[petsc-users] [petsc-maint] Inquiry about Multithreading Capabilities in PETSc's KSPSolver
Barry Smith
bsmith at petsc.dev
Mon Apr 22 15:19:54 CDT 2024
PETSc provided solvers do not directly use threads.
The BLAS used by LAPACK and PETSc may use threads depending on what BLAS is being used and how it was configured.
Some of the vector operations in GMRES in PETSc use BLAS that can use threads, including axpy, dot, etc. For sufficiently large problems, the use of threaded BLAS can help with these routines, but not significantly for the solver.
Dense matrix-vector products MatMult() and dense matrix direct solvers PCLU use BLAS and thus can benefit from threading. The benefit can be significant for large enough problems with good hardware, especially with PCLU.
If you run with -blas_view PETSc tries to indicate information about the threading of BLAS. You can also use -blas_num_threads <n> to set the number of threads, equivalent to setting the environmental variable. For dense solvers you can vary the number of threads and run with -log_view to see what it helps to improve and what it does not effect.
> On Apr 22, 2024, at 4:06 PM, Yongzhong Li <yongzhong.li at mail.utoronto.ca> wrote:
>
> This Message Is From an External Sender
> This message came from outside your organization.
> Hello all,
>
> I am writing to ask if PETSc’s KSPSolver makes use of OpenMP/multithreading, specifically when performing iterative solutions with the GMRES algorithm.
>
> The questions appeared when I was running a large numerical program based on boundary element method. I used the PETSc's GMRES algorithm in KSPSolve to solve a shell matrix system iteratively. I observed that threads were being utilized, controlled by the OPENBLAS_NUM_THREADS environment variable. However, I noticed no significant performance difference between running the solver with multiple threads versus a single thread.
>
> Could you please confirm if GMRES in KSPSolve leverages multithreading, and also whether it is influenced by the multithreadings of the low-level math libraries such as BLAS and LAPACK? If so, how can I enable multithreading effectively to see noticeable improvements in solution times when using GMRES? If not, why do I observe that threads are being used during the GMERS solutions?
>
> For reference, I am using PETSc version 3.16.0, configured in CMakelists as follows:
>
> ./configure PETSC_ARCH=config-release --with-scalar-type=complex --with-fortran-kernels=1 --with-debugging=0 COPTFLAGS=-O3 -march=native CXXOPTFLAGS=-O3 -march=native FOPTFLAGS=-O3 -march=native --with-cxx=g++ --download-openmpi --download-superlu --download-opencascade --with-openblas-include=${OPENBLAS_INC} --with-openblas-lib=${OPENBLAS_LIB} --with-threadsafety --with-log=0 --with-openmp
>
> To simplify the diagnosis of potential issues, I have also written a small example program using GMRES to solve a sparse matrix system derived from a 2D Poisson problem using the finite difference method. I found similar issues on this piece of codes. The code is as follows:
>
> #include <petscksp.h>
>
> /* Monitor function to print iteration number and residual norm */
> PetscErrorCode MyKSPMonitor(KSP ksp, PetscInt n, PetscReal rnorm, void *ctx) {
> PetscErrorCode ierr;
> ierr = PetscPrintf(PETSC_COMM_WORLD, "Iteration %D, Residual norm %g\n", n, (double)rnorm);
> CHKERRQ(ierr);
> return 0;
> }
>
> int main(int argc, char **args) {
> Vec x, b, x_true, e;
> Mat A;
> KSP ksp;
> PetscErrorCode ierr;
> PetscInt i, j, Ii, J, n = 500; // Size of the grid n x n
> PetscInt Istart, Iend, ncols;
> PetscScalar v;
> PetscMPIInt rank;
> PetscInitialize(&argc, &args, NULL, NULL);
> PetscLogDouble t1, t2; // Variables for timing
> MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
>
> // Create vectors and matrix
> ierr = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n*n, &x); CHKERRQ(ierr);
> ierr = VecDuplicate(x, &b); CHKERRQ(ierr);
> ierr = VecDuplicate(x, &x_true); CHKERRQ(ierr);
>
> // Set true solution as all ones
> ierr = VecSet(x_true, 1.0); CHKERRQ(ierr);
