Date: 2026-05-01T10:02:19+00:00

Actual source code: dsnhepts.c

      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: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: typedef struct {
     15:   PetscScalar *wr,*wi;     /* eigenvalues of B */
     16: } DS_NHEPTS;

     18: static PetscErrorCode DSAllocate_NHEPTS(DS ds,PetscInt ld)
     19: {
     20:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;

     22:   PetscFunctionBegin;
     23:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
     24:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
     25:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
     26:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Z));
     27:   PetscCall(PetscFree(ds->perm));
     28:   PetscCall(PetscMalloc1(ld,&ds->perm));
     29:   PetscCall(PetscMalloc1(ld,&ctx->wr));
     30: #if !defined(PETSC_USE_COMPLEX)
     31:   PetscCall(PetscMalloc1(ld,&ctx->wi));
     32: #endif
     33:   PetscFunctionReturn(PETSC_SUCCESS);
     34: }

     36: static PetscErrorCode DSView_NHEPTS(DS ds,PetscViewer viewer)
     37: {
     38:   PetscViewerFormat format;

     40:   PetscFunctionBegin;
     41:   PetscCall(PetscViewerGetFormat(viewer,&format));
     42:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
     43:   PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
     44:   PetscCall(DSViewMat(ds,viewer,DS_MAT_B));
     45:   if (ds->state>DS_STATE_INTERMEDIATE) {
     46:     PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
     47:     PetscCall(DSViewMat(ds,viewer,DS_MAT_Z));
     48:   }
     49:   if (ds->omat[DS_MAT_X]) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
     50:   if (ds->omat[DS_MAT_Y]) PetscCall(DSViewMat(ds,viewer,DS_MAT_Y));
     51:   PetscFunctionReturn(PETSC_SUCCESS);
     52: }

     54: static PetscErrorCode DSVectors_NHEPTS_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     55: {
     56:   PetscInt          i;
     57:   PetscBLASInt      mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
     58:   PetscScalar       sone=1.0,szero=0.0;
     59:   PetscReal         norm,done=1.0;
     60:   PetscBool         iscomplex = PETSC_FALSE;
     61:   PetscScalar       *X,*Y;
     62:   const PetscScalar *A,*Q;

     64:   PetscFunctionBegin;
     65:   PetscCall(PetscBLASIntCast(ds->n,&n));
     66:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     67:   PetscCall(DSAllocateWork_Private(ds,0,0,ld));
     68:   select = ds->iwork;
     69:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;

     71:   /* compute k-th eigenvector Y of A */
     72:   PetscCall(MatDenseGetArrayRead(ds->omat[left?DS_MAT_B:DS_MAT_A],&A));
     73:   PetscCall(MatDenseGetArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
     74:   Y = X+(*k)*ld;
     75:   select[*k] = (PetscBLASInt)PETSC_TRUE;
     76: #if !defined(PETSC_USE_COMPLEX)
     77:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
     78:   mm = iscomplex? 2: 1;
     79:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
     80:   PetscCall(DSAllocateWork_Private(ds,3*ld,0,0));
     81:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","S",select,&n,(PetscScalar*)A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
     82: #else
     83:   PetscCall(DSAllocateWork_Private(ds,2*ld,ld,0));
     84:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","S",select,&n,(PetscScalar*)A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
     85: #endif
     86:   SlepcCheckLapackInfo("trevc",info);
     87:   PetscCheck(mout==mm,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
     88:   PetscCall(MatDenseRestoreArrayRead(ds->omat[left?DS_MAT_B:DS_MAT_A],&A));

     90:   /* accumulate and normalize eigenvectors */
     91:   if (ds->state>=DS_STATE_CONDENSED) {
     92:     PetscCall(MatDenseGetArrayRead(ds->omat[left?DS_MAT_Z:DS_MAT_Q],&Q));
     93:     PetscCall(PetscArraycpy(ds->work,Y,mout*ld));
     94:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work,&inc,&szero,Y,&inc));
     95: #if !defined(PETSC_USE_COMPLEX)
     96:     if (iscomplex) PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work+ld,&inc,&szero,Y+ld,&inc));
     97: #endif
     98:     PetscCall(MatDenseRestoreArrayRead(ds->omat[left?DS_MAT_Z:DS_MAT_Q],&Q));
     99:     cols = 1;
    100:     norm = BLASnrm2_(&n,Y,&inc);
    101: #if !defined(PETSC_USE_COMPLEX)
    102:     if (iscomplex) {
    103:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Y+ld,&inc));
    104:       cols = 2;
    105:     }
    106: #endif
    107:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Y,&ld,&info));
    108:     SlepcCheckLapackInfo("lascl",info);
    109:   }

