Actual source code: dsghiep.c

slepc-3.13.3 2020-06-14
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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_GHIEP(DS ds,PetscInt ld)
 15: {

 19:   DSAllocateMat_Private(ds,DS_MAT_A);
 20:   DSAllocateMat_Private(ds,DS_MAT_B);
 21:   DSAllocateMat_Private(ds,DS_MAT_Q);
 22:   DSAllocateMatReal_Private(ds,DS_MAT_T);
 23:   DSAllocateMatReal_Private(ds,DS_MAT_D);
 24:   PetscFree(ds->perm);
 25:   PetscMalloc1(ld,&ds->perm);
 26:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 27:   return(0);
 28: }

 30: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
 31: {
 33:   PetscReal      *T,*S;
 34:   PetscScalar    *A,*B;
 35:   PetscInt       i,n,ld;

 38:   A = ds->mat[DS_MAT_A];
 39:   B = ds->mat[DS_MAT_B];
 40:   T = ds->rmat[DS_MAT_T];
 41:   S = ds->rmat[DS_MAT_D];
 42:   n = ds->n;
 43:   ld = ds->ld;
 44:   if (tocompact) { /* switch from dense (arrow) to compact storage */
 45:     PetscArrayzero(T,3*ld);
 46:     PetscArrayzero(S,ld);
 47:     for (i=0;i<n-1;i++) {
 48:       T[i]    = PetscRealPart(A[i+i*ld]);
 49:       T[ld+i] = PetscRealPart(A[i+1+i*ld]);
 50:       S[i]    = PetscRealPart(B[i+i*ld]);
 51:     }
 52:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
 53:     S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
 54:     for (i=ds->l;i<ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
 55:   } else { /* switch from compact (arrow) to dense storage */
 56:     PetscArrayzero(A,ld*ld);
 57:     PetscArrayzero(B,ld*ld);
 58:     for (i=0;i<n-1;i++) {
 59:       A[i+i*ld]     = T[i];
 60:       A[i+1+i*ld]   = T[ld+i];
 61:       A[i+(i+1)*ld] = T[ld+i];
 62:       B[i+i*ld]     = S[i];
 63:     }
 64:     A[n-1+(n-1)*ld] = T[n-1];
 65:     B[n-1+(n-1)*ld] = S[n-1];
 66:     for (i=ds->l;i<ds->k;i++) {
 67:       A[ds->k+i*ld] = T[2*ld+i];
 68:       A[i+ds->k*ld] = T[2*ld+i];
 69:     }
 70:   }
 71:   return(0);
 72: }

 74: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
 75: {
 76:   PetscErrorCode    ierr;
 77:   PetscViewerFormat format;
 78:   PetscInt          i,j;
 79:   PetscReal         value;
 80:   const char        *methodname[] = {
 81:                      "QR + Inverse Iteration",
 82:                      "HZ method",
 83:                      "QR"
 84:   };
 85:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

 88:   PetscViewerGetFormat(viewer,&format);
 89:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 90:     if (ds->method<nmeth) {
 91:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
 92:     }
 93:     return(0);
 94:   }
 95:   if (ds->compact) {
 96:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
 97:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
 98:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
 99:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
100:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
101:       for (i=0;i<ds->n;i++) {
102:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
103:       }
104:       for (i=0;i<ds->n-1;i++) {
105:         if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
106:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+2,i+1,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
107:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+2,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
108:         }
109:       }
110:       for (i = ds->l;i<ds->k;i++) {
111:         if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
112:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",ds->k+1,i+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
113:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,ds->k+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
114:         }
115:       }
116:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);

118:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
119:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
120:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
121:       for (i=0;i<ds->n;i++) {
122:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_D]+i));
123:       }
124:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

