Actual source code: dsnhep.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: static PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
     15: {
     16:   PetscFunctionBegin;
     17:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
     18:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
     19:   PetscCall(PetscFree(ds->perm));
     20:   PetscCall(PetscMalloc1(ld,&ds->perm));
     21:   PetscFunctionReturn(PETSC_SUCCESS);
     22: }

     24: static PetscErrorCode DSView_NHEP(DS ds,PetscViewer viewer)
     25: {
     26:   PetscViewerFormat format;

     28:   PetscFunctionBegin;
     29:   PetscCall(PetscViewerGetFormat(viewer,&format));
     30:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
     31:   PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
     32:   if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
     33:   if (ds->omat[DS_MAT_X]) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
     34:   if (ds->omat[DS_MAT_Y]) PetscCall(DSViewMat(ds,viewer,DS_MAT_Y));
     35:   PetscFunctionReturn(PETSC_SUCCESS);
     36: }

     38: static PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     39: {
     40:   PetscInt          i,j;
     41:   PetscBLASInt      info,ld,n,n1,lwork,inc=1;
     42:   PetscScalar       sdummy,done=1.0,zero=0.0;
     43:   PetscReal         *sigma;
     44:   PetscBool         iscomplex = PETSC_FALSE;
     45:   PetscScalar       *X,*W;
     46:   const PetscScalar *A,*Q;

     48:   PetscFunctionBegin;
     49:   PetscCheck(!left,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for left vectors");
     50:   PetscCall(PetscBLASIntCast(ds->n,&n));
     51:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     52:   n1 = n+1;
     53:   PetscCall(DSAllocateWork_Private(ds,5*ld,6*ld,0));
     54:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
     55:   lwork = 5*ld;
     56:   sigma = ds->rwork+5*ld;

     58:   /* build A-w*I in W */
     59:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
     60:   PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&W));
     61:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
     62:   PetscCheck(!iscomplex,PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
     63:   for (j=0;j<n;j++)
     64:     for (i=0;i<=n;i++)
     65:       W[i+j*ld] = A[i+j*ld];
     66:   for (i=0;i<n;i++)
     67:     W[i+i*ld] -= A[(*k)+(*k)*ld];
     68:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));

     70:   /* compute SVD of W */
     71: #if !defined(PETSC_USE_COMPLEX)
     72:   PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info));
     73: #else
     74:   PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info));
     75: #endif
     76:   SlepcCheckLapackInfo("gesvd",info);

     78:   /* the smallest singular value is the new error estimate */
     79:   if (rnorm) *rnorm = sigma[n-1];

     81:   /* update vector with right singular vector associated to smallest singular value,
     82:      accumulating the transformation matrix Q */
     83:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
     84:   PetscCall(MatDenseGetArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
     85:   PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
     86:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
     87:   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
     88:   PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&W));
     89:   PetscFunctionReturn(PETSC_SUCCESS);
     90: }

     92: static PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
     93: {
     94:   PetscInt       i;

     96:   PetscFunctionBegin;
     97:   for (i=0;i<ds->n;i++) PetscCall(DSVectors_NHEP_Refined_Some(ds,&i,NULL,left));
     98:   PetscFunctionReturn(PETSC_SUCCESS);
     99: }

    101: static PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
    102: {
    103:   PetscInt          i;
    104:   PetscBLASInt      mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
    105:   PetscScalar       sone=1.0,szero=0.0;
    106:   PetscReal         norm,done=1.0;
    107:   PetscBool         iscomplex = PETSC_FALSE;
    108:   PetscScalar       *X,*Y;
    109:   const PetscScalar *A,*Q;

    111:   PetscFunctionBegin;
    112:   PetscCall(PetscBLASIntCast(ds->n,&n));
    113:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    114:   PetscCall(DSAllocateWork_Private(ds,0,0,ld));
    115:   select = ds->iwork;
    116:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;

    118:   /* compute k-th eigenvector Y of A */
    119:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
    120:   PetscCall(MatDenseGetArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
    121:   Y = X+(*k)*ld;
    122:   select[*k] = (PetscBLASInt)PETSC_TRUE;
    123: #if !defined(PETSC_USE_COMPLEX)
    124:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
    125:   mm = iscomplex? 2: 1;
    126:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
    127:   PetscCall(DSAllocateWork_Private(ds,3*ld,0,0));
    128:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,(PetscScalar*)A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
    129: #else
    130:   PetscCall(DSAllocateWork_Private(ds,2*ld,ld,0));
    131:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,(PetscScalar*)A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
    132: #endif
    133:   SlepcCheckLapackInfo("trevc",info);
    134:   PetscCheck(mout==mm,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
    135:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));

