static char help[] = "Estimates the 2-norm condition number of a matrix A, that is, the ratio of the largest to the smallest singular values of A. "
"The matrix is a Grcar matrix.\n\n"
"The command line options are:\n"
" -n <n>, where <n> = matrix dimension.\n\n";
#include "slepcsvd.h"
#include "slepceps.h"
/*
This example computes the singular values of an nxn Grcar matrix,
which is a nonsymmetric Toeplitz matrix:
| 1 1 1 1 |
| -1 1 1 1 1 |
| -1 1 1 1 1 |
| . . . . . |
A = | . . . . . |
| -1 1 1 1 1 |
| -1 1 1 1 |
| -1 1 1 |
| -1 1 |
*/
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
PetscErrorCode ierr;
Mat A; /* Grcar matrix */
SVD svd; /* singular value solver context */
EPS eps; /* eigenproblem solver context */
PetscInt N=30, Istart, Iend, i, col[5];
int nconv1, nconv2;
PetscScalar value[] = { -1, 1, 1, 1, 1 };
PetscReal sigma_1, sigma_n;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%d\n\n",N);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Generate the matrix
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
for( i=Istart; i<Iend; i++ ) {
col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
if (i==0) {
ierr = MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);CHKERRQ(ierr);
}
else {
ierr = MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the singular value solver and set the solution method
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create singular value context
*/
ierr = SVDCreate(PETSC_COMM_WORLD,&svd);CHKERRQ(ierr);
/*
Set operator
*/
ierr = SVDSetOperator(svd,A);CHKERRQ(ierr);
/*
Set solver parameters at runtime
*/
ierr = SVDSetFromOptions(svd);CHKERRQ(ierr);
/* PENDIENTE: utilizar funciones SVD en lugar de EPS*/
ierr = SVDEigensolverGetEPS(svd,&eps);CHKERRQ(ierr);
ierr = EPSSetDimensions(eps,1,PETSC_DEFAULT);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the eigensystem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
First request an eigenvalue from one end of the spectrum
*/
ierr = EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);CHKERRQ(ierr);
ierr = SVDSolve(svd);CHKERRQ(ierr);
/*
Get number of converged singular values
*/
ierr = SVDGetConverged(svd,&nconv1);CHKERRQ(ierr);
/*
Get converged singular values: largest singular value is stored in sigma_1.
In this example, we are not interested in the singular vectors
*/
if (nconv1 > 0) {
ierr = SVDGetSingularTriplet(svd,0,&sigma_1,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
}
/*
Request an eigenvalue from the other end of the spectrum
*/
ierr = EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);CHKERRQ(ierr);
ierr = SVDSolve(svd);CHKERRQ(ierr);
/*
Get number of converged eigenpairs
*/
ierr = SVDGetConverged(svd,&nconv2);CHKERRQ(ierr);
/*
Get converged singular values: smallest singular value is stored in sigma_n.
As before, we are not interested in the singular vectors
*/
if (nconv2 > 0) {
ierr = SVDGetSingularTriplet(svd,0,&sigma_n,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
if (nconv1 > 0 && nconv2 > 0) {
ierr = PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%6f, sigma_n=%6f\n",sigma_1,sigma_n);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%6f\n\n",sigma_1/sigma_n);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_WORLD," Process did not converge! Try running with a larger value for -eps_ncv\n\n");CHKERRQ(ierr);
}
/*
Free work space
*/
ierr = SVDDestroy(svd);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}