PetscErrorCode EPSSolve_XD(EPS eps)
{
EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;
dvdDashboard *d = &data->ddb;
PetscInt l,k;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Call the starting routines */
ierr = EPSDavidsonFLCall(d->startList,d);CHKERRQ(ierr);
for (eps->its=0;eps->its<eps->max_it;eps->its++) {
/* Initialize V, if it is needed */
ierr = BVGetActiveColumns(d->eps->V,&l,&k);CHKERRQ(ierr);
if (l == k) { ierr = d->initV(d);CHKERRQ(ierr); }
/* Find the best approximated eigenpairs in V, X */
ierr = d->calcPairs(d);CHKERRQ(ierr);
/* Test for convergence */
if (eps->nconv >= eps->nev) break;
/* Expand the subspace */
ierr = d->updateV(d);CHKERRQ(ierr);
/* Monitor progress */
eps->nconv = d->nconv;
ierr = BVGetActiveColumns(d->eps->V,&l,&k);CHKERRQ(ierr);
ierr = EPSMonitor(eps,eps->its+1,eps->nconv,eps->eigr,eps->eigi,eps->errest,k);CHKERRQ(ierr);
}
/* Call the ending routines */
ierr = EPSDavidsonFLCall(d->endList,d);CHKERRQ(ierr);
if (eps->nconv >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
else eps->reason = EPS_DIVERGED_ITS;
PetscFunctionReturn(0);
}
PetscErrorCode EPSSolve_Lanczos(EPS eps)
{
EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
PetscErrorCode ierr;
PetscInt nconv,i,j,k,l,x,n,*perm,restart,ncv=eps->ncv,r,ld;
Vec vi,vj,w;
Mat U;
PetscScalar *Y,*ritz,stmp;
PetscReal *d,*e,*bnd,anorm,beta,norm,rtmp,resnorm;
PetscBool breakdown;
char *conv,ctmp;
PetscFunctionBegin;
ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
ierr = PetscMalloc4(ncv,&ritz,ncv,&bnd,ncv,&perm,ncv,&conv);CHKERRQ(ierr);
/* The first Lanczos vector is the normalized initial vector */
ierr = EPSGetStartVector(eps,0,NULL);CHKERRQ(ierr);
anorm = -1.0;
nconv = 0;
/* Restart loop */
while (eps->reason == EPS_CONVERGED_ITERATING) {
eps->its++;
/* Compute an ncv-step Lanczos factorization */
n = PetscMin(nconv+eps->mpd,ncv);
ierr = DSGetArrayReal(eps->ds,DS_MAT_T,&d);CHKERRQ(ierr);
e = d + ld;
ierr = EPSBasicLanczos(eps,d,e,nconv,&n,&breakdown,anorm);CHKERRQ(ierr);
beta = e[n-1];
ierr = DSRestoreArrayReal(eps->ds,DS_MAT_T,&d);CHKERRQ(ierr);
ierr = DSSetDimensions(eps->ds,n,0,nconv,0);CHKERRQ(ierr);
ierr = DSSetState(eps->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
ierr = BVSetActiveColumns(eps->V,nconv,n);CHKERRQ(ierr);
/* Solve projected problem */
ierr = DSSolve(eps->ds,ritz,NULL);CHKERRQ(ierr);
ierr = DSSort(eps->ds,ritz,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
/* Estimate ||A|| */
for (i=nconv;i<n;i++)
anorm = PetscMax(anorm,PetscAbsReal(PetscRealPart(ritz[i])));
/* Compute residual norm estimates as beta*abs(Y(m,:)) + eps*||A|| */
ierr = DSGetArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
for (i=nconv;i<n;i++) {
resnorm = beta*PetscAbsScalar(Y[n-1+i*ld]) + PETSC_MACHINE_EPSILON*anorm;
ierr = (*eps->converged)(eps,ritz[i],eps->eigi[i],resnorm,&bnd[i],eps->convergedctx);CHKERRQ(ierr);
if (bnd[i]<eps->tol) conv[i] = 'C';
else conv[i] = 'N';
}
ierr = DSRestoreArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
/* purge repeated ritz values */
if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) {
for (i=nconv+1;i<n;i++) {
if (conv[i] == 'C' && PetscAbsScalar((ritz[i]-ritz[i-1])/ritz[i]) < eps->tol) conv[i] = 'R';
}
}
/* Compute restart vector */
if (breakdown) {
ierr = PetscInfo2(eps,"Breakdown in Lanczos method (it=%D norm=%g)\n",eps->its,(double)beta);CHKERRQ(ierr);
} else {
restart = nconv;
while (restart<n && conv[restart] != 'N') restart++;
if (restart >= n) {