>
> // Create and assemble matrix A for the 2D Laplacian using 5-point stencil
> ierr = MatCreate(PETSC_COMM_WORLD, &A); CHKERRQ(ierr);
> ierr = MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n*n, n*n); CHKERRQ(ierr);
> ierr = MatSetFromOptions(A); CHKERRQ(ierr);
> ierr = MatSetUp(A); CHKERRQ(ierr);
> ierr = MatGetOwnershipRange(A, &Istart, &Iend); CHKERRQ(ierr);
> for (Ii = Istart; Ii < Iend; Ii++) {
> i = Ii / n; // Row index
> j = Ii % n; // Column index
> v = -4.0;
> ierr = MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES); CHKERRQ(ierr);
> if (i > 0) { // South
> J = Ii - n;
> v = 1.0;
> ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES); CHKERRQ(ierr);
> }
> if (i < n - 1) { // North
> J = Ii + n;
> v = 1.0;
> ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES); CHKERRQ(ierr);
> }
> if (j > 0) { // West
> J = Ii - 1;
> v = 1.0;
> ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES); CHKERRQ(ierr);
> }
> if (j < n - 1) { // East
> J = Ii + 1;
> v = 1.0;
> ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES); CHKERRQ(ierr);
> }
> }
> ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
> ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
>
> // Compute the RHS corresponding to the true solution
> ierr = MatMult(A, x_true, b); CHKERRQ(ierr);
>
> // Set up and solve the linear system
> ierr = KSPCreate(PETSC_COMM_WORLD, &ksp); CHKERRQ(ierr);
> ierr = KSPSetOperators(ksp, A, A); CHKERRQ(ierr);
> ierr = KSPSetType(ksp, KSPGMRES); CHKERRQ(ierr);
> ierr = KSPSetTolerances(ksp, 1e-5, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT); CHKERRQ(ierr);
>
> /* Set up the monitor */
> ierr = KSPMonitorSet(ksp, MyKSPMonitor, NULL, NULL); CHKERRQ(ierr);
>
> // Start timing
> PetscTime(&t1);
>
> ierr = KSPSolve(ksp, b, x); CHKERRQ(ierr);
>
> // Stop timing
> PetscTime(&t2);
>
> // Compute error
> ierr = VecDuplicate(x, &e); CHKERRQ(ierr);
> ierr = VecWAXPY(e, -1.0, x_true, x); CHKERRQ(ierr);
> PetscReal norm_error, norm_true;
> ierr = VecNorm(e, NORM_2, &norm_error); CHKERRQ(ierr);
> ierr = VecNorm(x_true, NORM_2, &norm_true); CHKERRQ(ierr);
> PetscReal relative_error = norm_error / norm_true;
> if (rank == 0) { // Print only from the first MPI process
> PetscPrintf(PETSC_COMM_WORLD, "Relative error ||x - x_true||_2 / ||x_true||_2: %g\n", (double)relative_error);
> }
>
> // Output the wall time taken for MatMult
> PetscPrintf(PETSC_COMM_WORLD, "Time taken for KSPSolve: %f seconds\n", t2 - t1);
>
> // Cleanup
> ierr = VecDestroy(&x); CHKERRQ(ierr);
> ierr = VecDestroy(&b); CHKERRQ(ierr);
> ierr = VecDestroy(&x_true); CHKERRQ(ierr);
> ierr = VecDestroy(&e); CHKERRQ(ierr);
> ierr = MatDestroy(&A); CHKERRQ(ierr);
> ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
> PetscFinalize();
> return 0;
> }
>
> Here are some profiling results for GMERS solution.
>
> OPENBLAS_NUM_THREADS = 1, iteration steps = 859, solution time = 16.1
> OPENBLAS_NUM_THREADS = 2, iteration steps = 859, solution time = 16.3
> OPENBLAS_NUM_THREADS = 4, iteration steps = 859, solution time = 16.7
> OPENBLAS_NUM_THREADS = 8, iteration steps = 859, solution time = 16.8
> OPENBLAS_NUM_THREADS = 16, iteration steps = 859, solution time = 17.8
>
> I am using one workstation with Intel® Core™ i9-11900K Processor, 8 cores, 16 threads. Note that I am not using multiple MPI processes, such as mpirun/mpiexec, the default number of MPI processes should be 1, correct if I am wrong.
>
> Thank you in advance!
>
> Sincerely,
> Yongzhong
>
> -----------------------------------------------------------
> Yongzhong Li
> PhD student | Electromagnetics Group
> Department of Electrical & Computer Engineering
> University of Toronto
> https://urldefense.us/v3/__http://www.modelics.org__;!!G_uCfscf7eWS!b7a3fGWAWaAfipIVdyC00gJjtfXWAyBg88kMFF39JD7pOYzY9yZi2J0Rnjf41f3GrdIIe4HltuF9P1xweNtROvc$ <https://urldefense.us/v3/__http://www.modelics.org__;!!G_uCfscf7eWS!efVv_hPkRBEhyquXer2c8sFeGrjOtTjEGicYg2niCyfT9swzjLFyf6k4XrhKElaF-cX_Q02y9KSTRNFHPlKhXMtuzaTekCWcXgw$>
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