/*
SLEPc eigensolver: "dsitrlanczos"
Method: Thick restart Lanczos with full reorthogonalization and dynamic shift and invert
Last update: Jan 2010
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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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*/
#include "private/epsimpl.h" /*I "slepceps.h" I*/
#include "slepcblaslapack.h"
PetscErrorCode EPSSolve_DSITRLANCZOS(EPS);
extern PetscErrorCode EPSProjectedKSSym(EPS eps,PetscInt n,PetscInt l,PetscReal *a,PetscReal *b,PetscScalar *eig,PetscScalar *Q,PetscReal *work,PetscInt *perm);
#undef __FUNCT__
#define __FUNCT__ "EPSSetUp_DSITRLANCZOS"
PetscErrorCode EPSSetUp_DSITRLANCZOS(EPS eps)
{
PetscErrorCode ierr;
PetscTruth isSinv;
PetscFunctionBegin;
if (eps->ncv) { /* ncv set */
if (eps->ncv<eps->nev) SETERRQ(1,"The value of ncv must be at least nev");
}
else if (eps->mpd) { /* mpd set */
eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd);
}
else { /* neither set: defaults depend on nev being small or large */
if (eps->nev<500) eps->ncv = PetscMin(eps->n,PetscMax(2*eps->nev,eps->nev+15));
else { eps->mpd = 500; eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd); }
}
if (!eps->mpd) eps->mpd = eps->ncv;
if (eps->ncv>eps->nev+eps->mpd) SETERRQ(1,"The value of ncv must not be larger than nev+mpd");
if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
if (!eps->ishermitian)
SETERRQ(PETSC_ERR_SUP,"Requested method is only available for Hermitian problems");
if (!eps->which) eps->which = EPS_LARGEST_MAGNITUDE;
if (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY)
SETERRQ(1,"Wrong value of eps->which");
if (!eps->extraction) {
ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);
} if (eps->extraction != EPS_RITZ) {
SETERRQ(PETSC_ERR_SUP,"Unsupported extraction type");
}
ierr = PetscTypeCompare((PetscObject)eps->OP,STSINVERT,&isSinv);CHKERRQ(ierr);
if (!isSinv) {
SETERRQ(PETSC_ERR_SUP,"Shift-and-invert ST is needed");
}
ierr = EPSAllocateSolution(eps);CHKERRQ(ierr);
ierr = EPSDefaultGetWork(eps,1);CHKERRQ(ierr);
/* dispatch solve method */
if (eps->leftvecs) SETERRQ(PETSC_ERR_SUP,"Left vectors not supported in this solver");
eps->ops->solve = EPSSolve_DSITRLANCZOS;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSSolve_DSITRLANCZOS"
PetscErrorCode EPSSolve_DSITRLANCZOS(EPS eps)
{
PetscErrorCode ierr;
PetscInt i,k,l,lds,lt,nv,m;
Vec u=eps->work[0];
PetscScalar *Q, sigma, lambda, zero = 0.0;
PetscReal *a,*b,*work,beta,distance = 1e-3;
PetscInt *iwork;
PetscTruth breakdown;
PetscFunctionBegin;
ierr = PetscOptionsGetReal(PETSC_NULL,"-eps_distance",&distance,PETSC_NULL);CHKERRQ(ierr);
lds = PetscMin(eps->mpd,eps->ncv);
ierr = PetscMalloc(lds*lds*sizeof(PetscReal),&work);CHKERRQ(ierr);
ierr = PetscMalloc(lds*lds*sizeof(PetscScalar),&Q);CHKERRQ(ierr);
ierr = PetscMalloc(2*lds*sizeof(PetscInt),&iwork);CHKERRQ(ierr);
lt = PetscMin(eps->nev+eps->mpd,eps->ncv);
ierr = PetscMalloc(lt*sizeof(PetscReal),&a);CHKERRQ(ierr);
ierr = PetscMalloc(lt*sizeof(PetscReal),&b);CHKERRQ(ierr);
/* Get the starting Lanczos vector */
ierr = EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);CHKERRQ(ierr);
