/*
SLEPc singular value solver: "lanczos"
Method: Golub-Kahan-Lanczos bidiagonalization
Last update: Jun 2007
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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.
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*/
#include "src/svd/svdimpl.h" /*I "slepcsvd.h" I*/
#include "slepcblaslapack.h"
typedef struct {
PetscTruth oneside;
} SVD_LANCZOS;
#undef __FUNCT__
#define __FUNCT__ "SVDSetUp_LANCZOS"
PetscErrorCode SVDSetUp_LANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_LANCZOS *lanczos = (SVD_LANCZOS *)svd->data;
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->U) {
for (i=0;i<svd->n;i++) { ierr = VecDestroy(svd->U[i]); CHKERRQ(ierr); }
ierr = PetscFree(svd->U);CHKERRQ(ierr);
}
if (!lanczos->oneside) {
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__ "SVDTwoSideLanczos"
PetscErrorCode SVDTwoSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,Vec *V,Vec v,Vec *U,int k,int n,PetscScalar* work,Vec wv,Vec wu)
{
PetscErrorCode ierr;
int i;
PetscFunctionBegin;
ierr = SVDMatMult(svd,PETSC_FALSE,V[k],U[k]);CHKERRQ(ierr);
ierr = IPOrthogonalize(svd->ip,k,PETSC_NULL,U,U[k],work,alpha,PETSC_NULL,wu);CHKERRQ(ierr);
ierr = VecScale(U[k],1.0/alpha[0]);CHKERRQ(ierr);
for (i=k+1;i<n;i++) {
ierr = SVDMatMult(svd,PETSC_TRUE,U[i-1],V[i]);CHKERRQ(ierr);
ierr = IPOrthogonalize(svd->ip,i,PETSC_NULL,V,V[i],work,beta+i-k-1,PETSC_NULL,wv);CHKERRQ(ierr);
ierr = VecScale(V[i],1.0/beta[i-k-1]);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,V[i],U[i]);CHKERRQ(ierr);
ierr = IPOrthogonalize(svd->ip,i,PETSC_NULL,U,U[i],work,alpha+i-k,PETSC_NULL,wu);CHKERRQ(ierr);
ierr = VecScale(U[i],1.0/alpha[i-k]);CHKERRQ(ierr);
}
ierr = SVDMatMult(svd,PETSC_TRUE,U[n-1],v);CHKERRQ(ierr);
ierr = IPOrthogonalize(svd->ip,n,PETSC_NULL,V,v,work,beta+n-k-1,PETSC_NULL,wv);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDOneSideLanczos"
static PetscErrorCode SVDOneSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,Vec *V,Vec v,Vec u,Vec u_1,int k,int n,PetscScalar* work,Vec wv)
{
PetscErrorCode ierr;
int i,j;
PetscReal a,b;
Vec temp;
PetscFunctionBegin;
ierr = SVDMatMult(svd,PETSC_FALSE,V[k],u);CHKERRQ(ierr);
for (i=k+1;i<n;i++) {
ierr = SVDMatMult(svd,PETSC_TRUE,u,V[i]);CHKERRQ(ierr);
ierr = IPNormBegin(svd->ip,u,&a);CHKERRQ(ierr);
ierr = IPMInnerProductBegin(svd->ip,V[i],i,V,work);CHKERRQ(ierr);
ierr = IPNormEnd(svd->ip,u,&a);CHKERRQ(ierr);
ierr = IPMInnerProductEnd(svd->ip,V[i],i,V,work);CHKERRQ(ierr);
ierr = VecScale(u,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_1);CHKERRQ(ierr);
ierr = VecAXPY(u_1,-b,u);CHKERRQ(ierr);
alpha[i-k-1] = a;
beta[i-k-1] = b;
temp = u;
u = u_1;
u_1 = temp;
}
ierr = SVDMatMult(svd,PETSC_TRUE,u,v);CHKERRQ(ierr);
ierr = IPNormBegin(svd->ip,u,&a);CHKERRQ(ierr);
ierr = IPMInnerProductBegin(svd->ip,v,n,V,work);CHKERRQ(ierr);
ierr = IPNormEnd(svd->ip,u,&a);CHKERRQ(ierr);
ierr = IPMInnerProductEnd(svd->ip,v,n,V,work);CHKERRQ(ierr);
ierr = VecScale(u,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_LANCZOS"
PetscErrorCode SVDSolve_LANCZOS(SVD svd)
{
#if defined(SLEPC_MISSING_LAPACK_BDSDC)
PetscFunctionBegin;
SETERRQ(PETSC_ERR_SUP,"BDSDC - Lapack routine is unavailable.");
#else
PetscErrorCode ierr;
SVD_LANCZOS *lanczos = (SVD_LANCZOS *)svd->data;
PetscReal *alpha,*beta,norm,*work,*Q,*PT;
PetscScalar *swork;
PetscInt *perm;
