Date: 2021-02-01T14:41:43+00:00

Actual source code: dsnhep.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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: PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
     15: {

     19:   DSAllocateMat_Private(ds,DS_MAT_A);
     20:   DSAllocateMat_Private(ds,DS_MAT_Q);
     21:   PetscFree(ds->perm);
     22:   PetscMalloc1(ld,&ds->perm);
     23:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     24:   return(0);
     25: }

     27: PetscErrorCode DSView_NHEP(DS ds,PetscViewer viewer)
     28: {
     29:   PetscErrorCode    ierr;
     30:   PetscViewerFormat format;

     33:   PetscViewerGetFormat(viewer,&format);
     34:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
     35:   DSViewMat(ds,viewer,DS_MAT_A);
     36:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
     37:   if (ds->mat[DS_MAT_X]) { DSViewMat(ds,viewer,DS_MAT_X); }
     38:   if (ds->mat[DS_MAT_Y]) { DSViewMat(ds,viewer,DS_MAT_Y); }
     39:   return(0);
     40: }

     42: static PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     43: {
     45:   PetscInt       i,j;
     46:   PetscBLASInt   info,ld,n,n1,lwork,inc=1;
     47:   PetscScalar    sdummy,done=1.0,zero=0.0;
     48:   PetscReal      *sigma;
     49:   PetscBool      iscomplex = PETSC_FALSE;
     50:   PetscScalar    *A = ds->mat[DS_MAT_A];
     51:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
     52:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
     53:   PetscScalar    *W;

     56:   if (left) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for left vectors");
     57:   PetscBLASIntCast(ds->n,&n);
     58:   PetscBLASIntCast(ds->ld,&ld);
     59:   n1 = n+1;
     60:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
     61:   if (iscomplex) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
     62:   DSAllocateWork_Private(ds,5*ld,6*ld,0);
     63:   DSAllocateMat_Private(ds,DS_MAT_W);
     64:   W = ds->mat[DS_MAT_W];
     65:   lwork = 5*ld;
     66:   sigma = ds->rwork+5*ld;

     68:   /* build A-w*I in W */
     69:   for (j=0;j<n;j++)
     70:     for (i=0;i<=n;i++)
     71:       W[i+j*ld] = A[i+j*ld];
     72:   for (i=0;i<n;i++)
     73:     W[i+i*ld] -= A[(*k)+(*k)*ld];

     75:   /* compute SVD of W */
     76: #if !defined(PETSC_USE_COMPLEX)
     77:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info));
     78: #else
     79:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info));
     80: #endif
     81:   SlepcCheckLapackInfo("gesvd",info);

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

     86:   /* update vector with right singular vector associated to smallest singular value,
     87:      accumulating the transformation matrix Q */
     88:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
     89:   return(0);
     90: }

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

     98:   for (i=0;i<ds->n;i++) {
     99:     DSVectors_NHEP_Refined_Some(ds,&i,NULL,left);
    100:   }
    101:   return(0);
    102: }

    104: static PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
    105: {
    107:   PetscInt       i;
    108:   PetscBLASInt   mm=1,mout,info,ld,n,*select,inc = 1;
    109:   PetscScalar    tmp,done=1.0,zero=0.0;
    110:   PetscReal      norm;
    111:   PetscBool      iscomplex = PETSC_FALSE;
    112:   PetscScalar    *A = ds->mat[DS_MAT_A];
    113:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    114:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
    115:   PetscScalar    *Y;

    118:   PetscBLASIntCast(ds->n,&n);
    119:   PetscBLASIntCast(ds->ld,&ld);
    120:   DSAllocateWork_Private(ds,0,0,ld);
    121:   select = ds->iwork;
    122:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;

    124:   /* compute k-th eigenvector Y of A */
    125:   Y = X+(*k)*ld;
    126:   select[*k] = (PetscBLASInt)PETSC_TRUE;
    127: #if !defined(PETSC_USE_COMPLEX)
    128:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
    129:   mm = iscomplex? 2: 1;
    130:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
    131:   DSAllocateWork_Private(ds,3*ld,0,0);
    132:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
    133: #else
    134:   DSAllocateWork_Private(ds,2*ld,ld,0);
    135:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
    136: #endif
    137:   SlepcCheckLapackInfo("trevc",info);
    138:   if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");