breakdown = PETSC_TRUE;
} else {
for (i=restart+1;i<n;i++) {
if (conv[i] == 'N') {
ierr = SlepcSCCompare(eps->sc,ritz[restart],0.0,ritz[i],0.0,&r);CHKERRQ(ierr);
if (r>0) restart = i;
}
}
ierr = DSGetArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
ierr = BVMultColumn(eps->V,1.0,0.0,n,Y+restart*ld+nconv);CHKERRQ(ierr);
ierr = DSRestoreArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
}
}
/* Count and put converged eigenvalues first */
for (i=nconv;i<n;i++) perm[i] = i;
for (k=nconv;k<n;k++) {
if (conv[perm[k]] != 'C') {
j = k + 1;
while (j<n && conv[perm[j]] != 'C') j++;
if (j>=n) break;
l = perm[k]; perm[k] = perm[j]; perm[j] = l;
}
}
/* Sort eigenvectors according to permutation */
ierr = DSGetArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
for (i=nconv;i<k;i++) {
x = perm[i];
if (x != i) {
j = i + 1;
while (perm[j] != i) j++;
/* swap eigenvalues i and j */
stmp = ritz[x]; ritz[x] = ritz[i]; ritz[i] = stmp;
rtmp = bnd[x]; bnd[x] = bnd[i]; bnd[i] = rtmp;
ctmp = conv[x]; conv[x] = conv[i]; conv[i] = ctmp;
perm[j] = x; perm[i] = i;
/* swap eigenvectors i and j */
for (l=0;l<n;l++) {
stmp = Y[l+x*ld]; Y[l+x*ld] = Y[l+i*ld]; Y[l+i*ld] = stmp;
}
}
}
ierr = DSRestoreArray(eps->ds,DS_MAT_Q,&Y);CHKERRQ(ierr);
/* compute converged eigenvectors */
ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
ierr = BVMultInPlace(eps->V,U,nconv,k);CHKERRQ(ierr);
ierr = MatDestroy(&U);CHKERRQ(ierr);
/* purge spurious ritz values */
if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) {
for (i=nconv;i<k;i++) {
ierr = BVGetColumn(eps->V,i,&vi);CHKERRQ(ierr);
ierr = VecNorm(vi,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecScale(vi,1.0/norm);CHKERRQ(ierr);
w = eps->work[0];
ierr = STApply(eps->st,vi,w);CHKERRQ(ierr);
ierr = VecAXPY(w,-ritz[i],vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,i,&vi);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
ierr = (*eps->converged)(eps,ritz[i],eps->eigi[i],norm,&bnd[i],eps->convergedctx);CHKERRQ(ierr);
if (bnd[i]>=eps->tol) conv[i] = 'S';
}
for (i=nconv;i<k;i++) {
if (conv[i] != 'C') {
j = i + 1;
while (j<k && conv[j] != 'C') j++;
if (j>=k) break;
/* swap eigenvalues i and j */
stmp = ritz[j]; ritz[j] = ritz[i]; ritz[i] = stmp;
rtmp = bnd[j]; bnd[j] = bnd[i]; bnd[i] = rtmp;
ctmp = conv[j]; conv[j] = conv[i]; conv[i] = ctmp;
/* swap eigenvectors i and j */
ierr = BVGetColumn(eps->V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(eps->V,j,&vj);CHKERRQ(ierr);
ierr = VecSwap(vi,vj);CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,j,&vj);CHKERRQ(ierr);
}
}
k = i;
}
/* store ritz values and estimated errors */
for (i=nconv;i<n;i++) {
eps->eigr[i] = ritz[i];
eps->errest[i] = bnd[i];
}
ierr = EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,n);CHKERRQ(ierr);
nconv = k;
if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
if (nconv >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
if (eps->reason == EPS_CONVERGED_ITERATING) { /* copy restart vector */
ierr = BVCopyColumn(eps->V,n,nconv);CHKERRQ(ierr);
if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL && !breakdown) {
/* Reorthonormalize restart vector */
ierr = BVOrthogonalizeColumn(eps->V,nconv,NULL,&norm,&breakdown);CHKERRQ(ierr);
ierr = BVScaleColumn(eps->V,nconv,1.0/norm);CHKERRQ(ierr);
}
if (breakdown) {
/* Use random vector for restarting */
ierr = PetscInfo(eps,"Using random vector for restart\n");CHKERRQ(ierr);
ierr = EPSGetStartVector(eps,nconv,&breakdown);CHKERRQ(ierr);
}
