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arnoldi-distribuito
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fixed final hesseberg bug

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Antonio De Lucreziis 1 year ago
parent 0346058926
commit f0444e2399
4 changed files with 85 additions and 25 deletions
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4
.gitignore vendored
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@ -5,4 +5,6 @@ build*/
*.log
*.out
*.lock?
*.lock?
*.mat

84
arnoldi.c
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@ -1,3 +1,5 @@
#include <time.h>
#include <lapack.h>
#include <lapacke.h>
@ -17,6 +19,7 @@
#include <petscdmda.h>
#include <petscksp.h>
#include <petscviewertypes.h>
#include <stdio.h>
#include <stdlib.h>
static char help[] = "Example PETSc program\n\n";
@ -129,7 +132,20 @@ int main(int argc, char **argv) {
VecSetSizes(b, PETSC_DECIDE, n);
VecSetType(b, VECMPI);
VecSet(b, 1.0);
// VecSet(b, 1.0);
// seed random number generator
srand((unsigned int)time(NULL));
// fill b with random values
for (PetscInt i = 0; i < n; i++) {
double val = (double)rand() / RAND_MAX;
VecSetValue(b, i, val, INSERT_VALUES);
}
VecAssemblyBegin(b);
VecAssemblyEnd(b);
// VecSetValue(b, 0, 1.0, INSERT_VALUES);
// MatView(A, PETSC_VIEWER_STDOUT_WORLD);
@ -156,14 +172,18 @@ int main(int argc, char **argv) {
// MatSetType(H, MATMPIAIJ);
double *H = (double *)malloc((l + 1) * l * sizeof(double));
double *h = (double *)malloc((l + 1) * l * sizeof(double));
for (PetscInt ii = 0; ii < (l + 1) * l; ii++) {
h[ii] = 0.0;
}
// PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[Arnoldi] Starting iteration\n"));
PetscLogDouble arnoldi_start_time;
PetscCall(PetscTime(&arnoldi_start_time));
{
PetscCall(ArnoldiIteration(A, b, l, n, Q, H));
PetscCall(ArnoldiIteration(A, b, l, n, Q, h));
}
PetscLogDouble arnoldi_end_time;
PetscCall(PetscTime(&arnoldi_end_time));
@ -181,6 +201,14 @@ int main(int argc, char **argv) {
// PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
if (rank == 0) {
// print Hessenberg matrix
printf("H = \n");
for (int i = 0; i < l + 1; i++) {
for (int j = 0; j < l; j++) {
printf("%.2f\t", h[i * (l + 1) + j]);
}
printf("\n");
}
double *wr = (double *)malloc(l * sizeof(double));
double *wi = (double *)malloc(l * sizeof(double));
@ -192,8 +220,9 @@ int main(int argc, char **argv) {
PetscCall(PetscTime(&lapack_start_time));
{
// call LAPACK function "DHSEQR" to compute the eigenvalues of the Hessenberg matrix
LAPACKE_dhseqr(LAPACK_ROW_MAJOR, 'E', 'I', l, 1, l, H, l, wr, wi, z, l);
LAPACKE_dhseqr(LAPACK_ROW_MAJOR, 'E', 'I', l, 1, l, h, l + 1, wr, wi, z, l);
}
PetscLogDouble lapack_end_time;
PetscCall(PetscTime(&lapack_end_time));
PetscLogDouble lapack_time = lapack_end_time - lapack_start_time;
@ -203,7 +232,7 @@ int main(int argc, char **argv) {
printf("H = \n");
for (int i = 0; i < l + 1; i++) {
for (int j = 0; j < l; j++) {
printf("%.2f ", H[i * (l + 1) + j]);
printf("%.2f\t", h[i * (l + 1) + j]);
}
printf("\n");
}
@ -254,11 +283,29 @@ PetscErrorCode ArnoldiIteration(Mat A, Vec b, PetscInt n, PetscInt m, Vec *Q, do
Vec q;
for (PetscInt i = 0; i < n + 1; i++) {
for (PetscInt j = 0; j < n; j++) {
h[i * (n + 1) + j] = 0.0;
}
}
if (rank == 0)
printf("n = %d, m = %d\n", n, m);
/*
eps = 1e-12
h = np.zeros((n + 1, n))
Q = np.zeros((A.shape[0], n + 1))
# Normalize the input vector
Q[:, 0] = b / np.linalg.norm(b, 2) # Use it as the first Krylov vector
for k in range(1, n + 1):
v = np.dot(A, Q[:, k - 1]) # Generate a new candidate vector
for j in range(k): # Subtract the projections on previous vectors
h[j, k - 1] = np.dot(Q[:, j].conj(), v)
v = v - h[j, k - 1] * Q[:, j]
h[k, k - 1] = np.linalg.norm(v, 2)
if h[k, k - 1] > eps: # Add the produced vector to the list, unless
Q[:, k] = v / h[k, k - 1]
else: # If that happens, stop iterating.
return Q, h
*/
PetscCall(VecDuplicate(b, &q));
PetscCall(VecCopy(b, q));
@ -278,15 +325,20 @@ PetscErrorCode ArnoldiIteration(Mat A, Vec b, PetscInt n, PetscInt m, Vec *Q, do
PetscCall(MatMult(A, Q[k - 1], v));
// Reorthogonalization using modified Gram-Schmidt
for (PetscInt j = 0; j < k - 1; j++) { // anche solo 3
// fill all rows from 0 to k - 1 at column k - 1
for (PetscInt j = 0; j < k; j++) { // anche solo 3
PetscScalar h_ij;
// h_(j, k - 1) = q_j . v
PetscCall(VecDot(Q[j], v, &h_ij));
if (rank == 0)
printf("h[%d, %d] = %f\n", j, k - 1, h_ij);
h[j * (n + 1) + k - 1] = h_ij;
// v -= h_ij * q_j
PetscCall(VecAXPY(v, -h_ij, Q[j]));
h[j * (n + 1) + k - 1] = h_ij;
}
// Normalize:
@ -296,6 +348,10 @@ PetscErrorCode ArnoldiIteration(Mat A, Vec b, PetscInt n, PetscInt m, Vec *Q, do
PetscScalar h_ij;
PetscCall(VecNorm(v, NORM_2, &h_ij));
if (rank == 0)
printf("h[%d, %d] = %f\n", k, k - 1, h_ij);
h[k * (n + 1) + k - 1] = h_ij;
// Check for convergence

