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 DSSort_NHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi) { #if defined(SLEPC_MISSING_LAPACK_TREXC) PetscFunctionBegin; SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREXC - Lapack routine is unavailable"); #else PetscErrorCode ierr; PetscScalar re; PetscInt i,j,pos,result; PetscBLASInt ifst,ilst,info,n,ld; PetscScalar *T = ds->mat[DS_MAT_A]; PetscScalar *Q = ds->mat[DS_MAT_Q]; #if !defined(PETSC_USE_COMPLEX) PetscScalar *work,im; #endif PetscFunctionBegin; ierr = PetscBLASIntCast(ds->n,&n);CHKERRQ(ierr); ierr = PetscBLASIntCast(ds->ld,&ld);CHKERRQ(ierr); #if !defined(PETSC_USE_COMPLEX) ierr = DSAllocateWork_Private(ds,ld,0,0);CHKERRQ(ierr); work = ds->work; #endif /* selection sort */ for (i=ds->l;i<n-1;i++) { re = wr[i]; #if !defined(PETSC_USE_COMPLEX) im = wi[i]; #endif pos = 0; j=i+1; /* j points to the next eigenvalue */ #if !defined(PETSC_USE_COMPLEX) if (im != 0) j=i+2; #endif /* find minimum eigenvalue */ for (;j<n;j++) { #if !defined(PETSC_USE_COMPLEX) ierr = SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);CHKERRQ(ierr); #else ierr = SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);CHKERRQ(ierr); #endif if (result > 0) { re = wr[j]; #if !defined(PETSC_USE_COMPLEX) im = wi[j]; #endif pos = j; } #if !defined(PETSC_USE_COMPLEX) if (wi[j] != 0) j++; #endif } if (pos) { /* interchange blocks */ ierr = PetscBLASIntCast(pos+1,&ifst);CHKERRQ(ierr); ierr = PetscBLASIntCast(i+1,&ilst);CHKERRQ(ierr); #if !defined(PETSC_USE_COMPLEX) PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info)); #else PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info)); #endif if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREXC %d",info); /* recover original eigenvalues from T matrix */ for (j=i;j<n;j++) { wr[j] = T[j+j*ld]; #if !defined(PETSC_USE_COMPLEX) if (j<n-1 && T[j+1+j*ld] != 0.0) { /* complex conjugate eigenvalue */ wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) * PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld])); wr[j+1] = wr[j]; wi[j+1] = -wi[j]; j++; } else { wi[j] = 0.0; } #endif } } #if !defined(PETSC_USE_COMPLEX) if (wi[i] != 0) i++; #endif } PetscFunctionReturn(0); #endif }