Date: 2015-09-03T15:03:35+00:00

Actual source code: dsnhep.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: #include <slepc/private/dsimpl.h>
     23: #include <slepcblaslapack.h>

     27: PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
     28: {

     32:   DSAllocateMat_Private(ds,DS_MAT_A);
     33:   DSAllocateMat_Private(ds,DS_MAT_Q);
     34:   PetscFree(ds->perm);
     35:   PetscMalloc1(ld,&ds->perm);
     36:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     37:   return(0);
     38: }

     42: PetscErrorCode DSView_NHEP(DS ds,PetscViewer viewer)
     43: {

     47:   DSViewMat(ds,viewer,DS_MAT_A);
     48:   if (ds->state>DS_STATE_INTERMEDIATE) {
     49:     DSViewMat(ds,viewer,DS_MAT_Q);
     50:   }
     51:   if (ds->mat[DS_MAT_X]) {
     52:     DSViewMat(ds,viewer,DS_MAT_X);
     53:   }
     54:   if (ds->mat[DS_MAT_Y]) {
     55:     DSViewMat(ds,viewer,DS_MAT_Y);
     56:   }
     57:   return(0);
     58: }

     62: PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     63: {
     64: #if defined(SLEPC_MISSING_LAPACK_GESVD)
     66:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
     67: #else
     69:   PetscInt       i,j;
     70:   PetscBLASInt   info,ld,n,n1,lwork,inc=1;
     71:   PetscScalar    sdummy,done=1.0,zero=0.0;
     72:   PetscReal      *sigma;
     73:   PetscBool      iscomplex = PETSC_FALSE;
     74:   PetscScalar    *A = ds->mat[DS_MAT_A];
     75:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
     76:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
     77:   PetscScalar    *W;

     80:   if (left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for left vectors");
     81:   PetscBLASIntCast(ds->n,&n);
     82:   PetscBLASIntCast(ds->ld,&ld);
     83:   n1 = n+1;
     84:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
     85:   if (iscomplex) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
     86:   DSAllocateWork_Private(ds,5*ld,6*ld,0);
     87:   DSAllocateMat_Private(ds,DS_MAT_W);
     88:   W = ds->mat[DS_MAT_W];
     89:   lwork = 5*ld;
     90:   sigma = ds->rwork+5*ld;

     92:   /* build A-w*I in W */
     93:   for (j=0;j<n;j++)
     94:     for (i=0;i<=n;i++)
     95:       W[i+j*ld] = A[i+j*ld];
     96:   for (i=0;i<n;i++)
     97:     W[i+i*ld] -= A[(*k)+(*k)*ld];

     99:   /* compute SVD of W */
    100: #if !defined(PETSC_USE_COMPLEX)
    101:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info));
    102: #else
    103:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info));
    104: #endif
    105:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);

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

    110:   /* update vector with right singular vector associated to smallest singular value,
    111:      accumulating the transformation matrix Q */
    112:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
    113:   return(0);
    114: #endif
    115: }

    119: PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
    120: {
    122:   PetscInt       i;

    125:   for (i=0;i<ds->n;i++) {
    126:     DSVectors_NHEP_Refined_Some(ds,&i,NULL,left);
    127:   }
    128:   return(0);
    129: }

    133: PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
    134: {
    135: #if defined(SLEPC_MISSING_LAPACK_TREVC)
    137:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
    138: #else
    140:   PetscInt       i;
    141:   PetscBLASInt   mm=1,mout,info,ld,n,inc = 1;
    142:   PetscScalar    tmp,done=1.0,zero=0.0;
    143:   PetscReal      norm;
    144:   PetscBool      iscomplex = PETSC_FALSE;
    145:   PetscBLASInt   *select;
    146:   PetscScalar    *A = ds->mat[DS_MAT_A];
    147:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    148:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
    149:   PetscScalar    *Y;

    152:   PetscBLASIntCast(ds->n,&n);
    153:   PetscBLASIntCast(ds->ld,&ld);
    154:   DSAllocateWork_Private(ds,0,0,ld);
    155:   select = ds->iwork;
    156:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;

