sbmv_description: + +.. rubric:: Description + +The ``sbmv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a symmetric band matrix. The +operation is defined as: + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` symmetric matrix with ``k`` +super-diagonals, + +``x`` and ``y`` are vectors of length ``n``. + +``sbmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_sbmv_buffer: + +sbmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void sbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void sbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + 1), + and positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_sbmv_usm: + +sbmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event sbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event sbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + std::int64_t k, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of super-diagonals of the matrix ``A``. Must be at least + zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + + 1), and positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/scal.rst.txt b/_sources/domains/blas/scal.rst.txt new file mode 100644 index 000000000..388d7f7f1 --- /dev/null +++ b/_sources/domains/blas/scal.rst.txt @@ -0,0 +1,162 @@ +.. _onemkl_blas_scal: + +scal +==== + +Computes the product of a vector by a scalar. + +.. _onemkl_blas_scal_description: + +.. rubric:: Description + +The ``scal`` routines computes a scalar-vector product: + +.. math:: + + x \leftarrow alpha*x + +where: + +``x`` is a vector of ``n`` elements, + +``alpha`` is a scalar. + +``scal`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + - T_scalar + * - ``float`` + - ``float`` + * - ``double`` + - ``double`` + * - ``std::complex`` + - ``std::complex`` + * - ``std::complex`` + - ``std::complex`` + * - ``std::complex`` + - ``float`` + * - ``std::complex`` + - ``double`` + +.. _onemkl_blas_scal_buffer: + +scal (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void scal(sycl::queue &queue, + std::int64_t n, + T_scalar alpha, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void scal(sycl::queue &queue, + std::int64_t n, + T_scalar alpha, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + alpha + Specifies the scalar ``alpha``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding updated buffer ``x``. + + +.. _onemkl_blas_scal_usm: + +scal (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event scal(sycl::queue &queue, + std::int64_t n, + T_scalar alpha, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event scal(sycl::queue &queue, + std::int64_t n, + T_scalar alpha, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + alpha + Specifies the scalar ``alpha``. + + x + Pointer to the input vector ``x``. The array must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated array ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/sdsdot.rst.txt b/_sources/domains/blas/sdsdot.rst.txt new file mode 100644 index 000000000..20028049d --- /dev/null +++ b/_sources/domains/blas/sdsdot.rst.txt @@ -0,0 +1,172 @@ +.. _onemkl_blas_sdsdot: + +sdsdot +====== + +Computes a vector-vector dot product with double precision. + +.. _onemkl_blas_sdsdot_description: + +.. rubric:: Description + +The ``sdsdot`` routines perform a dot product between two vectors with +double precision: + +.. math:: + + result = sb + \sum_{i=1}^{n}X_iY_i + +.. _onemkl_blas_sdsdot_buffer: + +sdsdot (Buffer Version) +----------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void sdsdot(sycl::queue &queue, + std::int64_t n, + float sb, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void sdsdot(sycl::queue &queue, + std::int64_t n, + float sb, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &result) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + sb + Single precision scalar to be added to the dot product. + + x + Buffer holding input vector ``x``. The buffer must be of size + at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size + at least (1 + (``n`` - 1)*abs(``incxy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + result + Buffer where the result (a scalar) will be stored. If ``n`` < 0 + the result is ``sb``. + + +.. _onemkl_blas_sdsdot_usm: + +sdsdot (USM Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event sdsdot(sycl::queue &queue, + std::int64_t n, + float sb, + const float *x, + std::int64_t incx, + const float *y, + std::int64_t incy, + float *result, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event sdsdot(sycl::queue &queue, + std::int64_t n, + float sb, + const float *x, + std::int64_t incx, + const float *y, + std::int64_t incy, + float *result, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vectors ``x`` and ``y``. + + sb + Single precision scalar to be added to the dot product. + + x + Pointer to the input vector ``x``. The array must be of size + at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` + for more details. + + incx + Stride of vector ``x``. + + y + Pointer to the input vector ``y``. The array must be of size + at least (1 + (``n`` - 1)*abs(``incxy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if + any. If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + result + Pointer to where the result (a scalar) will be stored. If + ``n`` < 0 the result is ``sb``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/spmv.rst.txt b/_sources/domains/blas/spmv.rst.txt new file mode 100644 index 000000000..ae2218723 --- /dev/null +++ b/_sources/domains/blas/spmv.rst.txt @@ -0,0 +1,220 @@ +.. _onemkl_blas_spmv: + +spmv +==== + +Computes a matrix-vector product with a symmetric packed matrix. + +.. _onemkl_blas_spmv_description: + +.. rubric:: Description + +The ``spmv`` routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a symmetric packed matrix. +The operation is defined as: + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` symmetric matrix, supplied in packed form, + +``x`` and ``y`` are vectors of length ``n``. + +``spmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_spmv_buffer: + +spmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void spmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void spmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``\ +1))/2. See :ref:`matrix-storage` for + more details. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_spmv_usm: + +spmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event spmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event spmv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``\ +1))/2. See + :ref:`matrix-storage` for + more details. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + beta + Scaling factor for vector ``y``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/spr.rst.txt b/_sources/domains/blas/spr.rst.txt new file mode 100644 index 000000000..9109566e1 --- /dev/null +++ b/_sources/domains/blas/spr.rst.txt @@ -0,0 +1,193 @@ +.. _onemkl_blas_spr: + +spr +=== + +Performs a rank-1 update of a symmetric packed matrix. + +.. _onemkl_blas_spr_description: + +.. rubric:: Description + +The ``spr`` routines compute a scalar-vector-vector product and add the +result to a symmetric packed matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*x^T + A + +where: + +``alpha`` is scalar, + +``A`` is an ``n``-by-``n`` symmetric matrix, supplied in packed form, + +``x`` is a vector of length ``n``. + +``spr`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_spr_buffer: + +spr (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void spr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void spr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n`` + 1))/2. See :ref:`matrix-storage` for + more details. + +.. container:: section + + .. rubric:: Output Parameters + :class: sectiontitle + + a + Buffer holding the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + + +.. _onemkl_blas_spr_usm: + +spr (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event spr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event spr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n`` + 1))/2. See + :ref:`matrix-storage` for + more details. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/spr2.rst.txt b/_sources/domains/blas/spr2.rst.txt new file mode 100644 index 000000000..6cd195cbb --- /dev/null +++ b/_sources/domains/blas/spr2.rst.txt @@ -0,0 +1,213 @@ +.. _onemkl_blas_spr2: + +spr2 +==== + +Computes a rank-2 update of a symmetric packed matrix. + +.. _onemkl_blas_spr2_description: + +.. rubric:: Description + +The ``spr2`` routines compute two scalar-vector-vector products and add +them to a symmetric packed matrix. The operation is defined as: + +.. math:: + + A \leftarrow alpha*x*y^T + alpha*y*x^T + A + +where: + +``alpha`` is scalar, + +``A`` is an ``n``-by-``n`` symmetric matrix, supplied in packed form, + +``x`` and ``y`` are vectors of length ``n``. + +``spr`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_spr2_buffer: + +spr2 (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void spr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void spr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for + more details. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper`` or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + +.. _onemkl_blas_spr2_usm: + +spr2 (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event spr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event spr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``-1))/2. See + :ref:`matrix-storage` for + more details. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper`` or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/swap.rst.txt b/_sources/domains/blas/swap.rst.txt new file mode 100644 index 000000000..c82aaf4f3 --- /dev/null +++ b/_sources/domains/blas/swap.rst.txt @@ -0,0 +1,184 @@ +.. _onemkl_blas_swap: + +swap +==== + +Swaps a vector with another vector. + +.. _onemkl_blas_swap_description: + +.. rubric:: Description + +Given two vectors of ``n`` elements, ``x`` and ``y``, the ``swap`` +routines return vectors ``y`` and ``x`` swapped, each replacing the +other. + +.. math:: + + \left[\begin{array}{c} + y\\x + \end{array}\right] + \leftarrow + \left[\begin{array}{c} + x\\y + \end{array}\right] + +``swap`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_swap_buffer: + +swap (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void swap(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void swap(sycl::queue &queue, + std::int64_t n, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input vector ``y``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding updated buffer ``x``, that is, the input vector + ``y``. + + y + Buffer holding updated buffer ``y``, that is, the input vector + ``x``. + + + +.. _onemkl_blas_swap_usm: + +swap (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event swap(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event swap(sycl::queue &queue, + std::int64_t n, + T *x, + std::int64_t incx, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + n + Number of elements in vector ``x``. + + x + Pointer to the input vector ``x``. The array must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to the input vector ``y``. The array must be of size at + least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated array ``x``, that is, the input vector + ``y``. + + y + Pointer to the updated array ``y``, that is, the input vector + ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-1-routines` diff --git a/_sources/domains/blas/symm.rst.txt b/_sources/domains/blas/symm.rst.txt new file mode 100644 index 000000000..bd50c2c02 --- /dev/null +++ b/_sources/domains/blas/symm.rst.txt @@ -0,0 +1,311 @@ +.. _onemkl_blas_symm: + +symm +==== + +Computes a matrix-matrix product where one input matrix is symmetric +and one matrix is general. + +.. _onemkl_blas_symm_description: + +.. rubric:: Description + +The ``symm`` routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, where one of the matrices in the +multiplication is symmetric. The argument ``left_right`` determines +if the symmetric matrix, ``A``, is on the left of the multiplication +(``left_right`` = ``side::left``) or on the right (``left_right`` = +``side::right``). Depending on ``left_right``, the operation is +defined as: + +.. math:: + + C \leftarrow alpha*A*B + beta*C + +or + +.. math:: + + C \leftarrow alpha*B*A + beta*C + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is a symmetric matrix, either ``m``-by-``m`` or ``n``-by-``n``, + +``B`` and ``C`` are ``m``-by-``n`` matrices. + +``symm`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_symm_buffer: + +symm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void symm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void symm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the multiplication + (``side::left``) or on the right side (``side::right``). See :ref:`onemkl_datatypes` for more details. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + m + Number of rows of ``B`` and ``C``. The value of ``m`` must be at + least zero. + + n + Number of columns of ``B`` and ``C``. The value of ``n`` must be + at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``A`` is on the left of the multiplication, + or ``lda``\ \*\ ``n`` if ``A`` is on the right. See :ref:`matrix-storage` + for more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if ``A`` is on + the left of the multiplication, or at least ``n`` if ``A`` is on + the right. Must be positive. + + b + Buffer holding input matrix ``B``. Must have size at least + ``ldb``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldb``\ \*\ ``m`` if row + major layout is used to store matrices. See :ref:`matrix-storage` for + more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + beta + Scaling factor for matrix ``C``. + + c + The buffer holding the input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices. See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by ``alpha``\ \*\ ``A``\ \*\ ``B`` + + ``beta``\ \*\ ``C`` (``left_right`` = ``side::left``) or + ``alpha``\ \*\ ``B``\ \*\ ``A`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::right``). + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized before + calling ``symm``. + + +.. _onemkl_blas_symm_usm: + +symm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event symm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event symm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the + multiplication (``side::left``) or on the right side + (``side::right``). See :ref:`onemkl_datatypes` for more details. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + m + Number of rows of ``B`` and ``C``. The value of ``m`` must be + at least zero. + + n + Number of columns of ``B`` and ``C``. The value of ``n`` must + be at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Pointer to input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``A`` is on the left of the + multiplication, or ``lda``\ \*\ ``n`` if ``A`` is on the right. + See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if ``A`` is + on the left of the multiplication, or at least ``n`` if ``A`` + is on the right. Must be positive. + + b + Pointer to input matrix ``B``. Must have size at least + ``ldb``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldb``\ \*\ ``m`` if row + major layout is used to store matrices. See :ref:`matrix-storage` for + more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + beta + Scaling factor for matrix ``C``. + + c + The pointer to input/output matrix ``C``. It must have a + size of at least ``ldc``\ \*\ ``n`` if column major layout is + used to store matrices or at least ``ldc``\ \*\ ``m`` if row + major layout is used to store matrices . See :ref:`matrix-storage` for more details. + + ldc + The leading dimension of ``C``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if column major layout is used to store matrices. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by + ``alpha``\ \*\ ``A``\ \*\ ``B`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::left``) or + ``alpha``\ \*\ ``B``\ \*\ ``A`` + ``beta``\ \*\ ``C`` + (``left_right`` = ``side::right``). + +.. container:: section + + .. rubric:: Notes + + If ``beta`` = 0, matrix ``C`` does not need to be initialized + before calling ``symm``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/symv.rst.txt b/_sources/domains/blas/symv.rst.txt new file mode 100644 index 000000000..2fa00ecbc --- /dev/null +++ b/_sources/domains/blas/symv.rst.txt @@ -0,0 +1,226 @@ +.. _onemkl_blas_symv: + +symv +==== + +Computes a matrix-vector product for a symmetric matrix. + +.. _onemkl_blas_symv_description: + +.. rubric:: Description + +The ``symv`` routines routines compute a scalar-matrix-vector product and +add the result to a scalar-vector product, with a symmetric matrix. +The operation is defined as: + +.. math:: + + y \leftarrow alpha*A*x + beta*y + +where: + +``alpha`` and ``beta`` are scalars, + +``A`` is an ``n``-by-``n`` symmetric matrix, + +``x`` and ``y`` are vectors of length ``n``. + +``symv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_symv_buffer: + +symv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void symv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void symv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx, + T beta, + sycl::buffer &y, + std::int64_t incy) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``m``, and + positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + +.. container:: section + + .. rubric:: Output Parameters + + y + Buffer holding the updated vector ``y``. + + +.. _onemkl_blas_symv_usm: + +symv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event symv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event symv(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *a, + std::int64_t lda, + const T *x, + std::int64_t incx, + T beta, + T *y, + std::int64_t incy, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``m``, and + positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + y + Pointer to the updated vector ``y``. + + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/syr.rst.txt b/_sources/domains/blas/syr.rst.txt new file mode 100644 index 000000000..ab1a4e2b8 --- /dev/null +++ b/_sources/domains/blas/syr.rst.txt @@ -0,0 +1,202 @@ +.. _onemkl_blas_syr: + +syr +=== + +Computes a rank-1 update of a symmetric matrix. + +.. _onemkl_blas_syr_description: + +.. rubric:: Description + +The ``syr`` routines compute a scalar-vector-vector product add them and +add the result to a matrix, with a symmetric matrix. The operation is +defined as: + +.. math:: + + A \leftarrow alpha*x*x^T + A + +where: + +``alpha`` is scalar, + +``A`` is an ``n``-by-``n`` symmetric matrix, + +``x`` is a vector of length ``n``. + +``syr`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_syr_buffer: + +syr (Buffer Version) +-------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void syr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void syr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper`` or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + +.. _onemkl_blas_syr_usm: + +syr (USM Version) +----------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event syr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event syr(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper`` or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/syr2.rst.txt b/_sources/domains/blas/syr2.rst.txt new file mode 100644 index 000000000..ca51cf45e --- /dev/null +++ b/_sources/domains/blas/syr2.rst.txt @@ -0,0 +1,228 @@ +.. _onemkl_blas_syr2: + +syr2 +==== + +Computes a rank-2 update of a symmetric matrix. + +.. _onemkl_blas_syr2_description: + +.. rubric:: Description + +The ``syr2`` routines compute two scalar-vector-vector product add them +and add the result to a matrix, with a symmetric matrix. The +operation is defined as: + +.. math:: + + A \leftarrow alpha*x*y^T + alpha*y*x^T + A + +where: + +``alpha`` is a scalar, + +``A`` is an ``n``-by-``n`` symmetric matrix, + +``x`` and ``y`` are vectors of length ``n``. + +``syr2`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + +.. _onemkl_blas_syr2_buffer: + +syr2 (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void syr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void syr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + sycl::buffer &x, + std::int64_t incx, + sycl::buffer &y, + std::int64_t incy, + sycl::buffer &a, + std::int64_t lda) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Buffer holding input/output vector ``y``. The buffer must be of + size at least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` + for more details. + + incy + Stride of vector ``y``. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + +.. container:: section + + .. rubric:: Output Parameters + + a + Buffer holding the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + + + +.. _onemkl_blas_syr2_usm: + +syr2 (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event syr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event syr2(sycl::queue &queue, + onemkl::uplo upper_lower, + std::int64_t n, + T alpha, + const T *x, + std::int64_t incx, + const T *y, + std::int64_t incy, + T *a, + std::int64_t lda, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + n + Number of columns of ``A``. Must be at least zero. + + alpha + Scaling factor for the matrix-vector product. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + y + Pointer to input/output vector ``y``. The array holding + input/output vector ``y`` must be of size at least (1 + (``n`` + - 1)*abs(``incy``)). See :ref:`matrix-storage` for + more details. + + incy + Stride of vector ``y``. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + a + Pointer to the updated upper triangular part of the symmetric + matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower + triangular part of the symmetric matrix ``A`` if + ``upper_lower``\ \=\ ``lower``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/syr2k.rst.txt b/_sources/domains/blas/syr2k.rst.txt new file mode 100644 index 000000000..5ce469795 --- /dev/null +++ b/_sources/domains/blas/syr2k.rst.txt @@ -0,0 +1,397 @@ +.. _onemkl_blas_syr2k: + +syr2k +===== + +Performs a symmetric rank-2k update. + +.. _onemkl_blas_syr2k_description: + +.. rubric:: Description + +The ``syr2k`` routines perform a rank-2k update of an ``n`` x ``n`` +symmetric matrix ``C`` by general matrices ``A`` and ``B``. + +If ``trans`` = ``transpose::nontrans``, the operation is defined as: + +.. math:: + + C \leftarrow alpha*(A*B^T + B*A^T) + beta*C + +where ``A`` is ``n`` x ``k`` and ``B`` is ``k`` x ``n``. + +If ``trans`` = ``transpose::trans``, the operation is defined as: + +.. math:: + + C \leftarrow alpha*(A^T*B + B^T*A) + beta * C + + +where ``A`` is ``k`` x ``n`` and ``B`` is ``n`` x ``k``. + + +In both cases: + +``alpha`` and ``beta`` are scalars, + +``C`` is a symmetric matrix and ``A``,\ ``B`` are general matrices, + +The inner dimension of both matrix multiplications is ``k``. + +``syr2k`` supports the following precisions: + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_syr2k_buffer: + +syr2k (Buffer Version) +---------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void syr2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void syr2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies the operation to apply, as described above. Conjugation + is never performed, even if ``trans`` = ``transpose::conjtrans``. + + n + Number of rows and columns in ``C``.The value of ``n`` must be at + least zero. + + k + Inner dimension of matrix multiplications.The value of ``k`` must + be at least zero. + + alpha + Scaling factor for the rank-2k update. + + a + Buffer holding input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for + more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Buffer holding input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + + See :ref:`matrix-storage` + for more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + Buffer holding input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details + + ldc + Leading dimension of ``C``. Must be positive and at least ``n``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by the updated ``C`` matrix. + + + +.. _onemkl_blas_syr2k_usm: + +syr2k (USM Version) +------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event syr2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event syr2k(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + const T* b, + std::int64_t ldb, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies the operation to apply, as described above. + Conjugation is never performed, even if ``trans`` = + ``transpose::conjtrans``. + + n + Number of rows and columns in ``C``. The value of ``n`` must be + at least zero. + + k + Inner dimension of matrix multiplications.The value of ``k`` + must be at least zero. + + alpha + Scaling factor for the rank-2k update. + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + b + Pointer to input matrix ``B``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k`` + * - Row major + - ``B`` is an ``k``-by-``n`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``k``. + - ``B`` is an ``n``-by-``k`` matrix so the array ``b`` + must have size at least ``ldb``\ \*\ ``n``. + + See :ref:`matrix-storage` for + more details. + + ldb + The leading dimension of ``B``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``ldb`` must be at least ``k``. + - ``ldb`` must be at least ``n``. + * - Row major + - ``ldb`` must be at least ``n``. + - ``ldb`` must be at least ``k``. + + beta + Scaling factor for matrix ``C``. + + c + Pointer to input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details + + ldc + Leading dimension of ``C``. Must be positive and at least + ``n``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by the updated ``C`` + matrix. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/syrk.rst.txt b/_sources/domains/blas/syrk.rst.txt new file mode 100644 index 000000000..ce052e1d0 --- /dev/null +++ b/_sources/domains/blas/syrk.rst.txt @@ -0,0 +1,296 @@ +.. _onemkl_blas_syrk: + +syrk +==== + +Performs a symmetric rank-k update. + +.. _onemkl_blas_syrk_description: + +.. rubric:: Description + +The ``syrk`` routines perform a rank-k update of a symmetric matrix ``C`` +by a general matrix ``A``. The operation is defined as: + +.. math:: + + C \leftarrow alpha*op(A)*op(A)^T + beta*C + +where: + +op(``X``) is one of op(``X``) = ``X`` or op(``X``) = ``X``\ :sup:`T` +, + +``alpha`` and ``beta`` are scalars, + +``C`` is a symmetric matrix and ``A``\ is a general matrix. + +Here op(``A``) is ``n``-by-``k``, and ``C`` is ``n``-by-``n``. + +``syrk`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_syrk_buffer: + +syrk (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void syrk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void syrk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + sycl::buffer &a, + std::int64_t lda, + T beta, + sycl::buffer &c, + std::int64_t ldc) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A`` (See :ref:`onemkl_datatypes` for more details). Conjugation is never performed, even if ``trans`` = ``transpose::conjtrans``. + + n + Number of rows and columns in ``C``. The value of ``n`` must be at + least zero. + + k + Number of columns in op(``A``).The value of ``k`` must be at least + zero. + + alpha + Scaling factor for the rank-k update. + + a + Buffer holding input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for + more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + beta + Scaling factor for matrix ``C``. + + c + Buffer holding input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least ``n``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Output buffer, overwritten by + ``alpha``\ \*op(``A``)*op(``A``)\ :sup:`T` + ``beta``\ \*\ ``C``. + + +.. _onemkl_blas_syrk_usm: + +syrk (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event syrk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event syrk(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + std::int64_t n, + std::int64_t k, + T alpha, + const T* a, + std::int64_t lda, + T beta, + T* c, + std::int64_t ldc, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A``'s data is stored in its upper or lower + triangle. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A`` (See :ref:`onemkl_datatypes` for more details). Conjugation is never performed, even if + ``trans`` = ``transpose::conjtrans``. + + n + Number of rows and columns in ``C``. The value of ``n`` must be + at least zero. + + k + Number of columns in op(``A``). The value of ``k`` must be at + least zero. + + alpha + Scaling factor for the rank-k update. + + a + Pointer to input matrix ``A``. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n`` + * - Row major + - ``A`` is an ``n``-by-``k`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``n``. + - ``A`` is an ``k``-by-``n`` matrix so the array ``a`` + must have size at least ``lda``\ \*\ ``k``. + + See :ref:`matrix-storage` for more details. + + lda + The leading dimension of ``A``. It must be positive. + + .. list-table:: + :header-rows: 1 + + * - + - ``trans`` = ``transpose::nontrans`` + - ``trans`` = ``transpose::trans`` or ``transpose::conjtrans`` + * - Column major + - ``lda`` must be at least ``n``. + - ``lda`` must be at least ``k``. + * - Row major + - ``lda`` must be at least ``k``. + - ``lda`` must be at least ``n``. + + beta + Scaling factor for matrix ``C``. + + c + Pointer to input/output matrix ``C``. Must have size at least + ``ldc``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + ldc + Leading dimension of ``C``. Must be positive and at least + ``n``. + +.. container:: section + + .. rubric:: Output Parameters + + c + Pointer to the output matrix, overwritten by + ``alpha``\ \*op(``A``)*op(``A``)\ :sup:`T` + + ``beta``\ \*\ ``C``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/tbmv.rst.txt b/_sources/domains/blas/tbmv.rst.txt new file mode 100644 index 000000000..d8bdd83e5 --- /dev/null +++ b/_sources/domains/blas/tbmv.rst.txt @@ -0,0 +1,223 @@ +.. _onemkl_blas_tbmv: + +tbmv +==== + +Computes a matrix-vector product using a triangular band matrix. + +.. _onemkl_blas_tbmv_description: + +.. rubric:: Description + +The ``tbmv`` routines compute a matrix-vector product with a triangular +band matrix. The operation is defined as: + +.. math:: + + x \leftarrow op(A)*x + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular band matrix, with (``k`` + 1) diagonals, + +``x`` is a vector of length ``n``. + +``tbmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_tbmv_buffer: + +tbmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void tbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void tbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + k + Number of sub/super-diagonals of the matrix ``A``. Must be at + least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + 1), + and positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the updated vector ``x``. + + + +.. _onemkl_blas_tbmv_usm: + +tbmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event tbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event tbmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + k + Number of sub/super-diagonals of the matrix ``A``. Must be at + least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + + 1), and positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/tbsv.rst.txt b/_sources/domains/blas/tbsv.rst.txt new file mode 100644 index 000000000..285150007 --- /dev/null +++ b/_sources/domains/blas/tbsv.rst.txt @@ -0,0 +1,225 @@ +.. _onemkl_blas_tbsv: + +tbsv +==== + +Solves a system of linear equations whose coefficients are in a +triangular band matrix. + +.. _onemkl_blas_tbsv_description: + +.. rubric:: Description + +The ``tbsv`` routines solve a system of linear equations whose +coefficients are in a triangular band matrix. The operation is +defined as: + +.. math:: + + op(A)*x = b + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular band matrix, with (``k`` + 1) diagonals, + +``b`` and ``x`` are vectors of length ``n``. + +``tbsv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_tbsv_buffer: + +tbsv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void tbsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void tbsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of sub/super-diagonals of the matrix ``A``. Must be at + least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + 1), + and positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the solution vector ``x``. + + + +.. _onemkl_blas_tbsv_usm: + +tbsv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event tbsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event tbsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Number of rows and columns of ``A``. Must be at least zero. + + k + Number of sub/super-diagonals of the matrix ``A``. Must be at + least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least (``k`` + + 1), and positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the solution vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/tpmv.rst.txt b/_sources/domains/blas/tpmv.rst.txt new file mode 100644 index 000000000..58bc28712 --- /dev/null +++ b/_sources/domains/blas/tpmv.rst.txt @@ -0,0 +1,199 @@ +.. _onemkl_blas_tpmv: + +tpmv +==== + +Computes a matrix-vector product using a triangular packed matrix. + +.. _onemkl_blas_tpmv_description: + +.. rubric:: Description + +The ``tpmv`` routines compute a matrix-vector product with a triangular +packed matrix. The operation is defined as: + +.. math:: + + x \leftarrow op(A)*x + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular band matrix, supplied in packed form, + +``x`` is a vector of length ``n``. + +``tpmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_tpmv_buffer: + +tpmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void tpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void tpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``\ +1))/2. See :ref:`matrix-storage` for + more details. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the updated vector ``x``. + + +.. _onemkl_blas_tpmv_usm: + +tpmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event tpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + const T *a, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event tpmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + const T *a, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``\ +1))/2. See + :ref:`matrix-storage` for + more details. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/tpsv.rst.txt b/_sources/domains/blas/tpsv.rst.txt new file mode 100644 index 000000000..d62ad541d --- /dev/null +++ b/_sources/domains/blas/tpsv.rst.txt @@ -0,0 +1,207 @@ +.. _onemkl_blas_tpsv: + +tpsv +==== + +Solves a system of linear equations whose coefficients are in a +triangular packed matrix. + +.. _onemkl_blas_tpsv_description: + +.. rubric:: Description + +The ``tpsv`` routines solve a system of linear equations whose +coefficients are in a triangular packed matrix. The operation is +defined as: + +.. math:: + + op(A)*x = b + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular band matrix, supplied in packed form, + +``b`` and ``x`` are vectors of length ``n``. + +``tpsv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_tpsv_buffer: + +tpsv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void tpsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void tpsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + (``n``\ \*(``n``\ +1))/2. See :ref:`matrix-storage` for + more details. + + x + Buffer holding the ``n``-element right-hand side vector ``b``. The + buffer must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the solution vector ``x``. + + +.. _onemkl_blas_tpsv_usm: + +tpsv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event tpsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event tpsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least (``n``\ \*(``n``\ +1))/2. See + :ref:`matrix-storage` for + more details. + + x + Pointer to the ``n``-element right-hand side vector ``b``. The + array holding the ``n``-element right-hand side vector ``b`` + must be of size at least (1 + (``n`` - 1)*abs(``incx``)). See + :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the solution vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/trmm.rst.txt b/_sources/domains/blas/trmm.rst.txt new file mode 100644 index 000000000..69bca20d2 --- /dev/null +++ b/_sources/domains/blas/trmm.rst.txt @@ -0,0 +1,288 @@ +.. _onemkl_blas_trmm: + +trmm +==== + +Computes a matrix-matrix product where one input matrix is triangular +and one input matrix is general. + +.. _onemkl_blas_trmm_description: + +.. rubric:: Description + +The ``trmm`` routines compute a scalar-matrix-matrix product where one of +the matrices in the multiplication is triangular. The argument +``left_right`` determines if the triangular matrix, ``A``, is on the +left of the multiplication (``left_right`` = ``side::left``) or on +the right (``left_right`` = ``side::right``). Depending on +``left_right``. The operation is defined as: + +.. math:: + + B \leftarrow alpha*op(A)*B + +or + +.. math:: + + B \leftarrow alpha*B*op(A) + +where: + +op(``A``) is one of op(``A``) = *A*, or op(``A``) = ``A``\ :sup:`T`, +or op(``A``) = ``A``\ :sup:`H`, + +``alpha`` is a scalar, + +``A`` is a triangular matrix, and ``B`` is a general matrix. + +Here ``B`` is ``m`` x ``n`` and ``A`` is either ``m`` x ``m`` or +``n`` x ``n``, depending on ``left_right``. + +``trmm`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_trmm_buffer: + +trmm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void trmm(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void trmm(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the multiplication + (``side::left``) or on the right side (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether the matrix ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_diag + Specifies whether ``A`` is assumed to be unit triangular (all + diagonal elements are 1). See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of ``B``. The value of ``m`` must be + at least zero. + + n + Specifies the number of columns of ``B``. The value of ``n`` must + be at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``left_right`` = ``side::left``, or + ``lda``\ \*\ ``n`` if ``left_right`` = ``side::right``. See + :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if + ``left_right`` = ``side::left``, and at least ``n`` if + ``left_right`` = ``side::right``. Must be positive. + + b + Buffer holding input/output matrix ``B``. Must have size at + least ``ldb``\ \*\ ``n`` if column major layout is used to store + matrices or at least ``ldb``\ \*\ ``m`` if row major layout is + used to store matrices. See :ref:`matrix-storage` for more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if row major layout is used to store matrices. + +.. container:: section + + .. rubric:: Output Parameters + + b + Output buffer, overwritten by ``alpha``\ \*op(``A``)\*\ ``B`` or + ``alpha``\ \*\ ``B``\ \*op(``A``). + +.. container:: section + + .. rubric:: Notes + + If ``alpha`` = 0, matrix ``B`` is set to zero, and ``A`` and ``B`` do + not need to be initialized at entry. + + + +.. _onemkl_blas_trmm_usm: + +trmm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event trmm(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + T* b, + std::int64_t ldb, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event trmm(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + T* b, + std::int64_t ldb, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` is on the left side of the + multiplication (``side::left``) or on the right side + (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether the matrix ``A`` is upper or lower + triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_diag + Specifies whether ``A`` is assumed to be unit triangular (all + diagonal elements are 1). See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of ``B``. The value of ``m`` must + be at least zero. + + n + Specifies the number of columns of ``B``. The value of ``n`` + must be at least zero. + + alpha + Scaling factor for the matrix-matrix product. + + a + Pointer to input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``left_right`` = ``side::left``, or + ``lda``\ \*\ ``n`` if ``left_right`` = ``side::right``. See + :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if + ``left_right`` = ``side::left``, and at least ``n`` if + ``left_right`` = ``side::right``. Must be positive. + + b + Pointer to input/output matrix ``B``. Must have size at + least ``ldb``\ \*\ ``n`` if column major layout is used to store + matrices or at least ``ldb``\ \*\ ``m`` if row major layout is + used to store matrices. See :ref:`matrix-storage` for more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if row major layout is used to store matrices. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + b + Pointer to the output matrix, overwritten by + ``alpha``\ \*op(``A``)\*\ ``B`` or + ``alpha``\ \*\ ``B``\ \*op(``A``). + +.. container:: section + + .. rubric:: Notes + + If ``alpha`` = 0, matrix ``B`` is set to zero, and ``A`` and ``B`` + do not need to be initialized at entry. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/trmv.rst.txt b/_sources/domains/blas/trmv.rst.txt new file mode 100644 index 000000000..746eda899 --- /dev/null +++ b/_sources/domains/blas/trmv.rst.txt @@ -0,0 +1,210 @@ +.. _onemkl_blas_trmv: + +trmv +==== + +Computes a matrix-vector product using a triangular matrix. + +.. _onemkl_blas_trmv_description: + +.. rubric:: Description + +The ``trmv`` routines compute a matrix-vector product with a triangular +matrix. The operation is defined as: + +.. math:: + + x \leftarrow op(A)*x + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular band matrix, + +``x`` is a vector of length ``n``. + +``trmv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_trmv_buffer: + +trmv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void trmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void trmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + x + Buffer holding input vector ``x``. The buffer must be of size at + least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the updated vector ``x``. + + +.. _onemkl_blas_trmv_usm: + +trmv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event trmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event trmv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + x + Pointer to input vector ``x``. The array holding input vector + ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for + more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the updated vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/blas/trsm.rst.txt b/_sources/domains/blas/trsm.rst.txt new file mode 100644 index 000000000..b504ed015 --- /dev/null +++ b/_sources/domains/blas/trsm.rst.txt @@ -0,0 +1,286 @@ +.. _onemkl_blas_trsm: + +trsm +==== + +Solves a triangular matrix equation (forward or backward solve). + +.. _onemkl_blas_trsm_description: + +.. rubric:: Description + +The ``trsm`` routines solve one of the following matrix equations: + +.. math:: + + op(A)*X = alpha*B + +or + +.. math:: + + X*op(A) = alpha*B + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``alpha`` is a scalar, + +``A`` is a triangular matrix, and + +``B`` and ``X`` are ``m`` x ``n`` general matrices. + +``A`` is either ``m`` x ``m`` or ``n`` x ``n``, depending on whether +it multiplies ``X`` on the left or right. On return, the matrix ``B`` +is overwritten by the solution matrix ``X``. + +``trsm`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_trsm_buffer: + +trsm (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void trsm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void trsm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &b, + std::int64_t ldb) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` multiplies ``X`` on the left + (``side::left``) or on the right (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether the matrix ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_diag + Specifies whether ``A`` is assumed to be unit triangular (all + diagonal elements are 1). See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of ``B``. The value of ``m`` must be + at least zero. + + n + Specifies the number of columns of ``B``. The value of ``n`` must + be at least zero. + + alpha + Scaling factor for the solution. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``left_right`` = ``side::left``, or + ``lda``\ \*\ ``n`` if ``left_right`` = ``side::right``. See + :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if + ``left_right`` = ``side::left``, and at least ``n`` if + ``left_right`` = ``side::right``. Must be positive. + + b + Buffer holding input/output matrix ``B``. Must have size at + least ``ldb``\ \*\ ``n`` if column major layout is used to store + matrices or at least ``ldb``\ \*\ ``m`` if row major layout is + used to store matrices. See :ref:`matrix-storage` for more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if row major layout is used to store matrices. + +.. container:: section + + .. rubric:: Output Parameters + + b + Output buffer. Overwritten by the solution matrix ``X``. + +.. container:: section + + .. rubric:: Notes + + If ``alpha`` = 0, matrix ``B`` is set to zero, and ``A`` and ``B`` do + not need to be initialized at entry. + + + +.. _onemkl_blas_trsm_usm: + +trsm (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event trsm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + T* b, + std::int64_t ldb, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event trsm(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose transa, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + const T* a, + std::int64_t lda, + T* b, + std::int64_t ldb, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether ``A`` multiplies ``X`` on the left + (``side::left``) or on the right (``side::right``). See :ref:`onemkl_datatypes` for more details. + + uplo + Specifies whether the matrix ``A`` is upper or lower + triangular. See :ref:`onemkl_datatypes` for more details. + + transa + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_diag + Specifies whether ``A`` is assumed to be unit triangular (all + diagonal elements are 1). See :ref:`onemkl_datatypes` for more details. + + m + Specifies the number of rows of ``B``. The value of ``m`` must + be at least zero. + + n + Specifies the number of columns of ``B``. The value of ``n`` + must be at least zero. + + alpha + Scaling factor for the solution. + + a + Pointer to input matrix ``A``. Must have size at least + ``lda``\ \*\ ``m`` if ``left_right`` = ``side::left``, or + ``lda``\ \*\ ``n`` if ``left_right`` = ``side::right``. See + :ref:`matrix-storage` for + more details. + + lda + Leading dimension of ``A``. Must be at least ``m`` if + ``left_right`` = ``side::left``, and at least ``n`` if + ``left_right`` = ``side::right``. Must be positive. + + b + Pointer to input/output matrix ``B``. Must have size at + least ``ldb``\ \*\ ``n`` if column major layout is used to store + matrices or at least ``ldb``\ \*\ ``m`` if row major layout is + used to store matrices. See :ref:`matrix-storage` for more details. + + ldb + Leading dimension of ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if row major layout is used to store matrices. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + b + Pointer to the output matrix. Overwritten by the solution + matrix ``X``. + +.. container:: section + + .. rubric:: Notes + + If ``alpha`` = 0, matrix ``B`` is set to zero, and ``A`` and ``B`` + do not need to be initialized at entry. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-3-routines` diff --git a/_sources/domains/blas/trsm_batch.rst.txt b/_sources/domains/blas/trsm_batch.rst.txt new file mode 100644 index 000000000..bbc13344a --- /dev/null +++ b/_sources/domains/blas/trsm_batch.rst.txt @@ -0,0 +1,183 @@ +.. _onemkl_blas_trsm_batch: + +trsm_batch +========== + +Computes a group of ``trsm`` operations. + +.. _onemkl_blas_trsm_batch_description: + +.. rubric:: Description + +The ``trsm_batch`` routines are batched versions of :ref:`onemkl_blas_trsm`, performing +multiple ``trsm`` operations in a single call. Each ``trsm`` +solves an equation of the form op(A) \* X = alpha \* B or X \* op(A) = alpha \* B. + +``trsm_batch`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_trsm_batch_buffer: + +trsm_batch (Buffer Version) +--------------------------- + +.. rubric:: Description + +The buffer version of ``trsm_batch`` supports only the strided API. + +The strided API operation is defined as: +:: + + for i = 0 … batch_size – 1 + A and B are matrices at offset i * stridea and i * strideb in a and b. + if (left_right == onemkl::side::left) then + compute X such that op(A) * X = alpha * B + else + compute X such that X * op(A) = alpha * B + end if + B := X + end for + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(A) = ``A``\ :sup:`T`, +or op(``A``) = ``A``\ :sup:`H`, + +``alpha`` is a scalar, + +``A`` is a triangular matrix, + +``B`` and ``X`` are ``m`` x ``n`` general matrices, + +``A`` is either ``m`` x ``m`` or ``n`` x ``n``,depending on whether +it multiplies ``X`` on the left or right. On return, the matrix ``B`` +is overwritten by the solution matrix ``X``. + +The ``a`` and ``b`` buffers contain all the input matrices. The stride +between matrices is given by the stride parameter. The total number +of matrices in ``a`` and ``b`` buffers are given by the ``batch_size`` parameter. + +**Strided API** + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void trsm_batch(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + std::int64_t stridea, + sycl::buffer &b, + std::int64_t ldb, + std::int64_t strideb, + std::int64_t batch_size) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void trsm_batch(sycl::queue &queue, + onemkl::side left_right, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_diag, + std::int64_t m, + std::int64_t n, + T alpha, + sycl::buffer &a, + std::int64_t lda, + std::int64_t stridea, + sycl::buffer &b, + std::int64_t ldb, + std::int64_t strideb, + std::int64_t batch_size) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + left_right + Specifies whether the matrices ``A`` multiply ``X`` on the left + (``side::left``) or on the right (``side::right``). See :ref:`onemkl_datatypes` for more details. + + upper_lower + Specifies whether the matrices ``A`` are upper or lower + triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to the + matrices ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_diag + Specifies whether the matrices ``A`` are assumed to be unit + triangular (all diagonal elements are 1). See :ref:`onemkl_datatypes` for more details. + + m + Number of rows of the ``B`` matrices. Must be at least zero. + + n + Number of columns of the ``B`` matrices. Must be at least zero. + + alpha + Scaling factor for the solutions. + + a + Buffer holding the input matrices ``A`` with size ``stridea`` * ``batch_size``. + + lda + Leading dimension of the matrices ``A``. Must be at least ``m`` if + ``left_right`` = ``side::left``, and at least ``n`` if ``left_right`` = + ``side::right``. Must be positive. + + stridea + Stride between different ``A`` matrices. + + b + Buffer holding the input matrices ``B`` with size ``strideb`` * ``batch_size``. + + ldb + Leading dimension of the matrices ``B``. It must be positive and at least + ``m`` if column major layout is used to store matrices or at + least ``n`` if row major layout is used to store matrices. + + strideb + Stride between different ``B`` matrices. + + batch_size + Specifies the number of triangular linear systems to solve. + +.. container:: section + + .. rubric:: Output Parameters + + b + Output buffer, overwritten by ``batch_size`` solution matrices + ``X``. + +.. container:: section + + .. rubric:: Notes + + If ``alpha`` = 0, matrix ``B`` is set to zero and the matrices ``A`` + and ``B`` do not need to be initialized before calling ``trsm_batch``. + + **Parent topic:** :ref:`blas-like-extensions` diff --git a/_sources/domains/blas/trsv.rst.txt b/_sources/domains/blas/trsv.rst.txt new file mode 100644 index 000000000..d75651463 --- /dev/null +++ b/_sources/domains/blas/trsv.rst.txt @@ -0,0 +1,215 @@ +.. _onemkl_blas_trsv: + +trsv +==== + +Solves a system of linear equations whose coefficients are in a +triangular matrix. + +.. _onemkl_blas_trsv_description: + +.. rubric:: Description + +The ``trsv`` routines compute a matrix-vector product with a triangular +band matrix. The operation is defined as: + +.. math:: + + op(A)*x = b + +where: + +op(``A``) is one of op(``A``) = ``A``, or op(``A``) = +``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, + +``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower +triangular matrix, + +``b`` and ``x`` are vectors of length ``n``. + +``trsv`` supports the following precisions. + + .. list-table:: + :header-rows: 1 + + * - T + * - ``float`` + * - ``double`` + * - ``std::complex`` + * - ``std::complex`` + +.. _onemkl_blas_trsv_buffer: + +trsv (Buffer Version) +--------------------- + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + void trsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + void trsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + sycl::buffer &a, + std::int64_t lda, + sycl::buffer &x, + std::int64_t incx) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Buffer holding input matrix ``A``. Must have size at least + ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + x + Buffer holding the ``n``-element right-hand side vector ``b``. The + buffer must be of size at least (1 + (``n`` - 1)*abs(``incx``)). + See :ref:`matrix-storage` for more details. + + incx + Stride of vector ``x``. + +.. container:: section + + .. rubric:: Output Parameters + + x + Buffer holding the solution vector ``x``. + + + +.. _onemkl_blas_trsv_usm: + +trsv (USM Version) +------------------ + +.. rubric:: Syntax + +.. code-block:: cpp + + namespace oneapi::mkl::blas::column_major { + sycl::event trsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } +.. code-block:: cpp + + namespace oneapi::mkl::blas::row_major { + sycl::event trsv(sycl::queue &queue, + onemkl::uplo upper_lower, + onemkl::transpose trans, + onemkl::diag unit_nonunit, + std::int64_t n, + std::int64_t k, + const T *a, + std::int64_t lda, + T *x, + std::int64_t incx, + const sycl::vector_class &dependencies = {}) + } + +.. container:: section + + .. rubric:: Input Parameters + + queue + The queue where the routine should be executed. + + upper_lower + Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. + + trans + Specifies op(``A``), the transposition operation applied to + ``A``. See :ref:`onemkl_datatypes` for more details. + + unit_nonunit + Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. + + n + Numbers of rows and columns of ``A``. Must be at least zero. + + a + Pointer to input matrix ``A``. The array holding input matrix + ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for + more details. + + lda + Leading dimension of matrix ``A``. Must be at least ``n``, and + positive. + + x + Pointer to the ``n``-element right-hand side vector ``b``. The + array holding the ``n``-element right-hand side vector ``b`` + must be of size at least (1 + (``n`` - 1)*abs(``incx``)). See + :ref:`matrix-storage` for more details. + + incx + Stride of vector ``x``. + + dependencies + List of events to wait for before starting computation, if any. + If omitted, defaults to no dependencies. + +.. container:: section + + .. rubric:: Output Parameters + + x + Pointer to the solution vector ``x``. + +.. container:: section + + .. rubric:: Return Values + + Output event to wait on to ensure computation is complete. + + + **Parent topic:** :ref:`blas-level-2-routines` diff --git a/_sources/domains/dense_linear_algebra.rst.txt b/_sources/domains/dense_linear_algebra.rst.txt new file mode 100644 index 000000000..2b7b59fd3 --- /dev/null +++ b/_sources/domains/dense_linear_algebra.rst.txt @@ -0,0 +1,17 @@ +.. _onemkl_dense_linear_algebra: + +Dense Linear Algebra +--------------------- + +This section contains information about dense linear algebra routines: + +:ref:`matrix-storage` provides information about dense matrix and vector storage formats that are used by oneMKL :ref:`onemkl_blas`. + +:ref:`onemkl_blas` provides vector, matrix-vector, and matrix-matrix routines for dense matrices and vector operations. + + +.. toctree:: + :hidden: + + matrix-storage.rst + blas/blas.rst diff --git a/_sources/domains/matrix-storage.rst.txt b/_sources/domains/matrix-storage.rst.txt new file mode 100644 index 000000000..2dcbd2eb0 --- /dev/null +++ b/_sources/domains/matrix-storage.rst.txt @@ -0,0 +1,581 @@ +.. _matrix-storage: + +Matrix Storage +============== + + +.. container:: + + + The oneMKL BLAS and LAPACK routines for DPC++ use several matrix and + vector storage formats. These are the same formats used in + traditional Fortran BLAS/LAPACK. + + .. container:: section + + .. rubric:: General Matrix + :name: general-matrix + :class: sectiontitle + + A general matrix ``A`` of ``m`` rows and ``n`` columns with + leading dimension ``lda`` is represented as a one dimensional + array ``a`` of size of at least ``lda`` \* ``n`` if column major + layout is used and at least ``lda`` \* ``m`` if row major layout + is used. Before entry in any BLAS function using a general + matrix, the leading ``m`` by ``n`` part of the array ``a`` must + contain the matrix ``A``. For column (respectively row) major + layout, the elements of each column (respectively row) are + contiguous in memory while the elements of each row + (respectively column) are at distance ``lda`` from the element + in the same row (respectively column) and the previous column + (respectively row). + + Visually, the matrix + + .. math:: + + A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + A_{21} & A_{22} & A_{23} & \ldots & A_{2n}\\ + A_{31} & A_{32} & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{m1} & A_{m2} & A_{m3} & \ldots & A_{mn} + \end{bmatrix} + + is stored in memory as an array + + - For column major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{21},A_{31},...,A_{m1},*,...,*}_\text{lda}, + \underbrace{A_{12},A_{22},A_{32},...,A_{m2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{1n},A_{2n},A_{3n},...,A_{mn},*,...,*}_\text{lda}} + _\text{lda x n}] + + - For row major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{12},A_{13},...,A_{1n},*,...,*}_\text{lda}, + \underbrace{A_{21},A_{22},A_{23},...,A_{2n},*,...,*}_\text{lda}, + ..., + \underbrace{A_{m1},A_{m2},A_{m3},...,A_{mn},*,...,*}_\text{lda}} + _\text{m x lda}] + + .. container:: section + + .. rubric:: Triangular Matrix + :name: triangular-matrix + :class: sectiontitle + + A triangular matrix ``A`` of ``n`` rows and ``n`` columns with + leading dimension ``lda`` is represented as a one dimensional + array ``a``, of a size of at least ``lda`` \* ``n``. When column + (respectively row) major layout is used, the elements of each + column (respectively row) are contiguous in memory while the + elements of each row (respectively column) are at distance + ``lda`` from the element in the same row (respectively column) + and the previous column (respectively row). + + Before entry in any BLAS function using a triangular matrix, + + - If ``upper_lower = uplo::upper``, the leading ``n`` by ``n`` + upper triangular part of the array ``a`` must contain the upper + triangular part of the matrix ``A``. The strictly lower + triangular part of the array ``a`` is not referenced. In other + words, the matrix + + .. math:: + + A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + * & A_{22} & A_{23} & \ldots & A_{2n}\\ + * & * & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + * & * & * & \ldots & A_{nn} + \end{bmatrix} + + is stored in memory as the array + + - For column major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},*,...,*}_\text{lda}, + \underbrace{A_{12},A_{22},*,...,*}_\text{lda}, + ..., + \underbrace{A_{1n},A_{2n},A_{3n},...,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}] + + - For row major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{12},A_{13},...,A_{1n},*,...,*}_\text{lda}, + \underbrace{*,A_{22},A_{23},...,A_{2n},*,...,*}_\text{lda}, + ..., + \underbrace{*,...,*,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}] + + - If ``upper_lower = uplo::lower``, the leading ``n`` by ``n`` + lower triangular part of the array ``a`` must contain the lower + triangular part of the matrix ``A``. The strictly upper + triangular part of the array ``a`` is not referenced. That is, + the matrix + + .. math:: + + A = \begin{bmatrix} + A_{11} & * & * & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & * \\ + A_{31} & A_{32} & A_{33} & \ldots & * \\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{n1} & A_{n2} & A_{n3} & \ldots & A_{nn} + \end{bmatrix} + + is stored in memory as the array + + - For column major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{21},A_{31},..,A_{n1},*,...,*}_\text{lda}, + \underbrace{*,A_{22},A_{32},...,A_{n2},*,...,*}_\text{lda}, + ..., + \underbrace{*,...,*,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}] + + - For row major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{\underbrace{A_{11},*,...,*}_\text{lda}, + \underbrace{A_{21},A_{22},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n1},A_{n2},A_{n3},...,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}] + + .. container:: section + + .. rubric:: Band Matrix + :name: band-matrix + :class: sectiontitle + + A general band matrix ``A`` of ``m`` rows and ``n`` columns with + ``kl`` sub-diagonals, ``ku`` super-diagonals, and leading + dimension ``lda`` is represented as a one dimensional array + ``a`` of a size of at least ``lda`` \* ``n`` (respectively + ``lda`` \* ``m``) if column (respectively row) major layout is + used. + + Before entry in any BLAS function using a general band matrix, + the leading (``kl`` + ``ku`` + 1\ ``)`` by ``n`` (respectively + ``m``) part of the array ``a`` must contain the matrix + ``A``. This matrix must be supplied column-by-column + (respectively row-by-row), with the main diagonal of the matrix + in row ``ku`` (respectively ``kl``) of the array (0-based + indexing), the first super-diagonal starting at position 1 + (respectively 0) in row (``ku`` - 1) (respectively column + (``kl`` + 1)), the first sub-diagonal starting at position 0 + (respectively 1) in row (``ku`` + 1) (respectively column + (``kl`` - 1)), and so on. Elements in the array ``a`` that do + not correspond to elements in the band matrix (such as the top + left ``ku`` by ``ku`` triangle) are not referenced. + + Visually, the matrix ``A`` + + .. math:: + + A = \left[\begin{smallmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1,ku+1} & * & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{21} & A_{22} & A_{23} & A_{24} & \ldots & A_{2,ku+2} & * & \ldots & \ldots & \ldots & \ldots & * \\ + A_{31} & A_{32} & A_{33} & A_{34} & A_{35} & \ldots & A_{3,ku+3} & * & \ldots & \ldots & \ldots & * \\ + \vdots & A_{42} & A_{43} & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \ldots & \vdots \\ + A_{kl+1,1} & \vdots & A_{53} & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \vdots \\ + * & A_{kl+2,2} & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & * & A_{kl+3,3} & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{n-ku,n}\\ + \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{m-2,n} \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{m-1,n} \\ + * & * & * & \ldots & \ldots & \ldots & * & A_{m,m-kl} & \ldots & A_{m,n-2} & A_{m,n-1} & A_{m,n} + \end{smallmatrix}\right] + + + is stored in memory as an array + + - For column major layout, + + .. math:: + + \scriptscriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{ku},A_{11}, A_{12},...,A_{min(kl+1,m),1},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{ku-1},A_{max(1,2-ku),2},...,A_{min(kl+2,m),2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,ku-n+1)},A_{max(1,n-ku),n},...,A_{min(kl+n,m),n},*,...*}_\text{lda} + }_\text{lda x n}] + + + - For row major layout, + + .. math:: + + \scriptscriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{kl},A_{11}, A_{12},...,A_{1,min(ku+1,n)},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{kl-1},A_{2,max(1,2-kl)},...,A_{2,min(ku+2,n)},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,kl-m+1)},A_{m,max(1,m-kl)},...,A_{m,min(ku+m,n)},*,...