int i,j,k,m,n,info,nwork=0,*iwork;
Vec v,u,u_1,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(PetscReal)*svd->n*svd->n,&Q);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscReal)*svd->n*svd->n,&PT);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(PetscReal)*(3*svd->n+4)*svd->n,&work);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(int)*8*svd->n,&iwork);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 = PetscMalloc(sizeof(Vec)*svd->n,&workV);CHKERRQ(ierr);
if (lanczos->oneside) {
ierr = SVDMatGetVecs(svd,PETSC_NULL,&u);CHKERRQ(ierr);
ierr = SVDMatGetVecs(svd,PETSC_NULL,&u_1);CHKERRQ(ierr);
} else {
ierr = VecDuplicate(svd->U[0],&wu);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);
while (svd->reason == SVD_CONVERGED_ITERATING) {
svd->its++;
/* inner loop */
if (lanczos->oneside) {
ierr = SVDOneSideLanczos(svd,alpha,beta,svd->V,v,u,u_1,svd->nconv,svd->n,swork,wv);CHKERRQ(ierr);
} else {
ierr = SVDTwoSideLanczos(svd,alpha,beta,svd->V,v,svd->U,svd->nconv,svd->n,swork,wv,wu);CHKERRQ(ierr);
}
/* compute SVD of bidiagonal matrix */
n = svd->n - svd->nconv;
ierr = PetscMemzero(PT,sizeof(PetscReal)*n*n);CHKERRQ(ierr);
ierr = PetscMemzero(Q,sizeof(PetscReal)*n*n);CHKERRQ(ierr);
for (i=0;i<n;i++)
PT[i*n+i] = Q[i*n+i] = 1.0;
ierr = PetscLogEventBegin(SVD_Dense,0,0,0,0);CHKERRQ(ierr);
LAPACKbdsdc_("U","I",&n,alpha,beta,Q,&n,PT,&n,PETSC_NULL,PETSC_NULL,work,iwork,&info,1,1);
ierr = PetscLogEventEnd(SVD_Dense,0,0,0,0);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];
svd->errest[i] = PetscAbsScalar(Q[j*n+n-1])*beta[n-1];
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 */
if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;
/* allocate work space for converged singular vectors */
if (nwork<k) {
for (i=nwork;i<k;i++)
if (lanczos->oneside) { ierr = SVDMatGetVecs(svd,workV+i,PETSC_NULL);CHKERRQ(ierr); }
else { ierr = SVDMatGetVecs(svd,workV+i,workU+i);CHKERRQ(ierr); }
nwork = k;
}
/* compute converged singular vectors */
for (i=0;i<k;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);
if (!lanczos->oneside) {
ierr = VecSet(workU[i],0.0);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
ierr = VecMAXPY(workU[i],n,Q+j*n,svd->U+svd->nconv);CHKERRQ(ierr);
#else
for (m=0;m<n;m++) swork[m] = Q[j*n+m];
ierr = VecMAXPY(workU[i],n,swork,svd->U+svd->nconv);CHKERRQ(ierr);
#endif
}
}
/* compute restart vector */
if (svd->reason == SVD_CONVERGED_ITERATING) {
if (svd->which == SVD_SMALLEST) j = n-k-1;
else j = k;
ierr = VecSet(v,0.0);CHKERRQ(ierr);
for (m=0;m<n;m++) swork[m] = PT[m*n+j];
ierr = VecMAXPY(v,m,swork,svd->V+svd->nconv);CHKERRQ(ierr);
ierr = VecCopy(v,svd->V[svd->nconv+k]);CHKERRQ(ierr);
}
/* copy converged singular vectors from temporary space */
for (i=0;i<k;i++) {
ierr = VecCopy(workV[i],svd->V[i+svd->nconv]);CHKERRQ(ierr);
if (!lanczos->oneside) {
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);
if (!lanczos->oneside) { 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];
if (!lanczos->oneside) 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];
if (!lanczos->oneside) svd->U[i] = permU[j];
}
/* free working space */
ierr = VecDestroy(v);CHKERRQ(ierr);
ierr = VecDestroy(wv);CHKERRQ(ierr);
for (i=0;i<nwork;i++) { ierr = VecDestroy(workV[i]);CHKERRQ(ierr); }
ierr = PetscFree(workV);CHKERRQ(ierr);
if (lanczos->oneside) {
ierr = VecDestroy(u);CHKERRQ(ierr);