126:     } else {
127:       PetscViewerASCIIPrintf(viewer,"T\n");
128:       for (i=0;i<ds->n;i++) {
129:         for (j=0;j<ds->n;j++) {
130:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
131:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
132:           else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+2*ds->ld+PetscMin(i,j));
133:           else value = 0.0;
134:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
135:         }
136:         PetscViewerASCIIPrintf(viewer,"\n");
137:       }
138:       PetscViewerASCIIPrintf(viewer,"omega\n");
139:       for (i=0;i<ds->n;i++) {
140:         for (j=0;j<ds->n;j++) {
141:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
142:           else value = 0.0;
143:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
144:         }
145:         PetscViewerASCIIPrintf(viewer,"\n");
146:       }
147:     }
148:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
149:     PetscViewerFlush(viewer);
150:   } else {
151:     DSViewMat(ds,viewer,DS_MAT_A);
152:     DSViewMat(ds,viewer,DS_MAT_B);
153:   }
154:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
155:   return(0);
156: }

158: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
159: {
161:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
162:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
163:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
164:   PetscInt       k;
165:   PetscBLASInt   two = 2,n_,ld,one=1;
166: #if !defined(PETSC_USE_COMPLEX)
167:   PetscBLASInt   four=4;
168: #endif

171:   X = ds->mat[DS_MAT_X];
172:   Q = ds->mat[DS_MAT_Q];
173:   k = *idx;
174:   PetscBLASIntCast(ds->n,&n_);
175:   PetscBLASIntCast(ds->ld,&ld);
176:   if (k < ds->n-1) e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
177:   else e = 0.0;
178:   if (e == 0.0) { /* Real */
179:     if (ds->state>=DS_STATE_CONDENSED) {
180:       PetscArraycpy(X+k*ld,Q+k*ld,ld);
181:     } else {
182:       PetscArrayzero(X+k*ds->ld,ds->ld);
183:       X[k+k*ds->ld] = 1.0;
184:     }
185:     if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
186:   } else { /* 2x2 block */
187:     if (ds->compact) {
188:       s1 = *(ds->rmat[DS_MAT_D]+k);
189:       d1 = *(ds->rmat[DS_MAT_T]+k);
190:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
191:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
192:     } else {
193:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
194:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
195:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
196:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
197:     }
198:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
199:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
200:     ep = LAPACKlamch_("S");
201:     /* Compute eigenvalues of the block */
202:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
203:     if (wi==0.0) SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
204:     else { /* Complex eigenvalues */
205:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
206:       wr1 /= scal1;
207:       wi  /= scal1;
208: #if !defined(PETSC_USE_COMPLEX)
209:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
210:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
211:       } else {
212:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
213:       }
214:       norm = BLASnrm2_(&four,Y,&one);
215:       norm = 1.0/norm;
216:       if (ds->state >= DS_STATE_CONDENSED) {
217:         alpha = norm;
218:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
219:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
220:       } else {
221:         PetscArrayzero(X+k*ld,2*ld);
222:         X[k*ld+k]       = Y[0]*norm;
223:         X[k*ld+k+1]     = Y[1]*norm;
224:         X[(k+1)*ld+k]   = Y[2]*norm;
225:         X[(k+1)*ld+k+1] = Y[3]*norm;
226:       }
227: #else
228:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
229:         Y[0] = PetscCMPLX(wr1-s2*d2,wi);
230:         Y[1] = s2*e;
231:       } else {
232:         Y[0] = s1*e;
233:         Y[1] = PetscCMPLX(wr1-s1*d1,wi);
234:       }
235:       norm = BLASnrm2_(&two,Y,&one);
236:       norm = 1.0/norm;
237:       if (ds->state >= DS_STATE_CONDENSED) {
238:         alpha = norm;
239:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
240:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
241:       } else {
242:         PetscArrayzero(X+k*ld,2*ld);
243:         X[k*ld+k]   = Y[0]*norm;
244:         X[k*ld+k+1] = Y[1]*norm;
245:       }
246:       X[(k+1)*ld+k]   = PetscConj(X[k*ld+k]);
247:       X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
248: #endif
249:       (*idx)++;
250:     }
251:   }
252:   return(0);
253: }

255: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
256: {
257:   PetscInt       i;
258:   PetscReal      e;