    140:   /* accumulate and normalize eigenvectors */
    141:   if (ds->state>=DS_STATE_CONDENSED) {
    142:     PetscArraycpy(ds->work,Y,mout*ld);
    143:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work,&inc,&zero,Y,&inc));
    144: #if !defined(PETSC_USE_COMPLEX)
    145:     if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work+ld,&inc,&zero,Y+ld,&inc));
    146: #endif
    147:     norm = BLASnrm2_(&n,Y,&inc);
    148: #if !defined(PETSC_USE_COMPLEX)
    149:     if (iscomplex) {
    150:       tmp = BLASnrm2_(&n,Y+ld,&inc);
    151:       norm = SlepcAbsEigenvalue(norm,tmp);
    152:     }
    153: #endif
    154:     tmp = 1.0 / norm;
    155:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y,&inc));
    156: #if !defined(PETSC_USE_COMPLEX)
    157:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y+ld,&inc));
    158: #endif
    159:   }

    161:   /* set output arguments */
    162:   if (iscomplex) (*k)++;
    163:   if (rnorm) {
    164:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
    165:     else *rnorm = PetscAbsScalar(Y[n-1]);
    166:   }
    167:   return(0);
    168: }

    170: static PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
    171: {
    173:   PetscInt       i;
    174:   PetscBLASInt   n,ld,mout,info,inc = 1;
    175:   PetscBool      iscomplex;
    176:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],tmp;
    177:   PetscReal      norm;
    178:   const char     *side,*back;

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

    207:   /* normalize eigenvectors */
    208:   for (i=0;i<n;i++) {
    209:     iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
    210:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
    211: #if !defined(PETSC_USE_COMPLEX)
    212:     if (iscomplex) {
    213:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
    214:       norm = SlepcAbsEigenvalue(norm,tmp);
    215:     }
    216: #endif
    217:     tmp = 1.0 / norm;
    218:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
    219: #if !defined(PETSC_USE_COMPLEX)
    220:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
    221: #endif
    222:     if (iscomplex) i++;
    223:   }
    224:   return(0);
    225: }

    227: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    228: {

    232:   switch (mat) {
    233:     case DS_MAT_X:
    234:       if (ds->refined) {
    235:         if (!ds->extrarow) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Refined vectors require activating the extra row");
    236:         if (j) {
    237:           DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
    238:         } else {
    239:           DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
    240:         }
    241:       } else {
    242:         if (j) {
    243:           DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
    244:         } else {
    245:           DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
    246:         }
    247:       }
    248:       break;
    249:     case DS_MAT_Y:
    250:       if (ds->refined) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    251:       if (j) {
    252:         DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
    253:       } else {
    254:         DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
    255:       }
    256:       break;
    257:     case DS_MAT_U:
    258:     case DS_MAT_VT:
    259:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    260:     default:
    261:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    262:   }
    263:   if (ds->state < DS_STATE_CONDENSED) {
    264:     DSSetState(ds,DS_STATE_CONDENSED);
    265:   }
    266:   return(0);
    267: }

    269: static PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    270: {
    272:   PetscInt       i;
    273:   PetscBLASInt   info,n,ld,mout,lwork,*selection;
    274:   PetscScalar    *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
    275: #if !defined(PETSC_USE_COMPLEX)
    276:   PetscBLASInt   *iwork,liwork;
    277: #endif

