[petsc-users] [petsc-maint] Inquiry about Multithreading Capabilities in PETSc's KSPSolver
Yongzhong Li
yongzhong.li at mail.utoronto.ca
Tue Apr 23 14:59:54 CDT 2024
Thanks Barry! Does this mean that the sparse matrix-vector products, which actually constitute the majority of the computations in my GMRES routine in PETSc, don’t utilize multithreading? Only basic vector operations such as VecAXPY and VecDot or dense matrix operations in PETSc will benefit from multithreading, is it correct?
Best,
Yongzhong
From: Barry Smith <bsmith at petsc.dev>
Date: Tuesday, April 23, 2024 at 3:35 PM
To: Yongzhong Li <yongzhong.li at mail.utoronto.ca>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>, petsc-maint at mcs.anl.gov <petsc-maint at mcs.anl.gov>, Piero Triverio <piero.triverio at utoronto.ca>
Subject: Re: [petsc-maint] Inquiry about Multithreading Capabilities in PETSc's KSPSolver
你通常不会收到来自 bsmith at petsc.dev 的电子邮件。了解这一点为什么很重要<https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!Z0pxvyXKLQlC3howyi3mIQNq0FUydwnaLxNwQMyue0BB8sPuYLFqrSbUZ6qgaSY_uT13q_q86c4AlhXG1YnYBngzS5fKg7NxpVY$ >
Intel MKL or OpenBLAS are the best bet, but for vector operations they will not be significant since the vector operations do not dominate the computations.
On Apr 23, 2024, at 3:23 PM, Yongzhong Li <yongzhong.li at mail.utoronto.ca> wrote:
Hi Barry,
Thank you for the information provided!
Do you think different BLAS implementation will affect the multithreading performance of some vectors operations in GMERS in PETSc?
I am now using OpenBLAS but didn’t see much improvement when theb multithreading are enabled, do you think other implementation such as netlib and intel-mkl will help?
Best,
Yongzhong
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Date: Monday, April 22, 2024 at 4:20 PM
To: Yongzhong Li <yongzhong.li at mail.utoronto.ca<mailto:yongzhong.li at mail.utoronto.ca>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>, petsc-maint at mcs.anl.gov<mailto:petsc-maint at mcs.anl.gov> <petsc-maint at mcs.anl.gov<mailto:petsc-maint at mcs.anl.gov>>, Piero Triverio <piero.triverio at utoronto.ca<mailto:piero.triverio at utoronto.ca>>
Subject: Re: [petsc-maint] Inquiry about Multithreading Capabilities in PETSc's KSPSolver
你通常不会收到来自 bsmith at petsc.dev<mailto:bsmith at petsc.dev> 的电子邮件。了解这一点为什么很重要<https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!Z0pxvyXKLQlC3howyi3mIQNq0FUydwnaLxNwQMyue0BB8sPuYLFqrSbUZ6qgaSY_uT13q_q86c4AlhXG1YnYBngzS5fKg7NxpVY$ >
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<mailto:yongzhong.li at mail.utoronto.ca>> wrote:
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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
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