/*
SLEPc eigensolver: "krylovschur"
Method: Krylov-Schur
Algorithm:
Single-vector Krylov-Schur method for both symmetric and non-symmetric
problems.
References:
[1] "Krylov-Schur Methods in SLEPc", SLEPc Technical Report STR-7,
available at http://www.grycap.upv.es/slepc.
[2] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",
SIAM J. Matrix Analysis and App., 23(3), pp. 601-614, 2001.
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SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2011, Universitat 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_KrylovSchur_Default(EPS);
extern PetscErrorCode EPSSolve_KrylovSchur_Harmonic(EPS);
extern PetscErrorCode EPSSolve_KrylovSchur_Symm(EPS);
extern PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS);
#undef __FUNCT__
#define __FUNCT__ "EPSSetUp_KrylovSchur"
PetscErrorCode EPSSetUp_KrylovSchur(EPS eps)
{
PetscErrorCode ierr;
PetscBool issinv;
PetscFunctionBegin;
/* spectrum slicing requires special treatment of default values */
if (eps->which==EPS_ALL) {
if (eps->inta==0.0 && eps->intb==0.0) SETERRQ(((PetscObject)eps)->comm,1,"Must define a computational interval when using EPS_ALL");
if (!eps->ishermitian) SETERRQ(((PetscObject)eps)->comm,1,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
if (!((PetscObject)(eps->OP))->type_name) { /* default to shift-and-invert */
ierr = STSetType(eps->OP,STSINVERT);CHKERRQ(ierr);
}
ierr = PetscTypeCompare((PetscObject)eps->OP,STSINVERT,&issinv);CHKERRQ(ierr);
if (!issinv) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Shift-and-invert ST is needed for spectrum slicing");
#if defined(PETSC_USE_REAL_DOUBLE)
if (eps->tol==PETSC_DEFAULT) eps->tol = 1e-10; /* use tighter tolerance */
#endif
if (eps->intb >= PETSC_MAX_REAL) { /* right-open interval */
if (eps->inta <= PETSC_MIN_REAL) SETERRQ(((PetscObject)eps)->comm,1,"The defined computational interval should have at least one of their sides bounded");
ierr = STSetDefaultShift(eps->OP,eps->inta);CHKERRQ(ierr);
}
else { ierr = STSetDefaultShift(eps->OP,eps->intb);CHKERRQ(ierr); }
if (eps->nev==1) eps->nev = 40; /* nev not set, use default value */
if (eps->nev<10) SETERRQ(((PetscObject)eps)->comm,1,"nev cannot be less than 10 in spectrum slicing runs");
eps->ops->backtransform = PETSC_NULL;
}
/* proceed with the general case */
if (eps->ncv) { /* ncv set */
if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,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(((PetscObject)eps)->comm,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->which) { ierr = EPSDefaultSetWhich(eps);CHKERRQ(ierr); }
if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))
SETERRQ(((PetscObject)eps)->comm,1,"Wrong value of eps->which");
if (!eps->extraction) {
ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);
} else if (eps->extraction!=EPS_RITZ && eps->extraction!=EPS_HARMONIC) {
SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type");
}
ierr = EPSAllocateSolution(eps);CHKERRQ(ierr);
ierr = PetscFree(eps->T);CHKERRQ(ierr);
if (!eps->ishermitian || eps->extraction==EPS_HARMONIC) {
ierr = PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->T);CHKERRQ(ierr);
}
ierr = EPSDefaultGetWork(eps,1);CHKERRQ(ierr);
/* dispatch solve method */
if (eps->leftvecs) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Left vectors not supported in this solver");
if (eps->ishermitian) {
if (eps->which==EPS_ALL) eps->ops->solve = EPSSolve_KrylovSchur_Slice;
else {
switch (eps->extraction) {
case EPS_RITZ: eps->ops->solve = EPSSolve_KrylovSchur_Symm; break;
case EPS_HARMONIC: eps->ops->solve = EPSSolve_KrylovSchur_Harmonic; break;
default: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type");
}
}
} else {
switch (eps->extraction) {
case EPS_RITZ: eps->ops->solve = EPSSolve_KrylovSchur_Default; break;
case EPS_HARMONIC: eps->ops->solve = EPSSolve_KrylovSchur_Harmonic; break;
default: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type");
}
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSProjectedKSNonsym"
/*
EPSProjectedKSNonsym - Solves the projected eigenproblem in the Krylov-Schur
method (non-symmetric case).