*}_\text{lda} + }_\text{lda x m}] + + The following program segment transfers a band matrix from + conventional full matrix storage (variable ``matrix``, with + leading dimension ``ldm``) to band storage (variable ``a``, with + leading dimension ``lda``): + + + - Using matrices stored with column major layout, + + :: + + for (j = 0; j < n; j++) { + k = ku – j; + for (i = max(0, j – ku); i < min(m, j + kl + 1); i++) { + a[(k + i) + j * lda] = matrix[i + j * ldm]; + } + } + + - Using matrices stored with row major layout, + + :: + + for (i = 0; i < n; i++) { + k = kl – i; + for (j = max(0, i – kl); j < min(n, i + ku + 1); j++) { + a[(k + j) + i * lda] = matrix[j + i * ldm]; + } + } + + + .. container:: section + + .. rubric:: Triangular Band Matrix + :name: triangular-band-matrix + :class: sectiontitle + + A triangular band matrix ``A`` of ``n`` rows and ``n`` columns + with ``k`` sub/super-diagonals and leading dimension ``lda`` is + represented as a one dimensional array ``a`` of size at least + ``lda`` \* ``n``. + + Before entry in any BLAS function using a triangular band matrix, + + + - If ``upper_lower = uplo::upper``, the leading (``k`` + 1) by ``n`` + part of the array ``a`` must contain the upper + triangular band part of the matrix ``A``. When using column + major layout, this matrix must be supplied column-by-column + (respectively row-by-row) with the main diagonal of the + matrix in row (``k``) (respectively column 0) of the array, + the first super-diagonal starting at position 1 + (respectively 0) in row (``k`` - 1) (respectively column 1), + and so on. Elements in the array ``a`` that do not correspond + to elements in the triangular band matrix (such as the top + left ``k`` by ``k`` triangle) are not referenced. + + Visually, the matrix + + .. math:: + + A = \left[\begin{smallmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1,k+1} & * & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + * & A_{22} & A_{23} & A_{24} & \ldots & A_{2,k+2} & * & \ldots & \ldots & \ldots & \ldots & * \\ + \vdots & * & A_{33} & A_{34} & A_{35} & \ldots & A_{3,k+3} & * & \ldots & \ldots & \ldots & * \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{n-k,n}\\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & A_{n-2,n} \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & A_{n-1,n} \\ + * & * & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * & A_{n,n} + \end{smallmatrix}\right] + + is stored as an array + + .. container:: fignone + + - For column major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{ku},A_{11},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{ku-1},A_{max(1,2-k),2},...,A_{2,2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,k-n+1)},A_{max(1,n-k),n},...,A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}] + + + - For row major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{ + \underbrace{A_{11},A_{21},...,A_{min(k+1,n),1},*,...,*}_\text{lda}, + \underbrace{A_{2,2},...,A_{min(k+2,n),2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}] + + The following program segment transfers a band matrix from + conventional full matrix storage (variable ``matrix``, with + leading dimension ``ldm``) to band storage (variable ``a``, + with leading dimension ``lda``): + + - Using matrices stored with column major layout, + + :: + + for (j = 0; j < n; j++) { + m = k – j; + for (i = max(0, j – k); i <= j; i++) { + a[(m + i) + j * lda] = matrix[i + j * ldm]; + } + } + + - Using matrices stored with column major layout, + + :: + + for (i = 0; i < n; i++) { + m = –i; + for (j = i; j < min(n, i + k + 1); j++) { + a[(m + j) + i * lda] = matrix[j + i * ldm]; + } + } + + - If ``upper_lower = uplo::lower``, the leading (``k`` + 1) by ``n`` + part of the array ``a`` must contain the upper triangular + band part of the matrix ``A``. This matrix must be supplied + column-by-column with the main diagonal of the matrix in row 0 + of the array, the first sub-diagonal starting at position 0 in + row 1, and so on. Elements in the array ``a`` that do not + correspond to elements in the triangular band matrix (such as + the bottom right ``k`` by ``k`` triangle) are not referenced. + + That is, the matrix + + .. math:: + + A = \left[\begin{smallmatrix} + A_{11} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{31} & A_{32} & A_{33} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + \vdots & A_{42} & A_{43} & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + A_{k+1,1} & \vdots & A_{53} & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + * & A_{k+2,2} & \vdots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + \vdots & * & A_{k+3,3} & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \vdots \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + * & * & * & \ldots & \ldots & \ldots & * & A_{n,n-k} & \ldots & A_{n,n-2} & A_{n,n-1} & A_{n,n} + \end{smallmatrix}\right] + + + is stored as the array + + + .. container:: fignone + + - For column major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{ + \underbrace{A_{11},A_{21},...,A_{min(k+1,n),1},*,...,*}_\text{lda}, + \underbrace{A_{2,2},...,A_{min(k+2,n),2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}] + + - For row major layout, + + .. math:: + + \scriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{k},A_{11},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{k-1},A_{max(1,2-k),2},...,A_{2,2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,k-n+1)},A_{max(1,n-k),n},...,A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}] + + + The following program segment transfers a band matrix from + conventional full matrix storage (variable ``matrix``, with + leading dimension ``ldm``) to band storage (variable ``a``, + with leading dimension ``lda``): + + - Using matrices stored with column major layout, + + :: + + for (j = 0; j < n; j++) { + m = –j; + for (i = j; i < min(n, j + k + 1); i++) { + a[(m + i) + j * lda] = matrix[i + j * ldm]; + } + } + + - Using matrices stored with row major layout, + + :: + + for (i = 0; i < n; i++) { + m = k – i; + for (j = max(0, i – k); j <= i; j++) { + a[(m + j) + i * lda] = matrix[j + i * ldm]; + } + } + + + .. container:: section + + .. rubric:: Packed Triangular Matrix + :name: packed-triangular-matrix + :class: sectiontitle + + A triangular matrix ``A`` of ``n`` rows and ``n`` columns is + represented in packed format as a one dimensional array ``a`` of + size at least (``n``\ \*(``n`` + 1))/2. All elements in the upper + or lower part of the matrix ``A`` are stored contiguously in the + array ``a``. + + Before entry in any BLAS function using a triangular packed + matrix, + + - If ``upper_lower = uplo::upper``, if column (respectively row) + major layout is used, the first (``n``\ \*(``n`` + 1))/2 + elements in the array ``a`` must contain the upper triangular + part of the matrix ``A`` packed sequentially, column by column + (respectively row by row) so that ``a``\ [0] contains ``A``\ + :sub:`11`, ``a``\ [1] and ``a``\ [2] contain ``A``\ :sub:`12` + and ``A``\ :sub:`22` (respectively ``A``\ :sub:`13`) + respectively, and so on. Hence, the matrix + + .. math:: + + A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + * & A_{22} & A_{23} & \ldots & A_{2n}\\ + * & * & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + * & * & * & \ldots & A_{nn} + \end{bmatrix} + + is stored as the array + + - For column major layout, + + .. math:: + + \scriptstyle a = [A_{11},A_{12},A_{22},A_{13},A_{23},A_{33},...,A_{(n-1),n},A_{nn}] + + - For row major layout, + + .. math:: + + \scriptstyle a = [A_{11},A_{12},A_{13},...,A_{1n}, + A_{22},A_{23},...,A_{2n},..., + A_{(n-1),(n-1)},A_{(n-1),n},A_{nn}] + + - If ``upper_lower = uplo::lower``, if column (respectively row) + major layout is used, the first (``n``\ \*(``n`` + 1))/2 + elements in the array ``a`` must contain the lower triangular + part of the matrix ``A`` packed sequentially, column by column + (row by row) so that ``a``\ [0] contains ``A``\ :sub:`11`, + ``a``\ [1] and ``a``\ [2] contain ``A``\ :sub:`21` and ``A``\ + :sub:`31` (respectively ``A``\ :sub:`22`) respectively, and so + on. The matrix + + .. math:: + + A = \begin{bmatrix} + A_{11} & * & * & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & * \\ + A_{31} & A_{32} & A_{33} & \ldots & * \\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{n1} & A_{n2} & A_{n3} & \ldots & A_{nn} + \end{bmatrix} + + is stored as the array + + - For column major layout, + + .. math:: + + \scriptstyle a = [A_{11},A_{21},A_{31},...,A_{n1}, + A_{22},A_{32},...,A_{n2},..., + A_{(n-1),(n-1)},A_{n,(n-1)},A_{nn}] + + - For row major layout, + + .. math:: + + \scriptstyle a = [A_{11},A_{21},A_{22},A_{31},A_{32},A_{33},...,A_{n,(n-1)},A_{nn}] + + .. container:: section + + .. rubric:: Vector + :name: vector + :class: sectiontitle + + A vector ``X`` of ``n`` elements with increment ``incx`` is + represented as a one dimensional array ``x`` of size at least (1 + + (``n`` - 1) \* abs(``incx``)). + + Visually, the vector + + .. math:: + + X = (X_{1},X_{2}, X_{3},...,X_{n}) + + is stored in memory as an array + + + .. math:: + + \scriptstyle x = [\underbrace{ + \underbrace{X_{1},*,...,*}_\text{incx}, + \underbrace{X_{2},*,...,*}_\text{incx}, + ..., + \underbrace{X_{n-1},*,...,*}_\text{incx},X_{n} + }_\text{1 + (n-1) x incx}] \quad if \:incx \:> \:0 + + .. math:: + + \scriptstyle x = [\underbrace{ + \underbrace{X_{n},*,...,*}_\text{|incx|}, + \underbrace{X_{n-1},*,...,*}_\text{|incx|}, + ..., + \underbrace{X_{2},*,...,*}_\text{|incx|},X_{1} + }_\text{1 + (1-n) x incx}] \quad if \:incx \:< \:0 + + + + diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 000000000..89eb8486c --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,23 @@ +.. + Copyright 2020 Intel Corporation + +.. _onemkl: + +***************** +oneMKL Interfaces +***************** + +Introduction +============ + +oneMKL Interfaces is an open-source implementation of oneMKL Data Parallel C++ (DPC++) interfaces accordingly to `oneMKL specification `_ that can work with multiple devices (backends) using device specific libraries underneath + + +.. toctree:: + :maxdepth: 2 + + onemkl-datatypes.rst + domains/dense_linear_algebra.rst + domains/matrix-storage.rst + domains/blas/blas.rst + create_new_backend.rst diff --git a/_sources/onemkl-datatypes.rst.txt b/_sources/onemkl-datatypes.rst.txt new file mode 100644 index 000000000..4e9d6b26c --- /dev/null +++ b/_sources/onemkl-datatypes.rst.txt @@ -0,0 +1,140 @@ +.. _onemkl_datatypes: + +oneMKL defined datatypes +======================== + + +oneMKL BLAS and LAPACK for Data Parallel C++ (DPC++) introduces +several new enumeration data types, which are type-safe versions of +the traditional Fortran characters in BLAS and LAPACK. They are +declared in ``types.hpp``, which is included automatically when +you include ``mkl.hpp``. Like all oneMKL DPC++ functionality, they belong to the namespace ``oneapi::mkl``. + + +Each enumeration value comes with two names: A single-character name +(the traditional BLAS/LAPACK character) and a longer, descriptive +name. The two names are exactly equivalent and may be used +interchangeably. + + +Transpose +--------- + +The ``transpose`` type specifies whether an input matrix should be +transposed and/or conjugated. It can take the following values: + + +.. list-table:: + :header-rows: 1 + + * - Short Name + - Long Name + - Description + * - ``transpose::N`` + - ``transpose::nontrans`` + - Do not transpose or conjugate the matrix. + * - ``transpose::T`` + - ``transpose::trans`` + - Transpose the matrix. + * - ``transpose::C`` + - ``transpose::conjtrans`` + - Perform Hermitian transpose (transpose and conjugate). Only applicable to complex matrices. + + + + +uplo +---- + +The ``uplo`` type specifies whether the lower or upper triangle of a riangular, symmetric, or Hermitian matrix should be accessed. + +It can take the following values: + + +.. list-table:: + :header-rows: 1 + + * - Short Name + - Long Name + - Description + * - ``uplo::U`` + - ``uplo::upper`` + - Access the upper triangle of the matrix. + * - ``uplo::L`` + - ``uplo::lower`` + - Access the lower triangle of the matrix. + + + + +In both cases, elements that are not in the selected triangle are not accessed or updated. + + +diag +---- + + +The ``diag`` type specifies the values on the diagonal of a triangular matrix. It can take the following values: + + +.. list-table:: + :header-rows: 1 + + * - Short Name + - Long Name + - Description + * - ``diag::N`` + - ``diag::nonunit`` + - The matrix is not unit triangular. The diagonal entries are stored with the matrix data. + * - ``diag::U`` + - ``diag::unit`` + - The matrix is unit triangular (the diagonal entries are all 1s). The diagonal entries in the matrix data are not accessed. + + + + +side +---- + + +The ``side`` type specifies the order of matrix multiplication when one matrix has a special form (triangular, symmetric, or Hermitian): + + +.. list-table:: + :header-rows: 1 + + * - Short Name + - Long Name + - Description + * - ``side::L`` + - ``side::left`` + - The special form matrix is on the left in the multiplication. + * - ``side::R`` + - ``side::right`` + - The special form matrix is on the right in the multiplication. + + +offset +------ + + +The ``offset`` type specifies whether the offset to apply to an output matrix is a fix offset, column offset or row offset. It can take the following values + + +.. list-table:: + :header-rows: 1 + + * - Short Name + - Long Name + - Description + * - ``offset::F`` + - ``offset::fix`` + - The offset to apply to the output matrix is fix, all the inputs in the ``C_offset`` matrix has the same value given by the first element in the ``co`` array. + * - ``offset::C`` + - ``offset::column`` + - The offset to apply to the output matrix is a column offset, that is to say all the columns in the ``C_offset`` matrix are the same and given by the elements in the ``co`` array. + * - ``offset::R`` + - ``offset::row`` + - The offset to apply to the output matrix is a row offset, that is to say all the rows in the ``C_offset`` matrix are the same and given by the elements in the ``co`` array. + +**Parent topic:** :ref:`onemkl` diff --git a/_static/__init__.py b/_static/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/_static/ajax-loader.gif b/_static/ajax-loader.gif new file mode 100644 index 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a{color:#130754}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none!important;-webkit-user-select:text!important;-webkit-user-select:none!important;-moz-user-select:none!important;-ms-user-select:none!important} \ No newline at end of file diff --git a/_static/css/theme.css b/_static/css/theme.css new file mode 100644 index 000000000..3f6e79dab --- /dev/null +++ b/_static/css/theme.css @@ -0,0 +1,117 @@ +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/_static/doctools.js b/_static/doctools.js new file mode 100644 index 000000000..4a6e23680 --- /dev/null +++ b/_static/doctools.js @@ -0,0 +1,315 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + */ +jQuery.urldecode = function(x) { + return decodeURIComponent(x).replace(/\+/g, ' '); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var bbox = span.getBBox(); + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + var parentOfText = node.parentNode.parentNode; + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + + this.initOnKeyListeners(); + + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keyup(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box or textarea + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT') { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); \ No newline at end of file diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 000000000..093655d0a --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,12 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '0.1', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: true +}; \ No newline at end of file diff --git a/_static/down-pressed.png b/_static/down-pressed.png new file mode 100644 index 000000000..5756c8cad Binary files /dev/null and b/_static/down-pressed.png differ diff --git a/_static/down.png b/_static/down.png new file mode 100644 index 000000000..1b3bdad2c Binary files /dev/null and b/_static/down.png differ diff --git a/_static/favicons.png b/_static/favicons.png new file mode 100644 index 000000000..f450376b1 Binary files /dev/null and b/_static/favicons.png differ diff --git a/_static/file.png b/_static/file.png new file mode 100644 index 000000000..a858a410e Binary files /dev/null and b/_static/file.png differ diff --git a/_static/images/logo_binder.svg b/_static/images/logo_binder.svg new file mode 100644 index 000000000..45fecf751 --- /dev/null +++ b/_static/images/logo_binder.svg @@ -0,0 +1,19 @@ + + + + +logo + + + + + + + + diff --git a/_static/images/logo_colab.png b/_static/images/logo_colab.png new file mode 100644 index 000000000..b7560ec21 Binary files /dev/null and b/_static/images/logo_colab.png differ diff --git a/_static/images/logo_jupyterhub.svg b/_static/images/logo_jupyterhub.svg new file mode 100644 index 000000000..60cfe9f22 --- /dev/null +++ b/_static/images/logo_jupyterhub.svg @@ -0,0 +1 @@ +logo_jupyterhubHub diff --git a/_static/jquery-3.2.1.js b/_static/jquery-3.2.1.js new file mode 100644 index 000000000..d2d8ca479 --- /dev/null +++ b/_static/jquery-3.2.1.js @@ -0,0 +1,10253 @@ +/*! + * jQuery JavaScript Library v3.2.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2017-03-20T18:59Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var document = window.document; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var concat = arr.concat; + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + + + + function DOMEval( code, doc ) { + doc = doc || document; + + var script = doc.createElement( "script" ); + + script.text = code; + doc.head.appendChild( script ).parentNode.removeChild( script ); + } +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.2.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }, + + // Support: Android <=4.0 only + // Make sure we trim BOM and NBSP + rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g, + + // Matches dashed string for camelizing + rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g, + + // Used by jQuery.camelCase as callback to replace() + fcamelCase = function( all, letter ) { + return letter.toUpperCase(); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !jQuery.isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + src = target[ name ]; + copy = options[ name ]; + + // Prevent never-ending loop + if ( target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + + if ( copyIsArray ) { + copyIsArray = false; + clone = src && Array.isArray( src ) ? src : []; + + } else { + clone = src && jQuery.isPlainObject( src ) ? src : {}; + } + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isFunction: function( obj ) { + return jQuery.type( obj ) === "function"; + }, + + isWindow: function( obj ) { + return obj != null && obj === obj.window; + }, + + isNumeric: function( obj ) { + + // As of jQuery 3.0, isNumeric is limited to + // strings and numbers (primitives or objects) + // that can be coerced to finite numbers (gh-2662) + var type = jQuery.type( obj ); + return ( type === "number" || type === "string" ) && + + // parseFloat NaNs numeric-cast false positives ("") + // ...but misinterprets leading-number strings, particularly hex literals ("0x...") + // subtraction forces infinities to NaN + !isNaN( obj - parseFloat( obj ) ); + }, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + + /* eslint-disable no-unused-vars */ + // See https://github.com/eslint/eslint/issues/6125 + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + type: function( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; + }, + + // Evaluates a script in a global context + globalEval: function( code ) { + DOMEval( code ); + }, + + // Convert dashed to camelCase; used by the css and data modules + // Support: IE <=9 - 11, Edge 12 - 13 + // Microsoft forgot to hump their vendor prefix (#9572) + camelCase: function( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // Support: Android <=4.0 only + trim: function( text ) { + return text == null ? + "" : + ( text + "" ).replace( rtrim, "" ); + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return concat.apply( [], ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // Bind a function to a context, optionally partially applying any + // arguments. + proxy: function( fn, context ) { + var tmp, args, proxy; + + if ( typeof context === "string" ) { + tmp = fn[ context ]; + context = fn; + fn = tmp; + } + + // Quick check to determine if target is callable, in the spec + // this throws a TypeError, but we will just return undefined. + if ( !jQuery.isFunction( fn ) ) { + return undefined; + } + + // Simulated bind + args = slice.call( arguments, 2 ); + proxy = function() { + return fn.apply( context || this, args.concat( slice.call( arguments ) ) ); + }; + + // Set the guid of unique handler to the same of original handler, so it can be removed + proxy.guid = fn.guid = fn.guid || jQuery.guid++; + + return proxy; + }, + + now: Date.now, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = jQuery.type( obj ); + + if ( type === "function" || jQuery.isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.3 + * https://sizzlejs.com/ + * + * Copyright jQuery Foundation and other contributors + * Released under the MIT license + * http://jquery.org/license + * + * Date: 2016-08-08 + */ +(function( window ) { + +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ({}).hasOwnProperty, + arr = [], + pop = arr.pop, + push_native = arr.push, + push = arr.push, + slice = arr.slice, + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[i] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier + identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + // "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace + + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ), + + rattributeQuotes = new RegExp( "=" + whitespace + "*([^\\]'\"]*?)" + whitespace + "*\\]", "g" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace + + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace + + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + + whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ), + funescape = function( _, escaped, escapedWhitespace ) { + var high = "0x" + escaped - 0x10000; + // NaN means non-codepoint + // Support: Firefox<24 + // Workaround erroneous numeric interpretation of +"0x" + return high !== high || escapedWhitespace ? + escaped : + high < 0 ? + // BMP codepoint + String.fromCharCode( high + 0x10000 ) : + // Supplemental Plane codepoint (surrogate pair) + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + disabledAncestor = addCombinator( + function( elem ) { + return elem.disabled === true && ("form" in elem || "label" in elem); + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + (arr = slice.call( preferredDoc.childNodes )), + preferredDoc.childNodes + ); + // Support: Android<4.0 + // Detect silently failing push.apply + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + push_native.apply( target, slice.call(els) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + // Can't trust NodeList.length + while ( (target[j++] = els[i++]) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + + if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) { + setDocument( context ); + } + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) { + + // ID selector + if ( (m = match[1]) ) { + + // Document context + if ( nodeType === 9 ) { + if ( (elem = context.getElementById( m )) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && (elem = newContext.getElementById( m )) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[2] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( (m = match[3]) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !compilerCache[ selector + " " ] && + (!rbuggyQSA || !rbuggyQSA.test( selector )) ) { + + if ( nodeType !== 1 ) { + newContext = context; + newSelector = selector; + + // qSA looks outside Element context, which is not what we want + // Thanks to Andrew Dupont for this workaround technique + // Support: IE <=8 + // Exclude object elements + } else if ( context.nodeName.toLowerCase() !== "object" ) { + + // Capture the context ID, setting it first if necessary + if ( (nid = context.getAttribute( "id" )) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", (nid = expando) ); + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[i] = "#" + nid + " " + toSelector( groups[i] ); + } + newSelector = groups.join( "," ); + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + } + + if ( newSelector ) { + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return (cache[ key + " " ] = value); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement("fieldset"); + + try { + return !!fn( el ); + } catch (e) { + return false; + } finally { + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split("|"), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[i] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( (cur = cur.nextSibling) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return (name === "input" || name === "button") && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + disabledAncestor( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction(function( argument ) { + argument = +argument; + return markFunction(function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ (j = matchIndexes[i]) ] ) { + seed[j] = !(matches[j] = seed[j]); + } + } + }); + }); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + // documentElement is verified for cases where it doesn't yet exist + // (such as loading iframes in IE - #4833) + var documentElement = elem && (elem.ownerDocument || elem).documentElement; + return documentElement ? documentElement.nodeName !== "HTML" : false; +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9-11, Edge + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + if ( preferredDoc !== document && + (subWindow = document.defaultView) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert(function( el ) { + el.className = "i"; + return !el.getAttribute("className"); + }); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert(function( el ) { + el.appendChild( document.createComment("") ); + return !el.getElementsByTagName("*").length; + }); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert(function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + }); + + // ID filter and find + if ( support.getById ) { + Expr.filter["ID"] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute("id") === attrId; + }; + }; + Expr.find["ID"] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter["ID"] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode("id"); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find["ID"] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode("id"); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( (elem = elems[i++]) ) { + node = elem.getAttributeNode("id"); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find["TAG"] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( (elem = results[i++]) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( (support.qsa = rnative.test( document.querySelectorAll )) ) { + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert(function( el ) { + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll("[msallowcapture^='']").length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll("[selected]").length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push("~="); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll(":checked").length ) { + rbuggyQSA.push(":checked"); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push(".#.+[+~]"); + } + }); + + assert(function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement("input"); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll("[name=d]").length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll(":enabled").length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll(":disabled").length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll("*,:x"); + rbuggyQSA.push(",.*:"); + }); + } + + if ( (support.matchesSelector = rnative.test( (matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector) )) ) { + + assert(function( el ) { + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + }); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + )); + } : + function( a, b ) { + if ( b ) { + while ( (b = b.parentNode) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + (!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) { + + // Choose the first element that is related to our preferred document + if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) { + return -1; + } + if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + return a === document ? -1 : + b === document ? 1 : + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( (cur = cur.parentNode) ) { + ap.unshift( cur ); + } + cur = b; + while ( (cur = cur.parentNode) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[i] === bp[i] ) { + i++; + } + + return i ? + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[i], bp[i] ) : + + // Otherwise nodes in our document sort first + ap[i] === preferredDoc ? -1 : + bp[i] === preferredDoc ? 1 : + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + // Set document vars if needed + if ( ( elem.ownerDocument || elem ) !== document ) { + setDocument( elem ); + } + + // Make sure that attribute selectors are quoted + expr = expr.replace( rattributeQuotes, "='$1']" ); + + if ( support.matchesSelector && documentIsHTML && + !compilerCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch (e) {} + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + // Set document vars if needed + if ( ( context.ownerDocument || context ) !== document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + // Set document vars if needed + if ( ( elem.ownerDocument || elem ) !== document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + (val = elem.getAttributeNode(name)) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return (sel + "").replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( (elem = results[i++]) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + // If no nodeType, this is expected to be an array + while ( (node = elem[i++]) ) { + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[1] = match[1].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape ); + + if ( match[2] === "~=" ) { + match[3] = " " + match[3] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[1] = match[1].toLowerCase(); + + if ( match[1].slice( 0, 3 ) === "nth" ) { + // nth-* requires argument + if ( !match[3] ) { + Sizzle.error( match[0] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) ); + match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" ); + + // other types prohibit arguments + } else if ( match[3] ) { + Sizzle.error( match[0] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[6] && match[2]; + + if ( matchExpr["CHILD"].test( match[0] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[3] ) { + match[2] = match[4] || match[5] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + // Get excess from tokenize (recursively) + (excess = tokenize( unquoted, true )) && + // advance to the next closing parenthesis + (excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) { + + // excess is a negative index + match[0] = match[0].slice( 0, excess ); + match[2] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { return true; } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + (pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) && + classCache( className, function( elem ) { + return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" ); + }); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + }; + }, + + "CHILD": function( type, what, argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( (node = node[ dir ]) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( (node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + (diff = nodeIndex = 0) || start.pop()) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + // Use previously-cached element index if available + if ( useCache ) { + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + // Use the same loop as above to seek `elem` from the start + while ( (node = ++nodeIndex && node && node[ dir ] || + (diff = nodeIndex = 0) || start.pop()) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction(function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[i] ); + seed[ idx ] = !( matches[ idx ] = matched[i] ); + } + }) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + // Potentially complex pseudos + "not": markFunction(function( selector ) { + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction(function( seed, matches, context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( (elem = unmatched[i]) ) { + seed[i] = !(matches[i] = elem); + } + } + }) : + function( elem, context, xml ) { + input[0] = elem; + matcher( input, null, xml, results ); + // Don't keep the element (issue #299) + input[0] = null; + return !results.pop(); + }; + }), + + "has": markFunction(function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + }), + + "contains": markFunction(function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || elem.innerText || getText( elem ) ).indexOf( text ) > -1; + }; + }), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + // lang value must be a valid identifier + if ( !ridentifier.test(lang || "") ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( (elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( (elem = elem.parentNode) && elem.nodeType === 1 ); + return false; + }; + }), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected); + }, + + "selected": function( elem ) { + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos["empty"]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo(function() { + return [ 0 ]; + }), + + "last": createPositionalPseudo(function( matchIndexes, length ) { + return [ length - 1 ]; + }), + + "eq": createPositionalPseudo(function( matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + }), + + "even": createPositionalPseudo(function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "odd": createPositionalPseudo(function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "lt": createPositionalPseudo(function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "gt": createPositionalPseudo(function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + }) + } +}; + +Expr.pseudos["nth"] = Expr.pseudos["eq"]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || (match = rcomma.exec( soFar )) ) { + if ( match ) { + // Don't consume trailing commas as valid + soFar = soFar.slice( match[0].length ) || soFar; + } + groups.push( (tokens = []) ); + } + + matched = false; + + // Combinators + if ( (match = rcombinators.exec( soFar )) ) { + matched = match.shift(); + tokens.push({ + value: matched, + // Cast descendant combinators to space + type: match[0].replace( rtrim, " " ) + }); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] || + (match = preFilters[ type ]( match ))) ) { + matched = match.shift(); + tokens.push({ + value: matched, + type: type, + matches: match + }); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[i].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || (elem[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {}); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( (oldCache = uniqueCache[ key ]) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return (newCache[ 2 ] = oldCache[ 2 ]); + } else { + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[i]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[0]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[i], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( (elem = unmatched[i]) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction(function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( (elem = temp[i]) ) { + matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( (elem = matcherOut[i]) ) { + // Restore matcherIn since elem is not yet a final match + temp.push( (matcherIn[i] = elem) ); + } + } + postFinder( null, (matcherOut = []), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( (elem = matcherOut[i]) && + (temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) { + + seed[temp] = !(results[temp] = elem); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + }); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[0].type ], + implicitRelative = leadingRelative || Expr.relative[" "], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + (checkContext = context).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( (matcher = Expr.relative[ tokens[i].type ]) ) { + matchers = [ addCombinator(elementMatcher( matchers ), matcher) ]; + } else { + matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[j].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" }) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( (tokens = tokens.slice( j )) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find["TAG"]( "*", outermost ), + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = (dirruns += contextBackup == null ? 1 : Math.random() || 0.1), + len = elems.length; + + if ( outermost ) { + outermostContext = context === document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && (elem = elems[i]) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + if ( !context && elem.ownerDocument !== document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( (matcher = elementMatchers[j++]) ) { + if ( matcher( elem, context || document, xml) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + // They will have gone through all possible matchers + if ( (elem = !matcher && elem) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( (matcher = setMatchers[j++]) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !(unmatched[i] || setMatched[i]) ) { + setMatched[i] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[i] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( selector, matcherFromGroupMatchers( elementMatchers, setMatchers ) ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( (selector = compiled.selector || selector) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[0] = match[0].slice( 0 ); + if ( tokens.length > 2 && (token = tokens[0]).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[1].type ] ) { + + context = ( Expr.find["ID"]( token.matches[0].replace(runescape, funescape), context ) || [] )[0]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr["needsContext"].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[i]; + + // Abort if we hit a combinator + if ( Expr.relative[ (type = token.type) ] ) { + break; + } + if ( (find = Expr.find[ type ]) ) { + // Search, expanding context for leading sibling combinators + if ( (seed = find( + token.matches[0].replace( runescape, funescape ), + rsibling.test( tokens[0].type ) && testContext( context.parentNode ) || context + )) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split("").sort( sortOrder ).join("") === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert(function( el ) { + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement("fieldset") ) & 1; +}); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert(function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute("href") === "#" ; +}) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + }); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert(function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +}) ) { + addHandle( "value", function( elem, name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + }); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert(function( el ) { + return el.getAttribute("disabled") == null; +}) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + (val = elem.getAttributeNode( name )) && val.specified ? + val.value : + null; + } + }); +} + +return Sizzle; + +})( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +var risSimple = /^.[^:#\[\.,]*$/; + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( jQuery.isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Simple selector that can be filtered directly, removing non-Elements + if ( risSimple.test( qualifier ) ) { + return jQuery.filter( qualifier, elements, not ); + } + + // Complex selector, compare the two sets, removing non-Elements + qualifier = jQuery.filter( qualifier, elements ); + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not && elem.nodeType === 1; + } ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( jQuery.isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( jQuery.isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( nodeName( elem, "iframe" ) ) { + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( jQuery.isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && jQuery.type( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && jQuery.isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && jQuery.isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = jQuery.isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && jQuery.isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( jQuery.isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + jQuery.isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + jQuery.isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + jQuery.isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + jQuery.isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( jQuery.type( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !jQuery.isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ jQuery.camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ jQuery.camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ jQuery.camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( jQuery.camelCase ); + } else { + key = jQuery.camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = jQuery.camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + jQuery.contains( elem.ownerDocument, elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + +var swap = function( elem, options, callback, args ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.apply( elem, args || [] ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, + scale = 1, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + do { + + // If previous iteration zeroed out, double until we get *something*. + // Use string for doubling so we don't accidentally see scale as unchanged below + scale = scale || ".5"; + + // Adjust and apply + initialInUnit = initialInUnit / scale; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Update scale, tolerating zero or NaN from tween.cur() + // Break the loop if scale is unchanged or perfect, or if we've just had enough. + } while ( + scale !== ( scale = currentValue() / initial ) && scale !== 1 && --maxIterations + ); + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]+)/i ); + +var rscriptType = ( /^$|\/(?:java|ecma)script/i ); + + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // Support: IE <=9 only + option: [ 1, "" ], + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +// Support: IE <=9 only +wrapMap.optgroup = wrapMap.option; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, contains, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( jQuery.type( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + contains = jQuery.contains( elem.ownerDocument, elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( contains ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; +} )(); +var documentElement = document.documentElement; + + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 only +// See #13393 for more info +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Don't attach events to noData or text/comment nodes (but allow plain objects) + if ( !elemData ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = {}; + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + // Make a writable jQuery.Event from the native event object + var event = jQuery.event.fix( nativeEvent ); + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + handlers = ( dataPriv.get( this, "events" ) || {} )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // Triggered event must either 1) have no namespace, or 2) have namespace(s) + // a subset or equal to those in the bound event (both can have no namespace). + if ( !event.rnamespace || event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: jQuery.isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + focus: { + + // Fire native event if possible so blur/focus sequence is correct + trigger: function() { + if ( this !== safeActiveElement() && this.focus ) { + this.focus(); + return false; + } + }, + delegateType: "focusin" + }, + blur: { + trigger: function() { + if ( this === safeActiveElement() && this.blur ) { + this.blur(); + return false; + } + }, + delegateType: "focusout" + }, + click: { + + // For checkbox, fire native event so checked state will be right + trigger: function() { + if ( this.type === "checkbox" && this.click && nodeName( this, "input" ) ) { + this.click(); + return false; + } + }, + + // For cross-browser consistency, don't fire native .click() on links + _default: function( event ) { + return nodeName( event.target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || jQuery.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + /* eslint-disable max-len */ + + // See https://github.com/eslint/eslint/issues/3229 + rxhtmlTag = /<(?!area|br|col|embed|hr|img|input|link|meta|param)(([a-z][^\/\0>\x20\t\r\n\f]*)[^>]*)\/>/gi, + + /* eslint-enable */ + + // Support: IE <=10 - 11, Edge 12 - 13 + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( ">tbody", elem )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + var match = rscriptTypeMasked.exec( elem.type ); + + if ( match ) { + elem.type = match[ 1 ]; + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, pdataCur, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.access( src ); + pdataCur = dataPriv.set( dest, pdataOld ); + events = pdataOld.events; + + if ( events ) { + delete pdataCur.handle; + pdataCur.events = {}; + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = concat.apply( [], args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + isFunction = jQuery.isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( isFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( isFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl ) { + jQuery._evalUrl( node.src ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && jQuery.contains( node.ownerDocument, node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html.replace( rxhtmlTag, "<$1>" ); + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = jQuery.contains( elem.ownerDocument, elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rmargin = ( /^margin/ ); + +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + div.style.cssText = + "box-sizing:border-box;" + + "position:relative;display:block;" + + "margin:auto;border:1px;padding:1px;" + + "top:1%;width:50%"; + div.innerHTML = ""; + documentElement.appendChild( container ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = divStyle.marginLeft === "2px"; + boxSizingReliableVal = divStyle.width === "4px"; + + // Support: Android 4.0 - 4.3 only + // Some styles come back with percentage values, even though they shouldn't + div.style.marginRight = "50%"; + pixelMarginRightVal = divStyle.marginRight === "4px"; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + var pixelPositionVal, boxSizingReliableVal, pixelMarginRightVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + container.style.cssText = "border:0;width:8px;height:0;top:0;left:-9999px;" + + "padding:0;margin-top:1px;position:absolute"; + container.appendChild( div ); + + jQuery.extend( support, { + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelMarginRight: function() { + computeStyleTests(); + return pixelMarginRightVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !jQuery.contains( elem.ownerDocument, elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelMarginRight() && rnumnonpx.test( ret ) && rmargin.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }, + + cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style; + +// Return a css property mapped to a potentially vendor prefixed property +function vendorPropName( name ) { + + // Shortcut for names that are not vendor prefixed + if ( name in emptyStyle ) { + return name; + } + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a property mapped along what jQuery.cssProps suggests or to +// a vendor prefixed property. +function finalPropName( name ) { + var ret = jQuery.cssProps[ name ]; + if ( !ret ) { + ret = jQuery.cssProps[ name ] = vendorPropName( name ) || name; + } + return ret; +} + +function setPositiveNumber( elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function augmentWidthOrHeight( elem, name, extra, isBorderBox, styles ) { + var i, + val = 0; + + // If we already have the right measurement, avoid augmentation + if ( extra === ( isBorderBox ? "border" : "content" ) ) { + i = 4; + + // Otherwise initialize for horizontal or vertical properties + } else { + i = name === "width" ? 1 : 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin, so add it if we want it + if ( extra === "margin" ) { + val += jQuery.css( elem, extra + cssExpand[ i ], true, styles ); + } + + if ( isBorderBox ) { + + // border-box includes padding, so remove it if we want content + if ( extra === "content" ) { + val -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // At this point, extra isn't border nor margin, so remove border + if ( extra !== "margin" ) { + val -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } else { + + // At this point, extra isn't content, so add padding + val += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // At this point, extra isn't content nor padding, so add border + if ( extra !== "padding" ) { + val += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + return val; +} + +function getWidthOrHeight( elem, name, extra ) { + + // Start with computed style + var valueIsBorderBox, + styles = getStyles( elem ), + val = curCSS( elem, name, styles ), + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Computed unit is not pixels. Stop here and return. + if ( rnumnonpx.test( val ) ) { + return val; + } + + // Check for style in case a browser which returns unreliable values + // for getComputedStyle silently falls back to the reliable elem.style + valueIsBorderBox = isBorderBox && + ( support.boxSizingReliable() || val === elem.style[ name ] ); + + // Fall back to offsetWidth/Height when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + if ( val === "auto" ) { + val = elem[ "offset" + name[ 0 ].toUpperCase() + name.slice( 1 ) ]; + } + + // Normalize "", auto, and prepare for extra + val = parseFloat( val ) || 0; + + // Use the active box-sizing model to add/subtract irrelevant styles + return ( val + + augmentWidthOrHeight( + elem, + name, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: { + "float": "cssFloat" + }, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = jQuery.camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + if ( type === "number" ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = jQuery.camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( i, name ) { + jQuery.cssHooks[ name ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, name, extra ); + } ) : + getWidthOrHeight( elem, name, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = extra && getStyles( elem ), + subtract = extra && augmentWidthOrHeight( + elem, + name, + extra, + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + styles + ); + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ name ] = value; + value = jQuery.css( elem, name ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( !rmargin.test( prefix ) ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && + ( tween.elem.style[ jQuery.cssProps[ tween.prop ] ] != null || + jQuery.cssHooks[ tween.prop ] ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = jQuery.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 13 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = jQuery.camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( jQuery.isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + jQuery.proxy( result.stop, result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( jQuery.isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( jQuery.isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + jQuery.isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !jQuery.isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( jQuery.isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue && type !== false ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = jQuery.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://html.spec.whatwg.org/multipage/infrastructure.html#strip-and-collapse-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( jQuery.isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( typeof value === "string" && value ) { + classes = value.match( rnothtmlwhite ) || []; + + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( jQuery.isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + if ( typeof value === "string" && value ) { + classes = value.match( rnothtmlwhite ) || []; + + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value; + + if ( typeof stateVal === "boolean" && type === "string" ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( jQuery.isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( type === "string" ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = value.match( rnothtmlwhite ) || []; + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, isFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + isFunction = jQuery.isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( isFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !jQuery.isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( dataPriv.get( cur, "events" ) || {} )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && jQuery.isFunction( elem[ type ] ) && !jQuery.isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + elem[ type ](); + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +jQuery.each( ( "blur focus focusin focusout resize scroll click dblclick " + + "mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " + + "change select submit keydown keypress keyup contextmenu" ).split( " " ), + function( i, name ) { + + // Handle event binding + jQuery.fn[ name ] = function( data, fn ) { + return arguments.length > 0 ? + this.on( name, null, data, fn ) : + this.trigger( name ); + }; +} ); + +jQuery.fn.extend( { + hover: function( fnOver, fnOut ) { + return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver ); + } +} ); + + + + +support.focusin = "onfocusin" in window; + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + var doc = this.ownerDocument || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = jQuery.now(); + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && jQuery.type( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = jQuery.isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( jQuery.isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() ] = match[ 2 ]; + } + } + match = responseHeaders[ key.toLowerCase() ]; + } + return match == null ? null : match; + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 13 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available, append data to url + if ( s.data ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce++ ) + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( jQuery.isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + + +jQuery._evalUrl = function( url ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + "throws": true + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( jQuery.isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( jQuery.isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var isFunction = jQuery.isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( isFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain requests + if ( s.crossDomain ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " +{% endmacro %} \ No newline at end of file diff --git a/_static/websupport.js b/_static/websupport.js new file mode 100644 index 000000000..78e14bb4a --- /dev/null +++ b/_static/websupport.js @@ -0,0 +1,808 @@ +/* + * websupport.js + * ~~~~~~~~~~~~~ + * + * sphinx.websupport utilities for all documentation. + * + * :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +(function($) { + $.fn.autogrow = function() { + return this.each(function() { + var textarea = this; + + $.fn.autogrow.resize(textarea); + + $(textarea) + .focus(function() { + textarea.interval = setInterval(function() { + $.fn.autogrow.resize(textarea); + }, 500); + }) + .blur(function() { + clearInterval(textarea.interval); + }); + }); + }; + + $.fn.autogrow.resize = function(textarea) { + var lineHeight = parseInt($(textarea).css('line-height'), 10); + var lines = textarea.value.split('\n'); + var columns = textarea.cols; + var lineCount = 0; + $.each(lines, function() { + lineCount += Math.ceil(this.length / columns) || 1; + }); + var height = lineHeight * (lineCount + 1); + $(textarea).css('height', height); + }; +})(jQuery); + +(function($) { + var comp, by; + + function init() { + initEvents(); + initComparator(); + } + + function initEvents() { + $(document).on("click", 'a.comment-close', function(event) { + event.preventDefault(); + hide($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.vote', function(event) { + event.preventDefault(); + handleVote($(this)); + }); + $(document).on("click", 'a.reply', function(event) { + event.preventDefault(); + openReply($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.close-reply', function(event) { + event.preventDefault(); + closeReply($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.sort-option', function(event) { + event.preventDefault(); + handleReSort($(this)); + }); + $(document).on("click", 'a.show-proposal', function(event) { + event.preventDefault(); + showProposal($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.hide-proposal', function(event) { + event.preventDefault(); + hideProposal($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.show-propose-change', function(event) { + event.preventDefault(); + showProposeChange($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.hide-propose-change', function(event) { + event.preventDefault(); + hideProposeChange($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.accept-comment', function(event) { + event.preventDefault(); + acceptComment($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.delete-comment', function(event) { + event.preventDefault(); + deleteComment($(this).attr('id').substring(2)); + }); + $(document).on("click", 'a.comment-markup', function(event) { + event.preventDefault(); + toggleCommentMarkupBox($(this).attr('id').substring(2)); + }); + } + + /** + * Set comp, which is a comparator function used for sorting and + * inserting comments into the list. + */ + function setComparator() { + // If the first three letters are "asc", sort in ascending order + // and remove the prefix. + if (by.substring(0,3) == 'asc') { + var i = by.substring(3); + comp = function(a, b) { return a[i] - b[i]; }; + } else { + // Otherwise sort in descending order. + comp = function(a, b) { return b[by] - a[by]; }; + } + + // Reset link styles and format the selected sort option. + $('a.sel').attr('href', '#').removeClass('sel'); + $('a.by' + by).removeAttr('href').addClass('sel'); + } + + /** + * Create a comp function. If the user has preferences stored in + * the sortBy cookie, use those, otherwise use the default. + */ + function initComparator() { + by = 'rating'; // Default to sort by rating. + // If the sortBy cookie is set, use that instead. + if (document.cookie.length > 0) { + var start = document.cookie.indexOf('sortBy='); + if (start != -1) { + start = start + 7; + var end = document.cookie.indexOf(";", start); + if (end == -1) { + end = document.cookie.length; + by = unescape(document.cookie.substring(start, end)); + } + } + } + setComparator(); + } + + /** + * Show a comment div. + */ + function show(id) { + $('#ao' + id).hide(); + $('#ah' + id).show(); + var context = $.extend({id: id}, opts); + var popup = $(renderTemplate(popupTemplate, context)).hide(); + popup.find('textarea[name="proposal"]').hide(); + popup.find('a.by' + by).addClass('sel'); + var form = popup.find('#cf' + id); + form.submit(function(event) { + event.preventDefault(); + addComment(form); + }); + $('#s' + id).after(popup); + popup.slideDown('fast', function() { + getComments(id); + }); + } + + /** + * Hide a comment div. + */ + function hide(id) { + $('#ah' + id).hide(); + $('#ao' + id).show(); + var div = $('#sc' + id); + div.slideUp('fast', function() { + div.remove(); + }); + } + + /** + * Perform an ajax request to get comments for a node + * and insert the comments into the comments tree. + */ + function getComments(id) { + $.ajax({ + type: 'GET', + url: opts.getCommentsURL, + data: {node: id}, + success: function(data, textStatus, request) { + var ul = $('#cl' + id); + var speed = 100; + $('#cf' + id) + .find('textarea[name="proposal"]') + .data('source', data.source); + + if (data.comments.length === 0) { + ul.html('
  • No comments yet.
    • '); + ul.data('empty', true); + } else { + // If there are comments, sort them and put them in the list. + var comments = sortComments(data.comments); + speed = data.comments.length * 100; + appendComments(comments, ul); + ul.data('empty', false); + } + $('#cn' + id).slideUp(speed + 200); + ul.slideDown(speed); + }, + error: function(request, textStatus, error) { + showError('Oops, there was a problem retrieving the comments.'); + }, + dataType: 'json' + }); + } + + /** + * Add a comment via ajax and insert the comment into the comment tree. + */ + function addComment(form) { + var node_id = form.find('input[name="node"]').val(); + var parent_id = form.find('input[name="parent"]').val(); + var text = form.find('textarea[name="comment"]').val(); + var proposal = form.find('textarea[name="proposal"]').val(); + + if (text == '') { + showError('Please enter a comment.'); + return; + } + + // Disable the form that is being submitted. + form.find('textarea,input').attr('disabled', 'disabled'); + + // Send the comment to the server. + $.ajax({ + type: "POST", + url: opts.addCommentURL, + dataType: 'json', + data: { + node: node_id, + parent: parent_id, + text: text, + proposal: proposal + }, + success: function(data, textStatus, error) { + // Reset the form. + if (node_id) { + hideProposeChange(node_id); + } + form.find('textarea') + .val('') + .add(form.find('input')) + .removeAttr('disabled'); + var ul = $('#cl' + (node_id || parent_id)); + if (ul.data('empty')) { + $(ul).empty(); + ul.data('empty', false); + } + insertComment(data.comment); + var ao = $('#ao' + node_id); + ao.find('img').attr({'src': opts.commentBrightImage}); + if (node_id) { + // if this was a "root" comment, remove the commenting box + // (the user can get it back by reopening the comment popup) + $('#ca' + node_id).slideUp(); + } + }, + error: function(request, textStatus, error) { + form.find('textarea,input').removeAttr('disabled'); + showError('Oops, there was a problem adding the comment.'); + } + }); + } + + /** + * Recursively append comments to the main comment list and children + * lists, creating the comment tree. + */ + function appendComments(comments, ul) { + $.each(comments, function() { + var div = createCommentDiv(this); + ul.append($(document.createElement('li')).html(div)); + appendComments(this.children, div.find('ul.comment-children')); + // To avoid stagnating data, don't store the comments children in data. + this.children = null; + div.data('comment', this); + }); + } + + /** + * After adding a new comment, it must be inserted in the correct + * location in the comment tree. + */ + function insertComment(comment) { + var div = createCommentDiv(comment); + + // To avoid stagnating data, don't store the comments children in data. + comment.children = null; + div.data('comment', comment); + + var ul = $('#cl' + (comment.node || comment.parent)); + var siblings = getChildren(ul); + + var li = $(document.createElement('li')); + li.hide(); + + // Determine where in the parents children list to insert this comment. + for(var i=0; i < siblings.length; i++) { + if (comp(comment, siblings[i]) <= 0) { + $('#cd' + siblings[i].id) + .parent() + .before(li.html(div)); + li.slideDown('fast'); + return; + } + } + + // If we get here, this comment rates lower than all the others, + // or it is the only comment in the list. + ul.append(li.html(div)); + li.slideDown('fast'); + } + + function acceptComment(id) { + $.ajax({ + type: 'POST', + url: opts.acceptCommentURL, + data: {id: id}, + success: function(data, textStatus, request) { + $('#cm' + id).fadeOut('fast'); + $('#cd' + id).removeClass('moderate'); + }, + error: function(request, textStatus, error) { + showError('Oops, there was a problem accepting the comment.'); + } + }); + } + + function deleteComment(id) { + $.ajax({ + type: 'POST', + url: opts.deleteCommentURL, + data: {id: id}, + success: function(data, textStatus, request) { + var div = $('#cd' + id); + if (data == 'delete') { + // Moderator mode: remove the comment and all children immediately + div.slideUp('fast', function() { + div.remove(); + }); + return; + } + // User mode: only mark the comment as deleted + div + .find('span.user-id:first') + .text('[deleted]').end() + .find('div.comment-text:first') + .text('[deleted]').end() + .find('#cm' + id + ', #dc' + id + ', #ac' + id + ', #rc' + id + + ', #sp' + id + ', #hp' + id + ', #cr' + id + ', #rl' + id) + .remove(); + var comment = div.data('comment'); + comment.username = '[deleted]'; + comment.text = '[deleted]'; + div.data('comment', comment); + }, + error: function(request, textStatus, error) { + showError('Oops, there was a problem deleting the comment.'); + } + }); + } + + function showProposal(id) { + $('#sp' + id).hide(); + $('#hp' + id).show(); + $('#pr' + id).slideDown('fast'); + } + + function hideProposal(id) { + $('#hp' + id).hide(); + $('#sp' + id).show(); + $('#pr' + id).slideUp('fast'); + } + + function showProposeChange(id) { + $('#pc' + id).hide(); + $('#hc' + id).show(); + var textarea = $('#pt' + id); + textarea.val(textarea.data('source')); + $.fn.autogrow.resize(textarea[0]); + textarea.slideDown('fast'); + } + + function hideProposeChange(id) { + $('#hc' + id).hide(); + $('#pc' + id).show(); + var textarea = $('#pt' + id); + textarea.val('').removeAttr('disabled'); + textarea.slideUp('fast'); + } + + function toggleCommentMarkupBox(id) { + $('#mb' + id).toggle(); + } + + /** Handle when the user clicks on a sort by link. */ + function handleReSort(link) { + var classes = link.attr('class').split(/\s+/); + for (var i=0; iThank you! Your comment will show up ' + + 'once it is has been approved by a moderator.'); + } + // Prettify the comment rating. + comment.pretty_rating = comment.rating + ' point' + + (comment.rating == 1 ? '' : 's'); + // Make a class (for displaying not yet moderated comments differently) + comment.css_class = comment.displayed ? '' : ' moderate'; + // Create a div for this comment. + var context = $.extend({}, opts, comment); + var div = $(renderTemplate(commentTemplate, context)); + + // If the user has voted on this comment, highlight the correct arrow. + if (comment.vote) { + var direction = (comment.vote == 1) ? 'u' : 'd'; + div.find('#' + direction + 'v' + comment.id).hide(); + div.find('#' + direction + 'u' + comment.id).show(); + } + + if (opts.moderator || comment.text != '[deleted]') { + div.find('a.reply').show(); + if (comment.proposal_diff) + div.find('#sp' + comment.id).show(); + if (opts.moderator && !comment.displayed) + div.find('#cm' + comment.id).show(); + if (opts.moderator || (opts.username == comment.username)) + div.find('#dc' + comment.id).show(); + } + return div; + } + + /** + * A simple template renderer. Placeholders such as <%id%> are replaced + * by context['id'] with items being escaped. Placeholders such as <#id#> + * are not escaped. + */ + function renderTemplate(template, context) { + var esc = $(document.createElement('div')); + + function handle(ph, escape) { + var cur = context; + $.each(ph.split('.'), function() { + cur = cur[this]; + }); + return escape ? esc.text(cur || "").html() : cur; + } + + return template.replace(/<([%#])([\w\.]*)\1>/g, function() { + return handle(arguments[2], arguments[1] == '%' ? true : false); + }); + } + + /** Flash an error message briefly. */ + function showError(message) { + $(document.createElement('div')).attr({'class': 'popup-error'}) + .append($(document.createElement('div')) + .attr({'class': 'error-message'}).text(message)) + .appendTo('body') + .fadeIn("slow") + .delay(2000) + .fadeOut("slow"); + } + + /** Add a link the user uses to open the comments popup. */ + $.fn.comment = function() { + return this.each(function() { + var id = $(this).attr('id').substring(1); + var count = COMMENT_METADATA[id]; + var title = count + ' comment' + (count == 1 ? '' : 's'); + var image = count > 0 ? opts.commentBrightImage : opts.commentImage; + var addcls = count == 0 ? ' nocomment' : ''; + $(this) + .append( + $(document.createElement('a')).attr({ + href: '#', + 'class': 'sphinx-comment-open' + addcls, + id: 'ao' + id + }) + .append($(document.createElement('img')).attr({ + src: image, + alt: 'comment', + title: title + })) + .click(function(event) { + event.preventDefault(); + show($(this).attr('id').substring(2)); + }) + ) + .append( + $(document.createElement('a')).attr({ + href: '#', + 'class': 'sphinx-comment-close hidden', + id: 'ah' + id + }) + .append($(document.createElement('img')).attr({ + src: opts.closeCommentImage, + alt: 'close', + title: 'close' + })) + .click(function(event) { + event.preventDefault(); + hide($(this).attr('id').substring(2)); + }) + ); + }); + }; + + var opts = { + processVoteURL: '/_process_vote', + addCommentURL: '/_add_comment', + getCommentsURL: '/_get_comments', + acceptCommentURL: '/_accept_comment', + deleteCommentURL: '/_delete_comment', + commentImage: '/static/_static/comment.png', + closeCommentImage: '/static/_static/comment-close.png', + loadingImage: '/static/_static/ajax-loader.gif', + commentBrightImage: '/static/_static/comment-bright.png', + upArrow: '/static/_static/up.png', + downArrow: '/static/_static/down.png', + upArrowPressed: '/static/_static/up-pressed.png', + downArrowPressed: '/static/_static/down-pressed.png', + voting: false, + moderator: false + }; + + if (typeof COMMENT_OPTIONS != "undefined") { + opts = jQuery.extend(opts, COMMENT_OPTIONS); + } + + var popupTemplate = '\ +
    \ +

