void DiagonalizationPoisson1Dfst(Vector u, const Vector lambda)
{
Vector btilde = createVector(u->len);
Vector buf = createVector(4*(u->len+1));
int i;
int N=u->len+1;
int NN=4*N;
copyVector(btilde, u);
fst(btilde->data, &N, buf->data, &NN);
for (i=0;i<btilde->len;++i)
btilde->data[i] /= (lambda->data[i]+alpha);
fstinv(btilde->data, &N, buf->data, &NN);
copyVector(u, btilde);
freeVector(btilde);
freeVector(buf);
}
int main(int argc, char** argv)
{
int rank, size;
init_app(argc, argv, &rank, &size);
if (argc < 2) {
printf("usage: %s <N> [L]\n",argv[0]);
close_app();
return 1;
}
/* the total number of grid points in each spatial direction is (N+1) */
/* the total number of degrees-of-freedom in each spatial direction is (N-1) */
int N = atoi(argv[1]);
int M = N-1;
double L=1;
if (argc > 2)
L = atof(argv[2]);
double h = L/N;
Vector lambda = createEigenValues(M);
Vector grid = createVector(M);
for (int i=0;i<M;++i)
grid->data[i] = (i+1)*h;
Matrix u = createMatrix(M, M);
Matrix ut = createMatrix(M, M);
evalMesh(u->as_vec, grid, grid, poisson_source);
scaleVector(u->as_vec, h*h);
int NN = 4*N;
Vector z = createVector(NN);
double time = WallTime();
for (int j=0; j < M; j++)
fst(u->data[j], &N, z->data, &NN);
transposeMatrix(ut, u);
for (int i=0; i < M; i++)
fstinv(ut->data[i], &N, z->data, &NN);
for (int j=0; j < M; j++)
for (int i=0; i < M; i++)
ut->data[j][i] /= lambda->data[i]+lambda->data[j];
for (int i=0; i < M; i++)
fst(ut->data[i], &N, z->data, &NN);
transposeMatrix(u, ut);
for (int j=0; j < M; j++)
fstinv(u->data[j], &N, z->data, &NN);
evalMesh2(u->as_vec, grid, grid, exact_solution, -1.0);
double max = maxNorm(u->as_vec);
if (rank == 0) {
printf("elapsed: %f\n", WallTime()-time);
printf("max: %f\n", max);
}
freeMatrix(u);
freeMatrix(ut);
freeVector(grid);
freeVector(z);
freeVector(lambda);
close_app();
return 0;
}