    111:   /* set output arguments */
    112:   if (iscomplex) (*k)++;
    113:   if (rnorm) {
    114:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
    115:     else *rnorm = PetscAbsScalar(Y[n-1]);
    116:   }
    117:   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
    118:   PetscFunctionReturn(PETSC_SUCCESS);
    119: }

    121: static PetscErrorCode DSVectors_NHEPTS_Eigen_All(DS ds,PetscBool left)
    122: {
    123:   PetscInt          i;
    124:   PetscBLASInt      n,ld,mout,info,inc=1,cols,zero=0;
    125:   PetscBool         iscomplex;
    126:   PetscScalar       *X;
    127:   const PetscScalar *A;
    128:   PetscReal         norm,done=1.0;
    129:   const char        *back;

    131:   PetscFunctionBegin;
    132:   PetscCall(PetscBLASIntCast(ds->n,&n));
    133:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    134:   PetscCall(MatDenseGetArrayRead(ds->omat[left?DS_MAT_B:DS_MAT_A],&A));
    135:   PetscCall(MatDenseGetArrayWrite(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
    136:   if (ds->state>=DS_STATE_CONDENSED) {
    137:     /* DSSolve() has been called, backtransform with matrix Q */
    138:     back = "B";
    139:     PetscCall(MatCopy(ds->omat[left?DS_MAT_Z:DS_MAT_Q],ds->omat[left?DS_MAT_Y:DS_MAT_X],SAME_NONZERO_PATTERN));
    140:   } else back = "A";
    141: #if !defined(PETSC_USE_COMPLEX)
    142:   PetscCall(DSAllocateWork_Private(ds,3*ld,0,0));
    143:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R",back,NULL,&n,(PetscScalar*)A,&ld,X,&ld,X,&ld,&n,&mout,ds->work,&info));
    144: #else
    145:   PetscCall(DSAllocateWork_Private(ds,2*ld,ld,0));
    146:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R",back,NULL,&n,(PetscScalar*)A,&ld,X,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
    147: #endif
    148:   SlepcCheckLapackInfo("trevc",info);

    150:   /* normalize eigenvectors */
    151:   for (i=0;i<n;i++) {
    152:     iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
    153:     cols = 1;
    154:     norm = BLASnrm2_(&n,X+i*ld,&inc);
    155: #if !defined(PETSC_USE_COMPLEX)
    156:     if (iscomplex) {
    157:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,X+(i+1)*ld,&inc));
    158:       cols = 2;
    159:     }
    160: #endif
    161:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,X+i*ld,&ld,&info));
    162:     SlepcCheckLapackInfo("lascl",info);
    163:     if (iscomplex) i++;
    164:   }
    165:   PetscCall(MatDenseRestoreArrayRead(ds->omat[left?DS_MAT_B:DS_MAT_A],&A));
    166:   PetscCall(MatDenseRestoreArrayWrite(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
    167:   PetscFunctionReturn(PETSC_SUCCESS);
    168: }

    170: static PetscErrorCode DSVectors_NHEPTS(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    171: {
    172:   PetscFunctionBegin;
    173:   switch (mat) {
    174:     case DS_MAT_X:
    175:       PetscCheck(!ds->refined,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    176:       if (j) PetscCall(DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_FALSE));
    177:       else PetscCall(DSVectors_NHEPTS_Eigen_All(ds,PETSC_FALSE));
    178:       break;
    179:     case DS_MAT_Y:
    180:       PetscCheck(!ds->refined,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    181:       if (j) PetscCall(DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_TRUE));
    182:       else PetscCall(DSVectors_NHEPTS_Eigen_All(ds,PETSC_TRUE));
    183:       break;
    184:     case DS_MAT_U:
    185:     case DS_MAT_V:
    186:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    187:     default:
    188:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    189:   }
    190:   PetscFunctionReturn(PETSC_SUCCESS);
    191: }

