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);
}
/*
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 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);
}
PetscErrorCode EPSSetUp_LAPACK(EPS eps)
{
PetscErrorCode ierr,ierra,ierrb;
PetscBool isshift,denseok=PETSC_FALSE;
Mat A,B,OP,Adense,Bdense;
PetscScalar shift,*Ap,*Bp;
PetscInt i,ld,nmat;
KSP ksp;
PC pc;
Vec v;
PetscFunctionBegin;
eps->ncv = eps->n;
if (eps->mpd) { ierr = PetscInfo(eps,"Warning: parameter mpd ignored\n");CHKERRQ(ierr); }
if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); }
if (eps->balance!=EPS_BALANCE_NONE) { ierr = PetscInfo(eps,"Warning: balancing ignored\n");CHKERRQ(ierr); }
if (eps->extraction) { ierr = PetscInfo(eps,"Warning: extraction type ignored\n");CHKERRQ(ierr); }
ierr = EPSAllocateSolution(eps,0);CHKERRQ(ierr);
/* attempt to get dense representations of A and B separately */
ierr = PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift);CHKERRQ(ierr);
if (isshift) {
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); }
PetscPushErrorHandler(PetscIgnoreErrorHandler,NULL);
ierra = SlepcMatConvertSeqDense(A,&Adense);CHKERRQ(ierr);
if (eps->isgeneralized) {
ierrb = SlepcMatConvertSeqDense(B,&Bdense);CHKERRQ(ierr);
} else {
ierrb = 0;
}
PetscPopErrorHandler();
denseok = (ierra == 0 && ierrb == 0)? PETSC_TRUE: PETSC_FALSE;
} else Adense = NULL;
/* setup DS */
if (denseok) {
if (eps->isgeneralized) {
if (eps->ishermitian) {
if (eps->ispositive) {
ierr = DSSetType(eps->ds,DSGHEP);CHKERRQ(ierr);
} else {
ierr = DSSetType(eps->ds,DSGNHEP);CHKERRQ(ierr); /* TODO: should be DSGHIEP */
}
} else {
ierr = DSSetType(eps->ds,DSGNHEP);CHKERRQ(ierr);
}
} else {
if (eps->ishermitian) {
ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr);
} else {
ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr);
}
}
} else {
ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr);
}
ierr = DSAllocate(eps->ds,eps->ncv);CHKERRQ(ierr);
ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
ierr = DSSetDimensions(eps->ds,eps->ncv,0,0,0);CHKERRQ(ierr);
if (denseok) {
ierr = STGetShift(eps->st,&shift);CHKERRQ(ierr);
if (shift != 0.0) {
ierr = MatShift(Adense,shift);CHKERRQ(ierr);
}
/* use dummy pc and ksp to avoid problems when B is not positive definite */
ierr = STGetKSP(eps->st,&ksp);CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
} else {
ierr = PetscInfo(eps,"Using slow explicit operator\n");CHKERRQ(ierr);
ierr = STComputeExplicitOperator(eps->st,&OP);CHKERRQ(ierr);
ierr = MatDestroy(&Adense);CHKERRQ(ierr);
ierr = SlepcMatConvertSeqDense(OP,&Adense);CHKERRQ(ierr);
}
/* fill DS matrices */
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,ld,NULL,&v);CHKERRQ(ierr);
ierr = DSGetArray(eps->ds,DS_MAT_A,&Ap);CHKERRQ(ierr);
for (i=0;i<ld;i++) {
ierr = VecPlaceArray(v,Ap+i*ld);CHKERRQ(ierr);
ierr = MatGetColumnVector(Adense,v,i);CHKERRQ(ierr);
ierr = VecResetArray(v);CHKERRQ(ierr);
}
ierr = DSRestoreArray(eps->ds,DS_MAT_A,&Ap);CHKERRQ(ierr);
if (denseok && eps->isgeneralized) {
ierr = DSGetArray(eps->ds,DS_MAT_B,&Bp);CHKERRQ(ierr);
for (i=0;i<ld;i++) {
ierr = VecPlaceArray(v,Bp+i*ld);CHKERRQ(ierr);
ierr = MatGetColumnVector(Bdense,v,i);CHKERRQ(ierr);
ierr = VecResetArray(v);CHKERRQ(ierr);
}
ierr = DSRestoreArray(eps->ds,DS_MAT_B,&Bp);CHKERRQ(ierr);
}
ierr = VecDestroy(&v);CHKERRQ(ierr);
ierr = MatDestroy(&Adense);CHKERRQ(ierr);
if (!denseok) { ierr = MatDestroy(&OP);CHKERRQ(ierr); }
if (denseok && eps->isgeneralized) { ierr = MatDestroy(&Bdense);CHKERRQ(ierr); }
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);
}
PetscErrorCode SVDSolve_TRLanczos(SVD svd)
{
PetscErrorCode ierr;
SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
PetscReal *alpha,*beta,lastbeta,norm;