    158:   /* Compute k-th eigenvector Y of A */
    159:   Y = X+(*k)*ld;
    160:   select[*k] = (PetscBLASInt)PETSC_TRUE;
    161: #if !defined(PETSC_USE_COMPLEX)
    162:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
    163:   mm = iscomplex? 2: 1;
    164:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
    165:   DSAllocateWork_Private(ds,3*ld,0,0);
    166:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
    167: #else
    168:   DSAllocateWork_Private(ds,2*ld,ld,0);
    169:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
    170: #endif
    171:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREVC %d",info);
    172:   if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");

    174:   /* accumulate and normalize eigenvectors */
    175:   if (ds->state>=DS_STATE_CONDENSED) {
    176:     PetscMemcpy(ds->work,Y,mout*ld*sizeof(PetscScalar));
    177:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work,&inc,&zero,Y,&inc));
    178: #if !defined(PETSC_USE_COMPLEX)
    179:     if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work+ld,&inc,&zero,Y+ld,&inc));
    180: #endif
    181:     norm = BLASnrm2_(&n,Y,&inc);
    182: #if !defined(PETSC_USE_COMPLEX)
    183:     if (iscomplex) {
    184:       tmp = BLASnrm2_(&n,Y+ld,&inc);
    185:       norm = SlepcAbsEigenvalue(norm,tmp);
    186:     }
    187: #endif
    188:     tmp = 1.0 / norm;
    189:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y,&inc));
    190: #if !defined(PETSC_USE_COMPLEX)
    191:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y+ld,&inc));
    192: #endif
    193:   }

    195:   /* set output arguments */
    196:   if (iscomplex) (*k)++;
    197:   if (rnorm) {
    198:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
    199:     else *rnorm = PetscAbsScalar(Y[n-1]);
    200:   }
    201:   return(0);
    202: #endif
    203: }

    207: PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
    208: {
    209: #if defined(SLEPC_MISSING_LAPACK_TREVC)
    211:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
    212: #else
    214:   PetscInt       i;
    215:   PetscBLASInt   n,ld,mout,info,inc = 1;
    216:   PetscBool      iscomplex = PETSC_FALSE;
    217:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],tmp;
    218:   PetscReal      norm;
    219:   const char     *side,*back;

    222:   PetscBLASIntCast(ds->n,&n);
    223:   PetscBLASIntCast(ds->ld,&ld);
    224:   if (left) {
    225:     X = NULL;
    226:     Y = ds->mat[DS_MAT_Y];
    227:     side = "L";
    228:   } else {
    229:     X = ds->mat[DS_MAT_X];
    230:     Y = NULL;
    231:     side = "R";
    232:   }
    233:   Z = left? Y: X;
    234:   if (ds->state>=DS_STATE_CONDENSED) {
    235:     /* DSSolve() has been called, backtransform with matrix Q */
    236:     back = "B";
    237:     PetscMemcpy(Z,ds->mat[DS_MAT_Q],ld*ld*sizeof(PetscScalar));
    238:   } else back = "A";
    239: #if !defined(PETSC_USE_COMPLEX)
    240:   DSAllocateWork_Private(ds,3*ld,0,0);
    241:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
    242: #else
    243:   DSAllocateWork_Private(ds,2*ld,ld,0);
    244:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
    245: #endif
    246:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTREVC %i",info);

    248:   /* normalize eigenvectors */
    249:   for (i=0;i<n;i++) {
    250:     if (i<n-1 && A[i+1+i*ld]!=0.0) iscomplex = PETSC_TRUE;
    251:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
    252: #if !defined(PETSC_USE_COMPLEX)
    253:     if (iscomplex) {
    254:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
    255:       norm = SlepcAbsEigenvalue(norm,tmp);
    256:     }
    257: #endif
    258:     tmp = 1.0 / norm;
    259:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
    260: #if !defined(PETSC_USE_COMPLEX)
    261:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
    262: #endif
    263:     if (iscomplex) i++;
    264:   }
    265:   return(0);
    266: #endif
    267: }

