Actual source code: dsnhep.c

slepc-3.17.0 2022-03-31
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

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

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

 14: PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
 15: {
 16:   DSAllocateMat_Private(ds,DS_MAT_A);
 17:   DSAllocateMat_Private(ds,DS_MAT_Q);
 18:   PetscFree(ds->perm);
 19:   PetscMalloc1(ld,&ds->perm);
 20:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 21:   PetscFunctionReturn(0);
 22: }

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

 28:   PetscViewerGetFormat(viewer,&format);
 29:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);
 30:   DSViewMat(ds,viewer,DS_MAT_A);
 31:   if (ds->state>DS_STATE_INTERMEDIATE) DSViewMat(ds,viewer,DS_MAT_Q);
 32:   if (ds->mat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
 33:   if (ds->mat[DS_MAT_Y]) DSViewMat(ds,viewer,DS_MAT_Y);
 34:   PetscFunctionReturn(0);
 35: }

 37: static PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 38: {
 39:   PetscInt       i,j;
 40:   PetscBLASInt   info,ld,n,n1,lwork,inc=1;
 41:   PetscScalar    sdummy,done=1.0,zero=0.0;
 42:   PetscReal      *sigma;
 43:   PetscBool      iscomplex = PETSC_FALSE;
 44:   PetscScalar    *A = ds->mat[DS_MAT_A];
 45:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
 46:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
 47:   PetscScalar    *W;

 50:   PetscBLASIntCast(ds->n,&n);
 51:   PetscBLASIntCast(ds->ld,&ld);
 52:   n1 = n+1;
 53:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
 55:   DSAllocateWork_Private(ds,5*ld,6*ld,0);
 56:   DSAllocateMat_Private(ds,DS_MAT_W);
 57:   W = ds->mat[DS_MAT_W];
 58:   lwork = 5*ld;
 59:   sigma = ds->rwork+5*ld;

 61:   /* build A-w*I in W */
 62:   for (j=0;j<n;j++)
 63:     for (i=0;i<=n;i++)
 64:       W[i+j*ld] = A[i+j*ld];
 65:   for (i=0;i<n;i++)
 66:     W[i+i*ld] -= A[(*k)+(*k)*ld];

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

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

 79:   /* update vector with right singular vector associated to smallest singular value,
 80:      accumulating the transformation matrix Q */
 81:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
 82:   PetscFunctionReturn(0);
 83: }

 85: static PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
 86: {
 87:   PetscInt       i;

 89:   for (i=0;i<ds->n;i++) DSVectors_NHEP_Refined_Some(ds,&i,NULL,left);
 90:   PetscFunctionReturn(0);
 91: }

 93: static PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 94: {
 95:   PetscInt       i;
 96:   PetscBLASInt   mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
 97:   PetscScalar    sone=1.0,szero=0.0;
 98:   PetscReal      norm,done=1.0;
 99:   PetscBool      iscomplex = PETSC_FALSE;
100:   PetscScalar    *A = ds->mat[DS_MAT_A];
101:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
102:   PetscScalar    *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
103:   PetscScalar    *Y;

105:   PetscBLASIntCast(ds->n,&n);
106:   PetscBLASIntCast(ds->ld,&ld);
107:   DSAllocateWork_Private(ds,0,0,ld);
108:   select = ds->iwork;
109:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;

111:   /* compute k-th eigenvector Y of A */
112:   Y = X+(*k)*ld;
113:   select[*k] = (PetscBLASInt)PETSC_TRUE;
114: #if !defined(PETSC_USE_COMPLEX)
115:   if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
116:   mm = iscomplex? 2: 1;
117:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
118:   DSAllocateWork_Private(ds,3*ld,0,0);
119:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
120: #else
121:   DSAllocateWork_Private(ds,2*ld,ld,0);
122:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
123: #endif
124:   SlepcCheckLapackInfo("trevc",info);

127:   /* accumulate and normalize eigenvectors */
128:   if (ds->state>=DS_STATE_CONDENSED) {
129:     PetscArraycpy(ds->work,Y,mout*ld);
130:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work,&inc,&szero,Y,&inc));
131: #if !defined(PETSC_USE_COMPLEX)
132:     if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work+ld,&inc,&szero,Y+ld,&inc));
133: #endif
134:     cols = 1;
135:     norm = BLASnrm2_(&n,Y,&inc);
136: #if !defined(PETSC_USE_COMPLEX)
137:     if (iscomplex) {
138:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Y+ld,&inc));
139:       cols = 2;
140:     }
141: #endif
142:     PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Y,&ld,&info));
143:     SlepcCheckLapackInfo("lascl",info);
144:   }