if (breakdown) { /* give up */
eps->reason = EPS_DIVERGED_BREAKDOWN;
ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);
}
}
}
eps->nconv = nconv;
ierr = PetscFree4(ritz,bnd,perm,conv);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode EPSSolve_Arnoldi(EPS eps)
{
PetscErrorCode ierr;
PetscInt k,nv,ld;
Mat U;
PetscScalar *H,*X;
PetscReal beta,gamma=1.0;
PetscBool breakdown,harmonic,refined;
BVOrthogRefineType orthog_ref;
EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data;
PetscFunctionBegin;
ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
ierr = DSGetRefined(eps->ds,&refined);CHKERRQ(ierr);
harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
ierr = BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL);CHKERRQ(ierr);
/* Get the starting Arnoldi vector */
ierr = EPSGetStartVector(eps,0,NULL);CHKERRQ(ierr);
/* 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 = DSSetDimensions(eps->ds,nv,0,eps->nconv,0);CHKERRQ(ierr);
ierr = DSGetArray(eps->ds,DS_MAT_A,&H);CHKERRQ(ierr);
if (!arnoldi->delayed) {
ierr = EPSBasicArnoldi(eps,PETSC_FALSE,H,ld,eps->nconv,&nv,&beta,&breakdown);CHKERRQ(ierr);
} else SETERRQ(PetscObjectComm((PetscObject)eps),1,"Not implemented");
/*if (orthog_ref == BV_ORTHOG_REFINE_NEVER) {
ierr = EPSDelayedArnoldi1(eps,H,ld,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);
} else {
ierr = EPSDelayedArnoldi(eps,H,ld,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);
}*/
ierr = DSRestoreArray(eps->ds,DS_MAT_A,&H);CHKERRQ(ierr);
ierr = DSSetState(eps->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
ierr = BVSetActiveColumns(eps->V,eps->nconv,nv);CHKERRQ(ierr);
/* Compute translation of Krylov decomposition if harmonic extraction used */
if (harmonic) {
ierr = DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,NULL,&gamma);CHKERRQ(ierr);
}
/* Solve projected problem */
ierr = DSSolve(eps->ds,eps->eigr,eps->eigi);CHKERRQ(ierr);
ierr = DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DSUpdateExtraRow(eps->ds);CHKERRQ(ierr);
/* Check convergence */
ierr = EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,gamma,&k);CHKERRQ(ierr);
if (refined) {
ierr = DSGetArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
ierr = BVMultColumn(eps->V,1.0,0.0,k,X+k*ld);CHKERRQ(ierr);
ierr = DSRestoreArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
ierr = BVMultInPlace(eps->V,U,eps->nconv,nv);CHKERRQ(ierr);
ierr = MatDestroy(&U);CHKERRQ(ierr);
ierr = BVOrthogonalizeColumn(eps->V,k,NULL,NULL,NULL);CHKERRQ(ierr);
} else {
ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
ierr = BVMultInPlace(eps->V,U,eps->nconv,nv);CHKERRQ(ierr);
ierr = MatDestroy(&U);CHKERRQ(ierr);
}
eps->nconv = k;
ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);
if (breakdown && k<eps->nev) {
ierr = PetscInfo2(eps,"Breakdown in Arnoldi method (it=%D norm=%g)\n",eps->its,(double)beta);CHKERRQ(ierr);
ierr = EPSGetStartVector(eps,k,&breakdown);CHKERRQ(ierr);
if (breakdown) {
eps->reason = EPS_DIVERGED_BREAKDOWN;
ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);
}
}
if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
if (eps->nconv >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
}
/* truncate Schur decomposition and change the state to raw so that
PSVectors() computes eigenvectors from scratch */
ierr = DSSetDimensions(eps->ds,eps->nconv,0,0,0);CHKERRQ(ierr);
ierr = DSSetState(eps->ds,DS_STATE_RAW);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
EPSSolve - Solves the eigensystem.