262:   switch (mat) {
263:     case DS_MAT_X:
264:     case DS_MAT_Y:
265:       if (k) {
266:         DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
267:       } else {
268:         for (i=0; i<ds->n; i++) {
269:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
270:           if (e == 0.0) { /* real */
271:             if (ds->state >= DS_STATE_CONDENSED) {
272:               PetscArraycpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld);
273:             } else {
274:               PetscArrayzero(ds->mat[mat]+i*ds->ld,ds->ld);
275:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
276:             }
277:           } else {
278:             DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
279:           }
280:         }
281:       }
282:       break;
283:     case DS_MAT_U:
284:     case DS_MAT_VT:
285:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
286:     default:
287:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
288:   }
289:   return(0);
290: }

292: /*
293:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
294:   Only the index range n0..n1 is processed.
295: */
296: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
297: {
298:   PetscInt     k,ld;
299:   PetscBLASInt two=2;
300:   PetscScalar  *A,*B;
301:   PetscReal    *D,*T;
302:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
303:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

306:   ld = ds->ld;
307:   A = ds->mat[DS_MAT_A];
308:   B = ds->mat[DS_MAT_B];
309:   D = ds->rmat[DS_MAT_D];
310:   T = ds->rmat[DS_MAT_T];
311:   for (k=n0;k<n1;k++) {
312:     if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
313:     else e = 0.0;
314:     if (e==0.0) { /* real eigenvalue */
315:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
316: #if !defined(PETSC_USE_COMPLEX)
317:       wi[k] = 0.0 ;
318: #endif
319:     } else { /* diagonal block */
320:       if (ds->compact) {
321:         s1 = D[k];
322:         d1 = T[k];
323:         s2 = D[k+1];
324:         d2 = T[k+1];
325:       } else {
326:         s1 = PetscRealPart(B[k*ld+k]);
327:         d1 = PetscRealPart(A[k+k*ld]);
328:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
329:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
330:       }
331:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
332:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
333:       ep = LAPACKlamch_("S");
334:       /* Compute eigenvalues of the block */
335:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
336:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
337:       if (wi1==0.0) { /* Real eigenvalues */
338:         if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
339:         wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
340: #if !defined(PETSC_USE_COMPLEX)
341:         wi[k] = wi[k+1] = 0.0;
342: #endif
343:       } else { /* Complex eigenvalues */
344: #if !defined(PETSC_USE_COMPLEX)
345:         wr[k]   = wr1/scal1;
346:         wr[k+1] = wr[k];
347:         wi[k]   = wi1/scal1;
348:         wi[k+1] = -wi[k];
349: #else
350:         wr[k]   = PetscCMPLX(wr1,wi1)/scal1;
351:         wr[k+1] = PetscConj(wr[k]);
352: #endif
353:       }
354:       k++;
355:     }
356:   }
357: #if defined(PETSC_USE_COMPLEX)
358:   if (wi) {
359:     for (k=n0;k<n1;k++) wi[k] = 0.0;
360:   }
361: #endif
362:   return(0);
363: }

365: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
366: {
368:   PetscInt       n,i,*perm;
369:   PetscReal      *d,*e,*s;

372: #if !defined(PETSC_USE_COMPLEX)
374: #endif
375:   n = ds->n;
376:   d = ds->rmat[DS_MAT_T];
377:   e = d + ds->ld;
378:   s = ds->rmat[DS_MAT_D];
379:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
380:   perm = ds->perm;
381:   if (!rr) {
382:     rr = wr;
383:     ri = wi;
384:   }
385:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
386:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
387:   PetscArraycpy(ds->work,wr,n);
388:   for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
389: #if !defined(PETSC_USE_COMPLEX)
390:   PetscArraycpy(ds->work,wi,n);
391:   for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
392: #endif
393:   PetscArraycpy(ds->rwork,s,n);
394:   for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
395:   PetscArraycpy(ds->rwork,d,n);
396:   for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
397:   PetscArraycpy(ds->rwork,e,n-1);
398:   PetscArrayzero(e+ds->l,n-1-ds->l);
399:   for (i=ds->l;i<n-1;i++) {
400:     if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
401:   }
402:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
403:   DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
404:   return(0);
405: }