On input:
l is the number of vectors kept in previous restart (0 means first restart)
S is the projected matrix (leading dimension is lds)
On output:
S has (real) Schur form with diagonal blocks sorted appropriately
Q contains the corresponding Schur vectors (order n, leading dimension n)
*/
PetscErrorCode EPSProjectedKSNonsym(EPS eps,PetscInt l,PetscScalar *S,PetscInt lds,PetscScalar *Q,PetscInt n)
{
PetscErrorCode ierr;
PetscInt i;
PetscFunctionBegin;
if (l==0) {
ierr = PetscMemzero(Q,n*n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=0;i<n;i++)
Q[i*(n+1)] = 1.0;
} else {
/* Reduce S to Hessenberg form, S <- Q S Q' */
ierr = EPSDenseHessenberg(n,eps->nconv,S,lds,Q);CHKERRQ(ierr);
}
/* Reduce S to (quasi-)triangular form, S <- Q S Q' */
ierr = EPSDenseSchur(n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);CHKERRQ(ierr);
/* Sort the remaining columns of the Schur form */
ierr = EPSSortDenseSchur(eps,n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSSolve_KrylovSchur_Default"
PetscErrorCode EPSSolve_KrylovSchur_Default(EPS eps)
{
PetscErrorCode ierr;
PetscInt i,k,l,lwork,nv;
Vec u=eps->work[0];
PetscScalar *S=eps->T,*Q,*work;
PetscReal beta;
PetscBool breakdown;
PetscFunctionBegin;
ierr = PetscMemzero(S,eps->ncv*eps->ncv*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&Q);CHKERRQ(ierr);
lwork = 7*eps->ncv;
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
/* Get the starting Arnoldi 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 Arnoldi factorization */
nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
ierr = EPSBasicArnoldi(eps,PETSC_FALSE,S,eps->ncv,eps->V,eps->nconv+l,&nv,u,&beta,&breakdown);CHKERRQ(ierr);
ierr = VecScale(u,1.0/beta);CHKERRQ(ierr);
/* Solve projected problem */
ierr = EPSProjectedKSNonsym(eps,l,S,eps->ncv,Q,nv);CHKERRQ(ierr);
/* Check convergence */
ierr = EPSKrylovConvergence(eps,PETSC_FALSE,eps->trackall,eps->nconv,nv-eps->nconv,S,eps->ncv,Q,eps->V,nv,beta,1.0,&k,work);CHKERRQ(ierr);
if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
/* Update l */
if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
else {
l = (nv-k)/2;
#if !defined(PETSC_USE_COMPLEX)
if (S[(k+l-1)*(eps->ncv+1)+1] != 0.0) {
if (k+l<nv-1) l = l+1;
else l = l-1;
}
#endif
}
if (eps->reason == EPS_CONVERGED_ITERATING) {
if (breakdown) {
/* Start a new Arnoldi factorization */
ierr = PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%G)\n",eps->its,beta);CHKERRQ(ierr);
ierr = EPSGetStartVector(eps,k,eps->V[k],&breakdown);CHKERRQ(ierr);
if (breakdown) {
eps->reason = EPS_DIVERGED_BREAKDOWN;
ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);
}
} else {
/* Prepare the Rayleigh quotient for restart */
for (i=k;i<k+l;i++) {
S[i*eps->ncv+k+l] = Q[(i+1)*nv-1]*beta;
}
}
}
/* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
ierr = SlepcUpdateVectors(nv,eps->V,eps->nconv,k+l,Q,nv,PETSC_FALSE);CHKERRQ(ierr);
if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
ierr = VecCopy(u,eps->V[k+l]);CHKERRQ(ierr);
}
eps->nconv = k;
ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);
}
ierr = PetscFree(Q);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSReset_KrylovSchur"
PetscErrorCode EPSReset_KrylovSchur(EPS eps)
{
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscFree(eps->T);CHKERRQ(ierr);
ierr = EPSReset_Default(eps);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "EPSCreate_KrylovSchur"
PetscErrorCode EPSCreate_KrylovSchur(EPS eps)
{
PetscFunctionBegin;
eps->ops->setup = EPSSetUp_KrylovSchur;
eps->ops->reset = EPSReset_KrylovSchur;
eps->ops->backtransform = EPSBackTransform_Default;
eps->ops->computevectors = EPSComputeVectors_Schur;
PetscFunctionReturn(0);
}
EXTERN_C_END