    \ + Sort by:\ + best rated\ + newest\ + oldest\ +

    \ +
    Comments
    \ +
    \ + loading comments...
    \ +
      \ +
      \ +

      Add a comment\ + (markup):

      \ +
      \ + reStructured text markup: *emph*, **strong**, \ + ``code``, \ + code blocks: :: and an indented block after blank line
      \ +
      \ + \ +

      \ + \ + Propose a change ▹\ + \ + \ + Propose a change ▿\ + \ +

      \ + \ + \ + \ + \ +
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      '; + + var commentTemplate = '\ +
      \ +
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      \ + \ + \ + \ + \ + \ + \ +
      \ +
      \ + \ + \ + \ + \ + \ + \ +
      \ +
      \ +
      \ +

      \ + <%username%>\ + <%pretty_rating%>\ + <%time.delta%>\ +

      \ +
      <#text#>
      \ +

      \ + \ + reply ▿\ + proposal ▹\ + proposal ▿\ + \ + \ +

      \ + 
      \
+<#proposal_diff#>\
+
      \ +
        \ +
        \ +
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        \ + '; + + var replyTemplate = '\ +
      • \ +
        \ +
        \ + \ + \ + \ + \ + \ +
        \ +
        \ +
        • '; + + $(document).ready(function() { + init(); + }); +})(jQuery); + +$(document).ready(function() { + // add comment anchors for all paragraphs that are commentable + $('.sphinx-has-comment').comment(); + + // highlight search words in search results + $("div.context").each(function() { + var params = $.getQueryParameters(); + var terms = (params.q) ? params.q[0].split(/\s+/) : []; + var result = $(this); + $.each(terms, function() { + result.highlightText(this.toLowerCase(), 'highlighted'); + }); + }); + + // directly open comment window if requested + var anchor = document.location.hash; + if (anchor.substring(0, 9) == '#comment-') { + $('#ao' + anchor.substring(9)).click(); + document.location.hash = '#s' + anchor.substring(9); + } +}); diff --git a/create_new_backend.html b/create_new_backend.html new file mode 100644 index 000000000..f5a8e1fe7 --- /dev/null +++ b/create_new_backend.html @@ -0,0 +1,1346 @@ + + + + + + + + + Integrating a Third-party Library to oneAPI Math Kernel Library (oneMKL) Interfaces — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        Integrating a Third-party Library to oneAPI Math Kernel Library (oneMKL) Interfaces

        +

        This step-by-step tutorial provides examples for enabling new third-party libraries in oneMKL.