    271: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    272: {

    276:   switch (mat) {
    277:     case DS_MAT_X:
    278:       if (ds->refined) {
    279:         if (!ds->extrarow) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Refined vectors require activating the extra row");
    280:         if (j) {
    281:           DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
    282:         } else {
    283:           DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
    284:         }
    285:       } else {
    286:         if (j) {
    287:           DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
    288:         } else {
    289:           DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
    290:         }
    291:       }
    292:       break;
    293:     case DS_MAT_Y:
    294:       if (ds->refined) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    295:       if (j) {
    296:         DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
    297:       } else {
    298:         DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
    299:       }
    300:       break;
    301:     case DS_MAT_U:
    302:     case DS_MAT_VT:
    303:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    304:       break;
    305:     default:
    306:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    307:   }
    308:   if (ds->state < DS_STATE_CONDENSED) {
    309:     DSSetState(ds,DS_STATE_CONDENSED);
    310:   }
    311:   return(0);
    312: }

    316: PetscErrorCode DSNormalize_NHEP(DS ds,DSMatType mat,PetscInt col)
    317: {
    319:   PetscInt       i,i0,i1;
    320:   PetscBLASInt   ld,n,one = 1;
    321:   PetscScalar    *A = ds->mat[DS_MAT_A],norm,*x;
    322: #if !defined(PETSC_USE_COMPLEX)
    323:   PetscScalar    norm0;
    324: #endif

    327:   switch (mat) {
    328:     case DS_MAT_X:
    329:     case DS_MAT_Y:
    330:     case DS_MAT_Q:
    331:       /* Supported matrices */
    332:       break;
    333:     case DS_MAT_U:
    334:     case DS_MAT_VT:
    335:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    336:       break;
    337:     default:
    338:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    339:   }

    341:   PetscBLASIntCast(ds->n,&n);
    342:   PetscBLASIntCast(ds->ld,&ld);
    343:   DSGetArray(ds,mat,&x);
    344:   if (col < 0) {
    345:     i0 = 0; i1 = ds->n;
    346:   } else if (col>0 && A[ds->ld*(col-1)+col] != 0.0) {
    347:     i0 = col-1; i1 = col+1;
    348:   } else {
    349:     i0 = col; i1 = col+1;
    350:   }
    351:   for (i=i0;i<i1;i++) {
    352: #if !defined(PETSC_USE_COMPLEX)
    353:     if (i<n-1 && A[ds->ld*i+i+1] != 0.0) {
    354:       norm = BLASnrm2_(&n,&x[ld*i],&one);
    355:       norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
    356:       norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
    357:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
    358:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
    359:       i++;
    360:     } else
    361: #endif
    362:     {
    363:       norm = BLASnrm2_(&n,&x[ld*i],&one);
    364:       norm = 1.0/norm;
    365:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
    366:     }
    367:   }
    368:   return(0);
    369: }

    373: PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    374: {
    375: #if defined(SLEPC_MISSING_LAPACK_TRSEN)
    377:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable");
    378: #else
    380:   PetscInt       i;
    381:   PetscBLASInt   info,n,ld,mout,lwork,*selection;
    382:   PetscScalar    *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
    383: #if !defined(PETSC_USE_COMPLEX)
    384:   PetscBLASInt   *iwork,liwork;
    385: #endif

    388:   if (!k) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must supply argument k");
    389:   PetscBLASIntCast(ds->n,&n);
    390:   PetscBLASIntCast(ds->ld,&ld);
    391: #if !defined(PETSC_USE_COMPLEX)
    392:   lwork = n;
    393:   liwork = 1;
    394:   DSAllocateWork_Private(ds,lwork,0,liwork+n);
    395:   work = ds->work;
    396:   lwork = ds->lwork;
    397:   selection = ds->iwork;
    398:   iwork = ds->iwork + n;
    399:   liwork = ds->liwork - n;
    400: #else
    401:   lwork = 1;
    402:   DSAllocateWork_Private(ds,lwork,0,n);
    403:   work = ds->work;
    404:   selection = ds->iwork;
    405: #endif
    406:   /* Compute the selected eigenvalue to be in the leading position */
    407:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
    408:   PetscMemzero(selection,n*sizeof(PetscBLASInt));
    409:   for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
    410: #if !defined(PETSC_USE_COMPLEX)
    411:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,NULL,NULL,work,&lwork,iwork,&liwork,&info));
    412: #else
    413:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,NULL,NULL,work,&lwork,&info));
    414: #endif
    415:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTRSEN %d",info);
    416:   *k = mout;
    417:   return(0);
    418: #endif
    419: }