407: /*
408:   Get eigenvectors with inverse iteration.
409:   The system matrix is in Hessenberg form.
410: */
411: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
412: {
414:   PetscInt       i,off;
415:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
416:   PetscScalar    *A,*B,*H,*X;
417:   PetscReal      *s,*d,*e;
418: #if defined(PETSC_USE_COMPLEX)
419:   PetscInt       j;
420: #endif

423:   PetscBLASIntCast(ds->ld,&ld);
424:   PetscBLASIntCast(ds->n-ds->l,&n1);
425:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
426:   DSAllocateMat_Private(ds,DS_MAT_W);
427:   A = ds->mat[DS_MAT_A];
428:   B = ds->mat[DS_MAT_B];
429:   H = ds->mat[DS_MAT_W];
430:   s = ds->rmat[DS_MAT_D];
431:   d = ds->rmat[DS_MAT_T];
432:   e = d + ld;
433:   select = ds->iwork;
434:   infoC = ds->iwork + ld;
435:   off = ds->l+ds->l*ld;
436:   if (ds->compact) {
437:     H[off] = d[ds->l]*s[ds->l];
438:     H[off+ld] = e[ds->l]*s[ds->l];
439:     for (i=ds->l+1;i<ds->n-1;i++) {
440:       H[i+(i-1)*ld] = e[i-1]*s[i];
441:       H[i+i*ld] = d[i]*s[i];
442:       H[i+(i+1)*ld] = e[i]*s[i];
443:     }
444:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
445:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
446:   } else {
447:     s[ds->l]  = PetscRealPart(B[off]);
448:     H[off]    = A[off]*s[ds->l];
449:     H[off+ld] = A[off+ld]*s[ds->l];
450:     for (i=ds->l+1;i<ds->n-1;i++) {
451:       s[i] = PetscRealPart(B[i+i*ld]);
452:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
453:       H[i+i*ld]     = A[i+i*ld]*s[i];
454:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
455:     }
456:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
457:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
458:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
459:   }
460:   DSAllocateMat_Private(ds,DS_MAT_X);
461:   X = ds->mat[DS_MAT_X];
462:   for (i=0;i<n1;i++) select[i] = 1;
463: #if !defined(PETSC_USE_COMPLEX)
464:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,NULL,infoC,&info));
465: #else
466:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,ds->rwork,NULL,infoC,&info));

468:   /* Separate real and imaginary part of complex eigenvectors */
469:   for (j=ds->l;j<ds->n;j++) {
470:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
471:       for (i=ds->l;i<ds->n;i++) {
472:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
473:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
474:       }
475:       j++;
476:     }
477:   }
478: #endif
479:   SlepcCheckLapackInfo("hsein",info);
480:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
481:   return(0);
482: }

484: /*
485:    Undo 2x2 blocks that have real eigenvalues.
486: */
487: PetscErrorCode DSGHIEPRealBlocks(DS ds)
488: {
490:   PetscInt       i;
491:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
492:   PetscReal      maxy,ep,scal1,scal2,snorm;
493:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
494:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
495:   PetscBLASInt   m,two=2,ld;
496:   PetscBool      isreal;