ierr = VecDestroy(u_1);CHKERRQ(ierr);
} else {
for (i=0;i<nwork;i++) { ierr = VecDestroy(workU[i]);CHKERRQ(ierr); }
ierr = PetscFree(workU);CHKERRQ(ierr);
ierr = PetscFree(permU);CHKERRQ(ierr);
ierr = VecDestroy(wu);CHKERRQ(ierr);
}
ierr = PetscFree(alpha);CHKERRQ(ierr);
ierr = PetscFree(beta);CHKERRQ(ierr);
ierr = PetscFree(Q);CHKERRQ(ierr);
ierr = PetscFree(PT);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
ierr = PetscFree(swork);CHKERRQ(ierr);
ierr = PetscFree(perm);CHKERRQ(ierr);
ierr = PetscFree(permV);CHKERRQ(ierr);
PetscFunctionReturn(0);
#endif
}
#undef __FUNCT__
#define __FUNCT__ "SVDSetFromOptions_LANCZOS"
PetscErrorCode SVDSetFromOptions_LANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_LANCZOS *lanczos = (SVD_LANCZOS *)svd->data;
PetscFunctionBegin;
ierr = PetscOptionsBegin(((PetscObject)svd)->comm,((PetscObject)svd)->prefix,"LANCZOS Singular Value Solver Options","SVD");CHKERRQ(ierr);
ierr = PetscOptionsTruth("-svd_lanczos_oneside","Lanczos one-side reorthogonalization","SVDLanczosSetOneSide",PETSC_FALSE,&lanczos->oneside,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "SVDLanczosSetOneSide_LANCZOS"
PetscErrorCode SVDLanczosSetOneSide_LANCZOS(SVD svd,PetscTruth oneside)
{
SVD_LANCZOS *lanczos = (SVD_LANCZOS *)svd->data;
PetscFunctionBegin;
if (lanczos->oneside != oneside) {
lanczos->oneside = oneside;
svd->setupcalled = 0;
}
PetscFunctionReturn(0);
}
EXTERN_C_END
#undef __FUNCT__
#define __FUNCT__ "SVDLanczosSetOneSide"
/*@
SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
to be used is one-sided or two-sided.
Collective on SVD
Input Parameters:
+ svd - singular value solver
- oneside - boolean flag indicating if the method is one-sided or not
Options Database Key:
. -svd_lanczos_oneside <boolean> - Indicates the boolean flag
Note:
By default, a two-sided variant is selected, which is sometimes slightly
more robust. However, the one-sided variant is faster because it avoids
the orthogonalization associated to left singular vectors. It also saves
the memory required for storing such vectors.
Level: advanced
.seealso: SVDTRLanczosSetOneSide()
@*/
PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscTruth oneside)
{
PetscErrorCode ierr, (*f)(SVD,PetscTruth);
PetscFunctionBegin;
PetscValidHeaderSpecific(svd,SVD_COOKIE,1);
ierr = PetscObjectQueryFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",(void (**)())&f);CHKERRQ(ierr);
if (f) {
ierr = (*f)(svd,oneside);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "SVDView_LANCZOS"
PetscErrorCode SVDView_LANCZOS(SVD svd,PetscViewer viewer)
{
PetscErrorCode ierr;
SVD_LANCZOS *lanczos = (SVD_LANCZOS *)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_LANCZOS"
PetscErrorCode SVDCreate_LANCZOS(SVD svd)
{
PetscErrorCode ierr;
SVD_LANCZOS *lanczos;
PetscFunctionBegin;
ierr = PetscNew(SVD_LANCZOS,&lanczos);CHKERRQ(ierr);
PetscLogObjectMemory(svd,sizeof(SVD_LANCZOS));
svd->data = (void *)lanczos;
svd->ops->setup = SVDSetUp_LANCZOS;
svd->ops->solve = SVDSolve_LANCZOS;
svd->ops->destroy = SVDDestroy_Default;
svd->ops->setfromoptions = SVDSetFromOptions_LANCZOS;
svd->ops->view = SVDView_LANCZOS;
lanczos->oneside = PETSC_FALSE;
ierr = PetscObjectComposeFunctionDynamic((PetscObject)svd,"SVDLanczosSetOneSide_C","SVDLanczosSetOneSide_LANCZOS",SVDLanczosSetOneSide_LANCZOS);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_END