Actual source code: dsnhepts.c

slepc-3.18.3 2023-03-24
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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: typedef struct {
 15:   PetscScalar *wr,*wi;     /* eigenvalues of B */
 16: } DS_NHEPTS;

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

 22:   DSAllocateMat_Private(ds,DS_MAT_A);
 23:   DSAllocateMat_Private(ds,DS_MAT_B);
 24:   DSAllocateMat_Private(ds,DS_MAT_Q);
 25:   DSAllocateMat_Private(ds,DS_MAT_Z);
 26:   PetscFree(ds->perm);
 27:   PetscMalloc1(ld,&ds->perm);
 28:   PetscMalloc1(ld,&ctx->wr);
 29: #if !defined(PETSC_USE_COMPLEX)
 30:   PetscMalloc1(ld,&ctx->wi);
 31: #endif
 32:   return 0;
 33: }

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

 39:   PetscViewerGetFormat(viewer,&format);
 40:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return 0;
 41:   DSViewMat(ds,viewer,DS_MAT_A);
 42:   DSViewMat(ds,viewer,DS_MAT_B);
 43:   if (ds->state>DS_STATE_INTERMEDIATE) {
 44:     DSViewMat(ds,viewer,DS_MAT_Q);
 45:     DSViewMat(ds,viewer,DS_MAT_Z);
 46:   }
 47:   if (ds->omat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
 48:   if (ds->omat[DS_MAT_Y]) DSViewMat(ds,viewer,DS_MAT_Y);
 49:   return 0;
 50: }

 52: static PetscErrorCode DSVectors_NHEPTS_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 53: {
 54:   PetscInt          i;
 55:   PetscBLASInt      mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
 56:   PetscScalar       sone=1.0,szero=0.0;
 57:   PetscReal         norm,done=1.0;
 58:   PetscBool         iscomplex = PETSC_FALSE;
 59:   PetscScalar       *X,*Y;
 60:   const PetscScalar *A,*Q;

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

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

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

108:   /* set output arguments */
109:   if (iscomplex) (*k)++;
110:   if (rnorm) {
111:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
112:     else *rnorm = PetscAbsScalar(Y[n-1]);
113:   }
114:   MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&X);
115:   return 0;
116: }

118: static PetscErrorCode DSVectors_NHEPTS_Eigen_All(DS ds,PetscBool left)
119: {
120:   PetscInt          i;
121:   PetscBLASInt      n,ld,mout,info,inc=1,cols,zero=0;
122:   PetscBool         iscomplex;
123:   PetscScalar       *X;
124:   const PetscScalar *A;
125:   PetscReal         norm,done=1.0;
126:   const char        *back;

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

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

166: PetscErrorCode DSVectors_NHEPTS(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
167: {
168:   switch (mat) {
169:     case DS_MAT_X:
171:       if (j) DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
172:       else DSVectors_NHEPTS_Eigen_All(ds,PETSC_FALSE);
173:       break;
174:     case DS_MAT_Y:
176:       if (j) DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
177:       else DSVectors_NHEPTS_Eigen_All(ds,PETSC_TRUE);
178:       break;
179:     case DS_MAT_U:
180:     case DS_MAT_V:
181:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
182:     default:
183:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
184:   }
185:   return 0;
186: }

188: PetscErrorCode DSSort_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
189: {
190:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;
191:   PetscInt       i,j,cont,id=0,*p,*idx,*idx2;
192:   PetscReal      s,t;
193: #if defined(PETSC_USE_COMPLEX)
194:   Mat            A,U;
195: #endif

