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); }