    193: static PetscErrorCode DSSort_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    194: {
    195:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;
    196:   PetscInt       i,j,cont,id=0,*p,*idx,*idx2;
    197:   PetscReal      s,t;
    198: #if defined(PETSC_USE_COMPLEX)
    199:   Mat            A,U;
    200: #endif

    202:   PetscFunctionBegin;
    203:   PetscCheck(!rr || wr==rr,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    204:   PetscCall(PetscMalloc3(ds->ld,&idx,ds->ld,&idx2,ds->ld,&p));
    205:   PetscCall(DSSort_NHEP_Total(ds,DS_MAT_A,DS_MAT_Q,wr,wi));
    206: #if defined(PETSC_USE_COMPLEX)
    207:   PetscCall(DSGetMat(ds,DS_MAT_B,&A));
    208:   PetscCall(MatConjugate(A));
    209:   PetscCall(DSRestoreMat(ds,DS_MAT_B,&A));
    210:   PetscCall(DSGetMat(ds,DS_MAT_Z,&U));
    211:   PetscCall(MatConjugate(U));
    212:   PetscCall(DSRestoreMat(ds,DS_MAT_Z,&U));
    213:   for (i=0;i<ds->n;i++) ctx->wr[i] = PetscConj(ctx->wr[i]);
    214: #endif
    215:   PetscCall(DSSort_NHEP_Total(ds,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi));
    216:   /* check correct eigenvalue correspondence */
    217:   cont = 0;
    218:   for (i=0;i<ds->n;i++) {
    219:     if (SlepcAbsEigenvalue(ctx->wr[i]-wr[i],ctx->wi[i]-wi[i])>PETSC_SQRT_MACHINE_EPSILON) {idx2[cont] = i; idx[cont++] = i;}
    220:     p[i] = -1;
    221:   }
    222:   if (cont) {
    223:     for (i=0;i<cont;i++) {
    224:       t = PETSC_MAX_REAL;
    225:       for (j=0;j<cont;j++) if (idx2[j]!=-1 && (s=SlepcAbsEigenvalue(ctx->wr[idx[j]]-wr[idx[i]],ctx->wi[idx[j]]-wi[idx[i]]))<t) { id = j; t = s; }
    226:       p[idx[i]] = idx[id];
    227:       idx2[id] = -1;
    228:     }
    229:     for (i=0;i<ds->n;i++) if (p[i]==-1) p[i] = i;
    230:     PetscCall(DSSortWithPermutation_NHEP_Private(ds,p,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi));
    231:   }
    232: #if defined(PETSC_USE_COMPLEX)
    233:   PetscCall(DSGetMat(ds,DS_MAT_B,&A));
    234:   PetscCall(MatConjugate(A));
    235:   PetscCall(DSRestoreMat(ds,DS_MAT_B,&A));
    236:   PetscCall(DSGetMat(ds,DS_MAT_Z,&U));
    237:   PetscCall(MatConjugate(U));
    238:   PetscCall(DSRestoreMat(ds,DS_MAT_Z,&U));
    239: #endif
    240:   PetscCall(PetscFree3(idx,idx2,p));
    241:   PetscFunctionReturn(PETSC_SUCCESS);
    242: }

    244: static PetscErrorCode DSUpdateExtraRow_NHEPTS(DS ds)
    245: {
    246:   PetscInt          i;
    247:   PetscBLASInt      n,ld,incx=1;
    248:   PetscScalar       *A,*x,*y,one=1.0,zero=0.0;
    249:   const PetscScalar *Q;

    251:   PetscFunctionBegin;
    252:   PetscCall(PetscBLASIntCast(ds->n,&n));
    253:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    254:   PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
    255:   x = ds->work;
    256:   y = ds->work+ld;
    257:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    258:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
    259:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    260:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    261:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    262:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    263:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
    264:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&A));
    265:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Z],&Q));
    266:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    267:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    268:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    269:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&A));
    270:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Z],&Q));
    271:   ds->k = n;
    272:   PetscFunctionReturn(PETSC_SUCCESS);
    273: }

    275: static PetscErrorCode DSSolve_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi)
    276: {
    277:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;

    279:   PetscFunctionBegin;
    280: #if !defined(PETSC_USE_COMPLEX)
    281:   PetscAssertPointer(wi,3);
    282: #endif
    283:   PetscCall(DSSolve_NHEP_Private(ds,DS_MAT_A,DS_MAT_Q,wr,wi));
    284:   PetscCall(DSSolve_NHEP_Private(ds,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi));
    285:   PetscFunctionReturn(PETSC_SUCCESS);
    286: }

