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| The main purpose of QDWH is to compute the polar decomposition A=UH using ScaLAPACK numerical library. | ||
| ScaLAPACK-QDWH is written in C and requires ScaLAPACK installation, as the main software dependency. | ||
| The main driver compares the ScaLAPACK performance of QDWH against the SVD-based polar decomposition | ||
| (using PDGESVD). | ||
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| 1. How to run the code: | ||
| 1.1 To run the test on N nodes, the number of tasks (nT) = N * (number_of_cores per node ). The programming model is pure MPI (no OpenMP, i.e., sequential BLAS). | ||
| 1.2 PxQ is the process grid configuration, where (nT - PxQ = 0) | ||
| 1.3 To find the polar decomposition: | ||
| a) Using ScaLAPACK-QDWH (--polarqdwh) | ||
| b) Using ScaLAPACK-SVD-based (--polarsvd) | ||
| c) On Cray systems, the launching command typically looks like: | ||
| The main purpose of QDWH is to compute the polar decomposition A=UH using ScaLAPACK numerical library. | ||
| ScaLAPACK-QDWH is written in C and requires ScaLAPACK installation, as the main software dependency. | ||
| The main driver compares the ScaLAPACK performance of QDWH against the SVD-based polar decomposition | ||
| (using PDGESVD). | ||
| 1. How to run the code | ||
| 1. To run the test on N nodes, the number of tasks (nT) = N * (number_of_cores per node ). The programming model is pure MPI (no OpenMP, i.e., sequential BLAS). | ||
| 2. PxQ is the process grid configuration, where (nT - PxQ = 0) | ||
| 3. To find the polar decomposition: | ||
| 1. Using ScaLAPACK-QDWH (--polarqdwh) | ||
| 2. Using ScaLAPACK-SVD-based (--polarsvd) | ||
| 3. On Cray systems, the launching command typically looks like: | ||
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| srun --ntasks=nT --hint=nomultithread ./main --nprow p --npcol q --b 64 --cond 1e16 --niter 1 --n_range start:stop:step --check --polarqdwh --polarsvd | ||
| This runs QDWH-based and SVD-based polar decomposition and will check on the numerical accuracy, for one single iteration, with ill-conditioned matrix, for PxQ processor grid size, block size 64, | ||
| no multithreading, on nT number of MPI processes, across a range of matrix sizes defined by start:stop:step. | ||
| 1.4 To Find the SVD using QDWH: | ||
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| This runs QDWH-based and SVD-based polar decomposition and will check on the numerical accuracy, for one single iteration, with ill-conditioned matrix, for PxQ processor grid size, block size 64, no multithreading, on nT number of MPI processes, across a range of matrix sizes defined by start:stop:step. | ||
| 4. To Find the SVD using QDWH: | ||
| Using ScaLAPACK-QDWH: the calculation of the polar decomposition is followed by MRRR (--qwmr) or DC (--qwdc) as the symmetric eigensolver. | ||
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| Using ScaLAPCK-PDGESVD: --slsvd | ||
| srun --ntasks=nT --hint=nomultithread ./main --nprow p --npcol q --b 64 --cond 1e16 --niter 1 --n_range start:stop:step --check --qwmr --qwdc --slsvd | ||
| 1.5 To use LU to estimate the condition number of the matrix: add the option --optcond 0 (default:optcond 1 to use qr) | ||
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| 1.6 The complete list of options is available below with -h option: | ||
| "======= QDWHsvd timing using ScaLAPACK\n" | ||
| " -p --nprow : Number of MPI process rows\n" | ||
| " -q --npcol : Number of MPI process cols\n" | ||
| " -jl --lvec : Compute left singular vectors\n" | ||
| " -jr --rvec : Compute right singular vectors\n" | ||
| " -n --N : Dimension of the matrix\n" | ||
| " -b --nb : Block size\n" | ||
| " -m --mode : [1:6] Mode from pdlatms used to generate the matrix\n" | ||
| " -k --cond : Condition number used to generate the matrix\n" | ||
| " -o --optcond : Estimate Condition number using QR\n" | ||
| " -i --niter : Number of iterations\n" | ||
| " -r --n_range : Range for matrix sizes Start:Stop:Step\n" | ||
| " -polarqdwh --polarqdwh : Find polar decomposition using QDWH A=UH \n" | ||
| " -polarsvd --polarsvd : Find the polar decomposition using scalapack-svd \n" | ||
| " -s --slsvd : Run reference ScaLAPACK SVD\n" | ||
| " -w --qwmr : Run QDWH SVD with ScaLAPACK MRRR EIG\n" | ||
| " -e --qwdc : Run QDWH SVD with ScaLAPACK DC EIG\n" | ||
| " -c --check : Check the solution\n" | ||
| " -fqwsvd --profqwsvd : Enable profiling QDWHsvd\n" | ||
| " -fqw --profqw : Enable profiling QDWH\n" | ||
| " -v --verbose : Verbose\n" | ||
| " -h --help : Print this help\n" ); | ||
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| srun --ntasks=nT --hint=nomultithread ./main --nprow p --npcol q --b 64 --cond 1e16 --niter 1 --n_range start:stop:step --check --qwmr --qwdc --slsvd | ||
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| 5. To use LU to estimate the condition number of the matrix: add the option --optcond 0 (default:optcond 1 to use qr) | ||
| 6. The complete list of options is available below with -h option: | ||
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| ``` | ||
| "======= QDWHsvd timing using ScaLAPACK" | ||
| " -p --nprow : Number of MPI process rows" | ||
| " -q --npcol : Number of MPI process cols" | ||
| " -jl --lvec : Compute left singular vectors" | ||
| " -jr --rvec : Compute right singular vectors" | ||
| " -n --N : Dimension of the matrix" | ||
| " -b --nb : Block size" | ||
| " -m --mode : [1:6] Mode from pdlatms used to generate the matrix" | ||
| " -k --cond : Condition number used to generate the matrix" | ||
| " -o --optcond : Estimate Condition number using QR" | ||
| " -i --niter : Number of iterations" | ||
| " -r --n_range : Range for matrix sizes Start:Stop:Step" | ||
| " -polarqdwh --polarqdwh : Find polar decomposition using QDWH A=UH " | ||
| " -polarsvd --polarsvd : Find the polar decomposition using scalapack-svd " | ||
| " -s --slsvd : Run reference ScaLAPACK SVD" | ||
| " -w --qwmr : Run QDWH SVD with ScaLAPACK MRRR EIG" | ||
| " -e --qwdc : Run QDWH SVD with ScaLAPACK DC EIG" | ||
| " -c --check : Check the solution" | ||
| " -fqwsvd --profqwsvd : Enable profiling QDWHsvd" | ||
| " -fqw --profqw : Enable profiling QDWH" | ||
| " -v --verbose : Verbose" | ||
| " -h --help : Print this help" | ||
| ``` |