    137:   /* accumulate and normalize eigenvectors */
    138:   if (ds->state>=DS_STATE_CONDENSED) {
    139:     PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
    140:     PetscCall(PetscArraycpy(ds->work,Y,mout*ld));
    141:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work,&inc,&szero,Y,&inc));
    142: #if !defined(PETSC_USE_COMPLEX)
    143:     if (iscomplex) PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work+ld,&inc,&szero,Y+ld,&inc));
    144: #endif
    145:     PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
    146:     cols = 1;
    147:     norm = BLASnrm2_(&n,Y,&inc);
    148: #if !defined(PETSC_USE_COMPLEX)
    149:     if (iscomplex) {
    150:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Y+ld,&inc));
    151:       cols = 2;
    152:     }
    153: #endif
    154:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Y,&ld,&info));
    155:     SlepcCheckLapackInfo("lascl",info);
    156:   }

    158:   /* set output arguments */
    159:   if (iscomplex) (*k)++;
    160:   if (rnorm) {
    161:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
    162:     else *rnorm = PetscAbsScalar(Y[n-1]);
    163:   }
    164:   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X));
    165:   PetscFunctionReturn(PETSC_SUCCESS);
    166: }

    168: static PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
    169: {
    170:   PetscInt          i;
    171:   PetscBLASInt      n,ld,mout,info,inc=1,cols,zero=0;
    172:   PetscBool         iscomplex;
    173:   PetscScalar       *X,*Y,*Z;
    174:   const PetscScalar *A,*Q;
    175:   PetscReal         norm,done=1.0;
    176:   const char        *side,*back;

    178:   PetscFunctionBegin;
    179:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
    180:   PetscCall(PetscBLASIntCast(ds->n,&n));
    181:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    182:   if (left) {
    183:     X = NULL;
    184:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Y],&Y));
    185:     side = "L";
    186:   } else {
    187:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
    188:     Y = NULL;
    189:     side = "R";
    190:   }
    191:   Z = left? Y: X;
    192:   if (ds->state>=DS_STATE_CONDENSED) {
    193:     /* DSSolve() has been called, backtransform with matrix Q */
    194:     back = "B";
    195:     PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
    196:     PetscCall(PetscArraycpy(Z,Q,ld*ld));
    197:     PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
    198:   } else back = "A";
    199: #if !defined(PETSC_USE_COMPLEX)
    200:   PetscCall(DSAllocateWork_Private(ds,3*ld,0,0));
    201:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,(PetscScalar*)A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
    202: #else
    203:   PetscCall(DSAllocateWork_Private(ds,2*ld,ld,0));
    204:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,(PetscScalar*)A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
    205: #endif
    206:   SlepcCheckLapackInfo("trevc",info);

    208:   /* normalize eigenvectors */
    209:   for (i=0;i<n;i++) {
    210:     iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
    211:     cols = 1;
    212:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
    213: #if !defined(PETSC_USE_COMPLEX)
    214:     if (iscomplex) {
    215:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+(i+1)*ld,&inc));
    216:       cols = 2;
    217:     }
    218: #endif
    219:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z+i*ld,&ld,&info));
    220:     SlepcCheckLapackInfo("lascl",info);
    221:     if (iscomplex) i++;
    222:   }
    223:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
    224:   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&Z));
    225:   PetscFunctionReturn(PETSC_SUCCESS);
    226: }

    228: static PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    229: {
    230:   PetscFunctionBegin;
    231:   switch (mat) {
    232:     case DS_MAT_X:
    233:       if (ds->refined) {
    234:         PetscCheck(ds->extrarow,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Refined vectors require activating the extra row");
    235:         if (j) PetscCall(DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE));
    236:         else PetscCall(DSVectors_NHEP_Refined_All(ds,PETSC_FALSE));
    237:       } else {
    238:         if (j) PetscCall(DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE));
    239:         else PetscCall(DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE));
    240:       }
    241:       break;
    242:     case DS_MAT_Y:
    243:       PetscCheck(!ds->refined,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    244:       if (j) PetscCall(DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE));
    245:       else PetscCall(DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE));
    246:       break;
    247:     case DS_MAT_U:
    248:     case DS_MAT_V:
    249:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    250:     default:
    251:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    252:   }
    253:   PetscFunctionReturn(PETSC_SUCCESS);
    254: }

    256: static PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    257: {
    258:   PetscInt       i;
    259:   PetscBLASInt   info,n,ld,mout,lwork,*selection;
    260:   PetscScalar    *T,*Q,*work;
    261:   PetscReal      dummy;
    262: #if !defined(PETSC_USE_COMPLEX)
    263:   PetscBLASInt   *iwork,liwork;
    264: #endif

