Date: 2022-10-01T06:39:45+00:00

Actual source code: ks-twosided.c
slepc-3.18.0 2022-10-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    SLEPc eigensolver: "krylovschur"

     13:    Method: Two-sided Arnoldi with Krylov-Schur restart (for left eigenvectors)

     15:    References:

     17:        [1] I.N. Zwaan and M.E. Hochstenbach, "Krylov-Schur-type restarts
     18:            for the two-sided Arnoldi method", SIAM J. Matrix Anal. Appl.
     19:            38(2):297-321, 2017.

     21: */

     23: #include <slepc/private/epsimpl.h>
     24: #include "krylovschur.h"
     25: #include <slepcblaslapack.h>

     27: static PetscErrorCode EPSTwoSidedRQUpdate1(EPS eps,Mat M,PetscInt nv,PetscReal beta,PetscReal betat)
     28: {
     29:   PetscScalar       *T,*S,*A,*w;
     30:   const PetscScalar *pM;
     31:   Vec               u;
     32:   PetscInt          ld,ncv=eps->ncv,i,l,nnv;
     33:   PetscBLASInt      info,n_,ncv_,*p,one=1;

     35:   DSGetLeadingDimension(eps->ds,&ld);
     36:   PetscMalloc3(nv,&p,ncv*ncv,&A,ncv,&w);
     37:   BVGetActiveColumns(eps->V,&l,&nnv);
     38:   BVSetActiveColumns(eps->V,0,nv);
     39:   BVSetActiveColumns(eps->W,0,nv);
     40:   BVGetColumn(eps->V,nv,&u);
     41:   BVDotVec(eps->W,u,w);
     42:   BVRestoreColumn(eps->V,nv,&u);
     43:   MatDenseGetArrayRead(M,&pM);
     44:   PetscArraycpy(A,pM,ncv*ncv);
     45:   MatDenseRestoreArrayRead(M,&pM);
     46:   PetscBLASIntCast(nv,&n_);
     47:   PetscBLASIntCast(ncv,&ncv_);
     48:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     49:   PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n_,&n_,A,&ncv_,p,&info));
     50:   SlepcCheckLapackInfo("getrf",info);
     51:   PetscLogFlops(2.0*n_*n_*n_/3.0);
     52:   PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
     53:   SlepcCheckLapackInfo("getrs",info);
     54:   PetscLogFlops(2.0*n_*n_-n_);
     55:   BVMultColumn(eps->V,-1.0,1.0,nv,w);
     56:   DSGetArray(eps->ds,DS_MAT_A,&S);
     57:   for (i=0;i<nv;i++) S[(nv-1)*ld+i] += beta*w[i];
     58:   DSRestoreArray(eps->ds,DS_MAT_A,&S);
     59:   BVGetColumn(eps->W,nv,&u);
     60:   BVDotVec(eps->V,u,w);
     61:   BVRestoreColumn(eps->W,nv,&u);
     62:   PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
     63:   PetscFPTrapPop();
     64:   BVMultColumn(eps->W,-1.0,1.0,nv,w);
     65:   DSGetArray(eps->ds,DS_MAT_B,&T);
     66:   for (i=0;i<nv;i++) T[(nv-1)*ld+i] += betat*w[i];
     67:   DSRestoreArray(eps->ds,DS_MAT_B,&T);
     68:   PetscFree3(p,A,w);
     69:   BVSetActiveColumns(eps->V,l,nnv);
     70:   BVSetActiveColumns(eps->W,l,nnv);
     71:   return 0;
     72: }

     74: static PetscErrorCode EPSTwoSidedRQUpdate2(EPS eps,Mat M,PetscInt k)
     75: {
     76:   PetscScalar    *Q,*pM,*w,zero=0.0,sone=1.0,*c,*A;
     77:   PetscBLASInt   n_,ncv_,ld_;
     78:   PetscReal      norm;
     79:   PetscInt       l,nv,ncv=eps->ncv,ld,i,j;

     81:   DSGetLeadingDimension(eps->ds,&ld);
     82:   BVGetActiveColumns(eps->V,&l,&nv);
     83:   BVSetActiveColumns(eps->V,0,nv);
     84:   BVSetActiveColumns(eps->W,0,nv);
     85:   PetscMalloc2(ncv*ncv,&w,ncv,&c);
     86:   /* u = u - V*V'*u */
     87:   BVOrthogonalizeColumn(eps->V,k,c,&norm,NULL);
     88:   BVScaleColumn(eps->V,k,1.0/norm);
     89:   DSGetArray(eps->ds,DS_MAT_A,&A);
     90:   /* H = H + V'*u*b' */
     91:   for (j=l;j<k;j++) {
     92:     for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
     93:     A[k+j*ld] *= norm;
     94:   }
     95:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
     96:   BVOrthogonalizeColumn(eps->W,k,c,&norm,NULL);
     97:   BVScaleColumn(eps->W,k,1.0/norm);
     98:   DSGetArray(eps->ds,DS_MAT_B,&A);
     99:   /* H = H + V'*u*b' */
    100:   for (j=l;j<k;j++) {
    101:     for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
    102:     A[k+j*ld] *= norm;
    103:   }
    104:   DSRestoreArray(eps->ds,DS_MAT_B,&A);

    106:   /* M = Q'*M*Q */
    107:   MatDenseGetArray(M,&pM);
    108:   PetscBLASIntCast(ncv,&ncv_);
    109:   PetscBLASIntCast(nv,&n_);
    110:   PetscBLASIntCast(ld,&ld_);
    111:   DSGetArray(eps->ds,DS_MAT_Q,&Q);
    112:   PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,pM,&ncv_,Q,&ld_,&zero,w,&ncv_));
    113:   DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    114:   DSGetArray(eps->ds,DS_MAT_Z,&Q);
    115:   PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,Q,&ld_,w,&ncv_,&zero,pM,&ncv_));
    116:   DSRestoreArray(eps->ds,DS_MAT_Z,&Q);
    117:   MatDenseRestoreArray(M,&pM);
    118:   PetscFree2(w,c);
    119:   BVSetActiveColumns(eps->V,l,nv);
    120:   BVSetActiveColumns(eps->W,l,nv);
    121:   return 0;
    122: }