    423: PetscErrorCode DSSort_NHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
    424: {
    425: #if defined(SLEPC_MISSING_LAPACK_TREXC)
    427:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREXC - Lapack routine is unavailable");
    428: #else
    430:   PetscScalar    re;
    431:   PetscInt       i,j,pos,result;
    432:   PetscBLASInt   ifst,ilst,info,n,ld;
    433:   PetscScalar    *T = ds->mat[DS_MAT_A];
    434:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    435: #if !defined(PETSC_USE_COMPLEX)
    436:   PetscScalar    *work,im;
    437: #endif

    440:   PetscBLASIntCast(ds->n,&n);
    441:   PetscBLASIntCast(ds->ld,&ld);
    442: #if !defined(PETSC_USE_COMPLEX)
    443:   DSAllocateWork_Private(ds,ld,0,0);
    444:   work = ds->work;
    445: #endif
    446:   /* selection sort */
    447:   for (i=ds->l;i<n-1;i++) {
    448:     re = wr[i];
    449: #if !defined(PETSC_USE_COMPLEX)
    450:     im = wi[i];
    451: #endif
    452:     pos = 0;
    453:     j=i+1; /* j points to the next eigenvalue */
    454: #if !defined(PETSC_USE_COMPLEX)
    455:     if (im != 0) j=i+2;
    456: #endif
    457:     /* find minimum eigenvalue */
    458:     for (;j<n;j++) {
    459: #if !defined(PETSC_USE_COMPLEX)
    460:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
    461: #else
    462:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
    463: #endif
    464:       if (result > 0) {
    465:         re = wr[j];
    466: #if !defined(PETSC_USE_COMPLEX)
    467:         im = wi[j];
    468: #endif
    469:         pos = j;
    470:       }
    471: #if !defined(PETSC_USE_COMPLEX)
    472:       if (wi[j] != 0) j++;
    473: #endif
    474:     }
    475:     if (pos) {
    476:       /* interchange blocks */
    477:       PetscBLASIntCast(pos+1,&ifst);
    478:       PetscBLASIntCast(i+1,&ilst);
    479: #if !defined(PETSC_USE_COMPLEX)
    480:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info));
    481: #else
    482:       PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info));
    483: #endif
    484:       if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREXC %d",info);
    485:       /* recover original eigenvalues from T matrix */
    486:       for (j=i;j<n;j++) {
    487:         wr[j] = T[j+j*ld];
    488: #if !defined(PETSC_USE_COMPLEX)
    489:         if (j<n-1 && T[j+1+j*ld] != 0.0) {
    490:           /* complex conjugate eigenvalue */
    491:           wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) *
    492:                   PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld]));
    493:           wr[j+1] = wr[j];
    494:           wi[j+1] = -wi[j];
    495:           j++;
    496:         } else {
    497:           wi[j] = 0.0;
    498:         }
    499: #endif
    500:       }
    501:     }
    502: #if !defined(PETSC_USE_COMPLEX)
    503:     if (wi[i] != 0) i++;
    504: #endif
    505:   }
    506:   return(0);
    507: #endif
    508: }

    512: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    513: {

    517:   if (!rr || wr == rr) {
    518:     DSSort_NHEP_Total(ds,wr,wi);
    519:   } else {
    520:     DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
    521:   }
    522:   return(0);
    523: }

    527: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
    528: {
    530:   PetscInt       i;
    531:   PetscBLASInt   n,ld,incx=1;
    532:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;

    535:   PetscBLASIntCast(ds->n,&n);
    536:   PetscBLASIntCast(ds->ld,&ld);
    537:   A  = ds->mat[DS_MAT_A];
    538:   Q  = ds->mat[DS_MAT_Q];
    539:   DSAllocateWork_Private(ds,2*ld,0,0);
    540:   x = ds->work;
    541:   y = ds->work+ld;
    542:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    543:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    544:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    545:   ds->k = n;
    546:   return(0);
    547: }

    551: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
    552: {
    553: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
    555:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
    556: #else
    558:   PetscScalar    *work,*tau;
    559:   PetscInt       i,j;
    560:   PetscBLASInt   ilo,lwork,info,n,ld;
    561:   PetscScalar    *A = ds->mat[DS_MAT_A];
    562:   PetscScalar    *Q = ds->mat[DS_MAT_Q];

