PetscErrorCode EPSSolve_LAPACK(EPS eps)
{
PetscErrorCode ierr;
PetscInt n=eps->n,i,low,high;
PetscScalar *array,*pX;
Vec v;
PetscFunctionBegin;
ierr = DSSolve(eps->ds,eps->eigr,eps->eigi);CHKERRQ(ierr);
ierr = DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);CHKERRQ(ierr);
/* right eigenvectors */
ierr = DSVectors(eps->ds,DS_MAT_X,NULL,NULL);CHKERRQ(ierr);
ierr = DSGetArray(eps->ds,DS_MAT_X,&pX);CHKERRQ(ierr);
for (i=0;i<eps->ncv;i++) {
ierr = BVGetColumn(eps->V,i,&v);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(v,&low,&high);CHKERRQ(ierr);
ierr = VecGetArray(v,&array);CHKERRQ(ierr);
ierr = PetscMemcpy(array,pX+i*n+low,(high-low)*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,i,&v);CHKERRQ(ierr);
}
ierr = DSRestoreArray(eps->ds,DS_MAT_X,&pX);CHKERRQ(ierr);
eps->nconv = eps->ncv;
eps->its = 1;
eps->reason = EPS_CONVERGED_TOL;
PetscFunctionReturn(0);
}
PetscErrorCode EPSGetArbitraryValues(EPS eps,PetscScalar *rr,PetscScalar *ri)
{
PetscErrorCode ierr;
PetscInt i,newi,ld,n,l;
Vec xr=eps->work[0],xi=eps->work[1];
PetscScalar re,im,*Zr,*Zi,*X;
PetscFunctionBegin;
ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
ierr = DSGetDimensions(eps->ds,&n,NULL,&l,NULL,NULL);CHKERRQ(ierr);
for (i=l;i<n;i++) {
re = eps->eigr[i];
im = eps->eigi[i];
ierr = STBackTransform(eps->st,1,&re,&im);CHKERRQ(ierr);
newi = i;
ierr = DSVectors(eps->ds,DS_MAT_X,&newi,NULL);CHKERRQ(ierr);
ierr = DSGetArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
Zr = X+i*ld;
if (newi==i+1) Zi = X+newi*ld;
else Zi = NULL;
ierr = EPSComputeRitzVector(eps,Zr,Zi,eps->V,xr,xi);CHKERRQ(ierr);
ierr = DSRestoreArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
ierr = (*eps->arbitrary)(re,im,xr,xi,rr+i,ri+i,eps->arbitraryctx);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode PEPComputeVectors_Schur(PEP pep)
{
PetscErrorCode ierr;
PetscInt n,i;
Mat Z;
Vec v;
#if !defined(PETSC_USE_COMPLEX)
Vec v1;
PetscScalar tmp;
PetscReal norm,normi;
#endif
PetscFunctionBegin;
ierr = DSGetDimensions(pep->ds,&n,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DSVectors(pep->ds,DS_MAT_X,NULL,NULL);CHKERRQ(ierr);
ierr = DSGetMat(pep->ds,DS_MAT_X,&Z);CHKERRQ(ierr);
ierr = BVSetActiveColumns(pep->V,0,n);CHKERRQ(ierr);
ierr = BVMultInPlace(pep->V,Z,0,n);CHKERRQ(ierr);
ierr = MatDestroy(&Z);CHKERRQ(ierr);
/* Fix eigenvectors if balancing was used */
if ((pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) && pep->Dr && (pep->refine!=PEP_REFINE_MULTIPLE)) {
for (i=0;i<n;i++) {
ierr = BVGetColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = VecPointwiseMult(v,v,pep->Dr);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i,&v);CHKERRQ(ierr);
}
}
/* normalization */
for (i=0;i<n;i++) {
#if !defined(PETSC_USE_COMPLEX)
if (pep->eigi[i] != 0.0) {
ierr = BVGetColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = BVGetColumn(pep->V,i+1,&v1);CHKERRQ(ierr);
ierr = VecNorm(v,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecNorm(v1,NORM_2,&normi);CHKERRQ(ierr);
tmp = 1.0 / SlepcAbsEigenvalue(norm,normi);
ierr = VecScale(v,tmp);CHKERRQ(ierr);
ierr = VecScale(v1,tmp);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i+1,&v1);CHKERRQ(ierr);
i++;
} else
#endif
{
ierr = BVGetColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = VecNormalize(v,NULL);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i,&v);CHKERRQ(ierr);
}
}
PetscFunctionReturn(0);
}
/*
PEPKrylovConvergence - This is the analogue to EPSKrylovConvergence, but
for polynomial Krylov methods.