146:   /* set output arguments */
147:   if (iscomplex) (*k)++;
148:   if (rnorm) {
149:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
150:     else *rnorm = PetscAbsScalar(Y[n-1]);
151:   }
152:   PetscFunctionReturn(0);
153: }

155: static PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
156: {
157:   PetscInt       i;
158:   PetscBLASInt   n,ld,mout,info,inc=1,cols,zero=0;
159:   PetscBool      iscomplex;
160:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A];
161:   PetscReal      norm,done=1.0;
162:   const char     *side,*back;

164:   PetscBLASIntCast(ds->n,&n);
165:   PetscBLASIntCast(ds->ld,&ld);
166:   if (left) {
167:     X = NULL;
168:     Y = ds->mat[DS_MAT_Y];
169:     side = "L";
170:   } else {
171:     X = ds->mat[DS_MAT_X];
172:     Y = NULL;
173:     side = "R";
174:   }
175:   Z = left? Y: X;
176:   if (ds->state>=DS_STATE_CONDENSED) {
177:     /* DSSolve() has been called, backtransform with matrix Q */
178:     back = "B";
179:     PetscArraycpy(Z,ds->mat[DS_MAT_Q],ld*ld);
180:   } else back = "A";
181: #if !defined(PETSC_USE_COMPLEX)
182:   DSAllocateWork_Private(ds,3*ld,0,0);
183:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
184: #else
185:   DSAllocateWork_Private(ds,2*ld,ld,0);
186:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
187: #endif
188:   SlepcCheckLapackInfo("trevc",info);

190:   /* normalize eigenvectors */
191:   for (i=0;i<n;i++) {
192:     iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
193:     cols = 1;
194:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
195: #if !defined(PETSC_USE_COMPLEX)
196:     if (iscomplex) {
197:       norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+(i+1)*ld,&inc));
198:       cols = 2;
199:     }
200: #endif
201:     PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z+i*ld,&ld,&info));
202:     SlepcCheckLapackInfo("lascl",info);
203:     if (iscomplex) i++;
204:   }
205:   PetscFunctionReturn(0);
206: }

208: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
209: {
210:   switch (mat) {
211:     case DS_MAT_X:
212:       if (ds->refined) {
214:         if (j) DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
215:         else DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
216:       } else {
217:         if (j) DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
218:         else DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
219:       }
220:       break;
221:     case DS_MAT_Y:
223:       if (j) DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
224:       else DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
225:       break;
226:     case DS_MAT_U:
227:     case DS_MAT_V:
228:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
229:     default:
230:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
231:   }
232:   PetscFunctionReturn(0);
233: }

235: static PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
236: {
237:   PetscInt       i;
238:   PetscBLASInt   info,n,ld,mout,lwork,*selection;
239:   PetscScalar    *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
240:   PetscReal      dummy;
241: #if !defined(PETSC_USE_COMPLEX)
242:   PetscBLASInt   *iwork,liwork;
243: #endif

246:   PetscBLASIntCast(ds->n,&n);
247:   PetscBLASIntCast(ds->ld,&ld);
248: #if !defined(PETSC_USE_COMPLEX)
249:   lwork = n;
250:   liwork = 1;
251:   DSAllocateWork_Private(ds,lwork,0,liwork+n);
252:   work = ds->work;
253:   lwork = ds->lwork;
254:   selection = ds->iwork;
255:   iwork = ds->iwork + n;
256:   liwork = ds->liwork - n;
257: #else
258:   lwork = 1;
259:   DSAllocateWork_Private(ds,lwork,0,n);
260:   work = ds->work;
261:   selection = ds->iwork;
262: #endif
263:   /* Compute the selected eigenvalue to be in the leading position */
264:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
265:   PetscArrayzero(selection,n);
266:   for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
267: #if !defined(PETSC_USE_COMPLEX)
268:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,&dummy,&dummy,work,&lwork,iwork,&liwork,&info));
269: #else
270:   PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,&dummy,&dummy,work,&lwork,&info));
271: #endif
272:   SlepcCheckLapackInfo("trsen",info);
273:   *k = mout;
274:   PetscFunctionReturn(0);
275: }