    266:   PetscFunctionBegin;
    267:   PetscCheck(k,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Must supply argument k");
    268:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&T));
    269:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    270:   PetscCall(PetscBLASIntCast(ds->n,&n));
    271:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    272: #if !defined(PETSC_USE_COMPLEX)
    273:   lwork = n;
    274:   liwork = 1;
    275:   PetscCall(DSAllocateWork_Private(ds,lwork,0,liwork+n));
    276:   work = ds->work;
    277:   PetscCall(PetscBLASIntCast(ds->lwork,&lwork));
    278:   selection = ds->iwork;
    279:   iwork = ds->iwork + n;
    280:   PetscCall(PetscBLASIntCast(ds->liwork-n,&liwork));
    281: #else
    282:   lwork = 1;
    283:   PetscCall(DSAllocateWork_Private(ds,lwork,0,n));
    284:   work = ds->work;
    285:   selection = ds->iwork;
    286: #endif
    287:   /* Compute the selected eigenvalue to be in the leading position */
    288:   PetscCall(DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE));
    289:   PetscCall(PetscArrayzero(selection,n));
    290:   for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
    291: #if !defined(PETSC_USE_COMPLEX)
    292:   PetscCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,&dummy,&dummy,work,&lwork,iwork,&liwork,&info));
    293: #else
    294:   PetscCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,&dummy,&dummy,work,&lwork,&info));
    295: #endif
    296:   SlepcCheckLapackInfo("trsen",info);
    297:   *k = mout;
    298:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&T));
    299:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    300:   PetscFunctionReturn(PETSC_SUCCESS);
    301: }

    303: static PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    304: {
    305:   PetscFunctionBegin;
    306:   if (!rr || wr == rr) PetscCall(DSSort_NHEP_Total(ds,DS_MAT_A,DS_MAT_Q,wr,wi));
    307:   else PetscCall(DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k));
    308:   PetscFunctionReturn(PETSC_SUCCESS);
    309: }

    311: static PetscErrorCode DSSortWithPermutation_NHEP(DS ds,PetscInt *perm,PetscScalar *wr,PetscScalar *wi)
    312: {
    313:   PetscFunctionBegin;
    314:   PetscCall(DSSortWithPermutation_NHEP_Private(ds,perm,DS_MAT_A,DS_MAT_Q,wr,wi));
    315:   PetscFunctionReturn(PETSC_SUCCESS);
    316: }

    318: static PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
    319: {
    320:   PetscInt          i;
    321:   PetscBLASInt      n,ld,incx=1;
    322:   PetscScalar       *A,*x,*y,one=1.0,zero=0.0;
    323:   const PetscScalar *Q;

    325:   PetscFunctionBegin;
    326:   PetscCall(PetscBLASIntCast(ds->n,&n));
    327:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    328:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    329:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
    330:   PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
    331:   x = ds->work;
    332:   y = ds->work+ld;
    333:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    334:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    335:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    336:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    337:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
    338:   ds->k = n;
    339:   PetscFunctionReturn(PETSC_SUCCESS);
    340: }

    342: static PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
    343: {
    344:   PetscFunctionBegin;
    345: #if !defined(PETSC_USE_COMPLEX)
    346:   PetscAssertPointer(wi,3);
    347: #endif
    348:   PetscCall(DSSolve_NHEP_Private(ds,DS_MAT_A,DS_MAT_Q,wr,wi));
    349:   PetscFunctionReturn(PETSC_SUCCESS);
    350: }

    352: #if !defined(PETSC_HAVE_MPIUNI)
    353: static PetscErrorCode DSSynchronize_NHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    354: {
    355:   PetscInt       ld=ds->ld,l=ds->l,k;
    356:   PetscMPIInt    n,rank,off=0,size,ldn;
    357:   PetscScalar    *A,*Q;

    359:   PetscFunctionBegin;
    360:   k = (ds->n-l)*ld;
    361:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    362:   if (eigr) k += ds->n-l;
    363:   if (eigi) k += ds->n-l;
    364:   PetscCall(DSAllocateWork_Private(ds,k,0,0));
    365:   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
    366:   PetscCall(PetscMPIIntCast(ds->n-l,&n));
    367:   PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
    368:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    369:   if (ds->state>DS_STATE_RAW) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    370:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
    371:   if (!rank) {
    372:     PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    373:     if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    374:     if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    375: #if !defined(PETSC_USE_COMPLEX)
    376:     if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    377: #endif
    378:   }
    379:   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
    380:   if (rank) {
    381:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    382:     if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    383:     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    384: #if !defined(PETSC_USE_COMPLEX)
    385:     if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    386: #endif
    387:   }
    388:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    389:   if (ds->state>DS_STATE_RAW) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    390:   PetscFunctionReturn(PETSC_SUCCESS);
    391: }
    392: #endif