    565: #if !defined(PETSC_USE_COMPLEX)
    567: #endif
    568:   PetscBLASIntCast(ds->n,&n);
    569:   PetscBLASIntCast(ds->ld,&ld);
    570:   PetscBLASIntCast(ds->l+1,&ilo);
    571:   DSAllocateWork_Private(ds,ld+ld*ld,0,0);
    572:   tau  = ds->work;
    573:   work = ds->work+ld;
    574:   lwork = ld*ld;

    576:   /* initialize orthogonal matrix */
    577:   PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
    578:   for (i=0;i<n;i++)
    579:     Q[i+i*ld] = 1.0;
    580:   if (n==1) { /* quick return */
    581:     wr[0] = A[0];
    582:     wi[0] = 0.0;
    583:     return(0);
    584:   }

    586:   /* reduce to upper Hessenberg form */
    587:   if (ds->state<DS_STATE_INTERMEDIATE) {
    588:     PetscStackCallBLAS("LAPACKgehrd",LAPACKgehrd_(&n,&ilo,&n,A,&ld,tau,work,&lwork,&info));
    589:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEHRD %d",info);
    590:     for (j=0;j<n-1;j++) {
    591:       for (i=j+2;i<n;i++) {
    592:         Q[i+j*ld] = A[i+j*ld];
    593:         A[i+j*ld] = 0.0;
    594:       }
    595:     }
    596:     PetscStackCallBLAS("LAPACKorghr",LAPACKorghr_(&n,&ilo,&n,Q,&ld,tau,work,&lwork,&info));
    597:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGHR %d",info);
    598:   }

    600:   /* compute the (real) Schur form */
    601: #if !defined(PETSC_USE_COMPLEX)
    602:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,wi,Q,&ld,work,&lwork,&info));
    603:   for (j=0;j<ds->l;j++) {
    604:     if (j==n-1 || A[j+1+j*ld] == 0.0) {
    605:       /* real eigenvalue */
    606:       wr[j] = A[j+j*ld];
    607:       wi[j] = 0.0;
    608:     } else {
    609:       /* complex eigenvalue */
    610:       wr[j] = A[j+j*ld];
    611:       wr[j+1] = A[j+j*ld];
    612:       wi[j] = PetscSqrtReal(PetscAbsReal(A[j+1+j*ld])) *
    613:               PetscSqrtReal(PetscAbsReal(A[j+(j+1)*ld]));
    614:       wi[j+1] = -wi[j];
    615:       j++;
    616:     }
    617:   }
    618: #else
    619:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,Q,&ld,work,&lwork,&info));
    620:   if (wi) for (i=ds->l;i<n;i++) wi[i] = 0.0;
    621: #endif
    622:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",info);
    623:   return(0);
    624: #endif
    625: }

    629: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n)
    630: {
    631:   PetscInt       i,newn,ld=ds->ld,l=ds->l;
    632:   PetscScalar    *A;

    635:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
    636:   A = ds->mat[DS_MAT_A];
    637:   /* be careful not to break a diagonal 2x2 block */
    638:   if (A[n+(n-1)*ld]==0.0) newn = n;
    639:   else {
    640:     if (n<ds->n-1) newn = n+1;
    641:     else newn = n-1;
    642:   }
    643:   if (ds->extrarow && ds->k==ds->n) {
    644:     /* copy entries of extra row to the new position, then clean last row */
    645:     for (i=l;i<newn;i++) A[newn+i*ld] = A[ds->n+i*ld];
    646:     for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    647:   }
    648:   ds->k = 0;
    649:   ds->n = newn;
    650:   return(0);
    651: }

    655: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
    656: {
    657: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(SLEPC_MISSING_LAPACK_GETRI) || defined(SLEPC_MISSING_LAPACK_LANGE) || defined(SLEPC_MISSING_LAPACK_LANHS)
    659:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI/LANGE/LANHS - Lapack routines are unavailable");
    660: #else
    662:   PetscScalar    *work;
    663:   PetscReal      *rwork;
    664:   PetscBLASInt   *ipiv;
    665:   PetscBLASInt   lwork,info,n,ld;
    666:   PetscReal      hn,hin;
    667:   PetscScalar    *A;