    288: #if !defined(PETSC_HAVE_MPIUNI)
    289: static PetscErrorCode DSSynchronize_NHEPTS(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    290: {
    291:   PetscInt       ld=ds->ld,l=ds->l,k;
    292:   PetscMPIInt    n,rank,off=0,size,ldn;
    293:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;
    294:   PetscScalar    *A,*B,*Q,*Z;

    296:   PetscFunctionBegin;
    297:   k = 2*(ds->n-l)*ld;
    298:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
    299:   if (eigr) k += ds->n-l;
    300:   if (eigi) k += ds->n-l;
    301:   if (ctx->wr) k += ds->n-l;
    302:   if (ctx->wi) k += ds->n-l;
    303:   PetscCall(DSAllocateWork_Private(ds,k,0,0));
    304:   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
    305:   PetscCall(PetscMPIIntCast(ds->n-l,&n));
    306:   PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
    307:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    308:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
    309:   if (ds->state>DS_STATE_RAW) {
    310:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    311:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
    312:   }
    313:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
    314:   if (!rank) {
    315:     PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    316:     PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    317:     if (ds->state>DS_STATE_RAW) {
    318:       PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    319:       PetscCallMPI(MPI_Pack(Z+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    320:     }
    321:     if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    322: #if !defined(PETSC_USE_COMPLEX)
    323:     if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    324: #endif
    325:     if (ctx->wr) PetscCallMPI(MPI_Pack(ctx->wr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    326:     if (ctx->wi) PetscCallMPI(MPI_Pack(ctx->wi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    327:   }
    328:   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
    329:   if (rank) {
    330:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    331:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    332:     if (ds->state>DS_STATE_RAW) {
    333:       PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    334:       PetscCallMPI(MPI_Unpack(ds->work,size,&off,Z+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    335:     }
    336:     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    337: #if !defined(PETSC_USE_COMPLEX)
    338:     if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    339: #endif
    340:     if (ctx->wr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,ctx->wr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    341:     if (ctx->wi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,ctx->wi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    342:   }
    343:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    344:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
    345:   if (ds->state>DS_STATE_RAW) {
    346:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    347:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
    348:   }
    349:   PetscFunctionReturn(PETSC_SUCCESS);
    350: }
    351: #endif

    353: static PetscErrorCode DSGetTruncateSize_NHEPTS(DS ds,PetscInt l,PetscInt n,PetscInt *k)
    354: {
    355: #if !defined(PETSC_USE_COMPLEX)
    356:   const PetscScalar *A,*B;
    357: #endif

    359:   PetscFunctionBegin;
    360: #if !defined(PETSC_USE_COMPLEX)
    361:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
    362:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
    363:   if (A[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0 || B[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0) {
    364:     if (l+(*k)<n-1) (*k)++;
    365:     else (*k)--;
    366:   }
    367:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
    368:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
    369: #endif
    370:   PetscFunctionReturn(PETSC_SUCCESS);
    371: }

    373: static PetscErrorCode DSTruncate_NHEPTS(DS ds,PetscInt n,PetscBool trim)
    374: {
    375:   PetscInt    i,ld=ds->ld,l=ds->l;
    376:   PetscScalar *A,*B;

    378:   PetscFunctionBegin;
    379:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    380:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
    381: #if defined(PETSC_USE_DEBUG)
    382:   /* make sure diagonal 2x2 block is not broken */
    383:   PetscCheck(ds->state<DS_STATE_CONDENSED || n==0 || n==ds->n || A[n+(n-1)*ld]==0.0 || B[n+(n-1)*ld]==0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
    384: #endif
    385:   if (trim) {
    386:     if (ds->extrarow) {   /* clean extra row */
    387:       for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
    388:     }
    389:     ds->l = 0;
    390:     ds->k = 0;
    391:     ds->n = n;
    392:     ds->t = ds->n;   /* truncated length equal to the new dimension */
    393:   } else {
    394:     if (ds->extrarow && ds->k==ds->n) {
    395:       /* copy entries of extra row to the new position, then clean last row */
    396:       for (i=l;i<n;i++) { A[n+i*ld] = A[ds->n+i*ld]; B[n+i*ld] = B[ds->n+i*ld]; }
    397:       for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
    398:     }
    399:     ds->k = (ds->extrarow)? n: 0;
    400:     ds->t = ds->n;   /* truncated length equal to previous dimension */
    401:     ds->n = n;
    402:   }
    403:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    404:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
    405:   PetscFunctionReturn(PETSC_SUCCESS);
    406: }