    280:   if (!k) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Must supply argument k");
    281:   PetscBLASIntCast(ds->n,&n);
    282:   PetscBLASIntCast(ds->ld,&ld);
    283: #if !defined(PETSC_USE_COMPLEX)
    284:   lwork = n;
    285:   liwork = 1;
    286:   DSAllocateWork_Private(ds,lwork,0,liwork+n);
    287:   work = ds->work;
    288:   lwork = ds->lwork;
    289:   selection = ds->iwork;
    290:   iwork = ds->iwork + n;
    291:   liwork = ds->liwork - n;
    292: #else
    293:   lwork = 1;
    294:   DSAllocateWork_Private(ds,lwork,0,n);
    295:   work = ds->work;
    296:   selection = ds->iwork;
    297: #endif
    298:   /* Compute the selected eigenvalue to be in the leading position */
    299:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
    300:   PetscArrayzero(selection,n);
    301:   for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
    302: #if !defined(PETSC_USE_COMPLEX)
    303:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,NULL,NULL,work,&lwork,iwork,&liwork,&info));
    304: #else
    305:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,NULL,NULL,work,&lwork,&info));
    306: #endif
    307:   SlepcCheckLapackInfo("trsen",info);
    308:   *k = mout;
    309:   return(0);
    310: }

    312: static PetscErrorCode DSSort_NHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
    313: {
    315:   PetscScalar    re;
    316:   PetscInt       i,j,pos,result;
    317:   PetscBLASInt   ifst,ilst,info,n,ld;
    318:   PetscScalar    *T = ds->mat[DS_MAT_A];
    319:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    320: #if !defined(PETSC_USE_COMPLEX)
    321:   PetscScalar    *work,im;
    322: #endif

    325:   PetscBLASIntCast(ds->n,&n);
    326:   PetscBLASIntCast(ds->ld,&ld);
    327: #if !defined(PETSC_USE_COMPLEX)
    328:   DSAllocateWork_Private(ds,ld,0,0);
    329:   work = ds->work;
    330: #endif
    331:   /* selection sort */
    332:   for (i=ds->l;i<n-1;i++) {
    333:     re = wr[i];
    334: #if !defined(PETSC_USE_COMPLEX)
    335:     im = wi[i];
    336: #endif
    337:     pos = 0;
    338:     j=i+1; /* j points to the next eigenvalue */
    339: #if !defined(PETSC_USE_COMPLEX)
    340:     if (im != 0) j=i+2;
    341: #endif
    342:     /* find minimum eigenvalue */
    343:     for (;j<n;j++) {
    344: #if !defined(PETSC_USE_COMPLEX)
    345:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
    346: #else
    347:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
    348: #endif
    349:       if (result > 0) {
    350:         re = wr[j];
    351: #if !defined(PETSC_USE_COMPLEX)
    352:         im = wi[j];
    353: #endif
    354:         pos = j;
    355:       }
    356: #if !defined(PETSC_USE_COMPLEX)
    357:       if (wi[j] != 0) j++;
    358: #endif
    359:     }
    360:     if (pos) {
    361:       /* interchange blocks */
    362:       PetscBLASIntCast(pos+1,&ifst);
    363:       PetscBLASIntCast(i+1,&ilst);
    364: #if !defined(PETSC_USE_COMPLEX)
    365:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info));
    366: #else
    367:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info));
    368: #endif
    369:       SlepcCheckLapackInfo("trexc",info);
    370:       /* recover original eigenvalues from T matrix */
    371:       for (j=i;j<n;j++) {
    372:         wr[j] = T[j+j*ld];
    373: #if !defined(PETSC_USE_COMPLEX)
    374:         if (j<n-1 && T[j+1+j*ld] != 0.0) {
    375:           /* complex conjugate eigenvalue */
    376:           wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) *
    377:                   PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld]));
    378:           wr[j+1] = wr[j];
    379:           wi[j+1] = -wi[j];
    380:           j++;
    381:         } else {
    382:           wi[j] = 0.0;
    383:         }
    384: #endif
    385:       }
    386:     }
    387: #if !defined(PETSC_USE_COMPLEX)
    388:     if (wi[i] != 0) i++;
    389: #endif
    390:   }
    391:   return(0);
    392: }

    394: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    395: {

    399:   if (!rr || wr == rr) {
    400:     DSSort_NHEP_Total(ds,wr,wi);
    401:   } else {
    402:     DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
    403:   }
    404:   return(0);
    405: }