PetscScalar *Q,*swork=NULL,*w;
PetscInt i,k,l,nv,ld;
Mat U,VT;
PetscBool conv;
BVOrthogType orthog;
PetscFunctionBegin;
/* allocate working space */
ierr = DSGetLeadingDimension(svd->ds,&ld);CHKERRQ(ierr);
ierr = BVGetOrthogonalization(svd->V,&orthog,NULL,NULL);CHKERRQ(ierr);
ierr = PetscMalloc1(ld,&w);CHKERRQ(ierr);
if (lanczos->oneside && orthog == BV_ORTHOG_CGS) {
ierr = PetscMalloc1(svd->ncv+1,&swork);CHKERRQ(ierr);
}
/* normalize start vector */
if (!svd->nini) {
ierr = BVSetRandomColumn(svd->V,0,svd->rand);CHKERRQ(ierr);
ierr = BVNormColumn(svd->V,0,NORM_2,&norm);CHKERRQ(ierr);
ierr = BVScaleColumn(svd->V,0,1.0/norm);CHKERRQ(ierr);
}
l = 0;
while (svd->reason == SVD_CONVERGED_ITERATING) {
svd->its++;
/* inner loop */
nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
ierr = BVSetActiveColumns(svd->V,svd->nconv,nv);CHKERRQ(ierr);
ierr = BVSetActiveColumns(svd->U,svd->nconv,nv);CHKERRQ(ierr);
ierr = DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
beta = alpha + ld;
if (lanczos->oneside) {
if (orthog == BV_ORTHOG_MGS) {
ierr = SVDOneSideTRLanczosMGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv);CHKERRQ(ierr);
} else {
ierr = SVDOneSideTRLanczosCGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork);CHKERRQ(ierr);
}
} else {
ierr = SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv+l,nv);CHKERRQ(ierr);
}
lastbeta = beta[nv-1];
ierr = DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
ierr = BVScaleColumn(svd->V,nv,1.0/lastbeta);CHKERRQ(ierr);
/* compute SVD of general matrix */
ierr = DSSetDimensions(svd->ds,nv,nv,svd->nconv,svd->nconv+l);CHKERRQ(ierr);
if (l==0) {
ierr = DSSetState(svd->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
} else {
ierr = DSSetState(svd->ds,DS_STATE_RAW);CHKERRQ(ierr);
}
ierr = DSSolve(svd->ds,w,NULL);CHKERRQ(ierr);
ierr = DSSort(svd->ds,w,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
/* compute error estimates */
k = 0;
conv = PETSC_TRUE;
ierr = DSGetArray(svd->ds,DS_MAT_U,&Q);CHKERRQ(ierr);
ierr = DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
beta = alpha + ld;
for (i=svd->nconv;i<nv;i++) {
svd->sigma[i] = PetscRealPart(w[i]);
beta[i] = PetscRealPart(Q[nv-1+i*ld])*lastbeta;
svd->errest[i] = PetscAbsScalar(beta[i]);
if (svd->sigma[i] > svd->tol) svd->errest[i] /= svd->sigma[i];
if (conv) {
if (svd->errest[i] < svd->tol) k++;
else conv = PETSC_FALSE;
}
}
ierr = DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
ierr = DSRestoreArray(svd->ds,DS_MAT_U,&Q);CHKERRQ(ierr);
/* check convergence and update l */
if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;
if (svd->reason != SVD_CONVERGED_ITERATING) l = 0;
else l = PetscMax((nv-svd->nconv-k)/2,0);
/* compute converged singular vectors and restart vectors */
ierr = DSGetMat(svd->ds,DS_MAT_VT,&VT);CHKERRQ(ierr);
ierr = BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k+l);CHKERRQ(ierr);
ierr = MatDestroy(&VT);CHKERRQ(ierr);
ierr = DSGetMat(svd->ds,DS_MAT_U,&U);CHKERRQ(ierr);
ierr = BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k+l);CHKERRQ(ierr);
ierr = MatDestroy(&U);CHKERRQ(ierr);
/* copy the last vector to be the next initial vector */
if (svd->reason == SVD_CONVERGED_ITERATING) {
ierr = BVCopyColumn(svd->V,nv,svd->nconv+k+l);CHKERRQ(ierr);
}
svd->nconv += k;
ierr = SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);CHKERRQ(ierr);
}
/* orthonormalize U columns in one side method */
if (lanczos->oneside) {
for (i=0;i<svd->nconv;i++) {
ierr = BVOrthogonalizeColumn(svd->U,i,NULL,&norm,NULL);CHKERRQ(ierr);
ierr = BVScaleColumn(svd->U,i,1.0/norm);CHKERRQ(ierr);
}
}
/* free working space */
ierr = PetscFree(w);CHKERRQ(ierr);
if (swork) { ierr = PetscFree(swork);CHKERRQ(ierr); }
PetscFunctionReturn(0);
}