        +

        oneMKL has a header-based implementation of the interface layer (include directory) and a source-based implementation of the backend layer for each third-party library (src directory). To enable a third-party library, you must update both parts of oneMKL and integrate the new third-party library to the oneMKL build and test systems.

        +

        1. Create Header Files

        +

        2. Integrate Header Files

        +

        3. Create Wrappers

        +

        4. Integrate Wrappers To the Build System

        +

        5. Update the Test System

        +
        +

        1. Create Header Files

        +

        For each new backend library, you should create the following two header files:

        +
          +

        • Header file with a declaration of entry points to the new third-party library wrappers

          • +

        • Compiler-time dispatching interface (see oneMKL Usage Models) for new third-party libraries

          • +
        +

        Header File Example: command to generate the header file with a declaration of BLAS entry points in the oneapi::mkl::newlib namespace

        +
        python scripts/generate_backend_api.py include/oneapi/mkl/blas.hpp \                                  # Base header file
+                                       include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Output header file
+                                       oneapi::mkl::newlib                                            # Wrappers namespace
+
        +
        +

        Code snippet of the generated header file include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp

        +
        namespace oneapi {
+namespace mkl {
+namespace newlib {
+
+void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer<float, 1> &x, std::int64_t incx,
+          cl::sycl::buffer<float, 1> &result);
+
        +
        +

        Compile-time Dispatching Interface Example: command to generate the compile-time dispatching interface template instantiations for newlib and supported device newdevice

        +
        python scripts/generate_ct_instant.py   include/oneapi/mkl/blas/detail/blas_ct_templates.hpp \         # Base header file
+                                        include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp \            # Output header file
+                                        include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Header file with declaration of entry points to wrappers
+                                        newlib \                                                       # Library name
+                                        newdevice \                                                    # Backend name
+                                        oneapi::mkl::newlib                                            # Wrappers namespace
+
        +
        +

        Code snippet of the generated header file include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp

        +
        namespace oneapi {
+namespace mkl {
+namespace blas {
+
+template <>
+void asum<library::newlib, backend::newdevice>(cl::sycl::queue &queue, std::int64_t n,
+                                               cl::sycl::buffer<float, 1> &x, std::int64_t incx,
+                                               cl::sycl::buffer<float, 1> &result) {
+    asum_precondition(queue, n, x, incx, result);
+    oneapi::mkl::newlib::asum(queue, n, x, incx, result);
+    asum_postcondition(queue, n, x, incx, result);
+}
+
        +
        +
        +
        +

        2. Integrate Header Files

        +

        Below you can see structure of oneMKL top-level include directory:

        +
        include/
+    oneapi/
+        mkl/
+            mkl.hpp -> oneMKL spec APIs
+            types.hpp  -> oneMKL spec types
+            blas.hpp   -> oneMKL BLAS APIs w/ pre-check/dispatching/post-check
+            detail/    -> implementation specific header files
+                exceptions.hpp        -> oneMKL exception classes
+                backends.hpp          -> list of oneMKL backends
+                backends_table.hpp    -> table of backend libraries for each domain and device
+                get_device_id.hpp     -> function to query device information from queue for Run-time dispatching
+            blas/
+                predicates.hpp -> oneMKL BLAS pre-check post-check
+                detail/        -> BLAS domain specific implementation details
+                    blas_loader.hpp       -> oneMKL Run-time BLAS API
+                    blas_ct_templates.hpp -> oneMKL Compile-time BLAS API general templates
+                    cublas/
+                        blas_ct.hpp            -> oneMKL Compile-time BLAS API template instantiations for <cublas>
+                        onemkl_blas_cublas.hpp -> backend wrappers library API
+                    mklcpu/
+                        blas_ct.hpp            -> oneMKL Compile-time BLAS API template instantiations for <mklcpu>
+                        onemkl_blas_mklcpu.hpp -> backend wrappers library API
+                    <other backends>/
+            <other domains>/
+
        +
        +

        To integrate the new third-party library to a oneMKL header-based part, following files from this structure should be updated:

        +
          +

        • include/oneapi/mkl/detail/backends.hpp: add the new backend

          +

          Example: add the newbackend backend

          +
             enum class backend { mklcpu,
++                       newbackend,
+
          +
          +
             static backendmap backend_map = { { backend::mklcpu, "mklcpu" },
++                                    { backend::newbackend, "newbackend" },
+
          +
          +
          • +

        • include/oneapi/mkl/detail/backends_table.hpp: add new backend library for supported domain(s) and device(s)

          +

          Example: enable newlib for blas domain and newdevice device

          +
             enum class device : uint16_t { x86cpu,
+                                  ...
++                                 newdevice
+                                };
+
+   static std::map<domain, std::map<device, std::vector<const char*>>> libraries = {
+       { domain::blas,
+         { { device::x86cpu,
+             {
+   #ifdef ENABLE_MKLCPU_BACKEND
+                 LIB_NAME("blas_mklcpu")
+   #endif
+              } },
++          { device::newdevice,
++            {
++  #ifdef ENABLE_NEWLIB_BACKEND
++                 LIB_NAME("blas_newlib")
++  #endif
++             } },
+
          +
          +
          • +

        • include/oneapi/mkl/detail/get_device_id.hpp: add new device detection mechanism for Run-time dispatching

          +

          Example: enable newdevice if the queue is targeted for the Host

          +
             inline oneapi::mkl::device get_device_id(cl::sycl::queue &queue) {
+       oneapi::mkl::device device_id;
++      if (queue.is_host())
++          device_id=device::newdevice;
+
          +
          +
          • +

        • include/oneapi/mkl/blas.hpp: include the generated header file for the compile-time dispatching interface (see oneMKL Usage Models)

          +

          Example: add include/oneapi/mkl/blas/detail/newlib/blas_ct.hpp generated at the 1. Create Header Files step

          +
             #include "oneapi/mkl/blas/detail/mklcpu/blas_ct.hpp"
+   #include "oneapi/mkl/blas/detail/mklgpu/blas_ct.hpp"
++  #include "oneapi/mkl/blas/detail/newlib/blas_ct.hpp"
+
          +
          +
          • +
        +

        The new files generated at the 1. Create Header Files step result in the following updated structure of the BLAS domain header files.

        +
        include/
+    oneapi/
+        mkl/
+            blas.hpp -> oneMKL BLAS APIs w/ pre-check/dispatching/post-check
+            blas/
+                predicates.hpp -> oneMKL BLAS pre-check post-check
+                detail/        -> BLAS domain specific implementation details
+                    blas_loader.hpp       -> oneMKL Run-time BLAS API
+                    blas_ct_templates.hpp -> oneMKL Compile-time BLAS API general templates
+                    cublas/
+                        blas_ct.hpp            -> oneMKL Compile-time BLAS API template instantiations for <cublas>
+                        onemkl_blas_cublas.hpp -> backend wrappers library API
+                    mklcpu/
+                        blas_ct.hpp            -> oneMKL Compile-time BLAS API template instantiations for <mklcpu>
+                        onemkl_blas_mklcpu.hpp -> backend wrappers library API
+    +              newlib/
+    +                  blas_ct.hpp            -> oneMKL Compile-time BLAS API template instantiations for <newbackend>
+    +                  onemkl_blas_newlib.hpp -> backend wrappers library API
+                    <other backends>/
+            <other domains>/
+
        +
        +
        +
        +

        3. Create Wrappers

        +

        Wrappers convert Data Parallel C++ (DPC++) input data types to third-party library data types and call corresponding implementation from the third-party library. Wrappers for each third-party library are built to separate oneMKL backend libraries. The libonemkl.so dispatcher library loads the wrappers at run-time if you are using the interface for run-time dispatching, or you will link with them directly in case you are using the interface for compile-time dispatching (for more information see oneMKL Usage Models).

        +

        All wrappers and dispatcher library implementations are in the src directory:

        +
        src/
+    include/
+        function_table_initializer.hpp -> general loader implementation w/ global libraries table
+    blas/
+        function_table.hpp -> loaded BLAS functions declaration
+        blas_loader.cpp -> BLAS wrappers for loader
+        backends/
+            cublas/ -> cuBLAS wrappers
+            mklcpu/ -> Intel oneMKL CPU wrappers
+            mklgpu/ -> Intel oneMKL GPU wrappers
+            <other backend libraries>/
+    <other domains>/
+
        +
        +

        Each backend library should contain a table of all functions from the chosen domain.

        +

        scripts/generate_wrappers.py can help to generate wrappers with the “Not implemented” exception for all functions based on the provided header file.

        +

        You can modify wrappers generated with this script to enable third-party library functionality.

        +

        Example: generate wrappers for newlib based on the header files generated and integrated previously, and enable only one asum function

        +

        The command below generates two new files:

        +
          +

        • src/blas/backends/newlib/newlib_wrappers.cpp - DPC++ wrappers for all functions from include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp

          • +

        • src/blas/backends/newlib/newlib_wrappers_table_dyn.cpp - structure of symbols for run-time dispatcher (in the same location as wrappers), suffix _dyn indicates that this file is required for dynamic library only.

          • +
        +
        python scripts/generate_wrappers.py include/oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp \ # Base header file
+                                    src/blas/function_table.hpp \                                  # Declaration for structure of symbols
+                                    src/blas/backends/newlib/newlib_wrappers.cpp \                 # Output wrappers
+                                    newlib                                                         # Library name
+
        +
        +

        You can then modify src/blas/backends/newlib/newlib_wrappers.cpp to enable the C function newlib_sasum from the third-party library libnewlib.so.

        +

        To enable this function:

        +
          +

        • Include the header file newlib.h with the newlib_sasum function declaration

          • +

        • Convert all DPC++ parameters to proper C types: use the get_access method for input and output DPC++ buffers to get row pointers

          • +

        • Submit the DPC++ kernel with a C function call to newlib as single_task

          • +
        +

        The following code snippet is updated for src/blas/backends/newlib/newlib_wrappers.cpp:

        +
            #include <CL/sycl.hpp>
+
+    #include "oneapi/mkl/types.hpp"
+
+    #include "oneapi/mkl/blas/detail/newlib/onemkl_blas_newlib.hpp"
++
++    #include "newlib.h"
+
+    namespace oneapi {
+    namespace mkl {
+    namespace newlib {
+
+    void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer<float, 1> &x, std::int64_t incx,
+               cl::sycl::buffer<float, 1> &result) {
+-       throw std::runtime_error("Not implemented for newlib");
++       queue.submit([&](cl::sycl::handler &cgh) {
++           auto accessor_x      = x.get_access<cl::sycl::access::mode::read>(cgh);
++           auto accessor_result = result.get_access<cl::sycl::access::mode::write>(cgh);
++           cgh.single_task<class newlib_sasum>([=]() {
++               accessor_result[0] = ::newlib_sasum((const int)n, accessor_x.get_pointer(), (const int)incx);
++           });
++       });
+    }
+
+    void asum(cl::sycl::queue &queue, std::int64_t n, cl::sycl::buffer<double, 1> &x, std::int64_t incx,
+              cl::sycl::buffer<double, 1> &result) {
+        throw std::runtime_error("Not implemented for newlib");
+    }
+
        +
        +

        Updated structure of the src folder with the newlib wrappers:

        +
        src/
+    blas/
+        loader.hpp -> general loader implementation w/ global libraries table
+        function_table.hpp -> loaded BLAS functions declaration
+        blas_loader.cpp -> BLAS wrappers for loader
+        backends/
+            cublas/ -> cuBLAS wrappers
+            mklcpu/ -> Intel oneMKL CPU wrappers
+            mklgpu/ -> Intel oneMKL GPU wrappers
+ +          newlib/
+ +              newlib.h
+ +              newlib_wrappers.cpp
+ +              newlib_wrappers_table_dyn.cpp
+            <other backend libraries>/
+    <other domains>/
+
        +
        +
        +
        +

        4. Integrate Wrappers to the Build System

        +

        Here is the list of files that should be created/updated to integrate the new wrappers for the third-party library to the oneMKL build system:

        +
          +

        • Add the new option ENABLE_XXX_BACKEND for the new third-party library to the top of the CMakeList.txt file.

          +

          Example: changes for newlib in the top of the CMakeList.txt file

          +
              option(ENABLE_MKLCPU_BACKEND "" ON)
+    option(ENABLE_MKLGPU_BACKEND "" ON)
++   option(ENABLE_NEWLIB_BACKEND "" ON)
+
          +
          +
          • +

        • Add the new directory (src/<domain>/backends/<new_directory>) with the wrappers for the new third-party library under the ENABLE_XXX_BACKEND condition to the src/<domain>/backends/CMakeList.txt file.

          +

          Example: changes for newlib in src/blas/backends/CMakeLists.txt

          +
              if(ENABLE_MKLCPU_BACKEND)
+        add_subdirectory(mklcpu)
+    endif()
++
++   if(ENABLE_NEWLIB_BACKEND)
++       add_subdirectory(newlib)
++   endif()
+
          +
          +
          • +

        • Create the cmake/FindXXX.cmake cmake config file to find the new third-party library and its dependencies.

          +

          Example: new config file cmake/FindNEWLIB.cmake for newlib

          +
          include_guard()
+# Find library by name in NEWLIB_ROOT cmake variable or environment variable NEWLIBROOT
+find_library(NEWLIB_LIBRARY NAMES newlib
+    HINTS ${NEWLIB_ROOT} $ENV{NEWLIBROOT}
+    PATH_SUFFIXES "lib")
+# Make sure that the library was found
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(NEWLIB REQUIRED_VARS NEWLIB_LIBRARY)
+# Set cmake target for the library
+add_library(ONEMKL::NEWLIB::NEWLIB UNKNOWN IMPORTED)
+set_target_properties(ONEMKL::NEWLIB::NEWLIB PROPERTIES
+    IMPORTED_LOCATION ${NEWLIB_LIBRARY})
+
          +
          +
          • +

        • Create the src/<domain>/backends/<new_directory>/CMakeList.txt cmake config file to specify how to build the backend layer for the new third-party library.

          +

          scripts/generate_cmake.py can help to generate the initial src/<domain>/backends/<new_directory>/CMakeList.txt config file automatically for all files in the directory. +Note: all source files with the _dyn suffix are added to build if the target is a dynamic library only.

          +

          Example: command to generate the cmake config file for the src/blas/backends/newlib directory

          +
          python scripts/generate_cmake.py src/blas/backends/newlib \ # Full path to the directory
+                                 newlib                     # Library name
+
          +
          +

          You should manually update the generated config file with information about the new cmake/FindXXX.cmake file and instructions about how to link with the third-party library.

          +

          Example: update the generated src/blas/backends/newlib/CMakeLists.txt file

          +
              # Add third-party library
+-   # find_package(XXX REQUIRED)
++   find_package(NEWLIB REQUIRED)
+
          +
          +
              target_link_libraries(${LIB_OBJ}
+        PUBLIC ONEMKL::SYCL::SYCL
+-       # Add third-party library to link with here
++       PUBLIC ONEMKL::NEWLIB::NEWLIB
+    )
+
          +
          +
          • +
        +

        Now you can build the backend library for newlib to make sure the third-party library integration was completed successfully (for more information, see Build with cmake)

        +
        cd build/
+cmake .. -DNEWLIB_ROOT=<path/to/newlib> \
+    -DENABLE_MKLCPU_BACKEND=OFF \
+    -DENABLE_MKLGPU_BACKEND=OFF \
+    -DENABLE_NEWLIB_BACKEND=ON \           # Enable new third-party library backend
+    -DBUILD_FUNCTIONAL_TESTS=OFF           # At this step we want build only
+cmake --build . -j4
+
        +
        +
        +
        +

        5. Update the Test System

        +

        Update the following files to enable the new third-party library for unit tests:

        +
          +

        • src/config.hpp.in: add a cmake option for the new third-party library so this macro can be propagated to unit tests

          +

          Example: add ENABLE_NEWLIB_BACKEND

          +
             #cmakedefine ENABLE_MKLCPU_BACKEND
++  #cmakedefine ENABLE_NEWLIB_BACKEND
+
          +
          +
          • +

        • tests/unit_tests/CMakeLists.txt: add instructions about how to link tests with the new backend library

          +

          Example: add the newlib backend library

          +
             if(ENABLE_MKLCPU_BACKEND)
+       add_dependencies(test_main_ct onemkl_blas_mklcpu)
+       if(BUILD_SHARED_LIBS)
+           list(APPEND ONEMKL_LIBRARIES onemkl_blas_mklcpu)
+       else()
+           list(APPEND ONEMKL_LIBRARIES -foffload-static-lib=${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libonemkl_blas_mklcpu.a)
+           find_package(MKL REQUIRED)
+           list(APPEND ONEMKL_LIBRARIES ${MKL_LINK_C})
+       endif()
+   endif()
++
++    if(ENABLE_NEWLIB_BACKEND)
++       add_dependencies(test_main_ct onemkl_blas_newlib)
++       if(BUILD_SHARED_LIBS)
++           list(APPEND ONEMKL_LIBRARIES onemkl_blas_newlib)
++       else()
++           list(APPEND ONEMKL_LIBRARIES -foffload-static-lib=${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libonemkl_blas_newlib.a)
++           find_package(NEWLIB REQUIRED)
++           list(APPEND ONEMKL_LIBRARIES ONEMKL::NEWLIB::NEWLIB)
++       endif()
++   endif()
+
          +
          +
          • +

        • tests/unit_tests/include/test_helper.hpp: add the helper function for the compile-time dispatching interface with the new backend, and specify the device for which it should be called

          +

          Example: add the helper function for the newlib compile-time dispatching interface with newdevice if it is the Host

          +
             #ifdef ENABLE_MKLGPU_BACKEND
+       #define TEST_RUN_INTELGPU(q, func, args) \
+           func<oneapi::mkl::backend::mklgpu> args
+   #else
+       #define TEST_RUN_INTELGPU(q, func, args)
+   #endif
++
++  #ifdef ENABLE_NEWLIB_BACKEND
++     #define TEST_RUN_NEWDEVICE(q, func, args) \
++         func<oneapi::mkl::backend::newbackend> args
++  #else
++      #define TEST_RUN_NEWDEVICE(q, func, args)
++  #endif
+
          +
          +
             #define TEST_RUN_CT(q, func, args)               \
+       do {                                         \
++          if (q.is_host())                         \
++              TEST_RUN_NEWDEVICE(q, func, args);   \
+
          +
          +
          • +

        • tests/unit_tests/main_test.cpp: add the targeted device to the vector of devices to test

          +

          Example: add the targeted device CPU for newlib

          +
                     }
+       }
++
++  #ifdef ENABLE_NEWLIB_BACKEND
++      devices.push_back(cl::sycl::device(cl::sycl::host_selector()));
++  #endif
+
          +
          +
          • +
        +

        Now you can build and run functional testing for enabled third-party libraries (for more information see Build with cmake).

        +
        cd build/
+cmake .. -DNEWLIB_ROOT=<path/to/newlib> \
+    -DENABLE_MKLCPU_BACKEND=OFF \
+    -DENABLE_MKLGPU_BACKEND=OFF \
+    -DENABLE_NEWLIB_BACKEND=ON  \
+    -DBUILD_FUNCTIONAL_TESTS=ON
+cmake --build . -j4
+ctest
+
        +
        +
        +
        + + +
        + + +
        + + gemm_bias + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/asum.html b/domains/blas/asum.html new file mode 100644 index 000000000..9621b7ed3 --- /dev/null +++ b/domains/blas/asum.html @@ -0,0 +1,1059 @@ + + + + + + + + + asum — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        asum

        +

        Computes the sum of magnitudes of the vector elements.

        +

        Description

        +

        The asum routine computes the sum of the magnitudes of elements of a +real vector, or the sum of magnitudes of the real and imaginary parts +of elements of a complex vector:

        +
        +\[result = \sum_{i=1}^{n}(|Re(x_i)| + |Im(x_i)|)\]
        +

        where x is a vector with n elements.

        +

        asum supports the following precisions for data:

        +
        +
        ++++ + + + + + + + + + + + + + + + + + + + +

        T

        T_res

        float

        float

        double

        double

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        asum (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void asum(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void asum(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the scalar result is stored (the sum of magnitudes of +the real and imaginary parts of all elements of the vector).

        +
        +
        +
        +
        +
        +

        asum (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event asum(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T_res *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event asum(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T_res *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to input vector x. The array holding the vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to the output matrix where the scalar result is stored +(the sum of magnitudes of the real and imaginary parts of all +elements of the vector).

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + BLAS Level 1 Routines + axpy + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/axpy.html b/domains/blas/axpy.html new file mode 100644 index 000000000..d7ad3fa6e --- /dev/null +++ b/domains/blas/axpy.html @@ -0,0 +1,1076 @@ + + + + + + + + + axpy — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        axpy

        +

        Computes a vector-scalar product and adds the result to a vector.

        +

        Description

        +

        The axpy routines compute a scalar-vector product and add the result +to a vector:

        +
        +\[y \leftarrow alpha * x + y\]
        +

        where:

        +

        x and y are vectors of n elements,

        +

        alpha is a scalar.

        +

        axpy supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        axpy (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void axpy(sycl::queue &queue,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void axpy(sycl::queue &queue,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        alpha

        Specifies the scalar alpha.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at least +(1 + (n – 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at least +(1 + (n – 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        axpy (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event axpy(sycl::queue &queue,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event axpy(sycl::queue &queue,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        alpha

        Specifies the scalar alpha.

        +
        +
        x

        Pointer to the input vector x. The array holding the vector +x must be of size at least (1 + (n – 1)*abs(incx)). See +Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to the input vector y. The array holding the vector +y must be of size at least (1 + (n – 1)*abs(incy)). See +Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + asum + copy + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/axpy_batch.html b/domains/blas/axpy_batch.html new file mode 100644 index 000000000..eb2f6878b --- /dev/null +++ b/domains/blas/axpy_batch.html @@ -0,0 +1,1121 @@ + + + + + + + + + axpy_batch — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
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        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        axpy_batch

        +

        Computes a group of axpy operations.

        +

        Description

        +

        The axpy_batch routines are batched versions of axpy, performing +multiple axpy operations in a single call. Each axpy +operation adds a scalar-vector product to a vector.

        +

        axpy_batch supports the following precisions for data.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        axpy_batch (USM Version)

        +

        Description

        +

        The USM version of axpy_batch supports the group API and strided API.

        +

        The group API operation is defined as

        +
        idx = 0
+for i = 0 … group_count – 1
+    for j = 0 … group_size – 1
+        X and Y are vectors in x[idx] and y[idx]
+        Y := alpha[i] * X + Y
+        idx := idx + 1
+    end for
+end for
+
        +
        +

        The strided API operation is defined as

        +
        for i = 0 … batch_size – 1
+   X and Y are vectors at offset i * stridex, i * stridey in x and y
+   Y := alpha * X + Y
+end for
+
        +
        +

        where:

        +

        alpha is scalar,

        +

        X and Y are vectors.

        +

        For group API, x and y arrays contain the pointers for all the input vectors. +The total number of vectors in x and y are given by:

        +
        +\[total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i]\]
        +

        For strided API, x and y arrays contain all the input vectors. +The total number of vectors in x and y are given by the batch_size parameter.

        +

        Group API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event axpy_batch(sycl::queue &queue,
+                           std::int64_t *n,
+                           T *alpha,
+                           const T **x,
+                           std::int64_t *incx,
+                           T **y,
+                           std::int64_t *incy,
+                           std::int64_t group_count,
+                           std::int64_t *group_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event axpy_batch(sycl::queue &queue,
+                           std::int64_t *n,
+                           T *alpha,
+                           const T **x,
+                           std::int64_t *incx,
+                           T **y,
+                           std::int64_t *incy,
+                           std::int64_t group_count,
+                           std::int64_t *group_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Array of group_count integers. n[i] specifies the number of elements in vectors X and Y for every vector in group i.

        +
        +
        alpha

        Array of group_count scalar elements. alpha[i] specifies the scaling factor for vector X in group i.

        +
        +
        x

        Array of pointers to input vectors X with size total_batch_count. +The size of array allocated for the X vector of the group i must be at least (1 + (n[i] – 1)*abs(incx[i]))``. +See Matrix Storage for more details.

        +
        +
        incx

        Array of group_count integers. incx[i] specifies the stride of vector X in group i.

        +
        +
        y

        Array of pointers to input/output vectors Y with size total_batch_count. +The size of array allocated for the Y vector of the group i must be at least (1 + (n[i] – 1)*abs(incy[i]))``. +See Matrix Storage for more details.

        +
        +
        incy

        Array of group_count integers. incy[i] specifies the stride of vector Y in group i.

        +
        +
        group_count

        Number of groups. Must be at least 0.

        +
        +
        group_size

        Array of group_count integers. group_size[i] specifies the number of axpy operations in group i. +Each element in group_size must be at least 0.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Array of pointers holding the Y vectors, overwritten by total_batch_count axpy operations of the form +alpha * X + Y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +
        +

        Strided API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event axpy_batch(sycl::queue &queue,
+                           std::int64_t n,
+                           T alpha,
+                           const T *x,
+                           std::int64_t incx,
+                           std::int64_t stridex,
+                           T *y,
+                           std::int64_t incy,
+                           std::int64_t stridey,
+                           std::int64_t batch_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event axpy_batch(sycl::queue &queue,
+                           std::int64_t n,
+                           T alpha,
+                           const T *x,
+                           std::int64_t incx,
+                           std::int64_t stridex,
+                           T *y,
+                           std::int64_t incy,
+                           std::int64_t stridey,
+                           std::int64_t batch_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in X and Y.

        +
        +
        alpha

        Specifies the scalar alpha.

        +
        +
        x

        Pointer to input vectors X with size stridex * batch_size.

        +
        +
        incx

        Stride of vector X.

        +
        +
        stridex

        Stride between different X vectors.

        +
        +
        y

        Pointer to input/output vectors Y with size stridey * batch_size.

        +
        +
        incy

        Stride of vector Y.

        +
        +
        stridey

        Stride between different Y vectors.

        +
        +
        batch_size

        Specifies the number of axpy operations to perform.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Output vectors, overwritten by batch_size axpy operations of the form +alpha * X + Y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic:BLAS-like Extensions

        +
        +
        +
        + + +
        + + +
        + + BLAS-like Extensions + gemm_batch + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/blas-level-1-routines.html b/domains/blas/blas-level-1-routines.html new file mode 100644 index 000000000..2c9328648 --- /dev/null +++ b/domains/blas/blas-level-1-routines.html @@ -0,0 +1,972 @@ + + + + + + + + + BLAS Level 1 Routines — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        BLAS Level 1 Routines

        +
        +

        BLAS Level 1 includes routines which perform +vector-vector operations as described in the following table.

        +
        + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

        Routines

        Description

        asum

        Sum of vector magnitudes

        axpy

        Scalar-vector product

        copy

        Copy vector

        dot

        Dot product

        sdsdot

        Dot product with double precision

        dotc

        Dot product conjugated

        dotu

        Dot product unconjugated

        nrm2

        Vector 2-norm (Euclidean norm)

        rot

        Plane rotation of points

        rotg

        Generate Givens rotation of points

        rotm

        Modified Givens plane rotation of points

        rotmg

        Generate modified Givens plane rotation of points

        scal

        Vector-scalar product

        swap

        Vector-vector swap

        iamax

        Index of the maximum absolute value element of a vector

        iamin

        Index of the minimum absolute value element of a vector

        +
        +
        +
        +
        +

        Parent topic: BLAS Routines

        +
        + + +
        + + +
        + + BLAS Routines + asum + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/blas-level-2-routines.html b/domains/blas/blas-level-2-routines.html new file mode 100644 index 000000000..c40314931 --- /dev/null +++ b/domains/blas/blas-level-2-routines.html @@ -0,0 +1,999 @@ + + + + + + + + + BLAS Level 2 Routines — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        BLAS Level 2 Routines

        +
        +

        BLAS Level 2 includes routines which perform +matrix-vector operations as described in the following table.

        +
        + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

        Routines

        Description

        gbmv

        Matrix-vector product using a general band matrix

        gemv

        Matrix-vector product using a general matrix

        ger

        Rank-1 update of a general matrix

        gerc

        Rank-1 update of a conjugated general matrix

        geru

        Rank-1 update of a general matrix, unconjugated

        hbmv

        Matrix-vector product using a Hermitian band matrix

        hemv

        Matrix-vector product using a Hermitian matrix

        her

        Rank-1 update of a Hermitian matrix

        her2

        Rank-2 update of a Hermitian matrix

        hpmv

        Matrix-vector product using a Hermitian packed matrix

        hpr

        Rank-1 update of a Hermitian packed matrix

        hpr2

        Rank-2 update of a Hermitian packed matrix

        sbmv

        Matrix-vector product using symmetric band matrix

        spmv

        Matrix-vector product using a symmetric packed matrix

        spr

        Rank-1 update of a symmetric packed matrix

        spr2

        Rank-2 update of a symmetric packed matrix

        symv

        Matrix-vector product using a symmetric matrix

        syr

        Rank-1 update of a symmetric matrix

        syr2

        Rank-2 update of a symmetric matrix

        tbmv

        Matrix-vector product using a triangular band matrix

        tbsv

        Solution of a linear system of equations with a triangular band matrix

        tpmv

        Matrix-vector product using a triangular packed matrix

        tpsv

        Solution of a linear system of equations with a triangular packed matrix

        trmv

        Matrix-vector product using a triangular matrix

        trsv

        Solution of a linear system of equations with a triangular matrix

        +
        +
        +
        +
        +

        Parent topic: BLAS Routines

        +
        + + +
        + + +
        + + iamin + gbmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/blas-level-3-routines.html b/domains/blas/blas-level-3-routines.html new file mode 100644 index 000000000..2d59b7512 --- /dev/null +++ b/domains/blas/blas-level-3-routines.html @@ -0,0 +1,951 @@ + + + + + + + + + BLAS Level 3 Routines — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        BLAS Level 3 Routines

        +
        +

        BLAS Level 3 includes routines which perform +matrix-matrix operations as described in the following table.

        +
        + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

        Routines

        Description

        gemm

        Computes a matrix-matrix product with general matrices.

        hemm

        Computes a matrix-matrix product where one input matrix is Hermitian and one is general.

        herk

        Performs a Hermitian rank-k update.

        her2k

        Performs a Hermitian rank-2k update.

        symm

        Computes a matrix-matrix product where one input matrix is symmetric and one matrix is general.

        syrk

        Performs a symmetric rank-k update.

        syr2k

        Performs a symmetric rank-2k update.

        trmm

        Computes a matrix-matrix product where one input matrix is triangular and one input matrix is general.

        trsm

        Solves a triangular matrix equation (forward or backward solve).