    407: static PetscErrorCode DSSortWithPermutation_NHEP(DS ds,PetscInt *perm,PetscScalar *wr,PetscScalar *wi)
    408: {
    410:   PetscInt       i,j,pos,inc=1;
    411:   PetscBLASInt   ifst,ilst,info,n,ld;
    412:   PetscScalar    *T = ds->mat[DS_MAT_A];
    413:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    414: #if !defined(PETSC_USE_COMPLEX)
    415:   PetscScalar    *work;
    416: #endif

    419:   PetscBLASIntCast(ds->n,&n);
    420:   PetscBLASIntCast(ds->ld,&ld);
    421: #if !defined(PETSC_USE_COMPLEX)
    422:   DSAllocateWork_Private(ds,ld,0,0);
    423:   work = ds->work;
    424: #endif
    425:   for (i=ds->l;i<n-1;i++) {
    426:     pos = perm[i];
    427: #if !defined(PETSC_USE_COMPLEX)
    428:     inc = (pos<n-1 && T[pos+1+pos*ld] != 0.0)? 2: 1;
    429: #endif
    430:     if (pos!=i) {
    431: #if !defined(PETSC_USE_COMPLEX)
    432:       if ((T[pos+(pos-1)*ld] != 0.0 && perm[i+1]!=pos-1) || (T[pos+1+pos*ld] != 0.0 && perm[i+1]!=pos+1))
    433:  SETERRQ1(PETSC_COMM_SELF,1,"Invalid permutation due to a 2x2 block at position %D",pos);
    434: #endif

    436:       /* interchange blocks */
    437:       PetscBLASIntCast(pos+1,&ifst);
    438:       PetscBLASIntCast(i+1,&ilst);
    439: #if !defined(PETSC_USE_COMPLEX)
    440:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info));
    441: #else
    442:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info));
    443: #endif
    444:       SlepcCheckLapackInfo("trexc",info);
    445:       for (j=i+1;j<n;j++) {
    446:         if (perm[j]>=i && perm[j]<pos) perm[j]+=inc;
    447:       }
    448:       perm[i] = i;
    449:       if (inc==2) perm[i+1] = i+1;
    450:     }
    451:     if (inc==2) i++;
    452:   }
    453:   /* recover original eigenvalues from T matrix */
    454:   for (j=ds->l;j<n;j++) {
    455:     wr[j] = T[j+j*ld];
    456: #if !defined(PETSC_USE_COMPLEX)
    457:     if (j<n-1 && T[j+1+j*ld] != 0.0) {
    458:       /* complex conjugate eigenvalue */
    459:       wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) * PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld]));
    460:       wr[j+1] = wr[j];
    461:       wi[j+1] = -wi[j];
    462:       j++;
    463:     } else {
    464:       wi[j] = 0.0;
    465:     }
    466: #endif
    467:   }
    468:   return(0);
    469: }

    471: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
    472: {
    474:   PetscInt       i;
    475:   PetscBLASInt   n,ld,incx=1;
    476:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;

    479:   PetscBLASIntCast(ds->n,&n);
    480:   PetscBLASIntCast(ds->ld,&ld);
    481:   A  = ds->mat[DS_MAT_A];
    482:   Q  = ds->mat[DS_MAT_Q];
    483:   DSAllocateWork_Private(ds,2*ld,0,0);
    484:   x = ds->work;
    485:   y = ds->work+ld;
    486:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    487:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    488:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    489:   ds->k = n;
    490:   return(0);
    491: }

    493: /*
    494:    Reduce a matrix A to upper Hessenberg form Q'*A*Q, where Q is an orthogonal matrix.
    495:    The result overwrites A. Matrix A has the form

    497:          [ S | * ]
    498:      A = [-------]
    499:          [ R | H ]

    501:   where S is an upper (quasi-)triangular matrix of order k, H is an upper Hessenberg
    502:   matrix of order n-k, and R is all zeros except the first row (the arrow).
    503:   The algorithm uses elementary reflectors to annihilate entries in the arrow, and
    504:   then proceeds upwards.
    505:   If ilo>1, then it is assumed that the first ilo-1 entries of the arrow are zero, and
    506:   hence the first ilo-1 rows and columns of Q are set to the identity matrix.

