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arnoldi-distribuito
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copied old arnoldi code

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Antonio De Lucreziis 1 year ago
parent 9f341be51f
commit 4f1adee70d
5 changed files with 229 additions and 3 deletions
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9
CMakeLists.txt
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@ -11,13 +11,16 @@ set(CMAKE_Fortran_COMPILER gfortran)
project(main) project(main)
add_executable(main main.c)
find_package(PkgConfig REQUIRED) find_package(PkgConfig REQUIRED)
pkg_search_module(OpenBLAS REQUIRED IMPORTED_TARGET openblas) pkg_search_module(OpenBLAS REQUIRED IMPORTED_TARGET openblas)
pkg_search_module(PETSc REQUIRED IMPORTED_TARGET petsc) pkg_search_module(PETSc REQUIRED IMPORTED_TARGET petsc)
pkg_search_module(OpenMPI REQUIRED IMPORTED_TARGET ompi) pkg_search_module(OpenMPI REQUIRED IMPORTED_TARGET ompi)
add_executable(main main.c)
target_include_directories(main PUBLIC ${PETSc_INCLUDE_DIRS} ${OpenBLAS_INCLUDE_DIRS} ${OpenMPI_INCLUDE_DIRS}) target_include_directories(main PUBLIC ${PETSc_INCLUDE_DIRS} ${OpenBLAS_INCLUDE_DIRS} ${OpenMPI_INCLUDE_DIRS})
target_link_libraries(main PUBLIC m PkgConfig::PETSc PkgConfig::OpenBLAS PkgConfig::OpenMPI) target_link_libraries(main PUBLIC m PkgConfig::PETSc PkgConfig::OpenBLAS PkgConfig::OpenMPI)
add_executable(arnoldi arnoldi.c)
target_include_directories(arnoldi PUBLIC ${PETSc_INCLUDE_DIRS} ${OpenBLAS_INCLUDE_DIRS} ${OpenMPI_INCLUDE_DIRS})
target_link_libraries(arnoldi PUBLIC m PkgConfig::PETSc PkgConfig::OpenBLAS PkgConfig::OpenMPI)

3
README.md
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@ -4,6 +4,9 @@
### Spack ### Spack
> I recently wrote
> [an article about this](https://aziis98.com/articles/using-spack/)
This assumes that you have spack installed and sourced. If not, you can install This assumes that you have spack installed and sourced. If not, you can install
it using the following commands it using the following commands

