/*
SLEPc singular value solver: "trlanczos"
Method: Golub-Kahan-Lanczos bidiagonalization with thick-restart
Last update: Mar 2007
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain
This file is part of SLEPc. See the README file for conditions of use
and additional information.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
#include "src/svd/svdimpl.h" /*I "slepcsvd.h" I*/
#include "slepcblaslapack.h"
typedef struct {
PetscTruth oneside;
} SVD_TRLANCZOS;
#undef __FUNCT__
#define __FUNCT__ "SVDSetUp_TRLANCZOS"
PetscErrorCode SVDSetUp_TRLANCZOS(SVD svd)
{
PetscErrorCode ierr;
PetscInt N;
int i;
PetscFunctionBegin;
ierr = SVDMatGetSize(svd,PETSC_NULL,&N);CHKERRQ(ierr);
if (svd->ncv == PETSC_DECIDE)
svd->ncv = PetscMin(N,PetscMax(2*svd->nsv,10));
if (svd->max_it == PETSC_DECIDE)
svd->max_it = PetscMax(N/svd->ncv,100);
if (svd->ncv!=svd->n) {
if (svd->U) {
for (i=0;i<svd->n;i++) { ierr = VecDestroy(svd->U[i]); CHKERRQ(ierr); }
ierr = PetscFree(svd->U);CHKERRQ(ierr);
}
ierr = PetscMalloc(sizeof(Vec)*svd->ncv,&svd->U);CHKERRQ(ierr);
for (i=0;i<svd->ncv;i++) { ierr = SVDMatGetVecs(svd,PETSC_NULL,svd->U+i);CHKERRQ(ierr); }
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDOneSideTRLanczos"
static PetscErrorCode SVDOneSideTRLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,PetscScalar* bb,Vec *V,Vec v,Vec* U,int nconv,int l,int n,PetscScalar* work,Vec wv,Vec wu)
{
PetscErrorCode ierr;
PetscReal a,b;
int i,j,k=nconv+l;
PetscFunctionBegin;
ierr = SVDMatMult(svd,PETSC_FALSE,V[k],U[k]);CHKERRQ(ierr);
if (l>0) {
ierr = VecSet(wu,0.0);CHKERRQ(ierr);
ierr = VecMAXPY(wu,l,bb,U+nconv);CHKERRQ(ierr);
ierr = VecAXPY(U[k],-1.0,wu);CHKERRQ(ierr);
}
for (i=k+1;i<n;i++) {
ierr = SVDMatMult(svd,PETSC_TRUE,U[i-1],V[i]);CHKERRQ(ierr);
ierr = IPNormBegin(svd->ip,U[i-1],&a);CHKERRQ(ierr);
ierr = IPMInnerProductBegin(svd->ip,i,V[i],V,work);CHKERRQ(ierr);
ierr = IPNormEnd(svd->ip,U[i-1],&a);CHKERRQ(ierr);
ierr = IPMInnerProductEnd(svd->ip,i,V[i],V,work);CHKERRQ(ierr);
ierr = VecScale(U[i-1],1.0/a);CHKERRQ(ierr);
ierr = VecScale(V[i],1.0/a);CHKERRQ(ierr);
for (j=0;j<i;j++) work[j] = - work[j] / a;
ierr = VecMAXPY(V[i],i,work,V);CHKERRQ(ierr);
ierr = IPOrthogonalizeCGS(svd->ip,i,PETSC_NULL,V,V[i],work,PETSC_NULL,&b,wv);CHKERRQ(ierr);
ierr = VecScale(V[i],1.0/b);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,V[i],U[i]);CHKERRQ(ierr);
ierr = VecAXPY(U[i],-b,U[i-1]);CHKERRQ(ierr);
alpha[i-k-1] = a;
beta[i-k-1] = b;
}
ierr = SVDMatMult(svd,PETSC_TRUE,U[n-1],v);CHKERRQ(ierr);
ierr = IPNormBegin(svd->ip,U[n-1],&a);CHKERRQ(ierr);
ierr = IPMInnerProductBegin(svd->ip,n,v,V,work);CHKERRQ(ierr);
ierr = IPNormEnd(svd->ip,U[n-1],&a);CHKERRQ(ierr);
ierr = IPMInnerProductEnd(svd->ip,n,v,V,work);CHKERRQ(ierr);
ierr = VecScale(U[n-1],1.0/a);CHKERRQ(ierr);
ierr = VecScale(v,1.0/a);CHKERRQ(ierr);
for (j=0;j<n;j++) work[j] = - work[j] / a;
ierr = VecMAXPY(v,n,work,V);CHKERRQ(ierr);
ierr = IPOrthogonalizeCGS(svd->ip,n,PETSC_NULL,V,v,work,PETSC_NULL,&b,wv);CHKERRQ(ierr);
alpha[n-k-1] = a;
beta[n-k-1] = b;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDSolve_TRLANCZOS"
PetscErrorCode SVDSolve_TRLANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS *)svd->data;
PetscReal *alpha,*beta,norm;
PetscScalar *b,*Q,*PT,*swork;
PetscInt *perm;
int i,j,k,l,m,n,nwork=0;
Vec v,wv,wu,*workV,*workU,*permV,*permU;
PetscTruth conv;
PetscFunctionBegin;
/* allocate working space */