277: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
278: {
279:   if (!rr || wr == rr) DSSort_NHEP_Total(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
280:   else DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
281:   PetscFunctionReturn(0);
282: }

284: static PetscErrorCode DSSortWithPermutation_NHEP(DS ds,PetscInt *perm,PetscScalar *wr,PetscScalar *wi)
285: {
286:   DSSortWithPermutation_NHEP_Private(ds,perm,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
287:   PetscFunctionReturn(0);
288: }

290: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
291: {
292:   PetscInt       i;
293:   PetscBLASInt   n,ld,incx=1;
294:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;

296:   PetscBLASIntCast(ds->n,&n);
297:   PetscBLASIntCast(ds->ld,&ld);
298:   A  = ds->mat[DS_MAT_A];
299:   Q  = ds->mat[DS_MAT_Q];
300:   DSAllocateWork_Private(ds,2*ld,0,0);
301:   x = ds->work;
302:   y = ds->work+ld;
303:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
304:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
305:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
306:   ds->k = n;
307:   PetscFunctionReturn(0);
308: }

310: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
311: {
312: #if !defined(PETSC_USE_COMPLEX)
314: #endif
315:   DSSolve_NHEP_Private(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
316:   PetscFunctionReturn(0);
317: }

319: PetscErrorCode DSSynchronize_NHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
320: {
321:   PetscInt       ld=ds->ld,l=ds->l,k;
322:   PetscMPIInt    n,rank,off=0,size,ldn;

324:   k = (ds->n-l)*ld;
325:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
326:   if (eigr) k += ds->n-l;
327:   if (eigi) k += ds->n-l;
328:   DSAllocateWork_Private(ds,k,0,0);
329:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
330:   PetscMPIIntCast(ds->n-l,&n);
331:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
332:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
333:   if (!rank) {
334:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
335:     if (ds->state>DS_STATE_RAW) MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
336:     if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
337: #if !defined(PETSC_USE_COMPLEX)
338:     if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
339: #endif
340:   }
341:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
342:   if (rank) {
343:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
344:     if (ds->state>DS_STATE_RAW) MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
345:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
346: #if !defined(PETSC_USE_COMPLEX)
347:     if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
348: #endif
349:   }
350:   PetscFunctionReturn(0);
351: }

353: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n,PetscBool trim)
354: {
355:   PetscInt    i,ld=ds->ld,l=ds->l;
356:   PetscScalar *A = ds->mat[DS_MAT_A];

358: #if defined(PETSC_USE_DEBUG)
359:   /* make sure diagonal 2x2 block is not broken */
361: #endif
362:   if (trim) {
363:     if (ds->extrarow) {   /* clean extra row */
364:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
365:     }
366:     ds->l = 0;
367:     ds->k = 0;
368:     ds->n = n;
369:     ds->t = ds->n;   /* truncated length equal to the new dimension */
370:   } else {
371:     if (ds->extrarow && ds->k==ds->n) {
372:       /* copy entries of extra row to the new position, then clean last row */
373:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
374:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
375:     }
376:     ds->k = (ds->extrarow)? n: 0;
377:     ds->t = ds->n;   /* truncated length equal to previous dimension */
378:     ds->n = n;
379:   }
380:   PetscFunctionReturn(0);
381: }

383: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
384: {
385:   PetscScalar    *work;
386:   PetscReal      *rwork;
387:   PetscBLASInt   *ipiv;
388:   PetscBLASInt   lwork,info,n,ld;
389:   PetscReal      hn,hin;
390:   PetscScalar    *A;

392:   PetscBLASIntCast(ds->n,&n);
393:   PetscBLASIntCast(ds->ld,&ld);
394:   lwork = 8*ld;
395:   DSAllocateWork_Private(ds,lwork,ld,ld);
396:   work  = ds->work;
397:   rwork = ds->rwork;
398:   ipiv  = ds->iwork;

400:   /* use workspace matrix W to avoid overwriting A */
401:   DSAllocateMat_Private(ds,DS_MAT_W);
402:   A = ds->mat[DS_MAT_W];
403:   PetscArraycpy(A,ds->mat[DS_MAT_A],ds->ld*ds->ld);

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

409:   /* norm of inv(A) */
410:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
411:   SlepcCheckLapackInfo("getrf",info);
412:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
413:   SlepcCheckLapackInfo("getri",info);
414:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