        +
        +
        +
        +
        +

        Parent topic: BLAS Routines

        +
        + + +
        + + +
        + + trsv + gemm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/blas-like-extensions.html b/domains/blas/blas-like-extensions.html new file mode 100644 index 000000000..0550c5d63 --- /dev/null +++ b/domains/blas/blas-like-extensions.html @@ -0,0 +1,942 @@ + + + + + + + + + BLAS-like Extensions — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        BLAS-like Extensions

        +
        +

        oneAPI Math Kernel Library DPC++ provides additional routines to +extend the functionality of the BLAS routines. These include routines +to compute many independent vector-vector and matrix-matrix operations.

        +

        The following table lists the BLAS-like extensions with their descriptions.

        +
        + ++++ + + + + + + + + + + + + + + + + + + + + + + +

        Routines

        Description

        axpy_batch

        Computes groups of vector-scalar products added to a vector.

        gemm_batch

        Computes groups of matrix-matrix products with general matrices.

        trsm_batch

        Solves a triangular matrix equation for a group of matrices.

        gemmt

        Computes a matrix-matrix product with general matrices, but updates +only the upper or lower triangular part of the result matrix.

        gemm_bias

        Computes a matrix-matrix product using general integer matrices with bias

        +
        +
        +
        +
        +

        Parent topic: BLAS Routines

        +
        + + +
        + + +
        + + trsm + axpy_batch + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/blas.html b/domains/blas/blas.html new file mode 100644 index 000000000..67247723d --- /dev/null +++ b/domains/blas/blas.html @@ -0,0 +1,911 @@ + + + + + + + + + BLAS Routines — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        BLAS Routines

        +

        oneMKL provides DPC++ interfaces to the Basic Linear Algebra Subprograms (BLAS) routines (Level1, Level2, Level3), as well as several BLAS-like extension routines.

        +
        + +
        +
        + + +
        + + +
        + + Matrix Storage + BLAS Level 1 Routines + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/copy.html b/domains/blas/copy.html new file mode 100644 index 000000000..6f31a256a --- /dev/null +++ b/domains/blas/copy.html @@ -0,0 +1,1056 @@ + + + + + + + + + copy — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        copy

        +

        Copies a vector to another vector.

        +

        Description

        +

        The copy routines copy one vector to another:

        +
        +\[y \leftarrow x\]
        +

        where x and y are vectors of n elements.

        +

        copy supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        copy (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void copy(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void copy(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at least +(1 + (n – 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        copy (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event copy(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event copy(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to the input vector x. The array holding the vector +x must be of size at least (1 + (n – 1)*abs(incx)). See +Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + axpy + dot + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/dot.html b/domains/blas/dot.html new file mode 100644 index 000000000..6949e4b22 --- /dev/null +++ b/domains/blas/dot.html @@ -0,0 +1,1076 @@ + + + + + + + + + dot — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        dot

        +

        Computes the dot product of two real vectors.

        +

        Description

        +

        The dot routines perform a dot product between two vectors:

        +
        +\[result = \sum_{i=1}^{n}X_iY_i\]
        +

        dot supports the following precisions for data.

        +
        +
        ++++ + + + + + + + + + + + + + + + + +

        T

        T_res

        float

        float

        double

        double

        float

        double

        +
        +
        +

        Note

        +

        For the mixed precision version (inputs are float while result is +double), the dot product is computed with double precision.

        +
        +
        +

        dot (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void dot(sycl::queue &queue,
+             std::int64_t n,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void dot(sycl::queue &queue,
+             std::int64_t n,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at least +(1 + (n – 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at least +(1 + (n – 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the result (a scalar) will be stored.

        +
        +
        +
        +
        +
        +

        dot (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event dot(sycl::queue &queue,
+                    std::int64_t n,
+                    const T *x,
+                    std::int64_t incx,
+                    const T *y,
+                    std::int64_t incy,
+                    T_res *result,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event dot(sycl::queue &queue,
+                    std::int64_t n,
+                    const T *x,
+                    std::int64_t incx,
+                    const T *y,
+                    std::int64_t incy,
+                    T_res *result,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        x

        Pointer to the input vector x. The array holding the vector x +must be of size at least (1 + (n – 1)*abs(incx)). See +Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to the input vector y. The array holding the vector y +must be of size at least (1 + (n – 1)*abs(incy)). See +Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to where the result (a scalar) will be stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + copy + sdsdot + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/dotc.html b/domains/blas/dotc.html new file mode 100644 index 000000000..536d691f1 --- /dev/null +++ b/domains/blas/dotc.html @@ -0,0 +1,1065 @@ + + + + + + + + + dotc — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        dotc

        +

        Computes the dot product of two complex vectors, conjugating the first vector.

        +

        Description

        +

        The dotc routines perform a dot product between two complex +vectors, conjugating the first of them:

        +
        +\[result = \sum_{i=1}^{n}\overline{X_i}Y_i\]
        +

        dotc supports the following precisions for data.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        dotc (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void dotc(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void dotc(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        The number of elements in vectors x and y.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details..

        +
        +
        incy

        The stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        The buffer where the result (a scalar) is stored.

        +
        +
        +
        +
        +
        +

        dotc (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void dotc(sycl::queue &queue,
+              std::int64_t n,
+              const T *x,
+              std::int64_t incx,
+              const T *y,
+              std::int64_t incy,
+              T *result,
+              const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void dotc(sycl::queue &queue,
+              std::int64_t n,
+              const T *x,
+              std::int64_t incx,
+              const T *y,
+              std::int64_t incy,
+              T *result,
+              const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        The number of elements in vectors x and y.

        +
        +
        x

        Pointer to input vector x. The array holding the input +vector x must be of size at least (1 + (n - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        y

        Pointer to input vector y. The array holding the input +vector y must be of size at least (1 + (n - +1)*abs(incy)). See Matrix Storage for +more details..

        +
        +
        incy

        The stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        The pointer to where the result (a scalar) is stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + sdsdot + dotu + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/dotu.html b/domains/blas/dotu.html new file mode 100644 index 000000000..1978b7ca9 --- /dev/null +++ b/domains/blas/dotu.html @@ -0,0 +1,1064 @@ + + + + + + + + + dotu — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        dotu

        +

        Computes the dot product of two complex vectors.

        +

        Description

        +

        The dotu routines perform a dot product between two complex vectors:

        +
        +\[result = \sum_{i=1}^{n}X_iY_i\]
        +

        dotu supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        dotu (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void dotu(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void dotu(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the result (a scalar) is stored.

        +
        +
        +
        +
        +
        +

        dotu (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event dotu(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event dotu(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        x

        Pointer to the input vector x. The array holding input +vector x must be of size at least (1 + (n - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input vector y. The array holding input vector +y must be of size at least (1 + (n - 1)*abs(incy)). +See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to where the result (a scalar) is stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + dotc + nrm2 + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gbmv.html b/domains/blas/gbmv.html new file mode 100644 index 000000000..33eb379b5 --- /dev/null +++ b/domains/blas/gbmv.html @@ -0,0 +1,1162 @@ + + + + + + + + + gbmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
        + + + + +
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        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        gbmv

        +

        Computes a matrix-vector product with a general band matrix.

        +

        Description

        +

        The gbmv routines compute a scalar-matrix-vector product and add +the result to a scalar-vector product, with a general band matrix. +The operation is defined as

        +
        +\[y \leftarrow alpha*op(A)*x + beta*y\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        alpha and beta are scalars,

        +

        A is an m-by-n matrix with kl sub-diagonals and +ku super-diagonals,

        +

        x and y are vectors.

        +

        gbmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        gbmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gbmv(sycl::queue &queue,
+              onemkl::transpose trans,
+              std::int64_t m,
+              std::int64_t n,
+              std::int64_t kl,
+              std::int64_t ku,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gbmv(sycl::queue &queue,
+              onemkl::transpose trans,
+              std::int64_t m,
+              std::int64_t n,
+              std::int64_t kl,
+              std::int64_t ku,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. +See +oneMKL defined datatypes for more +details.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        kl

        Number of sub-diagonals of the matrix A. Must be at least +zero.

        +
        +
        ku

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least lda*n +if column major layout is used or at least lda*m +if row major layout is used. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (kl + +ku + 1), and positive.

        +
        +
        x

        Buffer holding input vector x. The length len of vector +x is n if A is not transposed, and m if A is +transposed. The buffer must be of size at least (1 + (len - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The length len of +vector y is m, if A is not transposed, and n if +A is transposed. The buffer must be of size at least (1 + +(len - 1)*abs(incy)) where len is this length. See +Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        gbmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gbmv(sycl::queue &queue,
+                     onemkl::transpose trans,
+                     std::int64_t m,
+                     std::int64_t n,
+                     std::int64_t kl,
+                     std::int64_t ku,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gbmv(sycl::queue &queue,
+                     onemkl::transpose trans,
+                     std::int64_t m,
+                     std::int64_t n,
+                     std::int64_t kl,
+                     std::int64_t ku,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See +oneMKL defined datatypes for +more details.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        kl

        Number of sub-diagonals of the matrix A. Must be at least +zero.

        +
        +
        ku

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n if column +major layout is used or at least lda*m if row +major layout is used. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (kl + +ku + 1), and positive.

        +
        +
        x

        Pointer to input vector x. The length len of vector +x is n if A is not transposed, and m if A +is transposed. The array holding input vector x must be of +size at least (1 + (len - 1)*abs(incx)). See +Matrix Storage for more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The length len of +vector y is m, if A is not transposed, and n if +A is transposed. The array holding input/output vector +y must be of size at least (1 + (len - +1)*abs(incy)) where len is this length. +See Matrix Storage for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + BLAS Level 2 Routines + gemv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gemm.html b/domains/blas/gemm.html new file mode 100644 index 000000000..399441223 --- /dev/null +++ b/domains/blas/gemm.html @@ -0,0 +1,1396 @@ + + + + + + + + + gemm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        + + + + +
        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        gemm

        +

        Computes a matrix-matrix product with general matrices.

        +

        Description

        +

        The gemm routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, with general matrices. The +operation is defined as:

        +
        +\[C \leftarrow alpha*op(A)*op(B) + beta*C\]
        +

        where:

        +

        op(X) is one of op(X) = X, or op(X) = XT, or +op(X) = XH,

        +

        alpha and beta are scalars,

        +

        A, B and C are matrices,

        +

        op(A) is an m-by-k matrix,

        +

        op(B) is a k-by-n matrix,

        +

        C is an m-by-n matrix.

        +

        gemm supports the following precisions.

        +
        +
        ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

        Ts

        Ta

        Tb

        Tc

        float

        half

        half

        float

        half

        half

        half

        half

        float

        float

        float

        float

        double

        double

        double

        double

        std::complex<float>

        std::complex<float>

        std::complex<float>

        std::complex<float>

        std::complex<double>

        std::complex<double>

        std::complex<double>

        std::complex<double>

        +
        +
        +

        gemm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gemm(sycl::queue &queue,
+              onemkl::transpose transa,
+              onemkl::transpose transb,
+              std::int64_t m,
+              std::int64_t n,
+              std::int64_t k,
+              Ts alpha,
+              sycl::buffer<Ta,1> &a,
+              std::int64_t lda,
+              sycl::buffer<Tb,1> &b,
+              std::int64_t ldb,
+              Ts beta,
+              sycl::buffer<Tc,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gemm(sycl::queue &queue,
+              onemkl::transpose transa,
+              onemkl::transpose transb,
+              std::int64_t m,
+              std::int64_t n,
+              std::int64_t k,
+              Ts alpha,
+              sycl::buffer<Ta,1> &a,
+              std::int64_t lda,
+              sycl::buffer<Tb,1> &b,
+              std::int64_t ldb,
+              Ts beta,
+              sycl::buffer<Tc,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Specifies the form of op(A), the transposition operation +applied to A.

        +
        +
        transb

        Specifies the form of op(B), the transposition operation +applied to B.

        +
        +
        m

        Specifies the number of rows of the matrix op(A) and of the +matrix C. The value of m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix op(B) and the +number of columns of the matrix C. The value of n must be at +least zero.

        +
        +
        k

        Specifies the number of columns of the matrix op(A) and the +number of rows of the matrix op(B). The value of k must be at +least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        The buffer holding the input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        A is an m-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-m matrix so the array a +must have size at least lda*m

        Row major

        A is an m-by-k matrix so the array a +must have size at least lda*m.

        A is an k-by-m matrix so the array a +must have size at least lda*k

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least m.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least m.

        +
        +
        b

        The buffer holding the input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n

        +

        See Matrix Storage for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The buffer holding the input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        The buffer, which is overwritten by +alpha*op(A)*op(B) + beta*C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized before +calling gemm.

        +
        +
        +
        +

        gemm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gemm(sycl::queue &queue,
+                     onemkl::transpose transa,
+                     onemkl::transpose transb,
+                     std::int64_t m,
+                     std::int64_t n,
+                     std::int64_t k,
+                     Ts alpha,
+                     const Ta *a,
+                     std::int64_t lda,
+                     const Tb *b,
+                     std::int64_t ldb,
+                     Ts beta,
+                     Tc *c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gemm(sycl::queue &queue,
+                     onemkl::transpose transa,
+                     onemkl::transpose transb,
+                     std::int64_t m,
+                     std::int64_t n,
+                     std::int64_t k,
+                     Ts alpha,
+                     const Ta *a,
+                     std::int64_t lda,
+                     const Tb *b,
+                     std::int64_t ldb,
+                     Ts beta,
+                     Tc *c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Specifies the form of op(A), the transposition operation +applied to A.

        +
        +
        transb

        Specifies the form of op(B), the transposition operation +applied to B.

        +
        +
        m

        Specifies the number of rows of the matrix op(A) and of the +matrix C. The value of m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix op(B) and the +number of columns of the matrix C. The value of n must be +at least zero.

        +
        +
        k

        Specifies the number of columns of the matrix op(A) and the +number of rows of the matrix op(B). The value of k must be +at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        A is an m-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-m matrix so the array a +must have size at least lda*m

        Row major

        A is an m-by-k matrix so the array a +must have size at least lda*m.

        A is an k-by-m matrix so the array a +must have size at least lda*k

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least m.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least m.

        +
        +
        b

        Pointer to input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n

        +

        See Matrix Storage for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The pointer to input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by +alpha*op(A)*op(B) + beta*C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling gemm.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + BLAS Level 3 Routines + hemm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gemm_batch.html b/domains/blas/gemm_batch.html new file mode 100644 index 000000000..c2a81cd67 --- /dev/null +++ b/domains/blas/gemm_batch.html @@ -0,0 +1,1487 @@ + + + + + + + + + gemm_batch — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        gemm_batch

        +

        Computes a group of gemm operations.

        +

        Description

        +

        The gemm_batch routines are batched versions of gemm, performing +multiple gemm operations in a single call. Each gemm +operation perform a matrix-matrix product with general matrices.

        +

        gemm_batch supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        gemm_batch (Buffer Version)

        +

        Description

        +

        The buffer version of gemm_batch supports only the strided API.

        +

        The strided API operation is defined as:

        +
        for i = 0 … batch_size – 1
+    A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c.
+    C := alpha * op(A) * op(B) + beta * C
+end for
+
        +
        +

        where:

        +

        op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

        +

        alpha and beta are scalars,

        +

        A, B, and C are matrices,

        +

        op(A) is m x k, op(B) is +k x n, and C is m x n.

        +

        The a, b and c buffers contain all the input matrices. The stride +between matrices is given by the stride parameter. The total number +of matrices in a, b and c buffers is given by the batch_size parameter.

        +

        Strided API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gemm_batch(sycl::queue &queue,
+                    onemkl::transpose transa,
+                    onemkl::transpose transb,
+                    std::int64_t m,
+                    std::int64_t n,
+                    std::int64_t k,
+                    T alpha,
+                    sycl::buffer<T,1> &a,
+                    std::int64_t lda,
+                    std::int64_t stridea,
+                    sycl::buffer<T,1> &b,
+                    std::int64_t ldb,
+                    std::int64_t strideb,
+                    T beta,
+                    sycl::buffer<T,1> &c,
+                    std::int64_t ldc,
+                    std::int64_t stridec,
+                    std::int64_t batch_size)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gemm_batch(sycl::queue &queue,
+                    onemkl::transpose transa,
+                    onemkl::transpose transb,
+                    std::int64_t m,
+                    std::int64_t n,
+                    std::int64_t k,
+                    T alpha,
+                    sycl::buffer<T,1> &a,
+                    std::int64_t lda,
+                    std::int64_t stridea,
+                    sycl::buffer<T,1> &b,
+                    std::int64_t ldb,
+                    std::int64_t strideb,
+                    T beta,
+                    sycl::buffer<T,1> &c,
+                    std::int64_t ldc,
+                    std::int64_t stridec,
+                    std::int64_t batch_size)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Specifies op(A) the transposition operation applied to the +matrices A. See oneMKL defined datatypes for more details.

        +
        +
        transb

        Specifies op(B) the transposition operation applied to the +matrices B. See oneMKL defined datatypes for more details.

        +
        +
        m

        Number of rows of op(A) and C. Must be at least zero.

        +
        +
        n

        Number of columns of op(B) and C. Must be at least zero.

        +
        +
        k

        Number of columns of op(A) and rows of op(B). Must be at +least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix products.

        +
        +
        a

        Buffer holding the input matrices A with size stridea * batch_size.

        +
        +
        lda

        The leading dimension of the matrices A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least m.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least m.

        +
        +
        stridea

        Stride between different A matrices.

        +
        +
        b

        Buffer holding the input matrices B with size strideb * batch_size.

        +
        +
        ldb

        The leading dimension of the matrices``B``. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        strideb

        Stride between different B matrices.

        +
        +
        beta

        Scaling factor for the matrices C.

        +
        +
        c

        Buffer holding input/output matrices C with size stridec * batch_size.

        +
        +
        ldc

        The leading dimension of the mattrices C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        stridec

        Stride between different C matrices. Must be at least +ldc * n.

        +
        +
        batch_size

        Specifies the number of matrix multiply operations to perform.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by batch_size matrix multiply +operations of the form alpha * op(A)*op(B) + beta * C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized before +calling gemm_batch.

        +
        +
        +
        +

        gemm_batch (USM Version)

        +

        Description

        +

        The USM version of gemm_batch supports the group API and strided API.

        +

        The group API operation is defined as:

        +
        idx = 0
+for i = 0 … group_count – 1
+    for j = 0 … group_size – 1
+        A, B, and C are matrices in a[idx], b[idx] and c[idx]
+        C := alpha[i] * op(A) * op(B) + beta[i] * C
+        idx = idx + 1
+    end for
+end for
+
        +
        +

        The strided API operation is defined as

        +
        for i = 0 … batch_size – 1
+    A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c.
+    C := alpha * op(A) * op(B) + beta * C
+end for
+
        +
        +

        where:

        +

        op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

        +

        alpha and beta are scalars,

        +

        A, B, and C are matrices,

        +

        op(A) is m x k, op(B) is k x n, and C is m x n.

        +

        For group API, a, b and c arrays contain the pointers for all the input matrices. +The total number of matrices in a, b and c are given by:

        +
        +\[total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i]\]
        +

        For strided API, a, b, c arrays contain all the input matrices. The total number of matrices +in a, b and c are given by the batch_size parameter.

        +

        Group API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gemm_batch(sycl::queue &queue,
+                           onemkl::transpose *transa,
+                           onemkl::transpose *transb,
+                           std::int64_t *m,
+                           std::int64_t *n,
+                           std::int64_t *k,
+                           T *alpha,
+                           const T **a,
+                           std::int64_t *lda,
+                           const T **b,
+                           std::int64_t *ldb,
+                           T *beta,
+                           T **c,
+                           std::int64_t *ldc,
+                           std::int64_t group_count,
+                           std::int64_t *group_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gemm_batch(sycl::queue &queue,
+                           onemkl::transpose *transa,
+                           onemkl::transpose *transb,
+                           std::int64_t *m,
+                           std::int64_t *n,
+                           std::int64_t *k,
+                           T *alpha,
+                           const T **a,
+                           std::int64_t *lda,
+                           const T **b,
+                           std::int64_t *ldb,
+                           T *beta,
+                           T **c,
+                           std::int64_t *ldc,
+                           std::int64_t group_count,
+                           std::int64_t *group_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Array of group_count onemkl::transpose values. transa[i] specifies the form of op(A) used in +the matrix multiplication in group i. See oneMKL defined datatypes for more details.

        +
        +
        transb

        Array of group_count onemkl::transpose values. transb[i] specifies the form of op(B) used in +the matrix multiplication in group i. See oneMKL defined datatypes for more details.

        +
        +
        m

        Array of group_count integers. m[i] specifies the +number of rows of op(A) and C for every matrix in group i. All entries must be at least zero.

        +
        +
        n

        Array of group_count integers. n[i] specifies the +number of columns of op(B) and C for every matrix in group i. All entries must be at least zero.

        +
        +
        k

        Array of group_count integers. k[i] specifies the +number of columns of op(A) and rows of op(B) for every matrix in group i. All entries must be at +least zero.

        +
        +
        alpha

        Array of group_count scalar elements. alpha[i] specifies the scaling factor for every matrix-matrix +product in group i.

        +
        +
        a

        Array of pointers to input matrices A with size total_batch_count.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        Array of group_count integers. lda[i] specifies the +leading dimension of A for every matrix in group i. All +entries must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda[i] must be at least m[i].

        lda[i] must be at least k[i].

        Row major

        lda[i] must be at least k[i].

        lda[i] must be at least m[i].

        +
        +
        b

        Array of pointers to input matrices B with size total_batch_count.

        +

        See Matrix Storage for more details.

        +
        +
        +

        ldb

        +
        +

        Array of group_count integers. ldb[i] specifies the +leading dimension of B for every matrix in group i. All +entries must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb[i] must be at least k[i].

        ldb[i] must be at least n[i].

        Row major

        ldb[i] must be at least n[i].

        ldb[i] must be at least k[i].

        +
        +
        +
        beta

        Array of group_count scalar elements. beta[i] specifies the scaling factor for matrix C +for every matrix in group i.

        +
        +
        c

        Array of pointers to input/output matrices C with size total_batch_count.

        +

        See Matrix Storage for more details.

        +
        +
        ldc

        Array of group_count integers. ldc[i] specifies the +leading dimension of C for every matrix in group i. All +entries must be positive and ldc[i] must be at least +m[i] if column major layout is used to store matrices or at +least n[i] if row major layout is used to store matrices.

        +
        +
        group_count

        Specifies the number of groups. Must be at least 0.

        +
        +
        group_size

        Array of group_count integers. group_size[i] specifies the +number of matrix multiply products in group i. All entries must be at least 0.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Overwritten by the m[i]-by-n[i] matrix calculated by +(alpha[i] * op(A)*op(B) + beta[i] * C) for group i.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling gemm_batch.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +
        +

        Strided API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gemm_batch(sycl::queue &queue,
+                           onemkl::transpose transa,
+                           onemkl::transpose transb,
+                           std::int64_t m,
+                           std::int64_t n,
+                           std::int64_t k,
+                           T alpha,
+                           const T *a,
+                           std::int64_t lda,
+                           std::int64_t stridea,
+                           const T *b,
+                           std::int64_t ldb,
+                           std::int64_t strideb,
+                           T beta,
+                           T *c,
+                           std::int64_t ldc,
+                           std::int64_t stridec,
+                           std::int64_t batch_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gemm_batch(sycl::queue &queue,
+                           onemkl::transpose transa,
+                           onemkl::transpose transb,
+                           std::int64_t m,
+                           std::int64_t n,
+                           std::int64_t k,
+                           T alpha,
+                           const T *a,
+                           std::int64_t lda,
+                           std::int64_t stridea,
+                           const T *b,
+                           std::int64_t ldb,
+                           std::int64_t strideb,
+                           T beta,
+                           T *c,
+                           std::int64_t ldc,
+                           std::int64_t stridec,
+                           std::int64_t batch_size,
+                           const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Specifies op(A) the transposition operation applied to the +matrices A. See oneMKL defined datatypes for more details.

        +
        +
        transb

        Specifies op(B) the transposition operation applied to the +matrices B. See oneMKL defined datatypes for more details.

        +
        +
        m

        Number of rows of op(A) and C. Must be at least zero.

        +
        +
        n

        Number of columns of op(B) and C. Must be at least zero.

        +
        +
        k

        Number of columns of op(A) and rows of op(B). Must be at +least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix products.

        +
        +
        a

        Pointer to input matrices A with size stridea * batch_size.

        +
        +
        lda

        The leading dimension of the matrices A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least m.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least m.

        +
        +
        stridea

        Stride between different A matrices.

        +
        +
        b

        Pointer to input matrices B with size strideb * batch_size.

        +
        +
        ldb

        The leading dimension of the matrices``B``. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        strideb

        Stride between different B matrices.

        +
        +
        beta

        Scaling factor for the matrices C.

        +
        +
        c

        Pointer to input/output matrices C with size stridec * batch_size.

        +
        +
        ldc

        The leading dimension of the mattrices C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        stridec

        Stride between different C matrices.

        +
        +
        batch_size

        Specifies the number of matrix multiply operations to perform.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output matrices, overwritten by batch_size matrix multiply +operations of the form alpha * op(A)*op(B) + beta * C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized before +calling gemm_batch.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS-like Extensions

        +
        +
        +
        + + +
        + + +
        + + axpy_batch + trsm_batch + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gemm_bias.html b/domains/blas/gemm_bias.html new file mode 100644 index 000000000..24d14ea83 --- /dev/null +++ b/domains/blas/gemm_bias.html @@ -0,0 +1,1187 @@ + + + + + + + + + gemm_bias — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        +

        gemm_bias

        +

        Computes a matrix-matrix product using general integer matrices with bias.

        +

        Description

        +

        The gemm_bias routines compute a scalar-matrix-matrix product and +add the result to a scalar-matrix product, using general integer matrices with biases/offsets. +The operation is defined as:

        +
        +\[\scriptstyle C \leftarrow alpha*(op(A) - A\_offset)*(op(B) - B\_offset) + beta*C + C\_offset\]
        +

        where:

        +

        op(X) is one of op(X) = X, or op(X) = XT, or +op(X) = XH,

        +

        alpha and beta are scalars,

        +

        A_offset is an m-by-k matrix with every element equal to the value ao,

        +

        B_offset is a k-by-n matrix with every element equal to the value bo,

        +

        C_offset is an m-by-n matrix defined by the +co buffer as described below,

        +

        A, B, and C are matrices,

        +

        op(A) is m x k, op(B) is k x n, and +C is m x n.

        +

        gemm_bias supports the following precisions.

        +
        +
        ++++++ + + + + + + + + + + + + + + +

        Ts

        Ta

        Tb

        Tc

        float

        std::int8_t

        std::uint8_t

        std::int32_t

        +
        +
        +

        gemm_bias (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gemm_bias(sycl::queue &queue,
+                   onemkl::transpose transa,
+                   onemkl::transpose transb,
+                   onemkl::offset offset_type,
+                   std::int64_t m,
+                   std::int64_t n,
+                   std::int64_t k,
+                   Ts alpha,
+                   sycl::buffer<Ta,1> &a,
+                   std::int64_t lda,
+                   Ta ao,
+                   sycl::buffer<Tb,1> &b,
+                   std::int64_t ldb,
+                   Tb bo,
+                   Ts beta,
+                   sycl::buffer<Tc,1> &c,
+                   std::int64_t ldc,
+                   sycl::buffer<Tc,1> &co)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gemm_bias(sycl::queue &queue,
+                   onemkl::transpose transa,
+                   onemkl::transpose transb,
+                   onemkl::offset offset_type,
+                   std::int64_t m,
+                   std::int64_t n,
+                   std::int64_t k,
+                   Ts alpha,
+                   sycl::buffer<Ta,1> &a,
+                   std::int64_t lda,
+                   Ta ao,
+                   sycl::buffer<Tb,1> &b,
+                   std::int64_t ldb,
+                   Tb bo,
+                   Ts beta,
+                   sycl::buffer<Tc,1> &c,
+                   std::int64_t ldc,
+                   sycl::buffer<Tc,1> &co)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        transa

        Specifies op(A), the transposition operation applied to +A. See +oneMKL defined datatypes for +more details.

        +
        +
        transb

        Specifies op(B), the transposition operation applied to +B. See +oneMKL defined datatypes for +more details.

        +
        +
        offset_type

        Specifies the form of C_offset used in the matrix +multiplication. See +oneMKL defined datatypes for +more details.

        +
        +
        m

        Number of rows of op(A) and C. Must be at least zero.

        +
        +
        n

        Number of columns of op(B) and C. Must be at least +zero.

        +
        +
        k

        Number of columns of op(A) and rows of op(B). Must be +at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        The buffer holding the input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        A is an m-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-m matrix so the array a +must have size at least lda*m

        Row major

        A is an m-by-k matrix so the array a +must have size at least lda*m.

        A is an k-by-m matrix so the array a +must have size at least lda*k

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least m.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least m.

        +
        +
        ao

        Specifies the scalar offset value for matrix A.

        +
        +
        b

        Buffer holding the input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n

        +

        See Matrix Storage for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        bo

        Specifies the scalar offset value for matrix B.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Buffer holding the input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . +See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        co

        Buffer holding the offset values for matrix C.

        +

        If offset_type = offset::fix, the co array must have +size at least 1.

        +

        If offset_type = offset::col, the co array must have +size at least max(1,m).

        +

        If offset_type = offset::row, the co array must have +size at least max(1,n).

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by alpha * (op(A) - +A_offset)*(op(B) - B_offset) + beta * C + C_offset.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling gemm_bias.

        +

        Parent topic: BLAS-like Extensions

        +
        +
        +
        + + +
        + + +
        + + gemmt + Integrating a Third-party Library to oneAPI Math Kernel Library (oneMKL) Interfaces + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gemmt.html b/domains/blas/gemmt.html new file mode 100644 index 000000000..ced6ba72a --- /dev/null +++ b/domains/blas/gemmt.html @@ -0,0 +1,1366 @@ + + + + + + + + + gemmt — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
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        + +
        +

        gemmt

        +

        Computes a matrix-matrix product with general matrices, but updates +only the upper or lower triangular part of the result matrix.

        +

        Description

        +

        The gemmt routines compute a scalar-matrix-matrix product and add +the result to the upper or lower part of a scalar-matrix product, +with general matrices. The operation is defined as:

        +
        +\[C \leftarrow alpha*op(A)*op(B) + beta*C\]
        +

        where:

        +

        op(X) is one of op(X) = X, or op(X) = XT, or +op(X) = XH,

        +

        alpha and beta are scalars

        +

        A, B, and C are matrices

        +

        op(A) is n x k, op(B) is k x n, and +C is n x n.

        +

        gemmt supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        gemmt (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gemmt(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose transa,
+               onemkl::transpose transb,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gemmt(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose transa,
+               onemkl::transpose transb,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether C’s data is stored in its upper or +lower triangle. See oneMKL defined datatypes for more details.

        +
        +
        transa

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        transb

        Specifies op(B), the transposition operation applied to +B. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows of op(A), columns of op(B), and +columns and rows ofC. Must be at least zero.

        +
        +
        k

        Number of columns of op(A) and rows of op(B). Must be +at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Buffer holding the input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Buffer holding the input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n.

        +

        See Matrix Storage for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Buffer holding the input/output matrix C. Must have size at +least ldc * n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +m.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by the upper or lower triangular +part of alpha * op(A)*op(B) + beta * C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling gemmt.

        +
        +
        +
        +

        gemmt (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gemmt(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose transa,
+                      onemkl::transpose transb,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gemmt(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose transa,
+                      onemkl::transpose transb,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether C’s data is stored in its upper or +lower triangle. See +oneMKL defined datatypes for +more details.

        +
        +
        transa

        Specifies op(A), the transposition operation applied to +A. See +oneMKL defined datatypes for +more details.

        +
        +
        transb

        Specifies op(B), the transposition operation applied to +B. See +oneMKL defined datatypes for +more details.

        +
        +
        n

        Number of columns of op(A), columns of op(B), and +columns ofC. Must be at least zero.

        +
        +
        k

        Number of columns of op(A) and rows of op(B). Must be +at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        A not transposed

        A transposed

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Pointer to input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n

        +

        See Matrix Storage for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        B not transposed

        B transposed

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Pointer to input/output matrix C. Must have size at least +ldc * n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +m.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by the upper or lower +triangular part of alpha * op(A)*op(B) + beta * C.

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling gemmt.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS-like Extensions

        +
        +
        +
        + + +
        + + +
        + + trsm_batch + gemm_bias + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gemv.html b/domains/blas/gemv.html new file mode 100644 index 000000000..c935da9ef --- /dev/null +++ b/domains/blas/gemv.html @@ -0,0 +1,1142 @@ + + + + + + + + + gemv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
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        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        gemv

        +

        Computes a matrix-vector product using a general matrix.

        +

        Description

        +

        The gemv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a general matrix. The +operation is defined as:

        +
        +\[y \leftarrow alpha*op(A)*x + beta*y\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        alpha and beta are scalars,

        +

        A is an m-by-n matrix, and x, y are vectors.

        +

        gemv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        gemv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gemv(sycl::queue &queue,
+              onemkl::transpose trans,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gemv(sycl::queue &queue,
+              onemkl::transpose trans,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A.

        +
        +
        m

        Specifies the number of rows of the matrix A. The value of +m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix A. The value of +n must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        The buffer holding the input matrix A. Must have a size of at +least lda*n if column major layout is used or at +least lda*m if row major layout is used. See +Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        x

        Buffer holding input vector x. The length len of vector +x is n if A is not transposed, and m if A is +transposed. The buffer must be of size at least (1 + (len - +1)*abs(incx)). See Matrix Storage for more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        beta

        The scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The length len of +vector y is m, if A is not transposed, and n if +A is transposed. The buffer must be of size at least (1 + +(len - 1)*abs(incy)) where len is this length. See +Matrix Storage for more details.

        +
        +
        incy

        The stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        The buffer holding updated vector y.

        +
        +
        +
        +
        +
        +

        gemv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gemv(sycl::queue &queue,
+                     onemkl::transpose trans,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gemv(sycl::queue &queue,
+                     onemkl::transpose trans,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See +oneMKL defined datatypes for +more details.

        +
        +
        m

        Specifies the number of rows of the matrix A. The value of +m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix A. The value +of n must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        The pointer to the input matrix A. Must have a size of at +least lda*n if column major layout is used or at +least lda*m if row major layout is used. See +Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        x

        Pointer to the input vector x. The length len of vector +x is n if A is not transposed, and m if A +is transposed. The array holding vector x must be of size +at least (1 + (len - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        beta

        The scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The length len of +vector y is m, if A is not transposed, and n if +A is transposed. The array holding input/output vector +y must be of size at least (1 + (len - +1)*abs(incy)) where len is this length. See Matrix Storage for +more details.

        +
        +
        incy

        The stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        The pointer to updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + gbmv + ger + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/ger.html b/domains/blas/ger.html new file mode 100644 index 000000000..55613f78b --- /dev/null +++ b/domains/blas/ger.html @@ -0,0 +1,1107 @@ + + + + + + + + + ger — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        ger

        +

        Computes a rank-1 update of a general matrix.

        +

        Description

        +

        The ger routines compute a scalar-vector-vector product and add the +result to a general matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*y^T + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an m-by-n matrix,

        +

        x is a vector of length m,

        +

        y is a vector of length n.

        +

        ger supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        ger (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void ger(sycl::queue &queue,
+             std::int64_t m,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void ger(sycl::queue &queue,
+             std::int64_t m,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (m - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n if column major layout is used or at least lda*m +if row major layout is used. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated matrix A.