Collective on EPS
Input Parameter:
. eps - eigensolver context obtained from EPSCreate()
Options Database Keys:
+ -eps_view - print information about the solver used
. -eps_view_mat0 binary - save the first matrix (A) to the default binary viewer
. -eps_view_mat1 binary - save the second matrix (B) to the default binary viewer
- -eps_plot_eigs - plot computed eigenvalues
Level: beginner
.seealso: EPSCreate(), EPSSetUp(), EPSDestroy(), EPSSetTolerances()
@*/
PetscErrorCode EPSSolve(EPS eps)
{
PetscErrorCode ierr;
PetscInt i,nmat;
PetscReal re,im;
PetscScalar dot;
PetscBool flg,iscayley;
PetscViewer viewer;
PetscViewerFormat format;
PetscDraw draw;
PetscDrawSP drawsp;
STMatMode matmode;
Mat A,B;
Vec w,x;
PetscFunctionBegin;
PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
ierr = PetscLogEventBegin(EPS_Solve,eps,0,0,0);CHKERRQ(ierr);
/* call setup */
ierr = EPSSetUp(eps);CHKERRQ(ierr);
eps->nconv = 0;
eps->its = 0;
for (i=0;i<eps->ncv;i++) {
eps->eigr[i] = 0.0;
eps->eigi[i] = 0.0;
eps->errest[i] = 0.0;
}
ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->ncv);CHKERRQ(ierr);
/* call solver */
ierr = (*eps->ops->solve)(eps);CHKERRQ(ierr);
eps->state = EPS_STATE_SOLVED;
ierr = STGetMatMode(eps->st,&matmode);CHKERRQ(ierr);
if (matmode == ST_MATMODE_INPLACE && eps->ispositive) {
/* Purify eigenvectors before reverting operator */
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
}
ierr = STPostSolve(eps->st);CHKERRQ(ierr);
if (!eps->reason) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
/* Map eigenvalues back to the original problem, necessary in some
* spectral transformations */
if (eps->ops->backtransform) {
ierr = (*eps->ops->backtransform)(eps);CHKERRQ(ierr);
}
#if !defined(PETSC_USE_COMPLEX)
/* reorder conjugate eigenvalues (positive imaginary first) */
for (i=0; i<eps->nconv-1; i++) {
if (eps->eigi[i] != 0) {
if (eps->eigi[i] < 0) {
eps->eigi[i] = -eps->eigi[i];
eps->eigi[i+1] = -eps->eigi[i+1];
/* the next correction only works with eigenvectors */
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
ierr = BVScaleColumn(eps->V,i+1,-1.0);CHKERRQ(ierr);
}
i++;
}
}
#endif
ierr = STGetNumMatrices(eps->st,&nmat);CHKERRQ(ierr);
ierr = STGetOperators(eps->st,0,&A);CHKERRQ(ierr);
if (nmat>1) { ierr = STGetOperators(eps->st,1,&B);CHKERRQ(ierr); }
/* In the case of Cayley transform, eigenvectors need to be B-normalized */
ierr = PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);CHKERRQ(ierr);
if (iscayley && eps->isgeneralized && eps->ishermitian) {
ierr = MatGetVecs(B,NULL,&w);CHKERRQ(ierr);
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
for (i=0;i<eps->nconv;i++) {
ierr = BVGetColumn(eps->V,i,&x);CHKERRQ(ierr);
ierr = MatMult(B,x,w);CHKERRQ(ierr);
ierr = VecDot(w,x,&dot);CHKERRQ(ierr);
ierr = VecScale(x,1.0/PetscSqrtScalar(dot));CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,i,&x);CHKERRQ(ierr);
}
ierr = VecDestroy(&w);CHKERRQ(ierr);
}
/* sort eigenvalues according to eps->which parameter */
ierr = SlepcSortEigenvalues(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm);CHKERRQ(ierr);
ierr = PetscLogEventEnd(EPS_Solve,eps,0,0,0);CHKERRQ(ierr);
/* various viewers */
ierr = MatViewFromOptions(A,((PetscObject)eps)->prefix,"-eps_view_mat0");CHKERRQ(ierr);
if (nmat>1) { ierr = MatViewFromOptions(B,((PetscObject)eps)->prefix,"-eps_view_mat1");CHKERRQ(ierr); }
ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)eps),((PetscObject)eps)->prefix,"-eps_view",&viewer,&format,&flg);CHKERRQ(ierr);
if (flg && !PetscPreLoadingOn) {
ierr = PetscViewerPushFormat(viewer,format);CHKERRQ(ierr);
ierr = EPSView(eps,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)eps)->prefix,"-eps_plot_eigs",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,"Computed Eigenvalues",PETSC_DECIDE,PETSC_DECIDE,300,300,&viewer);CHKERRQ(ierr);
ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
ierr = PetscDrawSPCreate(draw,1,&drawsp);CHKERRQ(ierr);
for (i=0;i<eps->nconv;i++) {
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(eps->eigr[i]);