    670:   PetscBLASIntCast(ds->n,&n);
    671:   PetscBLASIntCast(ds->ld,&ld);
    672:   lwork = 8*ld;
    673:   DSAllocateWork_Private(ds,lwork,ld,ld);
    674:   work  = ds->work;
    675:   rwork = ds->rwork;
    676:   ipiv  = ds->iwork;

    678:   /* use workspace matrix W to avoid overwriting A */
    679:   DSAllocateMat_Private(ds,DS_MAT_W);
    680:   A = ds->mat[DS_MAT_W];
    681:   PetscMemcpy(A,ds->mat[DS_MAT_A],sizeof(PetscScalar)*ds->ld*ds->ld);

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

    687:   /* norm of inv(A) */
    688:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
    689:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRF %d",info);
    690:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
    691:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRI %d",info);
    692:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

    694:   *cond = hn*hin;
    695:   return(0);
    696: #endif
    697: }

    701: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gamma)
    702: {
    703: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRS)
    705:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRS - Lapack routines are unavailable");
    706: #else
    708:   PetscInt       i,j;
    709:   PetscBLASInt   *ipiv,info,n,ld,one=1,ncol;
    710:   PetscScalar    *A,*B,*Q,*g=gin,*ghat;
    711:   PetscScalar    done=1.0,dmone=-1.0,dzero=0.0;
    712:   PetscReal      gnorm;

    715:   PetscBLASIntCast(ds->n,&n);
    716:   PetscBLASIntCast(ds->ld,&ld);
    717:   A  = ds->mat[DS_MAT_A];

    719:   if (!recover) {

    721:     DSAllocateWork_Private(ds,0,0,ld);
    722:     ipiv = ds->iwork;
    723:     if (!g) {
    724:       DSAllocateWork_Private(ds,ld,0,0);
    725:       g = ds->work;
    726:     }
    727:     /* use workspace matrix W to factor A-tau*eye(n) */
    728:     DSAllocateMat_Private(ds,DS_MAT_W);
    729:     B = ds->mat[DS_MAT_W];
    730:     PetscMemcpy(B,A,sizeof(PetscScalar)*ld*ld);

    732:     /* Vector g initialy stores b = beta*e_n^T */
    733:     PetscMemzero(g,n*sizeof(PetscScalar));
    734:     g[n-1] = beta;

    736:     /* g = (A-tau*eye(n))'\b */
    737:     for (i=0;i<n;i++)
    738:       B[i+i*ld] -= tau;
    739:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
    740:     if (info<0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to LU factorization");
    741:     if (info>0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Bad LU factorization");
    742:     PetscLogFlops(2.0*n*n*n/3.0);
    743:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
    744:     if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"GETRS - Bad solve");
    745:     PetscLogFlops(2.0*n*n-n);

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

    751:   } else { /* recover */

    754:     DSAllocateWork_Private(ds,ld,0,0);
    755:     ghat = ds->work;
    756:     Q    = ds->mat[DS_MAT_Q];

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

    762:     /* A = A + g^*b' */
    763:     for (i=0;i<ds->l+ds->k;i++)
    764:       for (j=ds->l;j<ds->l+ds->k;j++)
    765:         A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;

    767:     /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
    768:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
    769:   }

    771:   /* Compute gamma factor */
    772:   if (gamma) {
    773:     gnorm = 0.0;
    774:     for (i=0;i<n;i++)
    775:       gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
    776:     *gamma = PetscSqrtReal(1.0+gnorm);
    777:   }
    778:   return(0);
    779: #endif
    780: }

    784: PETSC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
    785: {
    787:   ds->ops->allocate      = DSAllocate_NHEP;
    788:   ds->ops->view          = DSView_NHEP;
    789:   ds->ops->vectors       = DSVectors_NHEP;
    790:   ds->ops->solve[0]      = DSSolve_NHEP;
    791:   ds->ops->sort          = DSSort_NHEP;
    792:   ds->ops->truncate      = DSTruncate_NHEP;
    793:   ds->ops->update        = DSUpdateExtraRow_NHEP;
    794:   ds->ops->cond          = DSCond_NHEP;
    795:   ds->ops->transharm     = DSTranslateHarmonic_NHEP;
    796:   ds->ops->normalize     = DSNormalize_NHEP;
    797:   return(0);
    798: }