/*
Common subroutines for all Krylov-type solvers.
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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 <slepc-private/epsimpl.h>
#include <slepc-private/slepcimpl.h>
#include <slepcblaslapack.h>
#undef __FUNCT__
#define __FUNCT__ "EPSBasicArnoldi"
/*
EPSBasicArnoldi - Computes an m-step Arnoldi factorization. The first k
columns are assumed to be locked and therefore they are not modified. On
exit, the following relation is satisfied:
OP * V - V * H = f * e_m^T
where the columns of V are the Arnoldi vectors (which are B-orthonormal),
H is an upper Hessenberg matrix, f is the residual vector and e_m is
the m-th vector of the canonical basis. The vector f is B-orthogonal to
the columns of V. On exit, beta contains the B-norm of f and the next
Arnoldi vector can be computed as v_{m+1} = f / beta.
*/
PetscErrorCode EPSBasicArnoldi(EPS eps,PetscBool trans,PetscScalar *H,PetscInt ldh,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscReal *beta,PetscBool *breakdown)
{
PetscErrorCode ierr;
PetscInt j,m = *M;
PetscReal norm;
PetscFunctionBegin;
for (j=k;j<m-1;j++) {
if (trans) { ierr = STApplyTranspose(eps->OP,V[j],V[j+1]);CHKERRQ(ierr); }
else { ierr = STApply(eps->OP,V[j],V[j+1]);CHKERRQ(ierr); }
ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,j+1,PETSC_NULL,V,V[j+1],H+ldh*j,&norm,breakdown);CHKERRQ(ierr);
H[j+1+ldh*j] = norm;
if (*breakdown) {
*M = j+1;
*beta = norm;
PetscFunctionReturn(0);
} else {
ierr = VecScale(V[j+1],1/norm);CHKERRQ(ierr);
}
}
if (trans) { ierr = STApplyTranspose(eps->OP,V[m-1],f);CHKERRQ(ierr); }
else { ierr = STApply(eps->OP,V[m-1],f);CHKERRQ(ierr); }
ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,m,PETSC_NULL,V,f,H+ldh*(m-1),beta,PETSC_NULL);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSKrylovConvergence"
/*
EPSKrylovConvergence - Implements the loop that checks for convergence
in Krylov methods.
Input Parameters:
eps - the eigensolver; some error estimates are updated in eps->errest
getall - whether all residuals must be computed
kini - initial value of k (the loop variable)
nits - number of iterations of the loop
V - set of basis vectors (used only if trueresidual is activated)
nv - number of vectors to process (dimension of Q, columns of V)
beta - norm of f (the residual vector of the Arnoldi/Lanczos factorization)
corrf - correction factor for residual estimates (only in harmonic KS)
Output Parameters:
kout - the first index where the convergence test failed
*/
PetscErrorCode EPSKrylovConvergence(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,Vec *V,PetscInt nv,PetscReal beta,PetscReal corrf,PetscInt *kout)
{
PetscErrorCode ierr;
PetscInt k,newk,marker,ld;
PetscScalar re,im,*Z,*X;
PetscReal resnorm;
PetscBool isshift;
PetscFunctionBegin;
ierr = PSGetLeadingDimension(eps->ps,&ld);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)eps->OP,STSHIFT,&isshift);CHKERRQ(ierr);
marker = -1;
if (eps->trackall) getall = PETSC_TRUE;
for (k=kini;k<kini+nits;k++) {
/* eigenvalue */
re = eps->eigr[k];
im = eps->eigi[k];
if (eps->trueres || isshift) {
ierr = STBackTransform(eps->OP,1,&re,&im);CHKERRQ(ierr);
}
newk = k;
ierr = PSVectors(eps->ps,PS_MAT_X,&newk,&resnorm);CHKERRQ(ierr);
resnorm *= beta;
if (eps->trueres) {
ierr = PSGetArray(eps->ps,PS_MAT_X,&X);CHKERRQ(ierr);
Z = X+k*ld;
ierr = EPSComputeTrueResidual(eps,re,im,Z,V,nv,&resnorm);CHKERRQ(ierr);
ierr = PSRestoreArray(eps->ps,PS_MAT_X,&X);CHKERRQ(ierr);
}
else resnorm *= corrf;
/* error estimate */
ierr = (*eps->conv_func)(eps,re,im,resnorm,&eps->errest[k],eps->conv_ctx);CHKERRQ(ierr);
if (marker==-1 && eps->errest[k] >= eps->tol) marker = k;
if (newk==k+1) { eps->errest[k+1] = eps->errest[k]; k++; }
if (marker!=-1 && !getall) break;
}
if (marker!=-1) k = marker;
*kout = k;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "EPSFullLanczos"
/*
EPSFullLanczos - Computes an m-step Lanczos factorization with full
reorthogonalization. At each Lanczos step, the corresponding Lanczos
vector is orthogonalized with respect to all previous Lanczos vectors.
This is equivalent to computing an m-step Arnoldi factorization and
exploting symmetry of the operator.
The first k columns are assumed to be locked and therefore they are
not modified. On exit, the following relation is satisfied:
OP * V - V * T = f * e_m^T
where the columns of V are the Lanczos vectors (which are B-orthonormal),
T is a real symmetric tridiagonal matrix, f is the residual vector and e_m
is the m-th vector of the canonical basis. The tridiagonal is stored as
two arrays: alpha contains the diagonal elements, beta the off-diagonal.
The vector f is B-orthogonal to the columns of V. On exit, the last element
of beta contains the B-norm of f and the next Lanczos vector can be
computed as v_{m+1} = f / beta(end).
*/
PetscErrorCode EPSFullLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscBool *breakdown)
{
PetscErrorCode ierr;
PetscInt j,m = *M;
PetscReal norm;
PetscScalar *hwork,lhwork[100];
PetscFunctionBegin;
if (m > 100) {
ierr = PetscMalloc((eps->nds+m)*sizeof(PetscScalar),&hwork);CHKERRQ(ierr);
} else {
hwork = lhwork;
}
for (j=k;j<m-1;j++) {
ierr = STApply(eps->OP,V[j],V[j+1]);CHKERRQ(ierr);
ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,j+1,PETSC_NULL,V,V[j+1],hwork,&norm,breakdown);CHKERRQ(ierr);
alpha[j] = PetscRealPart(hwork[j]);
beta[j] = norm;
if (*breakdown) {
*M = j+1;
if (m > 100) {
ierr = PetscFree(hwork);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
} else {
ierr = VecScale(V[j+1],1.0/norm);CHKERRQ(ierr);
}
}
ierr = STApply(eps->OP,V[m-1],f);CHKERRQ(ierr);
ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,m,PETSC_NULL,V,f,hwork,&norm,PETSC_NULL);CHKERRQ(ierr);
alpha[m-1] = PetscRealPart(hwork[m-1]);
beta[m-1] = norm;
if (m > 100) {
ierr = PetscFree(hwork);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}