/*
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SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
This file is part of SLEPc.
SLEPc is free software: you can redistribute it and/or modify it under the
terms of version 3 of the GNU Lesser General Public License as published by
the Free Software Foundation.
SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
more details.
You should have received a copy of the GNU Lesser General Public License
along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
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*/
static char help[] = "Singular value decomposition of the Lauchli matrix.\n"
"The command line options are:\n"
" -n <n>, where <n> = matrix dimension.\n"
" -mu <mu>, where <mu> = subdiagonal value.\n\n";
#include <slepcsvd.h>
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
PetscErrorCode ierr;
Mat A; /* operator matrix */
Vec u,v; /* left and right singular vectors */
SVD svd; /* singular value problem solver context */
const SVDType type;
PetscReal error, tol, sigma, mu=PETSC_SQRT_MACHINE_EPSILON;
PetscInt n=100, i, j, Istart, Iend, nsv, maxit, its, nconv;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-mu",&mu,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%d x %d) mu=%g\n\n",n+1,n,mu);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Build the Lauchli matrix
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ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i == 0) {
for (j=0;j<n;j++) {
ierr = MatSetValue(A,0,j,1.0,INSERT_VALUES);CHKERRQ(ierr);
}
} else {
ierr = MatSetValue(A,i,i-1,mu,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetVecs(A,&v,&u);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the singular value solver and set various options
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/*
Create singular value solver context
*/
ierr = SVDCreate(PETSC_COMM_WORLD,&svd);CHKERRQ(ierr);
/*
Set operator
*/
ierr = SVDSetOperator(svd,A);CHKERRQ(ierr);
/*
Use thick-restart Lanczos as default solver
*/
ierr = SVDSetType(svd,SVDTRLANCZOS);CHKERRQ(ierr);
/*
Set solver parameters at runtime
*/
ierr = SVDSetFromOptions(svd);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the singular value system
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ierr = SVDSolve(svd);CHKERRQ(ierr);
ierr = SVDGetIterationNumber(svd, &its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr);
/*
Optional: Get some information from the solver and display it
*/
ierr = SVDGetType(svd,&type);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr);
ierr = SVDGetDimensions(svd,&nsv,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %d\n",nsv);CHKERRQ(ierr);
ierr = SVDGetTolerances(svd,&tol,&maxit);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
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/*
Get number of converged singular triplets
*/
ierr = SVDGetConverged(svd,&nconv);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %d\n\n",nconv);CHKERRQ(ierr);
if (nconv>0) {
/*
Display singular values and relative errors
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,
" sigma residual norm\n"
" --------------------- ------------------\n" );CHKERRQ(ierr);
for( i=0; i<nconv; i++ ) {
/*
Get converged singular triplets: i-th singular value is stored in sigma
*/
ierr = SVDGetSingularTriplet(svd,i,&sigma,u,v);CHKERRQ(ierr);
/*
Compute the error associated to each singular triplet
*/
ierr = SVDComputeRelativeError(svd,i,&error);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," % 6f ",sigma); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," % 12g\n",error);CHKERRQ(ierr);
}
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);
}
/*
Free work space
*/
ierr = SVDDestroy(&svd);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&v);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}