        +
        +
        +
        +
        +
        +

        ger (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event ger(sycl::queue &queue,
+                    std::int64_t m,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    const T *y,
+                    std::int64_t incy,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event ger(sycl::queue &queue,
+                    std::int64_t m,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    const T *y,
+                    std::int64_t incy,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (m - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. Must have size at least +lda*n if column major layout is used or at least lda*m +if row major layout is used. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated matrix A.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + gemv + gerc + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/gerc.html b/domains/blas/gerc.html new file mode 100644 index 000000000..63b41d408 --- /dev/null +++ b/domains/blas/gerc.html @@ -0,0 +1,1108 @@ + + + + + + + + + gerc — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        gerc

        +

        Computes a rank-1 update (conjugated) of a general complex matrix.

        +

        Description

        +

        The gerc routines compute a scalar-vector-vector product and add the +result to a general matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*y^H + A\]
        +

        where:

        +

        alpha is a scalar,

        +

        A is an m-by-n matrix,

        +

        x is a vector of length m,

        +

        y is vector of length n.

        +

        gerc supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        gerc (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void gerc(sycl::queue &queue,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void gerc(sycl::queue &queue,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (m - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n if column major layout is used or at least lda*m +if row major layout is used. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated matrix A.

        +
        +
        +
        +
        +
        +

        gerc (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event gerc(sycl::queue &queue,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event gerc(sycl::queue &queue,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to the input vector x. The array holding input +vector x must be of size at least (1 + (m - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to the input/output vector y. The array holding the +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +Amust have size at least lda*n if column +major layout is used or at least lda*m if row +major layout is used. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated matrix A.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + ger + geru + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/geru.html b/domains/blas/geru.html new file mode 100644 index 000000000..b61d8cd53 --- /dev/null +++ b/domains/blas/geru.html @@ -0,0 +1,1108 @@ + + + + + + + + + geru — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        geru

        +

        Computes a rank-1 update (unconjugated) of a general complex matrix.

        +

        Description

        +

        The geru routines routines compute a scalar-vector-vector product and +add the result to a general matrix. The operation is defined as

        +
        +\[A \leftarrow alpha*x*y^T + A\]
        +

        where:

        +

        alpha is a scalar,

        +

        A is an m-by-n matrix,

        +

        x is a vector of length m,

        +

        y is a vector of length n.

        +

        geru supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        geru (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void geru(sycl::queue &queue,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void geru(sycl::queue &queue,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (m - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n if column major layout is used or at least lda*m +if row major layout is used. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at least +m if column major layout is used or at least n if row +major layout is used.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated matrix A.

        +
        +
        +
        +
        +
        +

        geru (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event geru(sycl::queue &queue,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event geru(sycl::queue &queue,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        m

        Number of rows of A. Must be at least zero.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to the input vector x. The array holding input +vector x must be of size at least (1 + (m - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n if column +major layout is used or at least lda*m if row +major layout is used. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be positive and at +least m if column major layout is used or at least n +if row major layout is used.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated matrix A.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + gerc + hbmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/hbmv.html b/domains/blas/hbmv.html new file mode 100644 index 000000000..08e4a8638 --- /dev/null +++ b/domains/blas/hbmv.html @@ -0,0 +1,1124 @@ + + + + + + + + + hbmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
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        + + + +
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        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        hbmv

        +

        Computes a matrix-vector product using a Hermitian band matrix.

        +

        Description

        +

        The hbmv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian band matrix. The +operation is defined as

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n Hermitian band matrix, with k +super-diagonals,

        +

        x and y are vectors of length n.

        +

        hbmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hbmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + 1), +and positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (m - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        hbmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to the input matrix A. The array holding input +matrix A must have size at least lda*n. See +Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + +1), and positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (m - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + geru + hemv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/hemm.html b/domains/blas/hemm.html new file mode 100644 index 000000000..7a0d39ff0 --- /dev/null +++ b/domains/blas/hemm.html @@ -0,0 +1,1180 @@ + + + + + + + + + hemm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        hemm

        +

        Computes a matrix-matrix product where one input matrix is Hermitian +and one is general.

        +

        Description

        +

        The hemm routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, where one of the matrices in the +multiplication is Hermitian. The argument left_right determines +if the Hermitian matrix, A, is on the left of the multiplication +(left_right = side::left) or on the right (left_right = +side::right). Depending on left_right, the operation is +defined as:

        +
        +\[C \leftarrow alpha*A*B + beta*C\]
        +

        or

        +
        +\[C \leftarrow alpha*B*A + beta*C\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is a Hermitian matrix, either m-by-m or n-by-n +matrices,

        +

        B and C are m-by-n matrices.

        +

        hemm supports the following precisions:

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hemm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hemm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hemm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the multiplication +(side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of the matrix B and C.

        +

        The value of m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix B and C.

        +

        The value of n must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*m if A is on the left of the multiplication, +or lda*n if A is on the right. See Matrix Storage +for more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if A is on +the left of the multiplication, or at least n if A is on +the right. Must be positive.

        +
        +
        b

        Buffer holding input matrix B. Must have size at least +ldb*n if column major layout is +used to store matrices or at least ldb*m if row +major layout is used to store matrices. See Matrix Storage for +more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The buffer holding the input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by alpha*A*B + +beta*C (left_right = side::left) or +alpha*B*A + beta*C +(left_right = side::right).

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized before +calling hemm.

        +
        +
        +
        +

        hemm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hemm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     const T* b,
+                     std::int64_t ldb,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hemm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     const T* b,
+                     std::int64_t ldb,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the +multiplication (side::left) or on the right side +(side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of the matrix B and C.

        +

        The value of m must be at least zero.

        +
        +
        n

        Specifies the number of columns of the matrix B and C.

        +

        The value of n must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Pointer to input matrix A. Must have size at least +lda*m if A is on the left of the +multiplication, or lda*n if A is on the right. +See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if A is +on the left of the multiplication, or at least n if A +is on the right. Must be positive.

        +
        +
        b

        Pointer to input matrix B. Must have size at least +ldb*n if column major layout is +used to store matrices or at least ldb*m if row +major layout is used to store matrices. See Matrix Storage for +more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The pointer to input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by +alpha*A*B + beta*C +(left_right = side::left) or +alpha*B*A + beta*C +(left_right = side::right).

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling hemm.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + gemm + herk + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/hemv.html b/domains/blas/hemv.html new file mode 100644 index 000000000..8b40b1a26 --- /dev/null +++ b/domains/blas/hemv.html @@ -0,0 +1,1112 @@ + + + + + + + + + hemv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        hemv

        +

        Computes a matrix-vector product using a Hermitian matrix.

        +

        Description

        +

        The hemv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian matrix. The +operation is defined as

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n Hermitian matrix,

        +

        x and y are vectors of length n.

        +

        hemv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hemv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hemv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hemv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least m, and +positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        hemv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hemv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hemv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least m, and +positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + hbmv + her + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/her.html b/domains/blas/her.html new file mode 100644 index 000000000..2361d6d1a --- /dev/null +++ b/domains/blas/her.html @@ -0,0 +1,1090 @@ + + + + + + + + + her — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
        + + + + +
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        + Contents +
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        +

        her

        +

        Computes a rank-1 update of a Hermitian matrix.

        +

        Description

        +

        The her routines compute a scalar-vector-vector product and add the +result to a Hermitian matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*x^H + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an n-by-n Hermitian matrix,

        +

        x is a vector of length n.

        +

        her supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        her (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void her(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void her(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the Hermitian +matrix A if upper_lower = upper or the updated +lower triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +
        +

        her (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event her(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event her(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper or the updated +lower triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + hemv + her2 + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/her2.html b/domains/blas/her2.html new file mode 100644 index 000000000..ddb652a2c --- /dev/null +++ b/domains/blas/her2.html @@ -0,0 +1,1111 @@ + + + + + + + + + her2 — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
        + + + + +
        + + +
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        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        her2

        +

        Computes a rank-2 update of a Hermitian matrix.

        +

        Description

        +

        The her2 routines compute two scalar-vector-vector products and add +them to a Hermitian matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A\]
        +

        where:

        +

        alpha is a scalar,

        +

        A is an n-by-n Hermitian matrix,

        +

        x and y are vectors or length n.

        +

        her2 supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        her2 (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void her2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void her2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated +lower triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +
        +

        her2 (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event her2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event her2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated +lower triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + her + hpmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/her2k.html b/domains/blas/her2k.html new file mode 100644 index 000000000..211db4667 --- /dev/null +++ b/domains/blas/her2k.html @@ -0,0 +1,1344 @@ + + + + + + + + + her2k — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
        + + + + +
        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        her2k

        +

        Performs a Hermitian rank-2k update.

        +

        Description

        +

        The her2k routines perform a rank-2k update of an n x n +Hermitian matrix C by general matrices A and B.

        +

        If trans = transpose::nontrans, the operation is defined as:

        +
        +\[C \leftarrow alpha*A*B^H + conjg(alpha)*B*A^H + beta*C\]
        +

        where A is n x k and B is k x n.

        +

        If trans = transpose::conjtrans, the operation is defined as:

        +
        +\[C \leftarrow alpha*B*A^H + conjg(alpha)*A*B^H + beta*C\]
        +

        where A is k x n and B is n x k.

        +

        In both cases:

        +

        alpha is a complex scalar and beta is a real scalar.

        +

        C is a Hermitian matrix and A , B are general matrices.

        +

        The inner dimension of both matrix multiplications is k.

        +

        her2k supports the following precisions:

        +
        +
        ++++ + + + + + + + + + + + + + +

        T

        T_real

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        her2k (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void her2k(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose trans,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T_real beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void her2k(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose trans,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T_real beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies the operation to apply, as described above. Supported +operations are transpose::nontrans and +transpose::conjtrans.

        +
        +
        n

        The number of rows and columns in C. The value of n must +be at least zero.

        +
        +
        k

        The inner dimension of matrix multiplications. The value of k +must be at least equal to zero.

        +
        +
        alpha

        Complex scaling factor for the rank-2k update.

        +
        +
        a

        Buffer holding input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for +more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Buffer holding input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n.

        +

        See Matrix Storage +for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Real scaling factor for matrix C.

        +
        +
        c

        Buffer holding input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least n.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by the updated C matrix.

        +
        +
        +
        +
        +
        +

        her2k (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event her2k(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose trans,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T_real beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event her2k(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose trans,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T_real beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies the operation to apply, as described above. Supported +operations are transpose::nontrans and +transpose::conjtrans.

        +
        +
        n

        The number of rows and columns in C. The value of n +must be at least zero.

        +
        +
        k

        The inner dimension of matrix multiplications. The value of +k must be at least equal to zero.

        +
        +
        alpha

        Complex scaling factor for the rank-2k update.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Pointer to input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n.

        +

        See Matrix Storage for +more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Real scaling factor for matrix C.

        +
        +
        c

        Pointer to input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +n.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by the updated C +matrix.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + herk + symm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
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        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/herk.html b/domains/blas/herk.html new file mode 100644 index 000000000..35e89e492 --- /dev/null +++ b/domains/blas/herk.html @@ -0,0 +1,1224 @@ + + + + + + + + + herk — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        +

        herk

        +

        Performs a Hermitian rank-k update.

        +

        Description

        +

        The herk routines compute a rank-k update of a Hermitian matrix +C by a general matrix A. The operation is defined as:

        +
        +\[C \leftarrow alpha*op(A)*op(A)^H + beta*C\]
        +

        where:

        +

        op(X) is one of op(X) = X or op(X) = XH,

        +

        alpha and beta are real scalars,

        +

        C is a Hermitian matrix and A is a general matrix.

        +

        Here op(A) is n x k, and C is n x n.

        +

        herk supports the following precisions:

        +
        +
        ++++ + + + + + + + + + + + + + +

        T

        T_real

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        herk (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void herk(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              std::int64_t n,
+              std::int64_t k,
+              T_real alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              T_real beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void herk(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              std::int64_t n,
+              std::int64_t k,
+              T_real alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              T_real beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See +oneMKL defined datatypes for more +details. Supported operations are transpose::nontrans and +transpose::conjtrans.

        +
        +
        n

        The number of rows and columns in C.The value of n must be +at least zero.

        +
        +
        k

        Number of columns in op(A).

        +

        The value of k must be at least zero.

        +
        +
        alpha

        Real scaling factor for the rank-k update.

        +
        +
        a

        Buffer holding input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for +more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        beta

        Real scaling factor for matrix C.

        +
        +
        c

        Buffer holding input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least n.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        The output buffer, overwritten by +alpha*op(A)*op(A)T + beta*C. +The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +
        +

        herk (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event herk(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T_real alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T_real beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event herk(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T_real alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T_real beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details. Supported operations are transpose::nontrans +and transpose::conjtrans.

        +
        +
        n

        The number of rows and columns in C.The value of n must +be at least zero.

        +
        +
        k

        Number of columns in op(A).

        +

        The value of k must be at least zero.

        +
        +
        alpha

        Real scaling factor for the rank-k update.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        beta

        Real scaling factor for matrix C.

        +
        +
        c

        Pointer to input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +n.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by +alpha*op(A)*op(A)T + +beta*C. The imaginary parts of the diagonal +elements are set to zero.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + hemm + her2k + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/hpmv.html b/domains/blas/hpmv.html new file mode 100644 index 000000000..173bebe51 --- /dev/null +++ b/domains/blas/hpmv.html @@ -0,0 +1,1107 @@ + + + + + + + + + hpmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        + Contents +
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        +
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        +
        +
        + +
        + +
        +

        hpmv

        +

        Computes a matrix-vector product using a Hermitian packed matrix.

        +

        Description

        +

        The hpmv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a Hermitian packed matrix. +The operation is defined as

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n Hermitian matrix supplied in packed form,

        +

        x and y are vectors of length n.

        +

        hpmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hpmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hpmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hpmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n+1))/2. See Matrix Storage for +more details.

        +

        The imaginary parts of the diagonal elements need not be set and +are assumed to be zero.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        hpmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hpmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hpmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n+1))/2. See +Matrix Storage for +more details.

        +

        The imaginary parts of the diagonal elements need not be set +and are assumed to be zero.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + her2 + hpr + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/hpr.html b/domains/blas/hpr.html new file mode 100644 index 000000000..b47a97334 --- /dev/null +++ b/domains/blas/hpr.html @@ -0,0 +1,1085 @@ + + + + + + + + + hpr — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        + Contents +
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        +
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        +
        + +
        + +
        +

        hpr

        +

        Computes a rank-1 update of a Hermitian packed matrix.

        +

        Description

        +

        The hpr routines compute a scalar-vector-vector product and add the +result to a Hermitian packed matrix. The operation is defined as

        +
        +\[A \leftarrow alpha*x*x^H + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an n-by-n Hermitian matrix, supplied in packed form,

        +

        x is a vector of length n.

        +

        hpr supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hpr (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hpr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hpr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n-1))/2. See Matrix Storage for +more details.

        +

        The imaginary part of the diagonal elements need not be set and +are assumed to be zero.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated lower +triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +
        +

        hpr (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hpr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hpr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n-1))/2. See +Matrix Storage for +more details.

        +

        The imaginary part of the diagonal elements need not be set and +are assumed to be zero.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated lower +triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + hpmv + hpr2 + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/hpr2.html b/domains/blas/hpr2.html new file mode 100644 index 000000000..f90b03bda --- /dev/null +++ b/domains/blas/hpr2.html @@ -0,0 +1,1106 @@ + + + + + + + + + hpr2 — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
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        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        hpr2

        +

        Performs a rank-2 update of a Hermitian packed matrix.

        +

        Description

        +

        The hpr2 routines compute two scalar-vector-vector products and add +them to a Hermitian packed matrix. The operation is defined as

        +
        +\[A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A\]
        +

        where:

        +

        alpha is a scalar,

        +

        A is an n-by-n Hermitian matrix, supplied in packed form,

        +

        x and y are vectors of length n.

        +

        hpr2 supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        std::complex<float>

        std::complex<double>

        +
        +
        +

        hpr2 (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void hpr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void hpr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n-1))/2. See Matrix Storage for +more details.

        +

        The imaginary parts of the diagonal elements need not be set and +are assumed to be zero.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated lower +triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +
        +

        hpr2 (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event hpr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event hpr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n-1))/2. See +Matrix Storage for +more details.

        +

        The imaginary parts of the diagonal elements need not be set +and are assumed to be zero.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the Hermitian +matrix A if upper_lower=upper, or the updated lower +triangular part of the Hermitian matrix A if +upper_lower=lower.

        +

        The imaginary parts of the diagonal elements are set to zero.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + hpr + sbmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/iamax.html b/domains/blas/iamax.html new file mode 100644 index 000000000..0e558422d --- /dev/null +++ b/domains/blas/iamax.html @@ -0,0 +1,1063 @@ + + + + + + + + + iamax — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        iamax

        +

        Finds the index of the element with the largest absolute value in a vector.

        +

        Description

        +

        The iamax routines return an index i such that x[i] +has the maximum absolute value of all elements in vector x (real +variants), or such that (|Re(x[i])| + |Im(x[i])|) is maximal +(complex variants).

        +

        If either n or incx are not positive, the routine returns +0.

        +

        If more than one vector element is found with the same largest +absolute value, the index of the first one encountered is returned.

        +

        If the vector contains NaN values, then the routine returns the +index of the first NaN.

        +

        iamax supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std:complex<double>

        +
        +
        +

        Note

        +

        The index is zero-based.

        +
        +
        +

        iamax (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void iamax(sycl::queue &queue,
+               std::int64_t n,
+               sycl::buffer<T,
+               1> &x,
+               std::int64_t incx,
+               sycl::buffer<std::int64_t,
+               1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void iamax(sycl::queue &queue,
+               std::int64_t n,
+               sycl::buffer<T,
+               1> &x,
+               std::int64_t incx,
+               sycl::buffer<std::int64_t,
+               1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        The number of elements in vector x.

        +
        +
        x

        The buffer that holds the input vector x. The buffer must be +of size at least (1 + (n - 1)*abs(incx)). See Matrix Storage +for more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        The buffer where the zero-based index i of the maximal element +is stored.

        +
        +
        +
        +
        +
        +

        iamax (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event iamax(sycl::queue &queue,
+                      std::int64_t n,
+                      const T *x,
+                      std::int64_t incx,
+                      T_res *result,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event iamax(sycl::queue &queue,
+                      std::int64_t n,
+                      const T *x,
+                      std::int64_t incx,
+                      T_res *result,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        The number of elements in vector x.

        +
        +
        x

        The pointer to the input vector x. The array holding the +input vector x must be of size at least (1 + (n - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        The stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        The pointer to where the zero-based index i of the maximal +element is stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + swap + iamin + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/iamin.html b/domains/blas/iamin.html new file mode 100644 index 000000000..7b1fdfbd8 --- /dev/null +++ b/domains/blas/iamin.html @@ -0,0 +1,1056 @@ + + + + + + + + + iamin — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
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        + + +
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        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        iamin

        +

        Finds the index of the element with the smallest absolute value.

        +

        Description

        +

        The iamin routines return an index i such that x[i] has +the minimum absolute value of all elements in vector x (real +variants), or such that (|Re(x[i])| + |Im(x[i])|) is minimal +(complex variants).

        +

        If either n or incx are not positive, the routine returns +0.

        +

        If more than one vector element is found with the same smallest +absolute value, the index of the first one encountered is returned.

        +

        If the vector contains NaN values, then the routine returns the +index of the first NaN.

        +

        iamin supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        Note

        +

        The index is zero-based.

        +
        +
        +

        iamin (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void iamin(sycl::queue &queue,
+               std::int64_t n,
+               sycl::buffer<T,1> &x,
+               std::int64_t incx,
+               sycl::buffer<std::int64_t,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void iamin(sycl::queue &queue,
+               std::int64_t n,
+               sycl::buffer<T,1> &x,
+               std::int64_t incx,
+               sycl::buffer<std::int64_t,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the zero-based index i of the minimum element +will be stored.

        +
        +
        +
        +
        +
        +

        iamin (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event iamin(sycl::queue &queue,
+                      std::int64_t n,
+                      const T *x,
+                      std::int64_t incx,
+                      T_res *result,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event iamin(sycl::queue &queue,
+                      std::int64_t n,
+                      const T *x,
+                      std::int64_t incx,
+                      T_res *result,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        The pointer to input vector x. The array holding input +vector x must be of size at least (1 + (n - +1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to where the zero-based index i of the minimum +element will be stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + iamax + BLAS Level 2 Routines + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/nrm2.html b/domains/blas/nrm2.html new file mode 100644 index 000000000..e70d5c0c8 --- /dev/null +++ b/domains/blas/nrm2.html @@ -0,0 +1,1057 @@ + + + + + + + + + nrm2 — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        + + +
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        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        nrm2

        +

        Computes the Euclidean norm of a vector.

        +

        Description

        +

        The nrm2 routines computes Euclidean norm of a vector

        +
        +\[result = \| x\|\]
        +

        where:

        +

        x is a vector of n elements.

        +

        nrm2 supports the following precisions.

        +
        +
        ++++ + + + + + + + + + + + + + + + + + + + +

        T

        T_res

        float

        float

        double

        double

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        nrm2 (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void nrm2(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void nrm2(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T_res,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the Euclidean norm of the vector x will be +stored.

        +
        +
        +
        +
        +
        +

        nrm2 (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event nrm2(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T_res *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event nrm2(sycl::queue &queue,
+                     std::int64_t n,
+                     const T *x,
+                     std::int64_t incx,
+                     T_res *result,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to where the Euclidean norm of the vector x will be +stored.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + dotu + rot + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
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        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/rot.html b/domains/blas/rot.html new file mode 100644 index 000000000..7bd1d2845 --- /dev/null +++ b/domains/blas/rot.html @@ -0,0 +1,1099 @@ + + + + + + + + + rot — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
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        + + + + + + + +
        + + +
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        + Contents +
        + +
        +
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        +
        +
        + +
        + +
        +

        rot

        +

        Performs rotation of points in the plane.

        +

        Description

        +

        Given two vectors x and y of n elements, the rot routines +compute four scalar-vector products and update the input vectors with +the sum of two of these scalar-vector products as follow:

        +
        +\[\begin{split}\left[\begin{array}{c} + x\\y +\end{array}\right] +\leftarrow +\left[\begin{array}{c} + \phantom{-}c*x + s*y\\ + -s*x + c*y +\end{array}\right]\end{split}\]
        +

        rot supports the following precisions.

        +
        +
        ++++ + + + + + + + + + + + + + + + + + + + +

        T

        T_scalar

        float

        float

        double

        double

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        rot (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void rot(sycl::queue &queue,
+             std::int64_t n,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             T_scalar c,
+             T_scalar s)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void rot(sycl::queue &queue,
+             std::int64_t n,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &y,
+             std::int64_t incy,
+             T_scalar c,
+             T_scalar s)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        c

        Scaling factor.

        +
        +
        s

        Scaling factor.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding updated buffer x.

        +
        +
        y

        Buffer holding updated buffer y.

        +
        +
        +
        +
        +
        +

        rot (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event rot(sycl::queue &queue,
+                    std::int64_t n,
+                    T *x,
+                    std::int64_t incx,
+                    T *y,
+                    std::int64_t incy,
+                    T_scalar c,
+                    T_scalar s,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event rot(sycl::queue &queue,
+                    std::int64_t n,
+                    T *x,
+                    std::int64_t incx,
+                    T *y,
+                    std::int64_t incy,
+                    T_scalar c,
+                    T_scalar s,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input vector y. The array holding input vector +y must be of size at least (1 + (n - 1)*abs(incy)). +See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        c

        Scaling factor.

        +
        +
        s

        Scaling factor.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated matrix x.

        +
        +
        y

        Pointer to the updated matrix y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + nrm2 + rotg + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/rotg.html b/domains/blas/rotg.html new file mode 100644 index 000000000..69efea822 --- /dev/null +++ b/domains/blas/rotg.html @@ -0,0 +1,1072 @@ + + + + + + + + + rotg — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        rotg

        +

        Computes the parameters for a Givens rotation.

        +

        Description

        +

        Given the Cartesian coordinates (a, b) of a point, the rotg +routines return the parameters c, s, r, and z +associated with the Givens rotation. The parameters c and s +define a unitary matrix such that:

        +
        +\[\begin{split}\begin{bmatrix}c & s \\ -s & c\end{bmatrix}. +\begin{bmatrix}a \\ b\end{bmatrix} +=\begin{bmatrix}r \\ 0\end{bmatrix}\end{split}\]
        +

        The parameter z is defined such that if |a| > +|b|, z is s; otherwise if c is not 0 z is +1/c; otherwise z is 1.

        +

        rotg supports the following precisions.

        +
        +
        ++++ + + + + + + + + + + + + + + + + + + + +

        T

        T_res

        float

        float

        double

        double

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        rotg (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void rotg(sycl::queue &queue,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &b,
+              sycl::buffer<T_real,1> &c,
+              sycl::buffer<T,1> &s)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void rotg(sycl::queue &queue,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &b,
+              sycl::buffer<T_real,1> &c,
+              sycl::buffer<T,1> &s)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed

        +
        +
        a

        Buffer holding the x-coordinate of the point.

        +
        +
        b

        Buffer holding the y-coordinate of the point.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the parameter r associated with the Givens +rotation.

        +
        +
        b

        Buffer holding the parameter z associated with the Givens +rotation.

        +
        +
        c

        Buffer holding the parameter c associated with the Givens +rotation.

        +
        +
        s

        Buffer holding the parameter s associated with the Givens +rotation.

        +
        +
        +
        +
        +
        +

        rotg (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event rotg(sycl::queue &queue,
+                     T *a,
+                     T *b,
+                     T_real *c,
+                     T *s,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event rotg(sycl::queue &queue,
+                     T *a,
+                     T *b,
+                     T_real *c,
+                     T *s,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed

        +
        +
        a

        Pointer to the x-coordinate of the point.

        +
        +
        b

        Pointer to the y-coordinate of the point.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the parameter r associated with the Givens +rotation.

        +
        +
        b

        Pointer to the parameter z associated with the Givens +rotation.

        +
        +
        c

        Pointer to the parameter c associated with the Givens +rotation.

        +
        +
        s

        Pointer to the parameter s associated with the Givens +rotation.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + rot + rotm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/rotm.html b/domains/blas/rotm.html new file mode 100644 index 000000000..b98af9a7c --- /dev/null +++ b/domains/blas/rotm.html @@ -0,0 +1,1139 @@ + + + + + + + + + rotm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        rotm

        +

        Performs modified Givens rotation of points in the plane.

        +

        Description

        +

        Given two vectors x and y, each vector element of these +vectors is replaced as follows:

        +
        +\[\begin{split}\begin{bmatrix}x_i \\ y_i\end{bmatrix}= +H +\begin{bmatrix}x_i \\ y_i\end{bmatrix}\end{split}\]
        +

        for i from 1 to n, where H is a modified Givens +transformation matrix.

        +

        rotm supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        rotm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void rotm(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &param)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void rotm(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &param)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        param

        Buffer holding an array of size 5.

        +

        The elements of the param array are:

        +

        param[0] contains a switch, flag. The other array elements +param[1-4] contain the components of the modified Givens +transformation matrix H: +h11, h21, h12, and +h22, respectively.

        +

        Depending on the values of flag, the components of H +are set as follows:

        +
        +
        flag = -1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = 0.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix}\end{split}\]
        +
        +
        flag = 1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = -2.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix}\end{split}\]
        +

        In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 +are assumed based on the value of flag and are not required to +be set in the param vector.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding updated buffer x.

        +
        +
        y

        Buffer holding updated buffer y.

        +
        +
        +
        +
        +
        +

        rotm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event rotm(sycl::queue &queue,
+                     std::int64_t n,
+                     T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     T *param,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event rotm(sycl::queue &queue,
+                     std::int64_t n,
+                     T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     T *param,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to the input vector x. The array holding the vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        yparam

        Pointer to the input vector y. The array holding the vector +y must be of size at least (1 + (n - 1)*abs(incy)). +See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        param

        Buffer holding an array of size 5.

        +

        The elements of the param array are:

        +

        param[0] contains a switch, flag. The other array elements +param[1-4] contain the components of the modified Givens +transformation matrix H: +h11, h21, h12, and +h22, respectively.

        +

        Depending on the values of flag, the components of H +are set as follows:

        +
        +
        flag = -1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = 0.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix}\end{split}\]
        +
        +
        flag = 1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = -2.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix}\end{split}\]
        +

        In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 +are assumed based on the value of flag and are not required to +be set in the param vector.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated array x.

        +
        +
        y

        Pointer to the updated array y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + rotg + rotmg + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/rotmg.html b/domains/blas/rotmg.html new file mode 100644 index 000000000..9c37d9b62 --- /dev/null +++ b/domains/blas/rotmg.html @@ -0,0 +1,1131 @@ + + + + + + + + + rotmg — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        rotmg

        +

        Computes the parameters for a modified Givens rotation.

        +

        Description

        +

        Given Cartesian coordinates (x1, y1) of an +input vector, the rotmg routines compute the components of a modified +Givens transformation matrix H that zeros the y-component of +the resulting vector:

        +
        +\[\begin{split}\begin{bmatrix}x1 \\ 0\end{bmatrix}= +H +\begin{bmatrix}x1\sqrt{d1} \\ y1\sqrt{d2}\end{bmatrix}\end{split}\]
        +

        rotmg supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        rotmg (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void rotmg(sycl::queue &queue,
+               sycl::buffer<T,1> &d1,
+               sycl::buffer<T,1> &d2,
+               sycl::buffer<T,1> &x1,
+               sycl::buffer<T,1> &y1,
+               sycl::buffer<T,1> &param)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void rotmg(sycl::queue &queue,
+               sycl::buffer<T,1> &d1,
+               sycl::buffer<T,1> &d2,
+               sycl::buffer<T,1> &x1,
+               sycl::buffer<T,1> &y1,
+               sycl::buffer<T,1> &param)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        d1

        Buffer holding the scaling factor for the x-coordinate of the +input vector.

        +
        +
        d2

        Buffer holding the scaling factor for the y-coordinate of the +input vector.

        +
        +
        x1

        Buffer holding the x-coordinate of the input vector.

        +
        +
        y1

        Scalar specifying the y-coordinate of the input vector.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        d1

        Buffer holding the first diagonal element of the updated matrix.

        +
        +
        d2

        Buffer holding the second diagonal element of the updated matrix.

        +
        +
        x1

        Buffer holding the x-coordinate of the rotated vector before +scaling

        +
        +
        param

        Buffer holding an array of size 5.

        +

        The elements of the param array are:

        +

        param[0] contains a switch, flag. The other array elements +param[1-4] contain the components of the modified Givens +transformation matrix H: +h11, h21, h12, and +h22, respectively.

        +

        Depending on the values of flag, the components of H are +set as follows:

        +
        +
        flag = -1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = 0.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix}\end{split}\]
        +
        +
        flag = 1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = -2.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix}\end{split}\]
        +

        In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 +are assumed based on the value of flag and are not required to +be set in the param vector.

        +
        +
        +
        +
        +
        +

        rotmg (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event rotmg(sycl::queue &queue,
+                      T *d1,
+                      T *d2,
+                      T *x1,
+                      T *y1,
+                      T *param,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event rotmg(sycl::queue &queue,
+                      T *d1,
+                      T *d2,
+                      T *x1,
+                      T *y1,
+                      T *param,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        d1

        Pointer to the scaling factor for the x-coordinate of the +input vector.

        +
        +
        d2

        Pointer to the scaling factor for the y-coordinate of the +input vector.

        +
        +
        x1

        Pointer to the x-coordinate of the input vector.

        +
        +
        y1

        Scalar specifying the y-coordinate of the input vector.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        d1

        Pointer to the first diagonal element of the updated matrix.

        +
        +
        d2

        Pointer to the second diagonal element of the updated matrix.

        +
        +
        x1

        Pointer to the x-coordinate of the rotated vector before +scaling

        +
        +
        param

        Buffer holding an array of size 5.

        +

        The elements of the param array are:

        +

        param[0] contains a switch, flag. The other array elements +param[1-4] contain the components of the modified Givens +transformation matrix H: +h11, h21, h12, and +h22, respectively.

        +

        Depending on the values of flag, the components of H +are set as follows:

        +
        +
        flag = -1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = 0.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & h_{12} \\ h_{21} & 1.0\end{bmatrix}\end{split}\]
        +
        +
        flag = 1.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}h_{11} & 1.0 \\ -1.0 & h_{22}\end{bmatrix}\end{split}\]
        +
        +
        flag = -2.0:
        +
        +
        +\[\begin{split}H=\begin{bmatrix}1.0 & 0.0 \\ 0.0 & 1.0\end{bmatrix}\end{split}\]
        +

        In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 +are assumed based on the value of flag and are not required to +be set in the param vector.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + rotm + scal + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/sbmv.html b/domains/blas/sbmv.html new file mode 100644 index 000000000..abba8231f --- /dev/null +++ b/domains/blas/sbmv.html @@ -0,0 +1,1123 @@ + + + + + + + + + sbmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
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        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        sbmv

        +

        Computes a matrix-vector product with a symmetric band matrix.

        +

        Description

        +

        The sbmv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a symmetric band matrix. The +operation is defined as:

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n symmetric matrix with k +super-diagonals,

        +

        x and y are vectors of length n.

        +

        sbmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        sbmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void sbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void sbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + 1), +and positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        sbmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event sbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event sbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of super-diagonals of the matrix A. Must be at least +zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + +1), and positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + hpr2 + spmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/scal.html b/domains/blas/scal.html new file mode 100644 index 000000000..844049658 --- /dev/null +++ b/domains/blas/scal.html @@ -0,0 +1,1062 @@ + + + + + + + + + scal — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        scal

        +

        Computes the product of a vector by a scalar.

        +

        Description

        +

        The scal routines computes a scalar-vector product:

        +
        +\[x \leftarrow alpha*x\]
        +

        where:

        +

        x is a vector of n elements,

        +

        alpha is a scalar.

        +

        scal supports the following precisions.

        +
        +
        ++++ + + + + + + + + + + + + + + + + + + + + + + + + + +

        T

        T_scalar

        float

        float

        double

        double

        std::complex<float>

        std::complex<float>

        std::complex<double>

        std::complex<double>

        std::complex<float>

        float

        std::complex<double>

        double

        +
        +
        +

        scal (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void scal(sycl::queue &queue,
+              std::int64_t n,
+              T_scalar alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void scal(sycl::queue &queue,
+              std::int64_t n,
+              T_scalar alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        alpha

        Specifies the scalar alpha.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding updated buffer x.

        +
        +
        +
        +
        +
        +

        scal (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event scal(sycl::queue &queue,
+                     std::int64_t n,
+                     T_scalar alpha,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event scal(sycl::queue &queue,
+                     std::int64_t n,
+                     T_scalar alpha,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        alpha

        Specifies the scalar alpha.

        +
        +
        x

        Pointer to the input vector x. The array must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated array x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + rotmg + swap + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/sdsdot.html b/domains/blas/sdsdot.html new file mode 100644 index 000000000..a8dbbd28b --- /dev/null +++ b/domains/blas/sdsdot.html @@ -0,0 +1,1055 @@ + + + + + + + + + sdsdot — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        sdsdot

        +

        Computes a vector-vector dot product with double precision.