    124: PetscErrorCode EPSSolve_KrylovSchur_TwoSided(EPS eps)
    125: {
    126:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    127:   Mat             M,U,Op,OpHT,S,T;
    128:   PetscReal       norm,norm2,beta,betat;
    129:   PetscInt        ld,l,nv,nvt,k,nconv,dsn,dsk;
    130:   PetscBool       breakdownt,breakdown,breakdownl;

    132:   DSGetLeadingDimension(eps->ds,&ld);
    133:   EPSGetStartVector(eps,0,NULL);
    134:   EPSGetLeftStartVector(eps,0,NULL);
    135:   l = 0;
    136:   MatCreateSeqDense(PETSC_COMM_SELF,eps->ncv,eps->ncv,NULL,&M);

    138:   STGetOperator(eps->st,&Op);
    139:   MatCreateHermitianTranspose(Op,&OpHT);

    141:   /* Restart loop */
    142:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    143:     eps->its++;

    145:     /* Compute an nv-step Arnoldi factorization for Op */
    146:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
    147:     DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l);
    148:     DSGetMat(eps->ds,DS_MAT_A,&S);
    149:     BVMatArnoldi(eps->V,Op,S,eps->nconv+l,&nv,&beta,&breakdown);
    150:     DSRestoreMat(eps->ds,DS_MAT_A,&S);

    152:     /* Compute an nv-step Arnoldi factorization for Op' */
    153:     nvt = nv;
    154:     DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l);
    155:     DSGetMat(eps->ds,DS_MAT_B,&T);
    156:     BVMatArnoldi(eps->W,OpHT,T,eps->nconv+l,&nvt,&betat,&breakdownt);
    157:     DSRestoreMat(eps->ds,DS_MAT_B,&T);

    159:     /* Make sure both factorizations have the same length */
    160:     nv = PetscMin(nv,nvt);
    161:     DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l);
    162:     if (l==0) DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
    163:     else DSSetState(eps->ds,DS_STATE_RAW);
    164:     breakdown = (breakdown || breakdownt)? PETSC_TRUE: PETSC_FALSE;

    166:     /* Update M, modify Rayleigh quotients S and T */
    167:     BVSetActiveColumns(eps->V,eps->nconv+l,nv);
    168:     BVSetActiveColumns(eps->W,eps->nconv+l,nv);
    169:     BVMatProject(eps->V,NULL,eps->W,M);

    171:     EPSTwoSidedRQUpdate1(eps,M,nv,beta,betat);

    173:     /* Solve projected problem */
    174:     DSSolve(eps->ds,eps->eigr,eps->eigi);
    175:     DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
    176:     DSSynchronize(eps->ds,eps->eigr,eps->eigi);
    177:     DSUpdateExtraRow(eps->ds);

    179:     /* Check convergence */
    180:     BVNormColumn(eps->V,nv,NORM_2,&norm);
    181:     BVNormColumn(eps->W,nv,NORM_2,&norm2);
    182:     EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta*norm,betat*norm2,1.0,&k);
    183:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
    184:     nconv = k;

    186:     /* Update l */
    187:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
    188:     else {
    189:       l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    190:       DSGetTruncateSize(eps->ds,k,nv,&l);
    191:     }
    192:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
    193:     if (l) PetscInfo(eps,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);

    195:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    196:     BVSetActiveColumns(eps->V,eps->nconv,nv);
    197:     BVSetActiveColumns(eps->W,eps->nconv,nv);
    198:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    199:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    200:     DSRestoreMat(eps->ds,DS_MAT_Q,&U);
    201:     DSGetMat(eps->ds,DS_MAT_Z,&U);
    202:     BVMultInPlace(eps->W,U,eps->nconv,k+l);
    203:     DSRestoreMat(eps->ds,DS_MAT_Z,&U);
    204:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
    205:       BVCopyColumn(eps->V,nv,k+l);
    206:       BVCopyColumn(eps->W,nv,k+l);
    207:     }

    209:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    210:       if (breakdown || k==nv) {
    211:         /* Start a new Arnoldi factorization */
    212:         PetscInfo(eps,"Breakdown in Krylov-Schur method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta);
    213:         if (k<eps->nev) {
    214:           EPSGetStartVector(eps,k,&breakdown);
    215:           EPSGetLeftStartVector(eps,k,&breakdownl);
    216:           if (breakdown || breakdownl) {
    217:             eps->reason = EPS_DIVERGED_BREAKDOWN;
    218:             PetscInfo(eps,"Unable to generate more start vectors\n");
    219:           }
    220:         }
    221:       } else {
    222:         DSGetDimensions(eps->ds,&dsn,NULL,&dsk,NULL);
    223:         DSSetDimensions(eps->ds,dsn,k,dsk);
    224:         DSTruncate(eps->ds,k+l,PETSC_FALSE);
    225:       }
    226:       EPSTwoSidedRQUpdate2(eps,M,k+l);
    227:     }
    228:     eps->nconv = k;
    229:     EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv);
    230:   }

    232:   STRestoreOperator(eps->st,&Op);
    233:   MatDestroy(&OpHT);

    235:   DSTruncate(eps->ds,eps->nconv,PETSC_TRUE);
    236:   MatDestroy(&M);
    237:   return 0;
    238: }