feat: add blas/base/drotm

PR-URL: #2266
Ref: #2039
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com> 
Reviewed-by: Pranav Goswami <goswami.4@iitj.ac.in>

lib/node_modules/@stdlib/blas/base/drotm/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# drotm
+
+> Apply a modified Givens plane rotation.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var drotm = require( '@stdlib/blas/base/drotm' );
+```
+
+#### drotm( N, x, strideX, y, strideY, param )
+
+Applies a modified Givens plane rotation.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
+var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
+
+drotm( 2, x, 2, y, 1, param );
+// x => <Float64Array>[ ~-17.0, 2.0, ~-18.0, 4.0, 5.0 ]
+// y => <Float64Array>[ ~8.0, ~13.0, 8.0, 9.0, 10.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **x**: first input [`Float64Array`][mdn-float64array].
+-   **strideX**: index increment for `x`.
+-   **y**: second input [`Float64Array`][mdn-float64array].
+-   **strideY**: index increment for `y`.
+-   **param**: parameters for the modified Givens transformation
+
+The `N` and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a modified Givens plane rotation to every other element,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
+
+drotm( 3, x, 2, y, 2, param );
+// x => <Float64Array>[ ~-20.0, 2.0, ~-24.0, 4.0, ~-28.0, 6.0 ]
+// y => <Float64Array>[ ~9.0, 8.0, ~15.0, 10.0, ~21.0, 12.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y0 = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
+var param = new Float64Array( [ 1.0, 0.0, 2.0, 3.0, 0.0 ] );
+
+// Create offset views...
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element
+
+drotm( 2, x1, 1, y1, 1, param );
+// x0 => <Float64Array>[ 1.0, ~9.0, ~10.0, 4.0, 5.0 ]
+// y0 => <Float64Array>[ 6.0, 7.0, 8.0, ~-2.0, ~-3.0 ]
+```
+
+#### drotm.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, param )
+
+Applies a modified Givens plane rotation using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
+var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
+
+drotm.ndarray( 2, x, 1, 0, y, 2, 1, param );
+// x => <Float64Array>[ ~-20.0, ~-25.0, 3.0, 4.0, 5.0 ]
+// y => <Float64Array>[ 6.0, ~9.0, 8.0, ~13.0, 10.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetY**: starting index for `y`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to apply a modified Givens plane rotation to every other element starting from the second element,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
+
+drotm.ndarray( 3, x, 2, 1, y, 2, 1, param );
+// x => <Float64Array>[ 1.0, ~-22.0, 3.0, ~-26.0, 5.0, ~-30.0 ]
+// y => <Float64Array>[ 7.0, ~12.0, 9.0, ~18.0, 11.0, ~24.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions leave `x` and `y` unchanged.
+-   `drotm()` corresponds to the [BLAS][blas] level 1 function [`drotm`][drotm].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var drotm = require( '@stdlib/blas/base/drotm' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = discreteUniform( 10, 0, 500, opts );
+console.log( x );
+
+var y = discreteUniform( x.length, 0, 255, opts );
+console.log( y );
+
+var param = discreteUniform( 5, -5, 5, opts );
+console.log( param );
+
+// Apply a plane rotation:
+drotm( x.length, x, 1, y, 1, param );
+console.log( x );
+console.log( y );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/blas/base/drotm.h"
+```
+
+#### c_drotm( N, \*X, strideX, \*Y, strideY, param )
+
+Applies a modified Givens plane rotation.
+
+```c
+double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
+double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };
+const double param[5] = { 0.0, 0.0, 2.0, -3.0, 0.0 };
+
+c_drotm( 5, x, 1, y, 1, param );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[inout] double*` first input array.
+-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
+-   **Y**: `[inout] double*` second input array.
+-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
+-   **param**: `[in] double` parameters for the modified Givens transformation.
+
+```c
+void c_drotm( const CBLAS_INT N, double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY, const double *param );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/blas/base/drotm.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create strided arrays:
+    double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
+    double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };
+
+    // Specify the number of elements:
+    const int N = 5;
+
+    // Specify stride lengths:
+    const int strideX = 1;
+    const int strideY = 1;
+
+    // Specify parameters for the modified Givens transformation:
+    const double param[5] = { 0.0, 0.0, 2.0, -3.0, 0.0 };
+
+    // Apply plane rotation:
+    c_drotm( N, x, strideX, y, strideY, param );
+
+    // Print the result:
+    for ( int i = 0; i < 5; i++ ) {
+        printf( "x[ %i ] = %lf, y[ %i ] = %lf\n", i, x[ i ], i, y[ i ] );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[blas]: http://www.netlib.org/blas
+
+[drotm]: https://www.netlib.org/lapack/explore-html/d1/d45/group__rot_gae48ef017306866ac2d5a8c5a52617858.html#gae48ef017306866ac2d5a8c5a5261785
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->