207
arnoldi.c
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@ -0,0 +1,207 @@
#include <petscmat.h>
#include <petscsys.h>
#include <petscsystypes.h>
#include <petscvec.h>
#include <petscviewer.h>
#include <petscdm.h>
#include <petscdmda.h>
#include <petscksp.h>
static char help[] = "Example PETSc program\n\n";
// extern PetscErrorCode ComputeMatrix(KSP, Mat, Mat, void *);
// extern PetscErrorCode ComputeRHS(KSP, Vec, void *);
// extern PetscErrorCode ComputeInitialSolution(DM, Vec);
PetscErrorCode ArnoldiIteration(Mat A, Vec b, PetscInt n, Vec *Q, Mat H);
int main(int argc, char **argv) {
Vec b;
PetscInt n, l;
PetscFunctionBeginUser;
PetscInitialize(&argc, &argv, (char *)0, help);
PetscBool flg;
PetscOptionsGetInt(NULL, NULL, "-n", &n, &flg);
if (!flg)
n = 176;
PetscOptionsGetInt(NULL, NULL, "-l", &l, &flg);
if (!flg)
l = 4;
VecCreate(PETSC_COMM_WORLD, &b);
VecSetSizes(b, PETSC_DECIDE, n);
VecSetType(b, VECMPI);
VecSet(b, 1.0);
// VecSetValue(b, 0, 1.0, INSERT_VALUES);
Mat A;
MatCreate(PETSC_COMM_WORLD, &A);
// MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n, n);
// MatSetType(A, MATMPIAIJ);
PetscViewer v;
PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &v));
PetscCall(PetscViewerSetType(v, PETSCVIEWERHDF5));
PetscCall(PetscViewerPushFormat(v, PETSC_VIEWER_HDF5_MAT));
PetscCall(PetscViewerSetFromOptions(v));
PetscCall(PetscViewerFileSetMode(v, FILE_MODE_READ));
PetscCall(PetscViewerFileSetName(
v, "../matrices/laplacian/laplacian-discretization-3d.mat"));
PetscCall(MatSetOptionsPrefix(A, "a_"));
PetscCall(PetscObjectSetName((PetscObject)A, "A"));
// PetscCall(
// PetscOptionsGetString(NULL, NULL, "-f", name, sizeof(name), &flg));
// PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_SUP,
// "Must provide a binary file for the matrix");
// // PetscCall(MatLoad(A, v));
// PetscCall(PetscViewerBinaryOpen(
// PETSC_COMM_WORLD,
// "../matrices/laplacian/laplacian-discretization-3d.mat",
// FILE_MODE_READ, &v));
PetscCall(MatLoad(A, v));
// // A := diag(-1, 2, -1)
// for (PetscInt i = 0; i < n; i++) {
// PetscScalar v[3] = {-1.0, 2.0, -1.0};
// PetscInt col[3] = {i - 1, i, i + 1};
// PetscInt ncol = 0;
// if (i > 0) {
// col[ncol] = i - 1;
// v[ncol] = -1.0;
// ncol++;
// }
// col[ncol] = i;
// v[ncol] = 2.0;
// ncol++;
// if (i < n - 1) {
// col[ncol] = i + 1;
// v[ncol] = -1.0;
// ncol++;
// }
// MatSetValues(A, 1, &i, ncol, col, v, INSERT_VALUES);
// // MatSetValue(A, i, i, (PetscScalar)(i + 1), INSERT_VALUES);
// }
MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
MatView(A, PETSC_VIEWER_DRAW_WORLD);
MatView(A, PETSC_VIEWER_STDOUT_WORLD);
VecView(b, PETSC_VIEWER_DRAW_WORLD);
VecView(b, PETSC_VIEWER_STDOUT_WORLD);
printf("[Arnoldi] Allocating memory for Krylov subspace basis\n");
Vec *Q;
PetscMalloc1(l, &Q);
for (PetscInt i = 0; i < l; i++) {
VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n, &Q[i]);
}
printf("[Arnoldi] Constructing Hessenberg matrix\n");
Mat H;
PetscCall(MatCreate(PETSC_COMM_SELF, &H));
PetscCall(MatSetSizes(H, PETSC_DECIDE, PETSC_DECIDE, l + 1, l));
PetscCall(MatSetType(H, MATDENSE));
// MatSetType(H, MATMPIAIJ);
printf("[Arnoldi] Starting iteration\n");
PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
PetscCall(ArnoldiIteration(A, b, l, Q, H));
PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
printf("[Arnoldi] Done\n");
MatView(H, PETSC_VIEWER_DRAW_WORLD);
MatView(H, PETSC_VIEWER_STDOUT_WORLD);
// print Hessenberg matrix to file
PetscViewer v2;
PetscCall(PetscViewerCreate(PETSC_COMM_SELF, &v2));
PetscCall(PetscViewerSetType(v2, PETSCVIEWERHDF5));
PetscCall(PetscViewerPushFormat(v2, PETSC_VIEWER_HDF5_MAT));
PetscCall(PetscViewerFileSetMode(v2, FILE_MODE_WRITE));
PetscCall(PetscViewerFileSetName(v2, "hessenberg.mat"));
PetscCall(MatView(H, v2));
// for (PetscInt i = 0; i < l + 1; i++) {
// VecView(Q[i], PETSC_VIEWER_STDOUT_WORLD);
// }
// MatView(H, PETSC_VIEWER_STDOUT_WORLD);
// for (PetscInt i = 0; i < l + 1; i++) {
// PetscCall(VecDestroy(&Q[i]));
// }
// PetscCall(PetscFree(Q));
PetscCall(MatDestroy(&A));
PetscCall(VecDestroy(&b));
PetscFinalize();
return 0;
}
PetscErrorCode ArnoldiIteration(Mat A, Vec b, PetscInt n, Vec *Q, Mat H) {
PetscFunctionBeginUser;
PetscScalar eps = 1e-12;
PetscInt m;
PetscCall(VecGetSize(b, &m));
Vec q;
PetscCall(MatZeroEntries(H));
PetscCall(VecDuplicate(b, &q));
PetscCall(VecCopy(b, q));
PetscCall(VecNormalize(q, NULL));
Q[0] = q;
for (PetscInt k = 1; k < n + 1; k++) {
// printf("[Arnoldi] Iteration %d\n", k);
Vec v;
PetscCall(VecDuplicate(b, &v));
PetscCall(MatMult(A, Q[k - 1], v));
// Reorthogonalization using modified Gram-Schmidt
for (PetscInt j = 0; j < k; j++) {
// printf("[Arnoldi] Reorthogonalization %d\n", j);
PetscScalar h;
PetscCall(VecDot(Q[j], v, &h));
PetscCall(MatSetValue(H, j, k - 1, h, INSERT_VALUES));
PetscCall(VecAXPY(v, -h, Q[j]));
}
// Normalize
PetscScalar h;
PetscCall(VecNorm(v, NORM_2, &h));
PetscCall(MatSetValue(H, k, k - 1, h, INSERT_VALUES));
// Check for convergence
if (h > eps) {
PetscCall(VecNormalize(v, NULL));
Q[k] = v;
} else {
break;
}
}
PetscFunctionReturn(PETSC_SUCCESS);
}

13
matrices/laplacian/julia-laplaciano.jl
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@ -0,0 +1,13 @@
using SparseArrays
using MAT
# 11 x 16
nx = 10
ny = 15
ex = fill(1, nx)
ey = fill(1, ny)
Dxx = spdiagm(-1 => ex, 0 => -2 * ex, +1 => ex)
Dyy = spdiagm(-1 => ey, 0 => -2 * ey, +1 => ey)
L = kron(Dyy, spdiagm(0 => [ex; 1])) + kron(spdiagm(0 => [ey; 1]), Dxx);
matwrite("laplacian-discretization-3d.mat", Dict("A" => L))

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