198:   PetscMalloc3(ds->ld,&idx,ds->ld,&idx2,ds->ld,&p);
199:   DSSort_NHEP_Total(ds,DS_MAT_A,DS_MAT_Q,wr,wi);
200: #if defined(PETSC_USE_COMPLEX)
201:   DSGetMat(ds,DS_MAT_B,&A);
202:   MatConjugate(A);
203:   DSRestoreMat(ds,DS_MAT_B,&A);
204:   DSGetMat(ds,DS_MAT_Z,&U);
205:   MatConjugate(U);
206:   DSRestoreMat(ds,DS_MAT_Z,&U);
207:   for (i=0;i<ds->n;i++) ctx->wr[i] = PetscConj(ctx->wr[i]);
208: #endif
209:   DSSort_NHEP_Total(ds,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi);
210:   /* check correct eigenvalue correspondence */
211:   cont = 0;
212:   for (i=0;i<ds->n;i++) {
213:     if (SlepcAbsEigenvalue(ctx->wr[i]-wr[i],ctx->wi[i]-wi[i])>PETSC_SQRT_MACHINE_EPSILON) {idx2[cont] = i; idx[cont++] = i;}
214:     p[i] = -1;
215:   }
216:   if (cont) {
217:     for (i=0;i<cont;i++) {
218:       t = PETSC_MAX_REAL;
219:       for (j=0;j<cont;j++) if (idx2[j]!=-1 && (s=SlepcAbsEigenvalue(ctx->wr[idx[j]]-wr[idx[i]],ctx->wi[idx[j]]-wi[idx[i]]))<t) { id = j; t = s; }
220:       p[idx[i]] = idx[id];
221:       idx2[id] = -1;
222:     }
223:     for (i=0;i<ds->n;i++) if (p[i]==-1) p[i] = i;
224:     DSSortWithPermutation_NHEP_Private(ds,p,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi);
225:   }
226: #if defined(PETSC_USE_COMPLEX)
227:   DSGetMat(ds,DS_MAT_B,&A);
228:   MatConjugate(A);
229:   DSRestoreMat(ds,DS_MAT_B,&A);
230:   DSGetMat(ds,DS_MAT_Z,&U);
231:   MatConjugate(U);
232:   DSRestoreMat(ds,DS_MAT_Z,&U);
233: #endif
234:   PetscFree3(idx,idx2,p);
235:   return 0;
236: }

238: PetscErrorCode DSUpdateExtraRow_NHEPTS(DS ds)
239: {
240:   PetscInt          i;
241:   PetscBLASInt      n,ld,incx=1;
242:   PetscScalar       *A,*x,*y,one=1.0,zero=0.0;
243:   const PetscScalar *Q;

245:   PetscBLASIntCast(ds->n,&n);
246:   PetscBLASIntCast(ds->ld,&ld);
247:   DSAllocateWork_Private(ds,2*ld,0,0);
248:   x = ds->work;
249:   y = ds->work+ld;
250:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
251:   MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q);
252:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
253:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
254:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
255:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
256:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q);
257:   MatDenseGetArray(ds->omat[DS_MAT_B],&A);
258:   MatDenseGetArrayRead(ds->omat[DS_MAT_Z],&Q);
259:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
260:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
261:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
262:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&A);
263:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_Z],&Q);
264:   ds->k = n;
265:   return 0;
266: }

268: PetscErrorCode DSSolve_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi)
269: {
270:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;

272: #if !defined(PETSC_USE_COMPLEX)
274: #endif
275:   DSSolve_NHEP_Private(ds,DS_MAT_A,DS_MAT_Q,wr,wi);
276:   DSSolve_NHEP_Private(ds,DS_MAT_B,DS_MAT_Z,ctx->wr,ctx->wi);
277:   return 0;
278: }

280: #if !defined(PETSC_HAVE_MPIUNI)
281: PetscErrorCode DSSynchronize_NHEPTS(DS ds,PetscScalar eigr[],PetscScalar eigi[])
282: {
283:   PetscInt       ld=ds->ld,l=ds->l,k;
284:   PetscMPIInt    n,rank,off=0,size,ldn;
285:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;
286:   PetscScalar    *A,*B,*Q,*Z;

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

344: PetscErrorCode DSGetTruncateSize_NHEPTS(DS ds,PetscInt l,PetscInt n,PetscInt *k)
345: {
346: #if !defined(PETSC_USE_COMPLEX)
347:   const PetscScalar *A,*B;
348: #endif

350: #if !defined(PETSC_USE_COMPLEX)
351:   MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A);
352:   MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B);
353:   if (A[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0 || B[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0) {
354:     if (l+(*k)<n-1) (*k)++;
355:     else (*k)--;
356:   }
357:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A);
358:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B);
359: #endif
360:   return 0;
361: }

363: PetscErrorCode DSTruncate_NHEPTS(DS ds,PetscInt n,PetscBool trim)
364: {
365:   PetscInt    i,ld=ds->ld,l=ds->l;
366:   PetscScalar *A,*B;

368:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
369:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
370: #if defined(PETSC_USE_DEBUG)
371:   /* make sure diagonal 2x2 block is not broken */
373: #endif
374:   if (trim) {
375:     if (ds->extrarow) {   /* clean extra row */
376:       for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
377:     }
378:     ds->l = 0;
379:     ds->k = 0;
380:     ds->n = n;
381:     ds->t = ds->n;   /* truncated length equal to the new dimension */
382:   } else {
383:     if (ds->extrarow && ds->k==ds->n) {
384:       /* copy entries of extra row to the new position, then clean last row */
385:       for (i=l;i<n;i++) { A[n+i*ld] = A[ds->n+i*ld]; B[n+i*ld] = B[ds->n+i*ld]; }
386:       for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
387:     }
388:     ds->k = (ds->extrarow)? n: 0;
389:     ds->t = ds->n;   /* truncated length equal to previous dimension */
390:     ds->n = n;
391:   }
392:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
393:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
394:   return 0;
395: }

397: PetscErrorCode DSDestroy_NHEPTS(DS ds)
398: {
399:   DS_NHEPTS      *ctx = (DS_NHEPTS*)ds->data;

401:   if (ctx->wr) PetscFree(ctx->wr);
402:   if (ctx->wi) PetscFree(ctx->wi);
403:   PetscFree(ds->data);
404:   return 0;
405: }

407: PetscErrorCode DSMatGetSize_NHEPTS(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
408: {
409:   *rows = ((t==DS_MAT_A || t==DS_MAT_B) && ds->extrarow)? ds->n+1: ds->n;
410:   *cols = ds->n;
411:   return 0;
412: }

414: /*MC
415:    DSNHEPTS - Dense Non-Hermitian Eigenvalue Problem (special variant intended
416:    for two-sided Krylov solvers).

418:    Level: beginner

420:    Notes:
421:    Two related problems are solved, A*X = X*Lambda and B*Y = Y*Lambda', where A and
422:    B are supposed to come from the Arnoldi factorizations of a certain matrix and its
423:    (conjugate) transpose, respectively. Hence, in exact arithmetic the columns of Y
424:    are equal to the left eigenvectors of A. Lambda is a diagonal matrix whose diagonal
425:    elements are the arguments of DSSolve(). After solve, A is overwritten with the
426:    upper quasi-triangular matrix T of the (real) Schur form, A*Q = Q*T, and similarly
427:    another (real) Schur relation is computed, B*Z = Z*S, overwriting B.

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

431:    When left eigenvectors DS_MAT_Y are requested, right eigenvectors of B are returned,
432:    while DS_MAT_X contains right eigenvectors of A.

434:    Used DS matrices:
435: +  DS_MAT_A - first problem matrix obtained from Arnoldi
436: .  DS_MAT_B - second problem matrix obtained from Arnoldi on the transpose
437: .  DS_MAT_Q - orthogonal/unitary transformation that reduces A to Hessenberg form
438:    (intermediate step) or matrix of orthogonal Schur vectors of A
439: -  DS_MAT_Z - orthogonal/unitary transformation that reduces B to Hessenberg form
440:    (intermediate step) or matrix of orthogonal Schur vectors of B

442:    Implemented methods:
443: .  0 - Implicit QR (_hseqr)

445: .seealso: DSCreate(), DSSetType(), DSType
446: M*/
447: SLEPC_EXTERN PetscErrorCode DSCreate_NHEPTS(DS ds)
448: {
449:   DS_NHEPTS      *ctx;

451:   PetscNew(&ctx);
452:   ds->data = (void*)ctx;

454:   ds->ops->allocate        = DSAllocate_NHEPTS;
455:   ds->ops->view            = DSView_NHEPTS;
456:   ds->ops->vectors         = DSVectors_NHEPTS;
457:   ds->ops->solve[0]        = DSSolve_NHEPTS;
458:   ds->ops->sort            = DSSort_NHEPTS;
459: #if !defined(PETSC_HAVE_MPIUNI)
460:   ds->ops->synchronize     = DSSynchronize_NHEPTS;
461: #endif
462:   ds->ops->gettruncatesize = DSGetTruncateSize_NHEPTS;
463:   ds->ops->truncate        = DSTruncate_NHEPTS;
464:   ds->ops->update          = DSUpdateExtraRow_NHEPTS;
465:   ds->ops->destroy         = DSDestroy_NHEPTS;
466:   ds->ops->matgetsize      = DSMatGetSize_NHEPTS;
467:   return 0;
468: }