    508:   Required workspace is 2*n.
    509: */
    510: static PetscErrorCode ArrowHessenberg(PetscBLASInt n,PetscBLASInt k,PetscBLASInt ilo,PetscScalar *A,PetscBLASInt lda,PetscScalar *Q,PetscBLASInt ldq,PetscScalar *work)
    511: {
    512:   PetscBLASInt i,j,n0,m,inc=1,incn=-1;
    513:   PetscScalar  t,*v=work,*w=work+n,tau,tauc;

    516:   m = n-ilo+1;
    517:   for (i=k;i>ilo;i--) {
    518:     for (j=0;j<=i-ilo;j++) v[j] = A[i+(i-j-1)*lda];  /* _larfg does not allow negative inc, so use buffer */
    519:     n0 = i-ilo+1;
    520:     PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0,v,v+1,&inc,&tau));
    521:     for (j=1;j<=i-ilo;j++) v[j] = PetscConj(v[j]);
    522:     tauc = PetscConj(tau);
    523:     A[i+(i-1)*lda] = v[0];
    524:     v[0] = 1.0;
    525:     PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&i,&n0,v,&incn,&tauc,A+(ilo-1)*lda,&lda,w));
    526:     for (j=1;j<=i-ilo;j++) A[i+(i-j-1)*lda] = 0.0;
    527:     PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,v,&incn,&tau,A+ilo-1+(ilo-1)*lda,&lda,w));
    528:     PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,v,&incn,&tau,Q+ilo-1+(ilo-1)*ldq,&ldq,w));
    529:   }
    530:   /* trivial in-place transposition of Q */
    531:   for (j=ilo-1;j<k;j++) {
    532:     for (i=j;i<k;i++) {
    533:       t = Q[i+j*ldq];
    534:       if (i!=j) Q[i+j*ldq] = PetscConj(Q[j+i*ldq]);
    535:       Q[j+i*ldq] = PetscConj(t);
    536:     }
    537:   }
    538:   return(0);
    539: }

    541: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
    542: {
    544:   PetscScalar    *work,*tau;
    545:   PetscInt       i,j;
    546:   PetscBLASInt   ilo,lwork,info,n,k,ld;
    547:   PetscScalar    *A = ds->mat[DS_MAT_A];
    548:   PetscScalar    *Q = ds->mat[DS_MAT_Q];

    551: #if !defined(PETSC_USE_COMPLEX)
    553: #endif
    554:   PetscBLASIntCast(ds->n,&n);
    555:   PetscBLASIntCast(ds->ld,&ld);
    556:   PetscBLASIntCast(ds->l+1,&ilo);
    557:   PetscBLASIntCast(ds->k,&k);
    558:   DSAllocateWork_Private(ds,ld+6*ld,0,0);
    559:   tau  = ds->work;
    560:   work = ds->work+ld;
    561:   lwork = 6*ld;

    563:   /* initialize orthogonal matrix */
    564:   PetscArrayzero(Q,ld*ld);
    565:   for (i=0;i<n;i++) Q[i+i*ld] = 1.0;
    566:   if (n==1) { /* quick return */
    567:     wr[0] = A[0];
    568:     wi[0] = 0.0;
    569:     return(0);
    570:   }

    572:   /* reduce to upper Hessenberg form */
    573:   if (ds->state<DS_STATE_INTERMEDIATE) {
    574:     if (PETSC_FALSE && k>0) {
    575:       ArrowHessenberg(n,k,ilo,A,ld,Q,ld,work);
    576:     } else {
    577:       PetscStackCallBLAS("LAPACKgehrd",LAPACKgehrd_(&n,&ilo,&n,A,&ld,tau,work,&lwork,&info));
    578:       SlepcCheckLapackInfo("gehrd",info);
    579:       for (j=0;j<n-1;j++) {
    580:         for (i=j+2;i<n;i++) {
    581:           Q[i+j*ld] = A[i+j*ld];
    582:           A[i+j*ld] = 0.0;
    583:         }
    584:       }
    585:       PetscStackCallBLAS("LAPACKorghr",LAPACKorghr_(&n,&ilo,&n,Q,&ld,tau,work,&lwork,&info));
    586:       SlepcCheckLapackInfo("orghr",info);
    587:     }
    588:   }