Differences:
- Always non-symmetric
- Does not check for STSHIFT
- No correction factor
- No support for true residual
*/
PetscErrorCode PEPKrylovConvergence(PEP pep,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscInt *kout)
{
PetscErrorCode ierr;
PetscInt k,newk,marker,ld,inside;
PetscScalar re,im;
PetscReal resnorm;
PetscBool istrivial;
PetscFunctionBegin;
ierr = RGIsTrivial(pep->rg,&istrivial);CHKERRQ(ierr);
ierr = DSGetLeadingDimension(pep->ds,&ld);CHKERRQ(ierr);
marker = -1;
if (pep->trackall) getall = PETSC_TRUE;
for (k=kini;k<kini+nits;k++) {
/* eigenvalue */
re = pep->eigr[k];
im = pep->eigi[k];
if (!istrivial || pep->conv==PEP_CONV_NORM) {
ierr = STBackTransform(pep->st,1,&re,&im);CHKERRQ(ierr);
}
if (!istrivial) {
ierr = RGCheckInside(pep->rg,1,&re,&im,&inside);CHKERRQ(ierr);
if (marker==-1 && inside<=0) marker = k;
if (!pep->conv==PEP_CONV_NORM) { /* make sure pep->converged below uses the right value */
re = pep->eigr[k];
im = pep->eigi[k];
}
}
newk = k;
ierr = DSVectors(pep->ds,DS_MAT_X,&newk,&resnorm);CHKERRQ(ierr);
resnorm *= beta;
/* error estimate */
ierr = (*pep->converged)(pep,re,im,resnorm,&pep->errest[k],pep->convergedctx);CHKERRQ(ierr);
if (marker==-1 && pep->errest[k] >= pep->tol) marker = k;
if (newk==k+1) {
pep->errest[k+1] = pep->errest[k];
k++;
}
if (marker!=-1 && !getall) break;
}
if (marker!=-1) k = marker;
*kout = k;
PetscFunctionReturn(0);
}
PetscErrorCode PEPComputeVectors_Indefinite(PEP pep)
{
PetscErrorCode ierr;
PetscInt n,i;
Mat Z;
Vec v;
#if !defined(PETSC_USE_COMPLEX)
Vec v1;
PetscScalar tmp;
PetscReal norm,normi;
#endif
PetscFunctionBegin;
ierr = DSGetDimensions(pep->ds,&n,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DSVectors(pep->ds,DS_MAT_X,NULL,NULL);CHKERRQ(ierr);
ierr = DSGetMat(pep->ds,DS_MAT_X,&Z);CHKERRQ(ierr);
ierr = BVSetActiveColumns(pep->V,0,n);CHKERRQ(ierr);
ierr = BVMultInPlace(pep->V,Z,0,n);CHKERRQ(ierr);
ierr = MatDestroy(&Z);CHKERRQ(ierr);
/* normalization */
for (i=0;i<n;i++) {
#if !defined(PETSC_USE_COMPLEX)
if (pep->eigi[i] != 0.0) {
ierr = BVGetColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = BVGetColumn(pep->V,i+1,&v1);CHKERRQ(ierr);
ierr = VecNorm(v,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecNorm(v1,NORM_2,&normi);CHKERRQ(ierr);
tmp = 1.0 / SlepcAbsEigenvalue(norm,normi);
ierr = VecScale(v,tmp);CHKERRQ(ierr);
ierr = VecScale(v1,tmp);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i+1,&v1);CHKERRQ(ierr);
i++;
} else
#endif
{
ierr = BVGetColumn(pep->V,i,&v);CHKERRQ(ierr);
ierr = VecNormalize(v,NULL);CHKERRQ(ierr);
ierr = BVRestoreColumn(pep->V,i,&v);CHKERRQ(ierr);
}
}
PetscFunctionReturn(0);
}
/*
EPSComputeVectors_XD - Compute eigenvectors from the vectors
provided by the eigensolver. This version is intended for solvers
that provide Schur vectors from the QZ decomposition. Given the partial
Schur decomposition OP*V=V*T, the following steps are performed:
1) compute eigenvectors of (S,T): S*Z=T*Z*D
2) compute eigenvectors of OP: X=V*Z
*/
PetscErrorCode EPSComputeVectors_XD(EPS eps)
{
PetscErrorCode ierr;
Mat X;
PetscBool symm;
PetscFunctionBegin;
ierr = PetscObjectTypeCompareAny((PetscObject)eps->ds,&symm,DSHEP,"");CHKERRQ(ierr);
if (symm) PetscFunctionReturn(0);
ierr = DSVectors(eps->ds,DS_MAT_X,NULL,NULL);CHKERRQ(ierr);
ierr = DSNormalize(eps->ds,DS_MAT_X,-1);CHKERRQ(ierr);
/* V <- V * X */
ierr = DSGetMat(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
ierr = BVSetActiveColumns(eps->V,0,eps->nconv);CHKERRQ(ierr);
ierr = BVMultInPlace(eps->V,X,0,eps->nconv);CHKERRQ(ierr);
ierr = DSRestoreMat(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