    408: static PetscErrorCode DSDestroy_NHEPTS(DS ds)
    409: {
    410:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;

    412:   PetscFunctionBegin;
    413:   PetscCall(PetscFree(ctx->wr));
    414:   PetscCall(PetscFree(ctx->wi));
    415:   PetscCall(PetscFree(ds->data));
    416:   PetscFunctionReturn(PETSC_SUCCESS);
    417: }

    419: static PetscErrorCode DSMatGetSize_NHEPTS(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
    420: {
    421:   PetscFunctionBegin;
    422:   *rows = ((t==DS_MAT_A || t==DS_MAT_B) && ds->extrarow)? ds->n+1: ds->n;
    423:   *cols = ds->n;
    424:   PetscFunctionReturn(PETSC_SUCCESS);
    425: }

    427: /*MC
    428:    DSNHEPTS - Dense Non-Hermitian Eigenvalue Problem (special variant intended
    429:    for two-sided Krylov solvers).

    431:    Notes:
    432:    Two related problems are solved, $AX = X\Lambda$ and $BY = Y\Lambda^*$, where $A$ and
    433:    $B$ are supposed to come from the Arnoldi factorizations of a certain matrix and its
    434:    (conjugate) transpose, respectively. Hence, in exact arithmetic the columns of $Y$
    435:    are equal to the left eigenvectors of $A$. $\Lambda$ is a diagonal matrix whose diagonal
    436:    elements are the arguments of `DSSolve()`. After solve, $A$ is overwritten with the
    437:    upper quasi-triangular matrix $T$ of the (real) Schur form, $AQ = QT$, and similarly
    438:    another (real) Schur relation is computed, $BZ = ZS$, overwriting $B$.

    440:    In the intermediate state $A$ and $B$ are reduced to upper Hessenberg form.

    442:    When left eigenvectors `DS_MAT_Y` are requested, right eigenvectors of $B$ are returned,
    443:    while `DS_MAT_X` contains right eigenvectors of $A$.

    445:    Used DS matrices:
    446: +  `DS_MAT_A` - first problem matrix obtained from Arnoldi
    447: .  `DS_MAT_B` - second problem matrix obtained from Arnoldi on the transpose
    448: .  `DS_MAT_Q` - orthogonal/unitary transformation that reduces $A$ to Hessenberg form
    449:    (intermediate step) or matrix of orthogonal Schur vectors of $A$
    450: -  `DS_MAT_Z` - orthogonal/unitary transformation that reduces $B$ to Hessenberg form
    451:    (intermediate step) or matrix of orthogonal Schur vectors of $B$

    453:    Implemented methods:
    454: .  0 - Implicit QR (`_hseqr`)

    456:    Level: beginner

    458: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`
    459: M*/
    460: SLEPC_EXTERN PetscErrorCode DSCreate_NHEPTS(DS ds)
    461: {
    462:   DS_NHEPTS      *ctx;

    464:   PetscFunctionBegin;
    465:   PetscCall(PetscNew(&ctx));
    466:   ds->data = (void*)ctx;

    468:   ds->ops->allocate        = DSAllocate_NHEPTS;
    469:   ds->ops->view            = DSView_NHEPTS;
    470:   ds->ops->vectors         = DSVectors_NHEPTS;
    471:   ds->ops->solve[0]        = DSSolve_NHEPTS;
    472:   ds->ops->sort            = DSSort_NHEPTS;
    473: #if !defined(PETSC_HAVE_MPIUNI)
    474:   ds->ops->synchronize     = DSSynchronize_NHEPTS;
    475: #endif
    476:   ds->ops->gettruncatesize = DSGetTruncateSize_NHEPTS;
    477:   ds->ops->truncate        = DSTruncate_NHEPTS;
    478:   ds->ops->update          = DSUpdateExtraRow_NHEPTS;
    479:   ds->ops->destroy         = DSDestroy_NHEPTS;
    480:   ds->ops->matgetsize      = DSMatGetSize_NHEPTS;
    481:   PetscFunctionReturn(PETSC_SUCCESS);
    482: }