    590:   /* compute the (real) Schur form */
    591: #if !defined(PETSC_USE_COMPLEX)
    592:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,wi,Q,&ld,work,&lwork,&info));
    593:   for (j=0;j<ds->l;j++) {
    594:     if (j==n-1 || A[j+1+j*ld] == 0.0) {
    595:       /* real eigenvalue */
    596:       wr[j] = A[j+j*ld];
    597:       wi[j] = 0.0;
    598:     } else {
    599:       /* complex eigenvalue */
    600:       wr[j] = A[j+j*ld];
    601:       wr[j+1] = A[j+j*ld];
    602:       wi[j] = PetscSqrtReal(PetscAbsReal(A[j+1+j*ld])) *
    603:               PetscSqrtReal(PetscAbsReal(A[j+(j+1)*ld]));
    604:       wi[j+1] = -wi[j];
    605:       j++;
    606:     }
    607:   }
    608: #else
    609:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,Q,&ld,work,&lwork,&info));
    610:   if (wi) for (i=ds->l;i<n;i++) wi[i] = 0.0;
    611: #endif
    612:   SlepcCheckLapackInfo("hseqr",info);
    613:   return(0);
    614: }

    616: PetscErrorCode DSSynchronize_NHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    617: {
    619:   PetscInt       ld=ds->ld,l=ds->l,k;
    620:   PetscMPIInt    n,rank,off=0,size,ldn;

    623:   k = (ds->n-l)*ld;
    624:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    625:   if (eigr) k += ds->n-l;
    626:   if (eigi) k += ds->n-l;
    627:   DSAllocateWork_Private(ds,k,0,0);
    628:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
    629:   PetscMPIIntCast(ds->n-l,&n);
    630:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    631:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    632:   if (!rank) {
    633:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    634:     if (ds->state>DS_STATE_RAW) {
    635:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    636:     }
    637:     if (eigr) {
    638:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    639:     }
    640:     if (eigi) {
    641:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    642:     }
    643:   }
    644:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    645:   if (rank) {
    646:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    647:     if (ds->state>DS_STATE_RAW) {
    648:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    649:     }
    650:     if (eigr) {
    651:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    652:     }
    653:     if (eigi) {
    654:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    655:     }
    656:   }
    657:   return(0);
    658: }

    660: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n)
    661: {
    663:   PetscInt       i,newn,ld=ds->ld,l=ds->l;
    664:   PetscScalar    *A;

    667:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
    668:   A = ds->mat[DS_MAT_A];
    669:   /* be careful not to break a diagonal 2x2 block */
    670:   if (A[n+(n-1)*ld]==0.0) newn = n;
    671:   else {
    672:     if (n<ds->n-1) newn = n+1;
    673:     else newn = n-1;
    674:   }
    675:   if (ds->extrarow && ds->k==ds->n) {
    676:     /* copy entries of extra row to the new position, then clean last row */
    677:     for (i=l;i<newn;i++) A[newn+i*ld] = A[ds->n+i*ld];
    678:     for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    679:   }
    680:   ds->k = 0;
    681:   ds->n = newn;
    682:   PetscInfo1(ds,"Decomposition truncated to size n=%D\n",newn);
    683:   return(0);
    684: }

    686: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
    687: {
    689:   PetscScalar    *work;
    690:   PetscReal      *rwork;
    691:   PetscBLASInt   *ipiv;
    692:   PetscBLASInt   lwork,info,n,ld;
    693:   PetscReal      hn,hin;
    694:   PetscScalar    *A;

    697:   PetscBLASIntCast(ds->n,&n);
    698:   PetscBLASIntCast(ds->ld,&ld);
    699:   lwork = 8*ld;
    700:   DSAllocateWork_Private(ds,lwork,ld,ld);
    701:   work  = ds->work;
    702:   rwork = ds->rwork;
    703:   ipiv  = ds->iwork;