    394: static PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n,PetscBool trim)
    395: {
    396:   PetscInt    i,ld=ds->ld,l=ds->l;
    397:   PetscScalar *A;

    399:   PetscFunctionBegin;
    400:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    401: #if defined(PETSC_USE_DEBUG)
    402:   /* make sure diagonal 2x2 block is not broken */
    403:   PetscCheck(ds->state<DS_STATE_CONDENSED || n==0 || n==ds->n || A[n+(n-1)*ld]==0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
    404: #endif
    405:   if (trim) {
    406:     if (ds->extrarow) {   /* clean extra row */
    407:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    408:     }
    409:     ds->l = 0;
    410:     ds->k = 0;
    411:     ds->n = n;
    412:     ds->t = ds->n;   /* truncated length equal to the new dimension */
    413:   } else {
    414:     if (ds->extrarow && ds->k==ds->n) {
    415:       /* copy entries of extra row to the new position, then clean last row */
    416:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
    417:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    418:     }
    419:     ds->k = (ds->extrarow)? n: 0;
    420:     ds->t = ds->n;   /* truncated length equal to previous dimension */
    421:     ds->n = n;
    422:   }
    423:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    424:   PetscFunctionReturn(PETSC_SUCCESS);
    425: }

    427: static PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
    428: {
    429:   PetscScalar    *work;
    430:   PetscReal      *rwork;
    431:   PetscBLASInt   *ipiv;
    432:   PetscBLASInt   lwork,info,n,ld;
    433:   PetscReal      hn,hin;
    434:   PetscScalar    *A;

    436:   PetscFunctionBegin;
    437:   PetscCall(PetscBLASIntCast(ds->n,&n));
    438:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    439:   lwork = 8*ld;
    440:   PetscCall(DSAllocateWork_Private(ds,lwork,ld,ld));
    441:   work  = ds->work;
    442:   rwork = ds->rwork;
    443:   ipiv  = ds->iwork;

    445:   /* use workspace matrix W to avoid overwriting A */
    446:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
    447:   PetscCall(MatCopy(ds->omat[DS_MAT_A],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN));
    448:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&A));

    450:   /* norm of A */
    451:   if (ds->state<DS_STATE_INTERMEDIATE) hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);
    452:   else hn = LAPACKlanhs_("I",&n,A,&ld,rwork);

    454:   /* norm of inv(A) */
    455:   PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
    456:   SlepcCheckLapackInfo("getrf",info);
    457:   PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
    458:   SlepcCheckLapackInfo("getri",info);
    459:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);
    460:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&A));

    462:   *cond = hn*hin;
    463:   PetscFunctionReturn(PETSC_SUCCESS);
    464: }

    466: static PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gammaout)
    467: {
    468:   PetscInt          i,j;
    469:   PetscBLASInt      *ipiv,info,n,ld,one=1,ncol;
    470:   PetscScalar       *A,*B,*g=gin,*ghat,done=1.0,dmone=-1.0,dzero=0.0;
    471:   const PetscScalar *Q;
    472:   PetscReal         gamma=1.0;

    474:   PetscFunctionBegin;
    475:   PetscCall(PetscBLASIntCast(ds->n,&n));
    476:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    477:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));

    479:   if (!recover) {

    481:     PetscCall(DSAllocateWork_Private(ds,0,0,ld));
    482:     ipiv = ds->iwork;
    483:     if (!g) {
    484:       PetscCall(DSAllocateWork_Private(ds,ld,0,0));
    485:       g = ds->work;
    486:     }
    487:     /* use workspace matrix W to factor A-tau*eye(n) */
    488:     PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
    489:     PetscCall(MatCopy(ds->omat[DS_MAT_A],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN));
    490:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&B));

    492:     /* Vector g initially stores b = beta*e_n^T */
    493:     PetscCall(PetscArrayzero(g,n));
    494:     g[n-1] = beta;

    496:     /* g = (A-tau*eye(n))'\b */
    497:     for (i=0;i<n;i++) B[i+i*ld] -= tau;
    498:     PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
    499:     SlepcCheckLapackInfo("getrf",info);
    500:     PetscCall(PetscLogFlops(2.0*n*n*n/3.0));
    501:     PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
    502:     SlepcCheckLapackInfo("getrs",info);
    503:     PetscCall(PetscLogFlops(2.0*n*n-n));
    504:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&B));