ierr = PetscMalloc(sizeof(PetscReal)*svd->n,&alpha);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscReal)*svd->n,&beta);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscScalar)*svd->n,&b);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscScalar)*svd->n*svd->n,&Q);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscScalar)*svd->n*svd->n,&PT);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscScalar)*svd->n,&swork);CHKERRQ(ierr);
ierr = VecDuplicate(svd->V[0],&v);CHKERRQ(ierr);
ierr = VecDuplicate(svd->V[0],&wv);CHKERRQ(ierr);
ierr = VecDuplicate(svd->U[0],&wu);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(Vec)*svd->n,&workV);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(Vec)*svd->n,&workU);CHKERRQ(ierr);
/* normalize start vector */
ierr = VecCopy(svd->vec_initial,svd->V[0]);CHKERRQ(ierr);
ierr = VecNormalize(svd->V[0],&norm);CHKERRQ(ierr);
l = 0;
while (svd->reason == SVD_CONVERGED_ITERATING) {
svd->its++;
/* inner loop */
if (lanczos->oneside) {
ierr = SVDOneSideTRLanczos(svd,alpha,beta,b+svd->nconv,svd->V,v,svd->U,svd->nconv,l,svd->n,swork,wv,wu);CHKERRQ(ierr);
} else {
ierr = SVDTwoSideLanczos(svd,alpha,beta,svd->V,v,svd->U,svd->nconv+l,svd->n,swork,wv,wu);CHKERRQ(ierr);
}
ierr = VecScale(v,1.0/beta[svd->n-svd->nconv-l-1]);CHKERRQ(ierr);
/* compute SVD of general matrix */
n = svd->n - svd->nconv;
/* first l columns */
for (j=0;j<l;j++) {
for (i=0;i<j;i++) Q[j*n+i] = 0.0;
Q[j*n+j] = svd->sigma[svd->nconv+j];
for (i=j+1;i<n;i++) Q[j*n+i] = 0.0;
}
/* l+1 column */
for (i=0;i<l;i++) Q[l*n+i] = b[i+svd->nconv];
Q[l*n+l] = alpha[0];
for (i=l+1;i<n;i++) Q[l*n+i] = 0.0;
/* rest of matrix */
for (j=l+1;j<n;j++) {
for (i=0;i<j-1;i++) Q[j*n+i] = 0.0;
Q[j*n+j-1] = beta[j-l-1];
Q[j*n+j] = alpha[j-l];
for (i=j+1;i<n;i++) Q[j*n+i] = 0.0;
}
ierr = SVDDense(n,n,Q,alpha,PETSC_NULL,PT);CHKERRQ(ierr);
/* compute error estimates */
k = 0;
conv = PETSC_TRUE;
for (i=svd->nconv;i<svd->n;i++) {
if (svd->which == SVD_SMALLEST) j = n-i+svd->nconv-1;
else j = i-svd->nconv;
svd->sigma[i] = alpha[j];
b[i] = Q[j*n+n-1]*beta[n-l-1];
svd->errest[i] = PetscAbsScalar(b[i]);
if (alpha[j] > svd->tol) svd->errest[i] /= alpha[j];
if (conv) {
if (svd->errest[i] < svd->tol) k++;
else conv = PETSC_FALSE;
}
}
/* check convergence and update l */
if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;
if (svd->reason != SVD_CONVERGED_ITERATING) l = 0;
else l = PetscMax((svd->n - svd->nconv - k) / 2,1);
/* allocate work space for converged singular and restart vectors */
if (nwork<k+l) {
for (i=nwork;i<k+l;i++) {
ierr = SVDMatGetVecs(svd,workV+i,workU+i);CHKERRQ(ierr);
}
nwork = k+l;
}
/* compute converged singular vectors and restart vectors*/
for (i=0;i<k+l;i++) {
if (svd->which == SVD_SMALLEST) j = n-i-1;
else j = i;
ierr = VecSet(workV[i],0.0);CHKERRQ(ierr);
for (m=0;m<n;m++) swork[m] = PT[m*n+j];
ierr = VecMAXPY(workV[i],n,swork,svd->V+svd->nconv);CHKERRQ(ierr);
ierr = VecSet(workU[i],0.0);CHKERRQ(ierr);
ierr = VecMAXPY(workU[i],n,Q+j*n,svd->U+svd->nconv);CHKERRQ(ierr);
}
/* copy the last vector to be the next initial vector */
if (svd->reason == SVD_CONVERGED_ITERATING) {
ierr = VecCopy(v,svd->V[svd->nconv+k+l]);CHKERRQ(ierr);
}
/* copy converged singular vectors and restart vectors from temporary space */
for (i=0;i<k+l;i++) {
ierr = VecCopy(workV[i],svd->V[i+svd->nconv]);CHKERRQ(ierr);
ierr = VecCopy(workU[i],svd->U[i+svd->nconv]);CHKERRQ(ierr);
}
svd->nconv += k;
SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->n);
}
/* sort singular triplets */