        +

        Description

        +

        The sdsdot routines perform a dot product between two vectors with +double precision:

        +
        +\[result = sb + \sum_{i=1}^{n}X_iY_i\]
        +
        +

        sdsdot (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void sdsdot(sycl::queue &queue,
+                std::int64_t n,
+                float sb,
+                sycl::buffer<float,1> &x,
+                std::int64_t incx,
+                sycl::buffer<float,1> &y,
+                std::int64_t incy,
+                sycl::buffer<float,1> &result)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void sdsdot(sycl::queue &queue,
+                std::int64_t n,
+                float sb,
+                sycl::buffer<float,1> &x,
+                std::int64_t incx,
+                sycl::buffer<float,1> &y,
+                std::int64_t incy,
+                sycl::buffer<float,1> &result)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        sb

        Single precision scalar to be added to the dot product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size +at least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size +at least (1 + (n - 1)*abs(incxy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Buffer where the result (a scalar) will be stored. If n < 0 +the result is sb.

        +
        +
        +
        +
        +
        +

        sdsdot (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event sdsdot(sycl::queue &queue,
+                       std::int64_t n,
+                       float sb,
+                       const float *x,
+                       std::int64_t incx,
+                       const float *y,
+                       std::int64_t incy,
+                       float *result,
+                       const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event sdsdot(sycl::queue &queue,
+                       std::int64_t n,
+                       float sb,
+                       const float *x,
+                       std::int64_t incx,
+                       const float *y,
+                       std::int64_t incy,
+                       float *result,
+                       const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vectors x and y.

        +
        +
        sb

        Single precision scalar to be added to the dot product.

        +
        +
        x

        Pointer to the input vector x. The array must be of size +at least (1 + (n - 1)*abs(incx)). See Matrix Storage +for more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to the input vector y. The array must be of size +at least (1 + (n - 1)*abs(incxy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if +any. If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        result

        Pointer to where the result (a scalar) will be stored. If +n < 0 the result is sb.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + dot + dotc + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/spmv.html b/domains/blas/spmv.html new file mode 100644 index 000000000..7c8af5dbd --- /dev/null +++ b/domains/blas/spmv.html @@ -0,0 +1,1103 @@ + + + + + + + + + spmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
        +
        + + + + +
        + + +
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        + + + + + + + +
        + + +
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        + Contents +
        + +
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        +
        +
        +
        + +
        + +
        +

        spmv

        +

        Computes a matrix-vector product with a symmetric packed matrix.

        +

        Description

        +

        The spmv routines compute a scalar-matrix-vector product and add the +result to a scalar-vector product, with a symmetric packed matrix. +The operation is defined as:

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n symmetric matrix, supplied in packed form,

        +

        x and y are vectors of length n.

        +

        spmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        spmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void spmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void spmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n+1))/2. See Matrix Storage for +more details.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        spmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event spmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event spmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n+1))/2. See +Matrix Storage for +more details.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        beta

        Scaling factor for vector y.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + sbmv + spr + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/spr.html b/domains/blas/spr.html new file mode 100644 index 000000000..077238c69 --- /dev/null +++ b/domains/blas/spr.html @@ -0,0 +1,1079 @@ + + + + + + + + + spr — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        + + + + +
        + + +
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        + Contents +
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        +
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        +
        +
        + +
        + +
        +

        spr

        +

        Performs a rank-1 update of a symmetric packed matrix.

        +

        Description

        +

        The spr routines compute a scalar-vector-vector product and add the +result to a symmetric packed matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*x^T + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an n-by-n symmetric matrix, supplied in packed form,

        +

        x is a vector of length n.

        +

        spr supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        spr (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void spr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void spr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n + 1))/2. See Matrix Storage for +more details.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the symmetric +matrix A if upper_lower=upper, or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +
        +

        spr (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event spr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event spr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n + 1))/2. See +Matrix Storage for +more details.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the symmetric +matrix A if upper_lower=upper, or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + spmv + spr2 + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/spr2.html b/domains/blas/spr2.html new file mode 100644 index 000000000..ef259a309 --- /dev/null +++ b/domains/blas/spr2.html @@ -0,0 +1,1098 @@ + + + + + + + + + spr2 — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        +
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        + + + + + + + +
        + + +
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        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        spr2

        +

        Computes a rank-2 update of a symmetric packed matrix.

        +

        Description

        +

        The spr2 routines compute two scalar-vector-vector products and add +them to a symmetric packed matrix. The operation is defined as:

        +
        +\[A \leftarrow alpha*x*y^T + alpha*y*x^T + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an n-by-n symmetric matrix, supplied in packed form,

        +

        x and y are vectors of length n.

        +

        spr supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        spr2 (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void spr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void spr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n-1))/2. See Matrix Storage for +more details.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the symmetric +matrix A if upper_lower=upper or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +
        +

        spr2 (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event spr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event spr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n-1))/2. See +Matrix Storage for +more details.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the symmetric +matrix A if upper_lower=upper or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + spr + symv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/swap.html b/domains/blas/swap.html new file mode 100644 index 000000000..51fb8aa27 --- /dev/null +++ b/domains/blas/swap.html @@ -0,0 +1,1078 @@ + + + + + + + + + swap — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        swap

        +

        Swaps a vector with another vector.

        +

        Description

        +

        Given two vectors of n elements, x and y, the swap +routines return vectors y and x swapped, each replacing the +other.

        +
        +\[\begin{split}\left[\begin{array}{c} + y\\x +\end{array}\right] +\leftarrow +\left[\begin{array}{c} + x\\y +\end{array}\right]\end{split}\]
        +

        swap supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        swap (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void swap(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void swap(sycl::queue &queue,
+              std::int64_t n,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input vector y. The buffer must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding updated buffer x, that is, the input vector +y.

        +
        +
        y

        Buffer holding updated buffer y, that is, the input vector +x.

        +
        +
        +
        +
        +
        +

        swap (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event swap(sycl::queue &queue,
+                     std::int64_t n,
+                     T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event swap(sycl::queue &queue,
+                     std::int64_t n,
+                     T *x,
+                     std::int64_t incx,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        n

        Number of elements in vector x.

        +
        +
        x

        Pointer to the input vector x. The array must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to the input vector y. The array must be of size at +least (1 + (n - 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated array x, that is, the input vector +y.

        +
        +
        y

        Pointer to the updated array y, that is, the input vector +x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 1 Routines

        +
        +
        +
        + + +
        + + +
        + + scal + iamax + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/symm.html b/domains/blas/symm.html new file mode 100644 index 000000000..8232c22e1 --- /dev/null +++ b/domains/blas/symm.html @@ -0,0 +1,1183 @@ + + + + + + + + + symm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        +

        symm

        +

        Computes a matrix-matrix product where one input matrix is symmetric +and one matrix is general.

        +

        Description

        +

        The symm routines compute a scalar-matrix-matrix product and add the +result to a scalar-matrix product, where one of the matrices in the +multiplication is symmetric. The argument left_right determines +if the symmetric matrix, A, is on the left of the multiplication +(left_right = side::left) or on the right (left_right = +side::right). Depending on left_right, the operation is +defined as:

        +
        +\[C \leftarrow alpha*A*B + beta*C\]
        +

        or

        +
        +\[C \leftarrow alpha*B*A + beta*C\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is a symmetric matrix, either m-by-m or n-by-n,

        +

        B and C are m-by-n matrices.

        +

        symm supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        symm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void symm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void symm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the multiplication +(side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        m

        Number of rows of B and C. The value of m must be at +least zero.

        +
        +
        n

        Number of columns of B and C. The value of n must be +at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*m if A is on the left of the multiplication, +or lda*n if A is on the right. See Matrix Storage +for more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if A is on +the left of the multiplication, or at least n if A is on +the right. Must be positive.

        +
        +
        b

        Buffer holding input matrix B. Must have size at least +ldb*n if column major layout is +used to store matrices or at least ldb*m if row +major layout is used to store matrices. See Matrix Storage for +more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The buffer holding the input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices. See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by alpha*A*B + +beta*C (left_right = side::left) or +alpha*B*A + beta*C +(left_right = side::right).

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized before +calling symm.

        +
        +
        +
        +

        symm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event symm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     const T* b,
+                     std::int64_t ldb,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event symm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     const T* b,
+                     std::int64_t ldb,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the +multiplication (side::left) or on the right side +(side::right). See oneMKL defined datatypes for more details.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        m

        Number of rows of B and C. The value of m must be +at least zero.

        +
        +
        n

        Number of columns of B and C. The value of n must +be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Pointer to input matrix A. Must have size at least +lda*m if A is on the left of the +multiplication, or lda*n if A is on the right. +See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if A is +on the left of the multiplication, or at least n if A +is on the right. Must be positive.

        +
        +
        b

        Pointer to input matrix B. Must have size at least +ldb*n if column major layout is +used to store matrices or at least ldb*m if row +major layout is used to store matrices. See Matrix Storage for +more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        The pointer to input/output matrix C. It must have a +size of at least ldc*n if column major layout is +used to store matrices or at least ldc*m if row +major layout is used to store matrices . See Matrix Storage for more details.

        +
        +
        ldc

        The leading dimension of C. It must be positive and at least +m if column major layout is used to store matrices or at +least n if column major layout is used to store matrices.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by +alpha*A*B + beta*C +(left_right = side::left) or +alpha*B*A + beta*C +(left_right = side::right).

        +
        +
        +
        +
        +

        Notes

        +

        If beta = 0, matrix C does not need to be initialized +before calling symm.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + her2k + syrk + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/symv.html b/domains/blas/symv.html new file mode 100644 index 000000000..ce48ac881 --- /dev/null +++ b/domains/blas/symv.html @@ -0,0 +1,1108 @@ + + + + + + + + + symv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
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        + + +
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        + + +
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        + Contents +
        + +
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        +
        + +
        + +
        +

        symv

        +

        Computes a matrix-vector product for a symmetric matrix.

        +

        Description

        +

        The symv routines routines compute a scalar-matrix-vector product and +add the result to a scalar-vector product, with a symmetric matrix. +The operation is defined as:

        +
        +\[y \leftarrow alpha*A*x + beta*y\]
        +

        where:

        +

        alpha and beta are scalars,

        +

        A is an n-by-n symmetric matrix,

        +

        x and y are vectors of length n.

        +

        symv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        symv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void symv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void symv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              T beta,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least m, and +positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Buffer holding the updated vector y.

        +
        +
        +
        +
        +
        +

        symv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event symv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event symv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *a,
+                     std::int64_t lda,
+                     const T *x,
+                     std::int64_t incx,
+                     T beta,
+                     T *y,
+                     std::int64_t incy,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least m, and +positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        y

        Pointer to the updated vector y.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + spr2 + syr + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/syr.html b/domains/blas/syr.html new file mode 100644 index 000000000..a7549d8f3 --- /dev/null +++ b/domains/blas/syr.html @@ -0,0 +1,1089 @@ + + + + + + + + + syr — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
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        +
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        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        syr

        +

        Computes a rank-1 update of a symmetric matrix.

        +

        Description

        +

        The syr routines compute a scalar-vector-vector product add them and +add the result to a matrix, with a symmetric matrix. The operation is +defined as:

        +
        +\[A \leftarrow alpha*x*x^T + A\]
        +

        where:

        +

        alpha is scalar,

        +

        A is an n-by-n symmetric matrix,

        +

        x is a vector of length n.

        +

        syr supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        syr (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void syr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void syr(sycl::queue &queue,
+             onemkl::uplo upper_lower,
+             std::int64_t n,
+             T alpha,
+             sycl::buffer<T,1> &x,
+             std::int64_t incx,
+             sycl::buffer<T,1> &a,
+             std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the symmetric +matrix A if upper_lower=upper or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +
        +

        syr (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event syr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event syr(sycl::queue &queue,
+                    onemkl::uplo upper_lower,
+                    std::int64_t n,
+                    T alpha,
+                    const T *x,
+                    std::int64_t incx,
+                    T *a,
+                    std::int64_t lda,
+                    const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the symmetric +matrix A if upper_lower=upper or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + symv + syr2 + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/syr2.html b/domains/blas/syr2.html new file mode 100644 index 000000000..81e986c15 --- /dev/null +++ b/domains/blas/syr2.html @@ -0,0 +1,1110 @@ + + + + + + + + + syr2 — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        +

        syr2

        +

        Computes a rank-2 update of a symmetric matrix.

        +

        Description

        +

        The syr2 routines compute two scalar-vector-vector product add them +and add the result to a matrix, with a symmetric matrix. The +operation is defined as:

        +
        +\[A \leftarrow alpha*x*y^T + alpha*y*x^T + A\]
        +

        where:

        +

        alpha is a scalar,

        +

        A is an n-by-n symmetric matrix,

        +

        x and y are vectors of length n.

        +

        syr2 supports the following precisions.

        +
        +
        +++ + + + + + + + + + + +

        T

        float

        double

        +
        +
        +

        syr2 (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void syr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void syr2(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx,
+              sycl::buffer<T,1> &y,
+              std::int64_t incy,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Buffer holding input/output vector y. The buffer must be of +size at least (1 + (n - 1)*abs(incy)). See Matrix Storage +for more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Buffer holding the updated upper triangular part of the symmetric +matrix A if upper_lower=upper, or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +
        +

        syr2 (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event syr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event syr2(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     std::int64_t n,
+                     T alpha,
+                     const T *x,
+                     std::int64_t incx,
+                     const T *y,
+                     std::int64_t incy,
+                     T *a,
+                     std::int64_t lda,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of columns of A. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-vector product.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        y

        Pointer to input/output vector y. The array holding +input/output vector y must be of size at least (1 + (n +- 1)*abs(incy)). See Matrix Storage for +more details.

        +
        +
        incy

        Stride of vector y.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        a

        Pointer to the updated upper triangular part of the symmetric +matrix A if upper_lower=upper, or the updated lower +triangular part of the symmetric matrix A if +upper_lower=lower.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + syr + tbmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/syr2k.html b/domains/blas/syr2k.html new file mode 100644 index 000000000..9d1f86372 --- /dev/null +++ b/domains/blas/syr2k.html @@ -0,0 +1,1343 @@ + + + + + + + + + syr2k — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        +

        syr2k

        +

        Performs a symmetric rank-2k update.

        +

        Description

        +

        The syr2k routines perform a rank-2k update of an n x n +symmetric matrix C by general matrices A and B.

        +

        If trans = transpose::nontrans, the operation is defined as:

        +
        +\[C \leftarrow alpha*(A*B^T + B*A^T) + beta*C\]
        +

        where A is n x k and B is k x n.

        +

        If trans = transpose::trans, the operation is defined as:

        +
        +\[C \leftarrow alpha*(A^T*B + B^T*A) + beta * C\]
        +

        where A is k x n and B is n x k.

        +

        In both cases:

        +

        alpha and beta are scalars,

        +

        C is a symmetric matrix and A,B are general matrices,

        +

        The inner dimension of both matrix multiplications is k.

        +

        syr2k supports the following precisions:

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        syr2k (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void syr2k(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose trans,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void syr2k(sycl::queue &queue,
+               onemkl::uplo upper_lower,
+               onemkl::transpose trans,
+               std::int64_t n,
+               std::int64_t k,
+               T alpha,
+               sycl::buffer<T,1> &a,
+               std::int64_t lda,
+               sycl::buffer<T,1> &b,
+               std::int64_t ldb,
+               T beta,
+               sycl::buffer<T,1> &c,
+               std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies the operation to apply, as described above. Conjugation +is never performed, even if trans = transpose::conjtrans.

        +
        +
        n

        Number of rows and columns in C.The value of n must be at +least zero.

        +
        +
        k

        Inner dimension of matrix multiplications.The value of k must +be at least zero.

        +
        +
        alpha

        Scaling factor for the rank-2k update.

        +
        +
        a

        Buffer holding input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for +more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Buffer holding input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n.

        +

        See Matrix Storage +for more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Buffer holding input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least n.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by the updated C matrix.

        +
        +
        +
        +
        +
        +

        syr2k (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event syr2k(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose trans,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event syr2k(sycl::queue &queue,
+                      onemkl::uplo upper_lower,
+                      onemkl::transpose trans,
+                      std::int64_t n,
+                      std::int64_t k,
+                      T alpha,
+                      const T* a,
+                      std::int64_t lda,
+                      const T* b,
+                      std::int64_t ldb,
+                      T beta,
+                      T* c,
+                      std::int64_t ldc,
+                      const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies the operation to apply, as described above. +Conjugation is never performed, even if trans = +transpose::conjtrans.

        +
        +
        n

        Number of rows and columns in C. The value of n must be +at least zero.

        +
        +
        k

        Inner dimension of matrix multiplications.The value of k +must be at least zero.

        +
        +
        alpha

        Scaling factor for the rank-2k update.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        b

        Pointer to input matrix B.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        B is an k-by-n matrix so the array b +must have size at least ldb*n.

        B is an n-by-k matrix so the array b +must have size at least ldb*k

        Row major

        B is an k-by-n matrix so the array b +must have size at least ldb*k.

        B is an n-by-k matrix so the array b +must have size at least ldb*n.

        +

        See Matrix Storage for +more details.

        +
        +
        ldb

        The leading dimension of B. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        ldb must be at least k.

        ldb must be at least n.

        Row major

        ldb must be at least n.

        ldb must be at least k.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Pointer to input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +n.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by the updated C +matrix.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + syrk + trmm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/syrk.html b/domains/blas/syrk.html new file mode 100644 index 000000000..6d26564fa --- /dev/null +++ b/domains/blas/syrk.html @@ -0,0 +1,1217 @@ + + + + + + + + + syrk — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        syrk

        +

        Performs a symmetric rank-k update.

        +

        Description

        +

        The syrk routines perform a rank-k update of a symmetric matrix C +by a general matrix A. The operation is defined as:

        +
        +\[C \leftarrow alpha*op(A)*op(A)^T + beta*C\]
        +

        where:

        +

        op(X) is one of op(X) = X or op(X) = XT +,

        +

        alpha and beta are scalars,

        +

        C is a symmetric matrix and Ais a general matrix.

        +

        Here op(A) is n-by-k, and C is n-by-n.

        +

        syrk supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        syrk (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void syrk(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void syrk(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              std::int64_t n,
+              std::int64_t k,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              T beta,
+              sycl::buffer<T,1> &c,
+              std::int64_t ldc)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A (See oneMKL defined datatypes for more details). Conjugation is never performed, even if trans = transpose::conjtrans.

        +
        +
        n

        Number of rows and columns in C. The value of n must be at +least zero.

        +
        +
        k

        Number of columns in op(A).The value of k must be at least +zero.

        +
        +
        alpha

        Scaling factor for the rank-k update.

        +
        +
        a

        Buffer holding input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for +more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Buffer holding input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least n.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Output buffer, overwritten by +alpha*op(A)*op(A)T + beta*C.

        +
        +
        +
        +
        +
        +

        syrk (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event syrk(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event syrk(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     std::int64_t n,
+                     std::int64_t k,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T beta,
+                     T* c,
+                     std::int64_t ldc,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A’s data is stored in its upper or lower +triangle. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A (See oneMKL defined datatypes for more details). Conjugation is never performed, even if +trans = transpose::conjtrans.

        +
        +
        n

        Number of rows and columns in C. The value of n must be +at least zero.

        +
        +
        k

        Number of columns in op(A). The value of k must be at +least zero.

        +
        +
        alpha

        Scaling factor for the rank-k update.

        +
        +
        a

        Pointer to input matrix A.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        A is an n-by-k matrix so the array a +must have size at least lda*k.

        A is an k-by-n matrix so the array a +must have size at least lda*n

        Row major

        A is an n-by-k matrix so the array a +must have size at least lda*n.

        A is an k-by-n matrix so the array a +must have size at least lda*k.

        +

        See Matrix Storage for more details.

        +
        +
        lda

        The leading dimension of A. It must be positive.

        + +++++ + + + + + + + + + + + + + + + + +

        trans = transpose::nontrans

        trans = transpose::trans or transpose::conjtrans

        Column major

        lda must be at least n.

        lda must be at least k.

        Row major

        lda must be at least k.

        lda must be at least n.

        +
        +
        beta

        Scaling factor for matrix C.

        +
        +
        c

        Pointer to input/output matrix C. Must have size at least +ldc*n. See Matrix Storage for +more details.

        +
        +
        ldc

        Leading dimension of C. Must be positive and at least +n.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        c

        Pointer to the output matrix, overwritten by +alpha*op(A)*op(A)T + +beta*C.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + symm + syr2k + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/tbmv.html b/domains/blas/tbmv.html new file mode 100644 index 000000000..181d58102 --- /dev/null +++ b/domains/blas/tbmv.html @@ -0,0 +1,1107 @@ + + + + + + + + + tbmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        tbmv

        +

        Computes a matrix-vector product using a triangular band matrix.

        +

        Description

        +

        The tbmv routines compute a matrix-vector product with a triangular +band matrix. The operation is defined as:

        +
        +\[x \leftarrow op(A)*x\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular band matrix, with (k + 1) diagonals,

        +

        x is a vector of length n.

        +

        tbmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        tbmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void tbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void tbmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of sub/super-diagonals of the matrix A. Must be at +least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + 1), +and positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the updated vector x.

        +
        +
        +
        +
        +
        +

        tbmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event tbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event tbmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of sub/super-diagonals of the matrix A. Must be at +least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + +1), and positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + syr2 + tbsv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/tbsv.html b/domains/blas/tbsv.html new file mode 100644 index 000000000..0cf6d5d6b --- /dev/null +++ b/domains/blas/tbsv.html @@ -0,0 +1,1109 @@ + + + + + + + + + tbsv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        tbsv

        +

        Solves a system of linear equations whose coefficients are in a +triangular band matrix.

        +

        Description

        +

        The tbsv routines solve a system of linear equations whose +coefficients are in a triangular band matrix. The operation is +defined as:

        +
        +\[op(A)*x = b\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular band matrix, with (k + 1) diagonals,

        +

        b and x are vectors of length n.

        +

        tbsv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        tbsv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void tbsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void tbsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of sub/super-diagonals of the matrix A. Must be at +least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + 1), +and positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the solution vector x.

        +
        +
        +
        +
        +
        +

        tbsv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event tbsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event tbsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Number of rows and columns of A. Must be at least zero.

        +
        +
        k

        Number of sub/super-diagonals of the matrix A. Must be at +least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least (k + +1), and positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the solution vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + tbmv + tpmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/tpmv.html b/domains/blas/tpmv.html new file mode 100644 index 000000000..6912e5910 --- /dev/null +++ b/domains/blas/tpmv.html @@ -0,0 +1,1088 @@ + + + + + + + + + tpmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
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        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        tpmv

        +

        Computes a matrix-vector product using a triangular packed matrix.

        +

        Description

        +

        The tpmv routines compute a matrix-vector product with a triangular +packed matrix. The operation is defined as:

        +
        +\[x \leftarrow op(A)*x\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular band matrix, supplied in packed form,

        +

        x is a vector of length n.

        +

        tpmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        tpmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void tpmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void tpmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n+1))/2. See Matrix Storage for +more details.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the updated vector x.

        +
        +
        +
        +
        +
        +

        tpmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event tpmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     const T *a,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event tpmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     const T *a,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n+1))/2. See +Matrix Storage for +more details.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + tbsv + tpsv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/tpsv.html b/domains/blas/tpsv.html new file mode 100644 index 000000000..d5d1e316f --- /dev/null +++ b/domains/blas/tpsv.html @@ -0,0 +1,1096 @@ + + + + + + + + + tpsv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
        + + + + + + + + +
        + +
        +
        +
        +
        + + + + +
        + + +
        + + + + + + +
        +
        + + + +
        + +
        + + + +
        +
        + + + + + + + +
        + + +
        + +
        + Contents +
        + +
        +
        +
        +
        +
        + +
        + +
        +

        tpsv

        +

        Solves a system of linear equations whose coefficients are in a +triangular packed matrix.

        +

        Description

        +

        The tpsv routines solve a system of linear equations whose +coefficients are in a triangular packed matrix. The operation is +defined as:

        +
        +\[op(A)*x = b\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular band matrix, supplied in packed form,

        +

        b and x are vectors of length n.

        +

        tpsv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        tpsv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void tpsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void tpsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +(n*(n+1))/2. See Matrix Storage for +more details.

        +
        +
        x

        Buffer holding the n-element right-hand side vector b. The +buffer must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the solution vector x.

        +
        +
        +
        +
        +
        +

        tpsv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event tpsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event tpsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least (n*(n+1))/2. See +Matrix Storage for +more details.

        +
        +
        x

        Pointer to the n-element right-hand side vector b. The +array holding the n-element right-hand side vector b +must be of size at least (1 + (n - 1)*abs(incx)). See +Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the solution vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + tpmv + trmv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/trmm.html b/domains/blas/trmm.html new file mode 100644 index 000000000..026bfe1b9 --- /dev/null +++ b/domains/blas/trmm.html @@ -0,0 +1,1160 @@ + + + + + + + + + trmm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        trmm

        +

        Computes a matrix-matrix product where one input matrix is triangular +and one input matrix is general.

        +

        Description

        +

        The trmm routines compute a scalar-matrix-matrix product where one of +the matrices in the multiplication is triangular. The argument +left_right determines if the triangular matrix, A, is on the +left of the multiplication (left_right = side::left) or on +the right (left_right = side::right). Depending on +left_right. The operation is defined as:

        +
        +\[B \leftarrow alpha*op(A)*B\]
        +

        or

        +
        +\[B \leftarrow alpha*B*op(A)\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = AT, +or op(A) = AH,

        +

        alpha is a scalar,

        +

        A is a triangular matrix, and B is a general matrix.

        +

        Here B is m x n and A is either m x m or +n x n, depending on left_right.

        +

        trmm supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        trmm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void trmm(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose transa,
+              onemkl::diag unit_diag,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void trmm(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose transa,
+              onemkl::diag unit_diag,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the multiplication +(side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_diag

        Specifies whether A is assumed to be unit triangular (all +diagonal elements are 1). See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of B. The value of m must be +at least zero.

        +
        +
        n

        Specifies the number of columns of B. The value of n must +be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*m if left_right = side::left, or +lda*n if left_right = side::right. See +Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if +left_right = side::left, and at least n if +left_right = side::right. Must be positive.

        +
        +
        b

        Buffer holding input/output matrix B. Must have size at +least ldb*n if column major layout is used to store +matrices or at least ldb*m if row major layout is +used to store matrices. See Matrix Storage for more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if row major layout is used to store matrices.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        b

        Output buffer, overwritten by alpha*op(A)*B or +alpha*B*op(A).

        +
        +
        +
        +
        +

        Notes

        +

        If alpha = 0, matrix B is set to zero, and A and B do +not need to be initialized at entry.

        +
        +
        +
        +

        trmm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event trmm(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose transa,
+                     onemkl::diag unit_diag,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T* b,
+                     std::int64_t ldb,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event trmm(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose transa,
+                     onemkl::diag unit_diag,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T* b,
+                     std::int64_t ldb,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A is on the left side of the +multiplication (side::left) or on the right side +(side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether the matrix A is upper or lower +triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_diag

        Specifies whether A is assumed to be unit triangular (all +diagonal elements are 1). See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of B. The value of m must +be at least zero.

        +
        +
        n

        Specifies the number of columns of B. The value of n +must be at least zero.

        +
        +
        alpha

        Scaling factor for the matrix-matrix product.

        +
        +
        a

        Pointer to input matrix A. Must have size at least +lda*m if left_right = side::left, or +lda*n if left_right = side::right. See +Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if +left_right = side::left, and at least n if +left_right = side::right. Must be positive.

        +
        +
        b

        Pointer to input/output matrix B. Must have size at +least ldb*n if column major layout is used to store +matrices or at least ldb*m if row major layout is +used to store matrices. See Matrix Storage for more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if row major layout is used to store matrices.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        b

        Pointer to the output matrix, overwritten by +alpha*op(A)*B or +alpha*B*op(A).

        +
        +
        +
        +
        +

        Notes

        +

        If alpha = 0, matrix B is set to zero, and A and B +do not need to be initialized at entry.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + syr2k + trsm + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/trmv.html b/domains/blas/trmv.html new file mode 100644 index 000000000..e687cbec0 --- /dev/null +++ b/domains/blas/trmv.html @@ -0,0 +1,1097 @@ + + + + + + + + + trmv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        trmv

        +

        Computes a matrix-vector product using a triangular matrix.

        +

        Description

        +

        The trmv routines compute a matrix-vector product with a triangular +matrix. The operation is defined as:

        +
        +\[x \leftarrow op(A)*x\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular band matrix,

        +

        x is a vector of length n.

        +

        trmv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        trmv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void trmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void trmv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        x

        Buffer holding input vector x. The buffer must be of size at +least (1 + (n - 1)*abs(incx)). See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the updated vector x.

        +
        +
        +
        +
        +
        +

        trmv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event trmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event trmv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        x

        Pointer to input vector x. The array holding input vector +x must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for +more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the updated vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + tpsv + trsv + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
        +

        +
        +
        +
        + + +
        +
        + + + + + + \ No newline at end of file diff --git a/domains/blas/trsm.html b/domains/blas/trsm.html new file mode 100644 index 000000000..602aa3a40 --- /dev/null +++ b/domains/blas/trsm.html @@ -0,0 +1,1157 @@ + + + + + + + + + trsm — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
        +
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        + Contents +
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        +
        + +
        + +
        +

        trsm

        +

        Solves a triangular matrix equation (forward or backward solve).

        +

        Description

        +

        The trsm routines solve one of the following matrix equations:

        +
        +\[op(A)*X = alpha*B\]
        +

        or

        +
        +\[X*op(A) = alpha*B\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        alpha is a scalar,

        +

        A is a triangular matrix, and

        +

        B and X are m x n general matrices.

        +

        A is either m x m or n x n, depending on whether +it multiplies X on the left or right. On return, the matrix B +is overwritten by the solution matrix X.

        +

        trsm supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        trsm (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void trsm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              onemkl::transpose transa,
+              onemkl::diag unit_diag,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void trsm(sycl::queue &queue,
+              onemkl::side left_right,
+              onemkl::uplo upper_lower,
+              onemkl::transpose transa,
+              onemkl::diag unit_diag,
+              std::int64_t m,
+              std::int64_t n,
+              T alpha,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &b,
+              std::int64_t ldb)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A multiplies X on the left +(side::left) or on the right (side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_diag

        Specifies whether A is assumed to be unit triangular (all +diagonal elements are 1). See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of B. The value of m must be +at least zero.

        +
        +
        n

        Specifies the number of columns of B. The value of n must +be at least zero.

        +
        +
        alpha

        Scaling factor for the solution.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*m if left_right = side::left, or +lda*n if left_right = side::right. See +Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if +left_right = side::left, and at least n if +left_right = side::right. Must be positive.

        +
        +
        b

        Buffer holding input/output matrix B. Must have size at +least ldb*n if column major layout is used to store +matrices or at least ldb*m if row major layout is +used to store matrices. See Matrix Storage for more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if row major layout is used to store matrices.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        b

        Output buffer. Overwritten by the solution matrix X.

        +
        +
        +
        +
        +

        Notes

        +

        If alpha = 0, matrix B is set to zero, and A and B do +not need to be initialized at entry.

        +
        +
        +
        +

        trsm (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event trsm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose transa,
+                     onemkl::diag unit_diag,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T* b,
+                     std::int64_t ldb,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event trsm(sycl::queue &queue,
+                     onemkl::side left_right,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose transa,
+                     onemkl::diag unit_diag,
+                     std::int64_t m,
+                     std::int64_t n,
+                     T alpha,
+                     const T* a,
+                     std::int64_t lda,
+                     T* b,
+                     std::int64_t ldb,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether A multiplies X on the left +(side::left) or on the right (side::right). See oneMKL defined datatypes for more details.

        +
        +
        uplo

        Specifies whether the matrix A is upper or lower +triangular. See oneMKL defined datatypes for more details.

        +
        +
        transa

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_diag

        Specifies whether A is assumed to be unit triangular (all +diagonal elements are 1). See oneMKL defined datatypes for more details.

        +
        +
        m

        Specifies the number of rows of B. The value of m must +be at least zero.

        +
        +
        n

        Specifies the number of columns of B. The value of n +must be at least zero.

        +
        +
        alpha

        Scaling factor for the solution.

        +
        +
        a

        Pointer to input matrix A. Must have size at least +lda*m if left_right = side::left, or +lda*n if left_right = side::right. See +Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of A. Must be at least m if +left_right = side::left, and at least n if +left_right = side::right. Must be positive.

        +
        +
        b

        Pointer to input/output matrix B. Must have size at +least ldb*n if column major layout is used to store +matrices or at least ldb*m if row major layout is +used to store matrices. See Matrix Storage for more details.

        +
        +
        ldb

        Leading dimension of B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if row major layout is used to store matrices.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        b

        Pointer to the output matrix. Overwritten by the solution +matrix X.

        +
        +
        +
        +
        +

        Notes

        +

        If alpha = 0, matrix B is set to zero, and A and B +do not need to be initialized at entry.

        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 3 Routines

        +
        +
        +
        + + +
        + + +
        + + trmm + BLAS-like Extensions + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/trsm_batch.html b/domains/blas/trsm_batch.html new file mode 100644 index 000000000..dbb4541a4 --- /dev/null +++ b/domains/blas/trsm_batch.html @@ -0,0 +1,1068 @@ + + + + + + + + + trsm_batch — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        trsm_batch

        +

        Computes a group of trsm operations.

        +

        Description

        +

        The trsm_batch routines are batched versions of trsm, performing +multiple trsm operations in a single call. Each trsm +solves an equation of the form op(A) * X = alpha * B or X * op(A) = alpha * B.

        +

        trsm_batch supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        trsm_batch (Buffer Version)

        +

        Description

        +

        The buffer version of trsm_batch supports only the strided API.

        +

        The strided API operation is defined as:

        +
        for i = 0 … batch_size – 1
+    A and B are matrices at offset i * stridea and i * strideb in a and b.
+    if (left_right == onemkl::side::left) then
+        compute X such that op(A) * X = alpha * B
+    else
+        compute X such that X * op(A) = alpha * B
+    end if
+    B := X
+end for
+
        +
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = AT, +or op(A) = AH,

        +

        alpha is a scalar,

        +

        A is a triangular matrix,

        +

        B and X are m x n general matrices,

        +

        A is either m x m or n x n,depending on whether +it multiplies X on the left or right. On return, the matrix B +is overwritten by the solution matrix X.

        +

        The a and b buffers contain all the input matrices. The stride +between matrices is given by the stride parameter. The total number +of matrices in a and b buffers are given by the batch_size parameter.

        +

        Strided API

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void trsm_batch(sycl::queue &queue,
+                    onemkl::side left_right,
+                    onemkl::uplo upper_lower,
+                    onemkl::transpose trans,
+                    onemkl::diag unit_diag,
+                    std::int64_t m,
+                    std::int64_t n,
+                    T alpha,
+                    sycl::buffer<T,1> &a,
+                    std::int64_t lda,
+                    std::int64_t stridea,
+                    sycl::buffer<T,1> &b,
+                    std::int64_t ldb,
+                    std::int64_t strideb,
+                    std::int64_t batch_size)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void trsm_batch(sycl::queue &queue,
+                    onemkl::side left_right,
+                    onemkl::uplo upper_lower,
+                    onemkl::transpose trans,
+                    onemkl::diag unit_diag,
+                    std::int64_t m,
+                    std::int64_t n,
+                    T alpha,
+                    sycl::buffer<T,1> &a,
+                    std::int64_t lda,
+                    std::int64_t stridea,
+                    sycl::buffer<T,1> &b,
+                    std::int64_t ldb,
+                    std::int64_t strideb,
+                    std::int64_t batch_size)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        left_right

        Specifies whether the matrices A multiply X on the left +(side::left) or on the right (side::right). See oneMKL defined datatypes for more details.