    506:     /* A = A + g*b' */
    507:     for (i=0;i<n;i++) A[i+(n-1)*ld] += g[i]*beta;

    509:   } else { /* recover */

    511:     PetscCall(DSAllocateWork_Private(ds,ld,0,0));
    512:     ghat = ds->work;
    513:     PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));

    515:     /* g^ = -Q(:,idx)'*g */
    516:     PetscCall(PetscBLASIntCast(ds->l+ds->k,&ncol));
    517:     PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&ncol,&dmone,Q,&ld,g,&one,&dzero,ghat,&one));

    519:     /* A = A + g^*b' */
    520:     for (i=0;i<ds->l+ds->k;i++)
    521:       for (j=ds->l;j<ds->l+ds->k;j++)
    522:         A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;

    524:     /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
    525:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
    526:     PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
    527:   }

    529:   /* Compute gamma factor */
    530:   if (gammaout || (recover && ds->extrarow)) gamma = SlepcAbs(1.0,BLASnrm2_(&n,g,&one));
    531:   if (gammaout) *gammaout = gamma;
    532:   if (recover && ds->extrarow) {
    533:     for (j=ds->l;j<ds->l+ds->k;j++) A[ds->n+j*ld] *= gamma;
    534:   }
    535:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    536:   PetscFunctionReturn(PETSC_SUCCESS);
    537: }

    539: static PetscErrorCode DSReallocate_NHEP(DS ds,PetscInt ld)
    540: {
    541:   PetscInt i,*perm=ds->perm;

    543:   PetscFunctionBegin;
    544:   for (i=0;i<DS_NUM_MAT;i++) {
    545:     if (i!=DS_MAT_A && i!=DS_MAT_Q) PetscCall(MatDestroy(&ds->omat[i]));
    546:   }

    548:   PetscCall(DSReallocateMat_Private(ds,DS_MAT_A,ld));
    549:   PetscCall(DSReallocateMat_Private(ds,DS_MAT_Q,ld));

    551:   PetscCall(PetscMalloc1(ld,&ds->perm));
    552:   PetscCall(PetscArraycpy(ds->perm,perm,ds->ld));
    553:   PetscCall(PetscFree(perm));
    554:   PetscFunctionReturn(PETSC_SUCCESS);
    555: }

    557: /*MC
    558:    DSNHEP - Dense Non-Hermitian Eigenvalue Problem.

    560:    Notes:
    561:    The problem is expressed as $AX = X\Lambda$, where $A$ is the input matrix.
    562:    $\Lambda$ is a diagonal matrix whose diagonal elements are the arguments of
    563:    `DSSolve()`. After solve, $A$ is overwritten with the upper quasi-triangular
    564:    matrix $T$ of the (real) Schur form, $AQ = QT$.

    566:    In the intermediate state $A$ is reduced to upper Hessenberg form.

    568:    Computation of left eigenvectors is supported, but two-sided Krylov solvers
    569:    usually rely on the related `DSNHEPTS`.

    571:    Used DS matrices:
    572: +  `DS_MAT_A` - problem matrix
    573: -  `DS_MAT_Q` - orthogonal/unitary transformation that reduces to Hessenberg form
    574:    (intermediate step) or matrix of orthogonal Schur vectors

    576:    Implemented methods:
    577: .  0 - Implicit QR (`_hseqr`)

    579:    Level: beginner

    581: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`
    582: M*/
    583: SLEPC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
    584: {
    585:   PetscFunctionBegin;
    586:   ds->ops->allocate        = DSAllocate_NHEP;
    587:   ds->ops->view            = DSView_NHEP;
    588:   ds->ops->vectors         = DSVectors_NHEP;
    589:   ds->ops->solve[0]        = DSSolve_NHEP;
    590:   ds->ops->sort            = DSSort_NHEP;
    591:   ds->ops->sortperm        = DSSortWithPermutation_NHEP;
    592: #if !defined(PETSC_HAVE_MPIUNI)
    593:   ds->ops->synchronize     = DSSynchronize_NHEP;
    594: #endif
    595:   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
    596:   ds->ops->truncate        = DSTruncate_NHEP;
    597:   ds->ops->update          = DSUpdateExtraRow_NHEP;
    598:   ds->ops->cond            = DSCond_NHEP;
    599:   ds->ops->transharm       = DSTranslateHarmonic_NHEP;
    600:   ds->ops->reallocate      = DSReallocate_NHEP;
    601:   PetscFunctionReturn(PETSC_SUCCESS);
    602: }