/*
BVOrthogonalizeCGS1 - Compute |v'| (estimated), |v| and one step of CGS with
only one global synchronization
*/
PetscErrorCode BVOrthogonalizeCGS1(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *onorm,PetscReal *norm)
{
PetscErrorCode ierr;
PetscInt i;
PetscReal sum,nrm,beta;
Vec w=v;
PetscFunctionBegin;
/* h = W^* v ; alpha = (v, v) */
bv->k = j;
if (onorm || norm) {
if (!v) {
bv->k++;
ierr = BVGetColumn(bv,j,&w);CHKERRQ(ierr);
}
ierr = BVDotVec(bv,w,H);CHKERRQ(ierr);
if (!v) {
ierr = BVRestoreColumn(bv,j,&w);CHKERRQ(ierr);
bv->k--;
beta = PetscSqrtReal(PetscRealPart(H[bv->nc+j]));
} else {
ierr = BVNormVec(bv,w,NORM_2,&beta);CHKERRQ(ierr);
}
} else {
if (!v) { ierr = BVDotColumn(bv,j,H);CHKERRQ(ierr); }
else { ierr = BVDotVec(bv,w,H);CHKERRQ(ierr); }
}
/* q = v - V h */
if (bv->indef) {
for (i=0;i<bv->nc+j;i++) H[i] /= bv->omega[i]; /* apply inverse of signature */
}
if (!v) { ierr = BVMultColumn(bv,-1.0,1.0,j,H);CHKERRQ(ierr); }
else { ierr = BVMultVec(bv,-1.0,1.0,w,H);CHKERRQ(ierr); }
if (bv->indef) {
for (i=0;i<bv->nc+j;i++) H[i] *= bv->omega[i]; /* revert signature */
}
/* compute |v| */
if (onorm) *onorm = beta;
if (bv->indef) {
if (!v) { ierr = BVNormColumn(bv,j,NORM_2,&nrm);CHKERRQ(ierr); }
else { ierr = BVNormVec(bv,w,NORM_2,&nrm);CHKERRQ(ierr); }
if (norm) *norm = nrm;
bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
} else if (norm) {
/* estimate |v'| from |v| */
sum = 0.0;
for (i=0;i<bv->nc+j;i++) sum += PetscRealPart(H[i]*PetscConj(H[i]));
*norm = beta*beta-sum;
if (*norm <= 0.0) {
if (!v) { ierr = BVNormColumn(bv,j,NORM_2,norm);CHKERRQ(ierr); }
else { ierr = BVNormVec(bv,w,NORM_2,norm);CHKERRQ(ierr); }
} else *norm = PetscSqrtReal(*norm);
}
PetscFunctionReturn(0);
}
static PetscErrorCode SVDOneSideTRLanczosMGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n)
{
PetscErrorCode ierr;
PetscReal a,b;
PetscScalar gamma;
PetscInt i,k=nconv+l;
Vec ui,ui1,vi;
PetscFunctionBegin;
ierr = BVGetColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,k,&ui);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,k,&ui);CHKERRQ(ierr);
if (l>0) {
ierr = BVMultColumn(U,-1.0,1.0,k,&gamma);CHKERRQ(ierr);
beta[nconv] = PetscRealPart(gamma);
}
ierr = BVNormColumn(U,k,NORM_2,&a);CHKERRQ(ierr);
ierr = BVScaleColumn(U,k,1.0/a);CHKERRQ(ierr);
alpha[k] = a;
for (i=k+1;i<n;i++) {
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = BVOrthogonalizeColumn(V,i,NULL,&b,NULL);CHKERRQ(ierr);
ierr = BVScaleColumn(V,i,1.0/b);CHKERRQ(ierr);
beta[i-1] = b;
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i,&ui);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = VecAXPY(ui,-b,ui1);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i,&ui);CHKERRQ(ierr);
ierr = BVNormColumn(U,i,NORM_2,&a);CHKERRQ(ierr);
ierr = BVScaleColumn(U,i,1.0/a);CHKERRQ(ierr);
alpha[i] = a;
}
ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = BVOrthogonalizeColumn(V,n,NULL,&b,NULL);CHKERRQ(ierr);
beta[n-1] = b;
PetscFunctionReturn(0);
}
/*
Custom CGS orthogonalization, preprocess after first orthogonalization
*/
static PetscErrorCode SVDOrthogonalizeCGS(BV V,PetscInt i,PetscScalar* h,PetscReal a,BVOrthogRefineType refine,PetscReal eta,PetscReal *norm)
{
PetscErrorCode ierr;