20
matrices/laplacian/eigs.jl
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@ -11,15 +11,17 @@ ex = fill(1, nx)
ey = fill(1, ny)
ez = fill(1, nz)
Dxx = spdiagm(-1 => ex, 0 => -2 * ex, +1 => ex)
Dyy = spdiagm(-1 => ey, 0 => -2 * ey, +1 => ey)
Dzz = spdiagm(-1 => ez, 0 => -2 * ez, +1 => ez)
Dxx = diagm(-1 => ex, 0 => -2 * ex, +1 => ex)
Dyy = diagm(-1 => ey, 0 => -2 * ey, +1 => ey)
Dzz = diagm(-1 => ez, 0 => -2 * ez, +1 => ez)
Ix = spdiagm(0 => [ex; 1])
Iy = spdiagm(0 => [ey; 1])
Iz = spdiagm(0 => [ez; 1])
Ix = diagm(0 => [ex; 1])
Iy = diagm(0 => [ey; 1])
Iz = diagm(0 => [ez; 1])
# L = kron(Dxx, Iy, Iz) + kron(Ix, Dyy, Iz) + kron(Ix, Iy, Dzz)
L = kron(Dxx, Iy, Iz) + kron(Ix, Dyy, Iz) + kron(Ix, Iy, Dzz)
# display(eigvals(L))
# # 10 x 17 grid
# nx = 11 - 1
@ -40,7 +42,7 @@ println("Laplacian matrix L:")
display(sparse(L))
l = 100
l = 400
# arnoldi iteration
Q = Matrix{Float64}(undef, size(L, 1), l)
@ -66,6 +68,6 @@ end
H = H[1:(l-1), 1:(l-1)]
println("Hessenberg matrix H:")
display(H)
display(sparse(H))
display(eigvals(H))

2
matrices/laplacian/laplacian.jl
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@ -1,7 +1,7 @@
using SparseArrays
using MAT
if len(ARGS) == 0
if length(ARGS) == 0
println("Usage: julia laplacian.jl <N>")
exit(1)
end

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