416:   *cond = hn*hin;
417:   PetscFunctionReturn(0);
418: }

420: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gammaout)
421: {
422:   PetscInt       i,j;
423:   PetscBLASInt   *ipiv,info,n,ld,one=1,ncol;
424:   PetscScalar    *A,*B,*Q,*g=gin,*ghat;
425:   PetscScalar    done=1.0,dmone=-1.0,dzero=0.0;
426:   PetscReal      gamma=1.0;

428:   PetscBLASIntCast(ds->n,&n);
429:   PetscBLASIntCast(ds->ld,&ld);
430:   A  = ds->mat[DS_MAT_A];

432:   if (!recover) {

434:     DSAllocateWork_Private(ds,0,0,ld);
435:     ipiv = ds->iwork;
436:     if (!g) {
437:       DSAllocateWork_Private(ds,ld,0,0);
438:       g = ds->work;
439:     }
440:     /* use workspace matrix W to factor A-tau*eye(n) */
441:     DSAllocateMat_Private(ds,DS_MAT_W);
442:     B = ds->mat[DS_MAT_W];
443:     PetscArraycpy(B,A,ld*ld);

445:     /* Vector g initially stores b = beta*e_n^T */
446:     PetscArrayzero(g,n);
447:     g[n-1] = beta;

449:     /* g = (A-tau*eye(n))'\b */
450:     for (i=0;i<n;i++) B[i+i*ld] -= tau;
451:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
452:     SlepcCheckLapackInfo("getrf",info);
453:     PetscLogFlops(2.0*n*n*n/3.0);
454:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
455:     SlepcCheckLapackInfo("getrs",info);
456:     PetscLogFlops(2.0*n*n-n);

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

461:   } else { /* recover */

463:     DSAllocateWork_Private(ds,ld,0,0);
464:     ghat = ds->work;
465:     Q    = ds->mat[DS_MAT_Q];

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

471:     /* A = A + g^*b' */
472:     for (i=0;i<ds->l+ds->k;i++)
473:       for (j=ds->l;j<ds->l+ds->k;j++)
474:         A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;

476:     /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
477:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
478:   }

480:   /* Compute gamma factor */
481:   if (gammaout || (recover && ds->extrarow)) gamma = SlepcAbs(1.0,BLASnrm2_(&n,g,&one));
482:   if (gammaout) *gammaout = gamma;
483:   if (recover && ds->extrarow) {
484:     for (j=ds->l;j<ds->l+ds->k;j++) A[ds->n+j*ld] *= gamma;
485:   }
486:   PetscFunctionReturn(0);
487: }

489: /*MC
490:    DSNHEP - Dense Non-Hermitian Eigenvalue Problem.

492:    Level: beginner

494:    Notes:
495:    The problem is expressed as A*X = X*Lambda, where A is the input matrix.
496:    Lambda is a diagonal matrix whose diagonal elements are the arguments of
497:    DSSolve(). After solve, A is overwritten with the upper quasi-triangular
498:    matrix T of the (real) Schur form, A*Q = Q*T.

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

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

505:    Used DS matrices:
506: +  DS_MAT_A - problem matrix
507: -  DS_MAT_Q - orthogonal/unitary transformation that reduces to Hessenberg form
508:    (intermediate step) or matrix of orthogonal Schur vectors

510:    Implemented methods:
511: .  0 - Implicit QR (_hseqr)

513: .seealso: DSCreate(), DSSetType(), DSType
514: M*/
515: SLEPC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
516: {
517:   ds->ops->allocate        = DSAllocate_NHEP;
518:   ds->ops->view            = DSView_NHEP;
519:   ds->ops->vectors         = DSVectors_NHEP;
520:   ds->ops->solve[0]        = DSSolve_NHEP;
521:   ds->ops->sort            = DSSort_NHEP;
522:   ds->ops->sortperm        = DSSortWithPermutation_NHEP;
523:   ds->ops->synchronize     = DSSynchronize_NHEP;
524:   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
525:   ds->ops->truncate        = DSTruncate_NHEP;
526:   ds->ops->update          = DSUpdateExtraRow_NHEP;
527:   ds->ops->cond            = DSCond_NHEP;
528:   ds->ops->transharm       = DSTranslateHarmonic_NHEP;
529:   PetscFunctionReturn(0);
530: }