PetscReal sum,onorm;
PetscScalar dot;
PetscInt j;
PetscFunctionBegin;
switch (refine) {
case BV_ORTHOG_REFINE_NEVER:
ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
break;
case BV_ORTHOG_REFINE_ALWAYS:
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
ierr = BVDotColumn(V,i,h);CHKERRQ(ierr);
ierr = BVMultColumn(V,-1.0,1.0,i,h);CHKERRQ(ierr);
ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
break;
case BV_ORTHOG_REFINE_IFNEEDED:
dot = h[i];
onorm = PetscSqrtReal(PetscRealPart(dot)) / a;
sum = 0.0;
for (j=0;j<i;j++) {
sum += PetscRealPart(h[j] * PetscConj(h[j]));
}
*norm = PetscRealPart(dot)/(a*a) - sum;
if (*norm>0.0) *norm = PetscSqrtReal(*norm);
else {
ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
}
if (*norm < eta*onorm) {
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
ierr = BVDotColumn(V,i,h);CHKERRQ(ierr);
ierr = BVMultColumn(V,-1.0,1.0,i,h);CHKERRQ(ierr);
ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
}
break;
}
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 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);
}
static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
{
PetscErrorCode ierr;
PetscReal a,b,eta;
PetscScalar gamma;
PetscInt i,j,k=nconv+l;
Vec ui,ui1,vi;
BVOrthogRefineType refine;
PetscFunctionBegin;
ierr = BVGetColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,k,&ui);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,k,&ui);CHKERRQ(ierr);
if (l>0) {
ierr = BVMultColumn(U,-1.0,1.0,k,&gamma);CHKERRQ(ierr);
beta[nconv] = PetscRealPart(gamma);
}
ierr = BVGetOrthogonalization(V,NULL,&refine,&eta);CHKERRQ(ierr);
for (i=k+1;i<n;i++) {
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = BVNormColumn(U,i-1,NORM_2,&a);CHKERRQ(ierr);
if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
ierr = BVSetActiveColumns(V,0,i+1);CHKERRQ(ierr);
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
} else {
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
ierr = BVDotColumn(V,i,work);CHKERRQ(ierr);
}
ierr = BVScaleColumn(U,i-1,1.0/a);CHKERRQ(ierr);
for (j=0;j<i;j++) work[j] = work[j] / a;
ierr = BVMultColumn(V,-1.0,1.0/a,i,work);CHKERRQ(ierr);
ierr = SVDOrthogonalizeCGS(V,i,work,a,refine,eta,&b);CHKERRQ(ierr);
ierr = BVScaleColumn(V,i,1.0/b);CHKERRQ(ierr);
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i,&ui);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = VecAXPY(ui,-b,ui1);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i,&ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
alpha[i-1] = a;
beta[i-1] = b;
}
ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = BVNormColumn(svd->U,n-1,NORM_2,&a);CHKERRQ(ierr);
if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
ierr = BVSetActiveColumns(V,0,n+1);CHKERRQ(ierr);
ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
} else {
ierr = BVSetActiveColumns(V,0,n);CHKERRQ(ierr);
ierr = BVDotColumn(V,n,work);CHKERRQ(ierr);
}
ierr = BVScaleColumn(U,n-1,1.0/a);CHKERRQ(ierr);
for (j=0;j<n;j++) work[j] = work[j] / a;
ierr = BVMultColumn(V,-1.0,1.0/a,n,work);CHKERRQ(ierr);
ierr = SVDOrthogonalizeCGS(V,n,work,a,refine,eta,&b);CHKERRQ(ierr);
ierr = BVSetActiveColumns(V,nconv,n);CHKERRQ(ierr);
alpha[n-1] = a;
beta[n-1] = b;
PetscFunctionReturn(0);
}