l = 0;
/* Restart loop */
while (eps->reason == EPS_CONVERGED_ITERATING) {
eps->its++;
/* Compute an nv-step Lanczos factorization */
m = PetscMin(eps->nconv+eps->mpd,eps->ncv);
ierr = EPSFullLanczos(eps,a+l,b+l,eps->V,eps->nconv+l,&m,u,&breakdown);CHKERRQ(ierr);
nv = m - eps->nconv;
beta = b[nv-1];
/* Solve projected problem and compute residual norm estimates */
ierr = EPSProjectedKSSym(eps,nv,l,a,b,eps->eigr+eps->nconv,Q,work,iwork);CHKERRQ(ierr);
/* Check convergence */
ierr = EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv,PETSC_NULL,nv,Q,eps->V+eps->nconv,nv,beta,1.0,&k,PETSC_NULL);CHKERRQ(ierr);
if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
/* Transform converged eigenvalues to the original problem */
ierr = STBackTransform(eps->OP,k-eps->nconv,eps->eigr+eps->nconv,eps->eigi+eps->nconv);CHKERRQ(ierr);
/* Update l */
if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
else {
l = (eps->nconv+nv-k)/2;
/* Update shift */
ierr = STGetShift(eps->OP,&sigma);CHKERRQ(ierr);
lambda = eps->eigr[k+1];
ierr = STBackTransform(eps->OP,1,&lambda,&zero);CHKERRQ(ierr);
if (PetscAbsScalar(lambda - sigma)/PetscAbsScalar(sigma) > distance) {
ierr = PetscInfo2(eps,"Shift update its=%i sigma=%g\n",eps->its,lambda);
PetscPushErrorHandler(PetscReturnErrorHandler,PETSC_NULL);
ierr = STSetShift(eps->OP,lambda);
PetscPopErrorHandler();
switch (ierr) {
case PETSC_ERR_MAT_LU_ZRPVT:
case PETSC_ERR_MAT_CH_ZRPVT:
ierr = PetscInfo2(eps,"Factorization error in shift update its=%i sigma=%g\n",eps->its,lambda);
ierr = STSetShift(eps->OP,sigma);CHKERRQ(ierr);
break;
default:
CHKERRQ(ierr);
l = 0; /* do not use restart vectors */
}
}
}
if (eps->reason == EPS_CONVERGED_ITERATING) {
if (breakdown) {
/* Start a new Lanczos factorization */
PetscInfo2(eps,"Breakdown in TR Lanczos method (it=%i norm=%g)\n",eps->its,beta);
ierr = EPSGetStartVector(eps,k,eps->V[k],&breakdown);CHKERRQ(ierr);
if (breakdown) {
eps->reason = EPS_DIVERGED_BREAKDOWN;
PetscInfo(eps,"Unable to generate more start vectors\n");
}
} else {
/* Prepare the Rayleigh quotient for restart */
for (i=0;i<l;i++) {
a[i] = PetscRealPart(eps->eigr[i+k]);
b[i] = PetscRealPart(Q[nv-1+(i+k-eps->nconv)*nv]*beta);
}
}
}
/* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
ierr = SlepcUpdateVectors(nv,eps->V+eps->nconv,0,k+l-eps->nconv,Q,nv,PETSC_FALSE);CHKERRQ(ierr);
/* Normalize u and append it to V */
if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
ierr = VecAXPBY(eps->V[k+l],1.0/beta,0.0,u);CHKERRQ(ierr);
}
EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv+eps->nconv);
eps->nconv = k;
}
ierr = PetscFree(Q);CHKERRQ(ierr);
ierr = PetscFree(a);CHKERRQ(ierr);
ierr = PetscFree(b);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "EPSCreate_DSITRLANCZOS"
PetscErrorCode EPSCreate_DSITRLANCZOS(EPS eps)
{
PetscFunctionBegin;
eps->data = PETSC_NULL;
eps->ops->setup = EPSSetUp_DSITRLANCZOS;
eps->ops->setfromoptions = PETSC_NULL;
eps->ops->destroy = EPSDestroy_Default;
eps->ops->view = PETSC_NULL;
eps->ops->computevectors = EPSComputeVectors_Default;
PetscFunctionReturn(0);
}
EXTERN_C_END