im = PetscImaginaryPart(eps->eigi[i]);
#else
re = eps->eigr[i];
im = eps->eigi[i];
#endif
ierr = PetscDrawSPAddPoint(drawsp,&re,&im);CHKERRQ(ierr);
}
ierr = PetscDrawSPDraw(drawsp,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawSPDestroy(&drawsp);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* Remove deflation and initial subspaces */
eps->nds = 0;
eps->nini = 0;
PetscFunctionReturn(0);
}
PetscErrorCode EPSSolve_KrylovSchur_Default(EPS eps)
{
PetscErrorCode ierr;
EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
PetscInt i,j,*pj,k,l,nv,ld;
Mat U;
PetscScalar *S,*Q,*g;
PetscReal beta,gamma=1.0;
PetscBool breakdown,harmonic;
PetscFunctionBegin;
ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
if (harmonic) { ierr = PetscMalloc1(ld,&g);CHKERRQ(ierr); }
if (eps->arbitrary) pj = &j;
else pj = NULL;
/* Get the starting Arnoldi vector */
ierr = EPSGetStartVector(eps,0,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 = DSGetArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
ierr = EPSBasicArnoldi(eps,PETSC_FALSE,S,ld,eps->nconv+l,&nv,&beta,&breakdown);CHKERRQ(ierr);
ierr = DSRestoreArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
ierr = DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);CHKERRQ(ierr);
if (l==0) {
ierr = DSSetState(eps->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
} else {
ierr = DSSetState(eps->ds,DS_STATE_RAW);CHKERRQ(ierr);
}
ierr = BVSetActiveColumns(eps->V,eps->nconv,nv);CHKERRQ(ierr);
/* Compute translation of Krylov decomposition if harmonic extraction used */
if (harmonic) {
ierr = DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,g,&gamma);CHKERRQ(ierr);
}
/* Solve projected problem */
ierr = DSSolve(eps->ds,eps->eigr,eps->eigi);CHKERRQ(ierr);
if (eps->arbitrary) {
ierr = EPSGetArbitraryValues(eps,eps->rr,eps->ri);CHKERRQ(ierr);
j=1;
}
ierr = DSSort(eps->ds,eps->eigr,eps->eigi,eps->rr,eps->ri,pj);CHKERRQ(ierr);
/* Check convergence */
ierr = EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,gamma,&k);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 = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
#if !defined(PETSC_USE_COMPLEX)
ierr = DSGetArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
if (S[k+l+(k+l-1)*ld] != 0.0) {
if (k+l<nv-1) l = l+1;
else l = l-1;
}
ierr = DSRestoreArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
#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,(double)beta);CHKERRQ(ierr);
if (k<eps->nev) {
ierr = EPSGetStartVector(eps,k,&breakdown);CHKERRQ(ierr);
if (breakdown) {
eps->reason = EPS_DIVERGED_BREAKDOWN;
ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);
}
}
} else {
/* Undo translation of Krylov decomposition */
if (harmonic) {
ierr = DSSetDimensions(eps->ds,nv,0,k,l);CHKERRQ(ierr);
ierr = DSTranslateHarmonic(eps->ds,0.0,beta,PETSC_TRUE,g,&gamma);CHKERRQ(ierr);
/* gamma u^ = u - U*g~ */
ierr = BVMultColumn(eps->V,-1.0,1.0,nv,g);CHKERRQ(ierr);
ierr = BVScaleColumn(eps->V,nv,1.0/gamma);CHKERRQ(ierr);
}
/* Prepare the Rayleigh quotient for restart */
ierr = DSGetArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
ierr = DSGetArray(eps->ds,DS_MAT_Q,&Q);CHKERRQ(ierr);
for (i=k;i<k+l;i++) {
S[k+l+i*ld] = Q[nv-1+i*ld]*beta*gamma;
}
ierr = DSRestoreArray(eps->ds,DS_MAT_A,&S);CHKERRQ(ierr);
ierr = DSRestoreArray(eps->ds,DS_MAT_Q,&Q);CHKERRQ(ierr);
}
}
/* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
ierr = BVMultInPlace(eps->V,U,eps->nconv,k+l);CHKERRQ(ierr);
ierr = MatDestroy(&U);CHKERRQ(ierr);
if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
ierr = BVCopyColumn(eps->V,nv,k+l);CHKERRQ(ierr);
}
eps->nconv = k;
ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);
}
if (harmonic) { ierr = PetscFree(g);CHKERRQ(ierr); }
/* truncate Schur decomposition and change the state to raw so that
PSVectors() computes eigenvectors from scratch */
ierr = DSSetDimensions(eps->ds,eps->nconv,0,0,0);CHKERRQ(ierr);
ierr = DSSetState(eps->ds,DS_STATE_RAW);CHKERRQ(ierr);
PetscFunctionReturn(0);
}