ierr = PetscMalloc(sizeof(PetscInt)*svd->nconv,&perm);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(Vec)*svd->nconv,&permV);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(Vec)*svd->nconv,&permU);CHKERRQ(ierr);
for (i=0;i<svd->nconv;i++) {
alpha[i] = svd->sigma[i];
beta[i] = svd->errest[i];
permV[i] = svd->V[i];
permU[i] = svd->U[i];
perm[i] = i;
}
ierr = PetscSortRealWithPermutation(svd->nconv,svd->sigma,perm);CHKERRQ(ierr);
for (i=0;i<svd->nconv;i++) {
if (svd->which == SVD_SMALLEST) j = perm[i];
else j = perm[svd->nconv-i-1];
svd->sigma[i] = alpha[j];
svd->errest[i] = beta[j];
svd->V[i] = permV[j];
svd->U[i] = permU[j];
}
/* free working space */
ierr = VecDestroy(v);CHKERRQ(ierr);
ierr = VecDestroy(wv);CHKERRQ(ierr);
ierr = VecDestroy(wu);CHKERRQ(ierr);
for (i=0;i<nwork;i++) { ierr = VecDestroy(workV[i]);CHKERRQ(ierr); }
ierr = PetscFree(workV);CHKERRQ(ierr);
for (i=0;i<nwork;i++) { ierr = VecDestroy(workU[i]);CHKERRQ(ierr); }
ierr = PetscFree(workU);CHKERRQ(ierr);
ierr = PetscFree(alpha);CHKERRQ(ierr);
ierr = PetscFree(beta);CHKERRQ(ierr);
ierr = PetscFree(b);CHKERRQ(ierr);
ierr = PetscFree(Q);CHKERRQ(ierr);
ierr = PetscFree(PT);CHKERRQ(ierr);
ierr = PetscFree(swork);CHKERRQ(ierr);
ierr = PetscFree(perm);CHKERRQ(ierr);
ierr = PetscFree(permV);CHKERRQ(ierr);
ierr = PetscFree(permU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDSetFromOptions_TRLANCZOS"
PetscErrorCode SVDSetFromOptions_TRLANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS *)svd->data;
PetscFunctionBegin;
ierr = PetscOptionsBegin(svd->comm,svd->prefix,"TRLANCZOS Singular Value Solver Options","SVD");CHKERRQ(ierr);
ierr = PetscOptionsTruth("-svd_trlanczos_oneside","Lanczos one-side reorthogonalization","SVDTRLanczosSetOneSide",PETSC_FALSE,&lanczos->oneside,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "SVDTRLanczosSetOneSide_TRLANCZOS"
PetscErrorCode SVDTRLanczosSetOneSide_TRLANCZOS(SVD svd,PetscTruth oneside)
{
SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS *)svd->data;
PetscFunctionBegin;
lanczos->oneside = oneside;
PetscFunctionReturn(0);
}
EXTERN_C_END
#undef __FUNCT__
#define __FUNCT__ "SVDTRLanczosSetOneSide"
PetscErrorCode SVDTRLanczosSetOneSide(SVD svd,PetscTruth oneside)
{
PetscErrorCode ierr, (*f)(SVD,PetscTruth);
PetscFunctionBegin;
PetscValidHeaderSpecific(svd,SVD_COOKIE,1);
ierr = PetscObjectQueryFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",(void (**)())&f);CHKERRQ(ierr);
if (f) {
ierr = (*f)(svd,oneside);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDView_TRLANCZOS"
PetscErrorCode SVDView_TRLANCZOS(SVD svd,PetscViewer viewer)
{
PetscErrorCode ierr;
SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS *)svd->data;
PetscFunctionBegin;
ierr = PetscViewerASCIIPrintf(viewer,"Lanczos reorthogonalization: %s\n",lanczos->oneside ? "one-side" : "two-side");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "SVDCreate_TRLANCZOS"
PetscErrorCode SVDCreate_TRLANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_TRLANCZOS *lanczos;
PetscFunctionBegin;
ierr = PetscNew(SVD_TRLANCZOS,&lanczos);CHKERRQ(ierr);
PetscLogObjectMemory(svd,sizeof(SVD_TRLANCZOS));
svd->data = (void *)lanczos;
svd->ops->setup = SVDSetUp_TRLANCZOS;
svd->ops->solve = SVDSolve_TRLANCZOS;
svd->ops->setfromoptions = SVDSetFromOptions_TRLANCZOS;
svd->ops->view = SVDView_TRLANCZOS;
lanczos->oneside = PETSC_FALSE;
ierr = PetscObjectComposeFunctionDynamic((PetscObject)svd,"SVDTRLanczosSetOneSide_C","SVDTRLanczosSetOneSide_TRLANCZOS",SVDTRLanczosSetOneSide_TRLANCZOS);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_END