499:   PetscBLASIntCast(ds->ld,&ld);
500:   PetscBLASIntCast(ds->n-ds->l,&m);
501:   A = ds->mat[DS_MAT_A];
502:   B = ds->mat[DS_MAT_B];
503:   T = ds->rmat[DS_MAT_T];
504:   D = ds->rmat[DS_MAT_D];
505:   DSAllocateWork_Private(ds,2*m,0,0);
506:   for (i=ds->l;i<ds->n-1;i++) {
507:     e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
508:     if (e != 0.0) { /* 2x2 block */
509:       if (ds->compact) {
510:         s1 = D[i];
511:         d1 = T[i];
512:         s2 = D[i+1];
513:         d2 = T[i+1];
514:       } else {
515:         s1 = PetscRealPart(B[i*ld+i]);
516:         d1 = PetscRealPart(A[i*ld+i]);
517:         s2 = PetscRealPart(B[(i+1)*ld+i+1]);
518:         d2 = PetscRealPart(A[(i+1)*ld+i+1]);
519:       }
520:       isreal = PETSC_FALSE;
521:       if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
522:         dd = d1-d2;
523:         if (2*PetscAbsReal(e) <= dd) {
524:           t = 2*e/dd;
525:           t = t/(1 + PetscSqrtReal(1+t*t));
526:         } else {
527:           t = dd/(2*e);
528:           ss = (t>=0)?1.0:-1.0;
529:           t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
530:         }
531:         Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
532:         Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
533:         wr1 = d1+t*e; wr2 = d2-t*e;
534:         ss1 = s1; ss2 = s2;
535:         isreal = PETSC_TRUE;
536:       } else {
537:         ss1 = 1.0; ss2 = 1.0,
538:         M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
539:         b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
540:         ep = LAPACKlamch_("S");

542:         /* Compute eigenvalues of the block */
543:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
544:         if (wi==0.0) { /* Real eigenvalues */
545:           isreal = PETSC_TRUE;
546:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
547:           wr1 /= scal1;
548:           wr2 /= scal2;
549:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
550:             Y[0] = wr1-s2*d2;
551:             Y[1] = s2*e;
552:           } else {
553:             Y[0] = s1*e;
554:             Y[1] = wr1-s1*d1;
555:           }
556:           /* normalize with a signature*/
557:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
558:           scal1 = PetscRealPart(Y[0])/maxy;
559:           scal2 = PetscRealPart(Y[1])/maxy;
560:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
561:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
562:           snorm = maxy*PetscSqrtReal(snorm);
563:           Y[0] = Y[0]/snorm;
564:           Y[1] = Y[1]/snorm;
565:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
566:             Y[2] = wr2-s2*d2;
567:             Y[3] = s2*e;
568:           } else {
569:             Y[2] = s1*e;
570:             Y[3] = wr2-s1*d1;
571:           }
572:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
573:           scal1 = PetscRealPart(Y[2])/maxy;
574:           scal2 = PetscRealPart(Y[3])/maxy;
575:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
576:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
577:           snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
578:         }
579:         wr1 *= ss1; wr2 *= ss2;
580:       }
581:       if (isreal) {
582:         if (ds->compact) {
583:           D[i]    = ss1;
584:           T[i]    = wr1;
585:           D[i+1]  = ss2;
586:           T[i+1]  = wr2;
587:           T[ld+i] = 0.0;
588:         } else {
589:           B[i*ld+i]       = ss1;
590:           A[i*ld+i]       = wr1;
591:           B[(i+1)*ld+i+1] = ss2;
592:           A[(i+1)*ld+i+1] = wr2;
593:           A[(i+1)+ld*i]   = 0.0;
594:           A[i+ld*(i+1)]   = 0.0;
595:         }
596:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&oneS,ds->mat[DS_MAT_Q]+ds->l+i*ld,&ld,Y,&two,&zeroS,ds->work,&m));
597:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
598:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
599:       }
600:       i++;
601:     }
602:   }
603:   return(0);
604: }

606: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
607: {
609:   PetscInt       i,off;
610:   PetscBLASInt   n1,ld,one,info,lwork;
611:   PetscScalar    *H,*A,*B,*Q;
612:   PetscReal      *d,*e,*s;
613: #if defined(PETSC_USE_COMPLEX)
614:   PetscInt       j;
615: #endif

618: #if !defined(PETSC_USE_COMPLEX)
620: #endif
621:   one = 1;
622:   PetscBLASIntCast(ds->n-ds->l,&n1);
623:   PetscBLASIntCast(ds->ld,&ld);
624:   off = ds->l + ds->l*ld;
625:   A = ds->mat[DS_MAT_A];
626:   B = ds->mat[DS_MAT_B];
627:   Q = ds->mat[DS_MAT_Q];
628:   d = ds->rmat[DS_MAT_T];
629:   e = ds->rmat[DS_MAT_T] + ld;
630:   s = ds->rmat[DS_MAT_D];
631:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
632:   lwork = ld*ld;