        +
        +
        upper_lower

        Specifies whether the matrices A are upper or lower +triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to the +matrices A. See oneMKL defined datatypes for more details.

        +
        +
        unit_diag

        Specifies whether the matrices A are assumed to be unit +triangular (all diagonal elements are 1). See oneMKL defined datatypes for more details.

        +
        +
        m

        Number of rows of the B matrices. Must be at least zero.

        +
        +
        n

        Number of columns of the B matrices. Must be at least zero.

        +
        +
        alpha

        Scaling factor for the solutions.

        +
        +
        a

        Buffer holding the input matrices A with size stridea * batch_size.

        +
        +
        lda

        Leading dimension of the matrices A. Must be at least m if +left_right = side::left, and at least n if left_right = +side::right. Must be positive.

        +
        +
        stridea

        Stride between different A matrices.

        +
        +
        b

        Buffer holding the input matrices B with size strideb * batch_size.

        +
        +
        ldb

        Leading dimension of the matrices B. It must be positive and at least +m if column major layout is used to store matrices or at +least n if row major layout is used to store matrices.

        +
        +
        strideb

        Stride between different B matrices.

        +
        +
        batch_size

        Specifies the number of triangular linear systems to solve.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        b

        Output buffer, overwritten by batch_size solution matrices +X.

        +
        +
        +
        +
        +

        Notes

        +

        If alpha = 0, matrix B is set to zero and the matrices A +and B do not need to be initialized before calling trsm_batch.

        +

        Parent topic: BLAS-like Extensions

        +
        +
        +
        + + +
        + + +
        + + gemm_batch + gemmt + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
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        + + + + + + \ No newline at end of file diff --git a/domains/blas/trsv.html b/domains/blas/trsv.html new file mode 100644 index 000000000..135f35d67 --- /dev/null +++ b/domains/blas/trsv.html @@ -0,0 +1,1101 @@ + + + + + + + + + trsv — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        trsv

        +

        Solves a system of linear equations whose coefficients are in a +triangular matrix.

        +

        Description

        +

        The trsv routines compute a matrix-vector product with a triangular +band matrix. The operation is defined as:

        +
        +\[op(A)*x = b\]
        +

        where:

        +

        op(A) is one of op(A) = A, or op(A) = +AT, or op(A) = AH,

        +

        A is an n-by-n unit or non-unit, upper or lower +triangular matrix,

        +

        b and x are vectors of length n.

        +

        trsv supports the following precisions.

        +
        +
        +++ + + + + + + + + + + + + + + +

        T

        float

        double

        std::complex<float>

        std::complex<double>

        +
        +
        +

        trsv (Buffer Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    void trsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    void trsv(sycl::queue &queue,
+              onemkl::uplo upper_lower,
+              onemkl::transpose trans,
+              onemkl::diag unit_nonunit,
+              std::int64_t n,
+              std::int64_t k,
+              sycl::buffer<T,1> &a,
+              std::int64_t lda,
+              sycl::buffer<T,1> &x,
+              std::int64_t incx)
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Buffer holding input matrix A. Must have size at least +lda*n. See Matrix Storage for more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        x

        Buffer holding the n-element right-hand side vector b. The +buffer must be of size at least (1 + (n - 1)*abs(incx)). +See Matrix Storage for more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Buffer holding the solution vector x.

        +
        +
        +
        +
        +
        +

        trsv (USM Version)

        +

        Syntax

        +
        namespace oneapi::mkl::blas::column_major {
+    sycl::event trsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        namespace oneapi::mkl::blas::row_major {
+    sycl::event trsv(sycl::queue &queue,
+                     onemkl::uplo upper_lower,
+                     onemkl::transpose trans,
+                     onemkl::diag unit_nonunit,
+                     std::int64_t n,
+                     std::int64_t k,
+                     const T *a,
+                     std::int64_t lda,
+                     T *x,
+                     std::int64_t incx,
+                     const sycl::vector_class<sycl::event> &dependencies = {})
+}
+
        +
        +
        +

        Input Parameters

        +
        +
        queue

        The queue where the routine should be executed.

        +
        +
        upper_lower

        Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

        +
        +
        trans

        Specifies op(A), the transposition operation applied to +A. See oneMKL defined datatypes for more details.

        +
        +
        unit_nonunit

        Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes for more details.

        +
        +
        n

        Numbers of rows and columns of A. Must be at least zero.

        +
        +
        a

        Pointer to input matrix A. The array holding input matrix +A must have size at least lda*n. See Matrix Storage for +more details.

        +
        +
        lda

        Leading dimension of matrix A. Must be at least n, and +positive.

        +
        +
        x

        Pointer to the n-element right-hand side vector b. The +array holding the n-element right-hand side vector b +must be of size at least (1 + (n - 1)*abs(incx)). See +Matrix Storage for more details.

        +
        +
        incx

        Stride of vector x.

        +
        +
        dependencies

        List of events to wait for before starting computation, if any. +If omitted, defaults to no dependencies.

        +
        +
        +
        +
        +

        Output Parameters

        +
        +
        x

        Pointer to the solution vector x.

        +
        +
        +
        +
        +

        Return Values

        +

        Output event to wait on to ensure computation is complete.

        +

        Parent topic: BLAS Level 2 Routines

        +
        +
        +
        + + +
        + + +
        + + trmv + BLAS Level 3 Routines + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

        +
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        + + + + + + \ No newline at end of file diff --git a/domains/dense_linear_algebra.html b/domains/dense_linear_algebra.html new file mode 100644 index 000000000..37a6a05e1 --- /dev/null +++ b/domains/dense_linear_algebra.html @@ -0,0 +1,907 @@ + + + + + + + + + Dense Linear Algebra — oneAPI Math Kernel Library Interfaces 0.1 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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        +

        Dense Linear Algebra

        +

        This section contains information about dense linear algebra routines:

        +

        Matrix Storage provides information about dense matrix and vector storage formats that are used by oneMKL BLAS Routines.

        +

        BLAS Routines provides vector, matrix-vector, and matrix-matrix routines for dense matrices and vector operations.

        +
        +
        +
        + + +
        + + +
        + + oneMKL defined datatypes + Matrix Storage + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

        +

        Cookies

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        +

        Matrix Storage

        +
        +

        The oneMKL BLAS and LAPACK routines for DPC++ use several matrix and +vector storage formats. These are the same formats used in +traditional Fortran BLAS/LAPACK.

        +
        +

        General Matrix

        +

        A general matrix A of m rows and n columns with +leading dimension lda is represented as a one dimensional +array a of size of at least lda * n if column major +layout is used and at least lda * m if row major layout +is used. Before entry in any BLAS function using a general +matrix, the leading m by n part of the array a must +contain the matrix A. For column (respectively row) major +layout, the elements of each column (respectively row) are +contiguous in memory while the elements of each row +(respectively column) are at distance lda from the element +in the same row (respectively column) and the previous column +(respectively row).

        +

        Visually, the matrix

        +
        +\[\begin{split}A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + A_{21} & A_{22} & A_{23} & \ldots & A_{2n}\\ + A_{31} & A_{32} & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{m1} & A_{m2} & A_{m3} & \ldots & A_{mn} + \end{bmatrix}\end{split}\]
        +

        is stored in memory as an array

        +
          +

        • For column major layout,

          • +
        +
        +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{21},A_{31},...,A_{m1},*,...,*}_\text{lda}, + \underbrace{A_{12},A_{22},A_{32},...,A_{m2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{1n},A_{2n},A_{3n},...,A_{mn},*,...,*}_\text{lda}} + _\text{lda x n}]\]
        +
          +

        • For row major layout,

          • +
        +
        +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{12},A_{13},...,A_{1n},*,...,*}_\text{lda}, + \underbrace{A_{21},A_{22},A_{23},...,A_{2n},*,...,*}_\text{lda}, + ..., + \underbrace{A_{m1},A_{m2},A_{m3},...,A_{mn},*,...,*}_\text{lda}} + _\text{m x lda}]\]
        +
        +
        +

        Triangular Matrix

        +

        A triangular matrix A of n rows and n columns with +leading dimension lda is represented as a one dimensional +array a, of a size of at least lda * n. When column +(respectively row) major layout is used, the elements of each +column (respectively row) are contiguous in memory while the +elements of each row (respectively column) are at distance +lda from the element in the same row (respectively column) +and the previous column (respectively row).

        +

        Before entry in any BLAS function using a triangular matrix,

        +
          +

        • If upper_lower = uplo::upper, the leading n by n +upper triangular part of the array a must contain the upper +triangular part of the matrix A. The strictly lower +triangular part of the array a is not referenced. In other +words, the matrix

          +
          +\[\begin{split}A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + * & A_{22} & A_{23} & \ldots & A_{2n}\\ + * & * & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + * & * & * & \ldots & A_{nn} + \end{bmatrix}\end{split}\]
          +

          is stored in memory as the array

          +
            +

          • For column major layout,

            • +
          +
          +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},*,...,*}_\text{lda}, + \underbrace{A_{12},A_{22},*,...,*}_\text{lda}, + ..., + \underbrace{A_{1n},A_{2n},A_{3n},...,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}]\]
          +
            +

          • For row major layout,

            • +
          +
          +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{12},A_{13},...,A_{1n},*,...,*}_\text{lda}, + \underbrace{*,A_{22},A_{23},...,A_{2n},*,...,*}_\text{lda}, + ..., + \underbrace{*,...,*,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}]\]
          +
          • +

        • If upper_lower = uplo::lower, the leading n by n +lower triangular part of the array a must contain the lower +triangular part of the matrix A. The strictly upper +triangular part of the array a is not referenced. That is, +the matrix

          +
          +\[\begin{split}A = \begin{bmatrix} + A_{11} & * & * & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & * \\ + A_{31} & A_{32} & A_{33} & \ldots & * \\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{n1} & A_{n2} & A_{n3} & \ldots & A_{nn} + \end{bmatrix}\end{split}\]
          +

          is stored in memory as the array

          +
            +

          • For column major layout,

            • +
          +
          +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},A_{21},A_{31},..,A_{n1},*,...,*}_\text{lda}, + \underbrace{*,A_{22},A_{32},...,A_{n2},*,...,*}_\text{lda}, + ..., + \underbrace{*,...,*,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}]\]
          +
            +

          • For row major layout,

            • +
          +
          +\[\scriptstyle a = + [\underbrace{\underbrace{A_{11},*,...,*}_\text{lda}, + \underbrace{A_{21},A_{22},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n1},A_{n2},A_{n3},...,A_{nn},*,...,*}_\text{lda}} + _\text{lda x n}]\]
          +
          • +
        +
        +
        +

        Band Matrix

        +

        A general band matrix A of m rows and n columns with +kl sub-diagonals, ku super-diagonals, and leading +dimension lda is represented as a one dimensional array +a of a size of at least lda * n (respectively +lda * m) if column (respectively row) major layout is +used.

        +

        Before entry in any BLAS function using a general band matrix, +the leading (kl + ku + 1) by n (respectively +m) part of the array a must contain the matrix +A. This matrix must be supplied column-by-column +(respectively row-by-row), with the main diagonal of the matrix +in row ku (respectively kl) of the array (0-based +indexing), the first super-diagonal starting at position 1 +(respectively 0) in row (ku - 1) (respectively column +(kl + 1)), the first sub-diagonal starting at position 0 +(respectively 1) in row (ku + 1) (respectively column +(kl - 1)), and so on. Elements in the array a that do +not correspond to elements in the band matrix (such as the top +left ku by ku triangle) are not referenced.

        +

        Visually, the matrix A

        +
        +\[\begin{split}A = \left[\begin{smallmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1,ku+1} & * & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{21} & A_{22} & A_{23} & A_{24} & \ldots & A_{2,ku+2} & * & \ldots & \ldots & \ldots & \ldots & * \\ + A_{31} & A_{32} & A_{33} & A_{34} & A_{35} & \ldots & A_{3,ku+3} & * & \ldots & \ldots & \ldots & * \\ + \vdots & A_{42} & A_{43} & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \ldots & \vdots \\ + A_{kl+1,1} & \vdots & A_{53} & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \vdots \\ + * & A_{kl+2,2} & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & * & A_{kl+3,3} & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{n-ku,n}\\ + \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{m-2,n} \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{m-1,n} \\ + * & * & * & \ldots & \ldots & \ldots & * & A_{m,m-kl} & \ldots & A_{m,n-2} & A_{m,n-1} & A_{m,n} + \end{smallmatrix}\right]\end{split}\]
        +

        is stored in memory as an array

        +
          +

        • For column major layout,

          • +
        +
        +\[\scriptscriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{ku},A_{11}, A_{12},...,A_{min(kl+1,m),1},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{ku-1},A_{max(1,2-ku),2},...,A_{min(kl+2,m),2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,ku-n+1)},A_{max(1,n-ku),n},...,A_{min(kl+n,m),n},*,...*}_\text{lda} + }_\text{lda x n}]\]
        +
          +

        • For row major layout,

          • +
        +
        +\[\scriptscriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{kl},A_{11}, A_{12},...,A_{1,min(ku+1,n)},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{kl-1},A_{2,max(1,2-kl)},...,A_{2,min(ku+2,n)},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,kl-m+1)},A_{m,max(1,m-kl)},...,A_{m,min(ku+m,n)},*,...*}_\text{lda} + }_\text{lda x m}]\]
        +

        The following program segment transfers a band matrix from +conventional full matrix storage (variable matrix, with +leading dimension ldm) to band storage (variable a, with +leading dimension lda):

        +
          +

        • Using matrices stored with column major layout,

          • +
        +
        for (j = 0; j < n; j++) {
+    k = ku – j;
+    for (i = max(0, j – ku); i < min(m, j + kl + 1); i++) {
+        a[(k + i) + j * lda] = matrix[i + j * ldm];
+    }
+}
+
        +
        +
          +

        • Using matrices stored with row major layout,

          • +
        +
        for (i = 0; i < n; i++) {
+    k = kl – i;
+    for (j = max(0, i – kl); j < min(n, i + ku + 1); j++) {
+        a[(k + j) + i * lda] = matrix[j + i * ldm];
+    }
+}
+
        +
        +
        +
        +

        Triangular Band Matrix

        +

        A triangular band matrix A of n rows and n columns +with k sub/super-diagonals and leading dimension lda is +represented as a one dimensional array a of size at least +lda * n.

        +

        Before entry in any BLAS function using a triangular band matrix,

        +
          +

        • If upper_lower = uplo::upper, the leading (k + 1) by n +part of the array a must contain the upper +triangular band part of the matrix A. When using column +major layout, this matrix must be supplied column-by-column +(respectively row-by-row) with the main diagonal of the +matrix in row (k) (respectively column 0) of the array, +the first super-diagonal starting at position 1 +(respectively 0) in row (k - 1) (respectively column 1), +and so on. Elements in the array a that do not correspond +to elements in the triangular band matrix (such as the top +left k by k triangle) are not referenced.

          +

          Visually, the matrix

          +
          +\[\begin{split}A = \left[\begin{smallmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1,k+1} & * & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + * & A_{22} & A_{23} & A_{24} & \ldots & A_{2,k+2} & * & \ldots & \ldots & \ldots & \ldots & * \\ + \vdots & * & A_{33} & A_{34} & A_{35} & \ldots & A_{3,k+3} & * & \ldots & \ldots & \ldots & * \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & A_{n-k,n}\\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & A_{n-2,n} \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & A_{n-1,n} \\ + * & * & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * & A_{n,n} + \end{smallmatrix}\right]\end{split}\]
          +

          is stored as an array

          +
          • +
        +
        +
          +

        • For column major layout,

          +
          +
          +\[\scriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{ku},A_{11},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{ku-1},A_{max(1,2-k),2},...,A_{2,2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,k-n+1)},A_{max(1,n-k),n},...,A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}]\]
          +
          +
          • +

        • For row major layout,

          +
          +
          +\[\scriptstyle a = + [\underbrace{ + \underbrace{A_{11},A_{21},...,A_{min(k+1,n),1},*,...,*}_\text{lda}, + \underbrace{A_{2,2},...,A_{min(k+2,n),2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}]\]
          +
          +
          • +
        +

        The following program segment transfers a band matrix from +conventional full matrix storage (variable matrix, with +leading dimension ldm) to band storage (variable a, +with leading dimension lda):

        +
          +

        • Using matrices stored with column major layout,

          • +
        +
        for (j = 0; j < n; j++) {
+    m = k – j;
+    for (i = max(0, j – k); i <= j; i++) {
+        a[(m + i) + j * lda] = matrix[i + j * ldm];
+    }
+}
+
        +
        +
          +

        • Using matrices stored with column major layout,

          • +
        +
        for (i = 0; i < n; i++) {
+    m = –i;
+    for (j = i; j < min(n, i + k + 1); j++) {
+        a[(m + j) + i * lda] = matrix[j + i * ldm];
+    }
+}
+
        +
        +
        +
          +

        • If upper_lower = uplo::lower, the leading (k + 1) by n +part of the array a must contain the upper triangular +band part of the matrix A. This matrix must be supplied +column-by-column with the main diagonal of the matrix in row 0 +of the array, the first sub-diagonal starting at position 0 in +row 1, and so on. Elements in the array a that do not +correspond to elements in the triangular band matrix (such as +the bottom right k by k triangle) are not referenced.

          +

          That is, the matrix

          +
          +\[\begin{split}A = \left[\begin{smallmatrix} + A_{11} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + A_{31} & A_{32} & A_{33} & * & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & * \\ + \vdots & A_{42} & A_{43} & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + A_{k+1,1} & \vdots & A_{53} & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + * & A_{k+2,2} & \vdots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \ldots & \vdots \\ + \vdots & * & A_{k+3,3} & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \ldots & \vdots \\ + \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ldots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & * & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & * \\ + * & * & * & \ldots & \ldots & \ldots & * & A_{n,n-k} & \ldots & A_{n,n-2} & A_{n,n-1} & A_{n,n} + \end{smallmatrix}\right]\end{split}\]
          +

          is stored as the array

          +
          • +
        +
        +
          +

        • For column major layout,

          +
          +\[\scriptstyle a = + [\underbrace{ + \underbrace{A_{11},A_{21},...,A_{min(k+1,n),1},*,...,*}_\text{lda}, + \underbrace{A_{2,2},...,A_{min(k+2,n),2},*,...,*}_\text{lda}, + ..., + \underbrace{A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}]\]
          +
          • +

        • For row major layout,

          +
          +
          +\[\scriptstyle a = + [\underbrace{ + \underbrace{\underbrace{*,...,*}_\text{k},A_{11},*,...,*}_\text{lda}, + \underbrace{\underbrace{*,...,*}_\text{k-1},A_{max(1,2-k),2},...,A_{2,2},*,...*}_\text{lda}, + ..., + \underbrace{\underbrace{*,...,*}_\text{max(0,k-n+1)},A_{max(1,n-k),n},...,A_{n,n},*,...*}_\text{lda} + }_\text{lda x n}]\]
          +
          +
          • +
        +

        The following program segment transfers a band matrix from +conventional full matrix storage (variable matrix, with +leading dimension ldm) to band storage (variable a, +with leading dimension lda):

        +
          +

        • Using matrices stored with column major layout,

          • +
        +
        for (j = 0; j < n; j++) {
+    m = –j;
+    for (i = j; i < min(n, j + k + 1); i++) {
+        a[(m + i) + j * lda] = matrix[i + j * ldm];
+    }
+}
+
        +
        +
          +

        • Using matrices stored with row major layout,

          • +
        +
        for (i = 0; i < n; i++) {
+    m = k – i;
+    for (j = max(0, i – k); j <= i; j++) {
+        a[(m + j) + i * lda] = matrix[j + i * ldm];
+    }
+}
+
        +
        +
        +
        +
        +

        Packed Triangular Matrix

        +

        A triangular matrix A of n rows and n columns is +represented in packed format as a one dimensional array a of +size at least (n*(n + 1))/2. All elements in the upper +or lower part of the matrix A are stored contiguously in the +array a.

        +

        Before entry in any BLAS function using a triangular packed +matrix,

        +
          +

        • If upper_lower = uplo::upper, if column (respectively row) +major layout is used, the first (n*(n + 1))/2 +elements in the array a must contain the upper triangular +part of the matrix A packed sequentially, column by column +(respectively row by row) so that a[0] contains A11, a[1] and a[2] contain A12 +and A22 (respectively A13) +respectively, and so on. Hence, the matrix

          +
          +\[\begin{split}A = \begin{bmatrix} + A_{11} & A_{12} & A_{13} & \ldots & A_{1n}\\ + * & A_{22} & A_{23} & \ldots & A_{2n}\\ + * & * & A_{33} & \ldots & A_{3n}\\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + * & * & * & \ldots & A_{nn} + \end{bmatrix}\end{split}\]
          +

          is stored as the array

          +
            +

          • For column major layout,

            +
            +\[\scriptstyle a = [A_{11},A_{12},A_{22},A_{13},A_{23},A_{33},...,A_{(n-1),n},A_{nn}]\]
            +
            • +

          • For row major layout,

            +
            +\[\scriptstyle a = [A_{11},A_{12},A_{13},...,A_{1n}, + A_{22},A_{23},...,A_{2n},..., + A_{(n-1),(n-1)},A_{(n-1),n},A_{nn}]\]
            +
            • +
          +
          • +

        • If upper_lower = uplo::lower, if column (respectively row) +major layout is used, the first (n*(n + 1))/2 +elements in the array a must contain the lower triangular +part of the matrix A packed sequentially, column by column +(row by row) so that a[0] contains A11, +a[1] and a[2] contain A21 and A31 (respectively A22) respectively, and so +on. The matrix

          +
          +
          +\[\begin{split}A = \begin{bmatrix} + A_{11} & * & * & \ldots & * \\ + A_{21} & A_{22} & * & \ldots & * \\ + A_{31} & A_{32} & A_{33} & \ldots & * \\ + \vdots & \vdots & \vdots & \ddots & \vdots\\ + A_{n1} & A_{n2} & A_{n3} & \ldots & A_{nn} + \end{bmatrix}\end{split}\]
          +

          is stored as the array

          +
            +

          • For column major layout,

            • +
          +
          +
          +\[\scriptstyle a = [A_{11},A_{21},A_{31},...,A_{n1}, + A_{22},A_{32},...,A_{n2},..., + A_{(n-1),(n-1)},A_{n,(n-1)},A_{nn}]\]
          +
          +
            +

          • For row major layout,

            • +
          +
          +
          +\[\scriptstyle a = [A_{11},A_{21},A_{22},A_{31},A_{32},A_{33},...,A_{n,(n-1)},A_{nn}]\]
          +
          +
          +
          • +
        +
        +
        +

        Vector

        +

        A vector X of n elements with increment incx is +represented as a one dimensional array x of size at least (1 + +(n - 1) * abs(incx)).

        +

        Visually, the vector

        +
        +\[X = (X_{1},X_{2}, X_{3},...,X_{n})\]
        +

        is stored in memory as an array

        +
        +\[\scriptstyle x = [\underbrace{ + \underbrace{X_{1},*,...,*}_\text{incx}, + \underbrace{X_{2},*,...,*}_\text{incx}, + ..., + \underbrace{X_{n-1},*,...,*}_\text{incx},X_{n} + }_\text{1 + (n-1) x incx}] \quad if \:incx \:> \:0\]
        +
        +\[\scriptstyle x = [\underbrace{ + \underbrace{X_{n},*,...,*}_\text{|incx|}, + \underbrace{X_{n-1},*,...,*}_\text{|incx|}, + ..., + \underbrace{X_{2},*,...,*}_\text{|incx|},X_{1} + }_\text{1 + (1-n) x incx}] \quad if \:incx \:< \:0\]
        +
        +
        +
        + + +
        + + +
        + + Dense Linear Algebra + BLAS Routines + +
        + +
        +
        +
        +
        +

        + + By Intel Corporation
        + + © Copyright 2020, Intel Corporation.
        +

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        Index

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        oneMKL Interfaces

        +
        +

        Introduction

        +

        oneMKL Interfaces is an open-source implementation of oneMKL Data Parallel C++ (DPC++) interfaces accordingly to oneMKL specification that can work with multiple devices (backends) using device specific libraries underneath

        +
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        +
        +
        + + +
        + + +
        + + oneMKL defined datatypes + +
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        +
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        +

        oneMKL defined datatypes

        +

        oneMKL BLAS and LAPACK for Data Parallel C++ (DPC++) introduces +several new enumeration data types, which are type-safe versions of +the traditional Fortran characters in BLAS and LAPACK. They are +declared in types.hpp, which is included automatically when +you include mkl.hpp. Like all oneMKL DPC++ functionality, they belong to the namespace oneapi::mkl.

        +

        Each enumeration value comes with two names: A single-character name +(the traditional BLAS/LAPACK character) and a longer, descriptive +name. The two names are exactly equivalent and may be used +interchangeably.

        +
        +

        Transpose

        +

        The transpose type specifies whether an input matrix should be +transposed and/or conjugated. It can take the following values:

        + +++++ + + + + + + + + + + + + + + + + + + + + +

        Short Name

        Long Name

        Description

        transpose::N

        transpose::nontrans

        Do not transpose or conjugate the matrix.

        transpose::T

        transpose::trans

        Transpose the matrix.

        transpose::C

        transpose::conjtrans

        Perform Hermitian transpose (transpose and conjugate). Only applicable to complex matrices.

        +
        +
        +

        uplo

        +

        The uplo type specifies whether the lower or upper triangle of a riangular, symmetric, or Hermitian matrix should be accessed.

        +

        It can take the following values:

        + +++++ + + + + + + + + + + + + + + + + +

        Short Name

        Long Name

        Description

        uplo::U

        uplo::upper

        Access the upper triangle of the matrix.

        uplo::L

        uplo::lower

        Access the lower triangle of the matrix.

        +

        In both cases, elements that are not in the selected triangle are not accessed or updated.

        +
        +
        +

        diag

        +

        The diag type specifies the values on the diagonal of a triangular matrix. It can take the following values:

        + +++++ + + + + + + + + + + + + + + + + +

        Short Name

        Long Name

        Description

        diag::N

        diag::nonunit

        The matrix is not unit triangular. The diagonal entries are stored with the matrix data.

        diag::U

        diag::unit

        The matrix is unit triangular (the diagonal entries are all 1s). The diagonal entries in the matrix data are not accessed.

        +
        +
        +

        side

        +

        The side type specifies the order of matrix multiplication when one matrix has a special form (triangular, symmetric, or Hermitian):

        + +++++ + + + + + + + + + + + + + + + + +

        Short Name

        Long Name

        Description

        side::L

        side::left

        The special form matrix is on the left in the multiplication.

        side::R

        side::right

        The special form matrix is on the right in the multiplication.

        +
        +
        +

        offset

        +

        The offset type specifies whether the offset to apply to an output matrix is a fix offset, column offset or row offset. It can take the following values

        + +++++ + + + + + + + + + + + + + + + + + + + + +

        Short Name

        Long Name

        Description

        offset::F

        offset::fix

        The offset to apply to the output matrix is fix, all the inputs in the C_offset matrix has the same value given by the first element in the co array.

        offset::C

        offset::column

        The offset to apply to the output matrix is a column offset, that is to say all the columns in the C_offset matrix are the same and given by the elements in the co array.

        offset::R

        offset::row

        The offset to apply to the output matrix is a row offset, that is to say all the rows in the C_offset matrix are the same and given by the elements in the co array.

        +

        Parent topic: oneMKL Interfaces

        +
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        + + oneMKL Interfaces + Dense Linear Algebra + +
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        +
        + + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 000000000..0adc19e74 --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ 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largest:32,last:[37,38],layer:0,layout:[13,14,15,16,18,19,20,21,23,46,56,58,59,62],lda:[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,39,46,47,48,49,50,51,52,53,56,57,58,59,60,62],ldb:[14,15,16,17,23,27,46,50,56,58,59],ldc:[14,15,16,17,23,27,28,46,50,51],ldm:62,ldot:62,lead:[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,39,46,47,48,49,50,51,52,53,56,57,58,59,60,62],least:[1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62],left:[23,35,45,46,56,58,59,62,64],left_right:[23,46,56,58,59],leftarrow:[2,9,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,35,39,40,42,43,44,45,46,47,48,49,50,51,52,54,56,57],len:[13,18],length:[13,18,19,20,21,22,24,25,26,29,30,31,39,42,43,44,47,48,49,52,53,54,55,57,60],level1:4,level2:4,level3:4,level:[0,1,2,4,9,10,11,12,13,14,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,60,63],lib:0,lib_nam:0,lib_obj:0,libnewlib:0,libonemkl:0,libonemkl_blas_mklcpu:0,libonemkl_blas_newlib:0,librari:[8,63],like:[3,4,15,16,17,59,63,64],linear:[4,6,53,55,59,60,63],link:0,list:[0,1,2,3,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56,57,58,60],load:0,loader:0,locat:0,longer:64,lower:[8,17,22,23,24,25,26,27,28,29,30,31,39,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,64],m1:62,m2:62,m3:62,m:[13,14,15,16,17,18,19,20,21,22,23,24,46,47,56,58,59,62],macro:0,magnitud:[1,5],mai:64,main:62,main_test:0,major:[13,14,15,16,17,18,19,20,21,23,27,28,46,50,51,56,58,59,62],make:0,mani:8,manual:0,map:0,math:[8,63],matric:[7,8,14,15,16,17,23,27,46,50,56,58,59,61,62,64],matrix:[1,2,3,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,63,64],mattric:15,max:[16,62],maxim:32,maximum:[5,32],mechan:0,memori:62,method:0,min:62,minim:33,minimum:[5,33],mix:10,mkl:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],mkl_link_c:0,mklcpu:0,mklgpu:0,mn:62,mode:0,model:0,modifi:[0,5,37,38],more:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],multipl:[3,15,16,23,27,46,50,56,59,63,64],multipli:[15,58,59],must:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62],n1:62,n2:62,n3:62,n:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,64],name:[0,64],namespac:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],nan:[32,33],need:[14,15,16,17,23,29,30,31,46,56,58,59],never:[50,51],new_directori:0,newbackend:0,newdevic:0,newlib:0,newlib_librari:0,newlib_root:0,newlib_sasum:0,newlib_wrapp:0,newlib_wrappers_table_dyn:0,newlibroot:0,nn:62,non:[52,53,54,55,57,60],nontran:[27,28,50,51,64],nonunit:64,norm:[5,34],note:[0,10,14,15,16,17,23,32,33,46,56,58,59],now:0,nrm2:5,number:[1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],off:0,offset:[3,15,16,59,63],offset_typ:16,omit:[1,2,3,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56,57,58,60],one:[0,7,9,13,14,15,16,17,18,23,28,32,33,46,51,52,53,54,55,56,57,58,59,60,62,64],oneapi:[1,2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,63,64],onemkl:[4,13,14,15,16,17,18,22,23,24,25,26,27,28,29,30,31,39,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62],onemkl_blas_cubla:0,onemkl_blas_mklcpu:0,onemkl_blas_newlib:0,onemkl_librari:0,onli:[0,8,15,17,59,64],op:[13,14,15,16,17,18,28,51,52,53,54,55,56,57,58,59,60],open:63,oper:[3,5,6,7,8,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,39,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61],option:0,order:64,other:[0,37,38,45,62],otherwis:36,output:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],overlin:11,overwritten:[3,14,15,16,17,23,27,28,46,50,51,56,58,59],pack:[6,29,30,31,42,43,44,54,55,62],parallel:[0,63,64],param:[37,38],paramet:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],parent:[1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],part:[0,1,8,17,25,26,28,29,30,31,43,44,48,49,62],parti:63,path:0,path_suffix:0,perform:[3,5,6,7,10,11,12,15,27,28,31,35,37,41,43,50,51,59,64],phantom:35,plane:[5,35,37],point:[0,5,35,36,37],pointer:[0,1,2,3,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,60],posit:[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,32,33,39,46,47,48,49,50,51,52,53,56,57,58,59,60,62],post:0,pre:0,precis:[1,2,3,5,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],predic:0,previou:62,previous:0,product:[2,3,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,29,30,31,35,39,40,41,42,43,44,46,47,48,49,52,54,56,57,60],program:62,propag:0,proper:0,properti:0,provid:[0,4,8,61],push_back:0,py:0,python:0,q:0,quad:62,queri:0,queue:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],r:[36,64],rank:[6,7,19,20,21,25,26,27,28,30,31,43,44,48,49,50,51],re:[1,32,33],read:0,real:[1,10,27,28,32,33],referenc:62,replac:[37,45],repres:62,requir:[0,37,38],required_var:0,respect:[37,38,62],result:[0,1,2,8,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,29,30,32,33,34,38,39,41,42,43,46,47,48,49],riangular:64,right:[23,35,45,46,55,56,58,59,60,62,64],rot:5,rotat:[5,35,36,37,38],rotg:5,rotm:5,rotmg:5,routin:[1,2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63],row:[0,13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30,31,39,42,43,44,46,47,50,51,52,53,54,55,56,57,58,59,60,62,64],row_major:[1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],run:0,runtime_error:0,s:[0,17,23,27,28,35,36,46,50,51],safe:64,sai:64,same:[0,32,33,62,64],sb:41,sbmv:6,scal:5,scalar:[1,2,3,5,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,35,38,39,40,41,42,43,44,46,47,48,49,50,51,56,58,59],scale:[3,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,35,38,39,42,43,44,46,47,48,49,50,51,56,58,59],script:0,scriptscriptstyl:62,scriptstyl:[16,62],sdsdot:5,second:38,section:61,see:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],segment:62,select:64,separ:0,sequenti:62,set:[0,25,26,28,29,30,31,37,38,56,58,59],set_target_properti:0,sever:[4,62,64],should:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],side:[23,46,55,56,58,59,60,63],singl:[3,15,41,59,64],single_task:0,size:[1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62],smallest:33,smallmatrix:62,snippet:0,so:[0,14,16,17,27,28,50,51,62],solut:[6,53,55,58,59,60],solv:[7,8,53,55,58,59,60],sourc:[0,63],spec:0,special:64,specif:[0,63],specifi:[0,2,3,13,14,15,16,17,18,22,23,24,25,26,27,28,29,30,31,38,39,40,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,64],spmv:6,spr2:6,spr:[6,44],sqrt:38,src:0,start:[1,2,3,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56,57,58,60,62],std:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],step:0,storag:[1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,60,61,63],store:[1,10,11,12,14,15,16,17,23,27,28,32,33,34,41,46,50,51,56,58,59,62,64],strictli:62,stride:[1,2,3,9,10,11,12,13,15,18,19,20,21,22,24,25,26,29,30,31,32,33,34,35,37,39,40,41,42,43,44,45,47,48,49,52,53,54,55,57,59,60],stridea:[15,59],strideb:[15,59],stridec:15,stridei:3,stridex:3,structur:0,sub:[13,52,53,62],submit:0,subprogram:4,successfulli:0,suffix:0,sum:[1,5,35],sum_:[1,3,10,11,12,15,41],suppli:[29,30,31,42,43,44,54,55,62],support:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],sure:0,swap:5,sycl:[0,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],symbol:0,symm:7,symmetr:[6,7,39,42,43,44,46,47,48,49,50,51,64],symv:6,syntax:[1,2,3,9,10,11,12,13,14,1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