    705:   /* use workspace matrix W to avoid overwriting A */
    706:   DSAllocateMat_Private(ds,DS_MAT_W);
    707:   A = ds->mat[DS_MAT_W];
    708:   PetscArraycpy(A,ds->mat[DS_MAT_A],ds->ld*ds->ld);

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

    714:   /* norm of inv(A) */
    715:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
    716:   SlepcCheckLapackInfo("getrf",info);
    717:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
    718:   SlepcCheckLapackInfo("getri",info);
    719:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

    721:   *cond = hn*hin;
    722:   return(0);
    723: }

    725: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gamma)
    726: {
    728:   PetscInt       i,j;
    729:   PetscBLASInt   *ipiv,info,n,ld,one=1,ncol;
    730:   PetscScalar    *A,*B,*Q,*g=gin,*ghat;
    731:   PetscScalar    done=1.0,dmone=-1.0,dzero=0.0;
    732:   PetscReal      gnorm;

    735:   PetscBLASIntCast(ds->n,&n);
    736:   PetscBLASIntCast(ds->ld,&ld);
    737:   A  = ds->mat[DS_MAT_A];

    739:   if (!recover) {

    741:     DSAllocateWork_Private(ds,0,0,ld);
    742:     ipiv = ds->iwork;
    743:     if (!g) {
    744:       DSAllocateWork_Private(ds,ld,0,0);
    745:       g = ds->work;
    746:     }
    747:     /* use workspace matrix W to factor A-tau*eye(n) */
    748:     DSAllocateMat_Private(ds,DS_MAT_W);
    749:     B = ds->mat[DS_MAT_W];
    750:     PetscArraycpy(B,A,ld*ld);

    752:     /* Vector g initialy stores b = beta*e_n^T */
    753:     PetscArrayzero(g,n);
    754:     g[n-1] = beta;

    756:     /* g = (A-tau*eye(n))'\b */
    757:     for (i=0;i<n;i++) B[i+i*ld] -= tau;
    758:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
    759:     SlepcCheckLapackInfo("getrf",info);
    760:     PetscLogFlops(2.0*n*n*n/3.0);
    761:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
    762:     SlepcCheckLapackInfo("getrs",info);
    763:     PetscLogFlops(2.0*n*n-n);

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

    768:   } else { /* recover */

    770:     DSAllocateWork_Private(ds,ld,0,0);
    771:     ghat = ds->work;
    772:     Q    = ds->mat[DS_MAT_Q];

    774:     /* g^ = -Q(:,idx)'*g */
    775:     PetscBLASIntCast(ds->l+ds->k,&ncol);
    776:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&ncol,&dmone,Q,&ld,g,&one,&dzero,ghat,&one));

    778:     /* A = A + g^*b' */
    779:     for (i=0;i<ds->l+ds->k;i++)
    780:       for (j=ds->l;j<ds->l+ds->k;j++)
    781:         A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;

    783:     /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
    784:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
    785:   }

    787:   /* Compute gamma factor */
    788:   if (gamma) {
    789:     gnorm = 0.0;
    790:     for (i=0;i<n;i++) gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
    791:     *gamma = PetscSqrtReal(1.0+gnorm);
    792:   }
    793:   return(0);
    794: }

    796: SLEPC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
    797: {
    799:   ds->ops->allocate      = DSAllocate_NHEP;
    800:   ds->ops->view          = DSView_NHEP;
    801:   ds->ops->vectors       = DSVectors_NHEP;
    802:   ds->ops->solve[0]      = DSSolve_NHEP;
    803:   ds->ops->sort          = DSSort_NHEP;
    804:   ds->ops->sortperm      = DSSortWithPermutation_NHEP;
    805:   ds->ops->synchronize   = DSSynchronize_NHEP;
    806:   ds->ops->truncate      = DSTruncate_NHEP;
    807:   ds->ops->update        = DSUpdateExtraRow_NHEP;
    808:   ds->ops->cond          = DSCond_NHEP;
    809:   ds->ops->transharm     = DSTranslateHarmonic_NHEP;
    810:   return(0);
    811: }