634:   /* Quick return if possible */
635:   if (n1 == 1) {
636:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
637:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
638:     if (!ds->compact) {
639:       d[ds->l] = PetscRealPart(A[off]);
640:       s[ds->l] = PetscRealPart(B[off]);
641:     }
642:     wr[ds->l] = d[ds->l]/s[ds->l];
643:     if (wi) wi[ds->l] = 0.0;
644:     return(0);
645:   }
646:   /* Reduce to pseudotriadiagonal form */
647:   DSIntermediate_GHIEP(ds);

649:   /* Compute Eigenvalues (QR)*/
650:   DSAllocateMat_Private(ds,DS_MAT_W);
651:   H = ds->mat[DS_MAT_W];
652:   if (ds->compact) {
653:     H[off]    = d[ds->l]*s[ds->l];
654:     H[off+ld] = e[ds->l]*s[ds->l];
655:     for (i=ds->l+1;i<ds->n-1;i++) {
656:       H[i+(i-1)*ld] = e[i-1]*s[i];
657:       H[i+i*ld]     = d[i]*s[i];
658:       H[i+(i+1)*ld] = e[i]*s[i];
659:     }
660:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
661:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
662:   } else {
663:     s[ds->l]  = PetscRealPart(B[off]);
664:     H[off]    = A[off]*s[ds->l];
665:     H[off+ld] = A[off+ld]*s[ds->l];
666:     for (i=ds->l+1;i<ds->n-1;i++) {
667:       s[i] = PetscRealPart(B[i+i*ld]);
668:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
669:       H[i+i*ld]     = A[i+i*ld]*s[i];
670:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
671:     }
672:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
673:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
674:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
675:   }

677: #if !defined(PETSC_USE_COMPLEX)
678:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
679: #else
680:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
681:   for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
682:   /* Sort to have consecutive conjugate pairs */
683:   for (i=ds->l;i<ds->n;i++) {
684:       j=i+1;
685:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
686:       if (j==ds->n) {
687:         if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
688:         else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
689:       } else { /* complex eigenvalue */
690:         wr[j] = wr[i+1];
691:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
692:         wr[i+1] = PetscConj(wr[i]);
693:         i++;
694:       }
695:   }
696: #endif
697:   SlepcCheckLapackInfo("hseqr",info);
698:   /* Compute Eigenvectors with Inverse Iteration */
699:   DSGHIEPInverseIteration(ds,wr,wi);

701:   /* Recover eigenvalues from diagonal */
702:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
703: #if defined(PETSC_USE_COMPLEX)
704:   if (wi) {
705:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
706:   }
707: #endif
708:   return(0);
709: }

711: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
712: {
714:   PetscInt       i,j,off,nwu=0,n,lw,lwr,nwru=0;
715:   PetscBLASInt   n_,ld,info,lwork,ilo,ihi;
716:   PetscScalar    *H,*A,*B,*Q,*X;
717:   PetscReal      *d,*s,*scale,nrm,*rcde,*rcdv;
718: #if defined(PETSC_USE_COMPLEX)
719:   PetscInt       k;
720: #endif

723: #if !defined(PETSC_USE_COMPLEX)
725: #endif
726:   n = ds->n-ds->l;
727:   PetscBLASIntCast(n,&n_);
728:   PetscBLASIntCast(ds->ld,&ld);
729:   off = ds->l + ds->l*ld;
730:   A = ds->mat[DS_MAT_A];
731:   B = ds->mat[DS_MAT_B];
732:   Q = ds->mat[DS_MAT_Q];
733:   d = ds->rmat[DS_MAT_T];
734:   s = ds->rmat[DS_MAT_D];
735:   lw = 14*ld+ld*ld;
736:   lwr = 7*ld;
737:   DSAllocateWork_Private(ds,lw,lwr,0);
738:   scale = ds->rwork+nwru;
739:   nwru += ld;
740:   rcde = ds->rwork+nwru;
741:   nwru += ld;
742:   rcdv = ds->rwork+nwru;
743:   nwru += ld;
744:   /* Quick return if possible */
745:   if (n_ == 1) {
746:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
747:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
748:     if (!ds->compact) {
749:       d[ds->l] = PetscRealPart(A[off]);
750:       s[ds->l] = PetscRealPart(B[off]);
751:     }
752:     wr[ds->l] = d[ds->l]/s[ds->l];
753:     if (wi) wi[ds->l] = 0.0;
754:     return(0);
755:   }

757:   /* Form pseudo-symmetric matrix */
758:   H =  ds->work+nwu;
759:   nwu += n*n;
760:   PetscArrayzero(H,n*n);
761:   if (ds->compact) {
762:     for (i=0;i<n-1;i++) {
763:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
764:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
765:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
766:     }
767:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
768:     for (i=0;i<ds->k-ds->l;i++) {
769:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
770:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
771:     }
772:   } else {
773:     for (j=0;j<n;j++) {
774:       for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
775:     }
776:   }

778:   /* Compute eigenpairs */
779:   PetscBLASIntCast(lw-nwu,&lwork);
780:   DSAllocateMat_Private(ds,DS_MAT_X);
781:   X = ds->mat[DS_MAT_X];
782: #if !defined(PETSC_USE_COMPLEX)
783:   PetscStackCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,NULL,&info));
784: #else
785:   PetscStackCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,ds->rwork+nwru,&info));

787:   /* Sort to have consecutive conjugate pairs
788:      Separate real and imaginary part of complex eigenvectors*/
789:   for (i=ds->l;i<ds->n;i++) {
790:     j=i+1;
791:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
792:     if (j==ds->n) {
793:       if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
794:         wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
795:         for (k=ds->l;k<ds->n;k++) {
796:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
797:         }
798:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
799:     } else { /* complex eigenvalue */
800:       if (j!=i+1) {
801:         wr[j] = wr[i+1];
802:         PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
803:       }
804:       if (PetscImaginaryPart(wr[i])<0) {
805:         wr[i] = PetscConj(wr[i]);
806:         for (k=ds->l;k<ds->n;k++) {
807:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
808:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
809:         }
810:       } else {
811:         for (k=ds->l;k<ds->n;k++) {
812:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
813:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
814:         }
815:       }
816:       wr[i+1] = PetscConj(wr[i]);
817:       i++;
818:     }
819:   }
820: #endif
821:   SlepcCheckLapackInfo("geevx",info);

823:   /* Compute real s-orthonormal basis */
824:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE);

826:   /* Recover eigenvalues from diagonal */
827:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
828: #if defined(PETSC_USE_COMPLEX)
829:   if (wi) {
830:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
831:   }
832: #endif
833:   return(0);
834: }

836: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
837: {
839:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
840:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;

843:   if (ds->compact) kr = 4*ld;
844:   else k = 2*(ds->n-l)*ld;
845:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
846:   if (eigr) k += (ds->n-l);
847:   if (eigi) k += (ds->n-l);
848:   DSAllocateWork_Private(ds,k+kr,0,0);
849:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
850:   PetscMPIIntCast(ds->n-l,&n);
851:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
852:   PetscMPIIntCast(ld*3,&ld3);
853:   PetscMPIIntCast(ld,&ld_);
854:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
855:   if (!rank) {
856:     if (ds->compact) {
857:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
858:       MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
859:     } else {
860:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
861:       MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
862:     }
863:     if (ds->state>DS_STATE_RAW) {
864:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
865:     }
866:     if (eigr) {
867:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
868:     }
869:     if (eigi) {
870:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
871:     }
872:   }
873:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
874:   if (rank) {
875:     if (ds->compact) {
876:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
877:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));
878:     } else {
879:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
880:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
881:     }
882:     if (ds->state>DS_STATE_RAW) {
883:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
884:     }
885:     if (eigr) {
886:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
887:     }
888:     if (eigi) {
889:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
890:     }
891:   }
892:   return(0);
893: }

895: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
896: {
898:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
899:   else *flg = PETSC_FALSE;
900:   return(0);
901: }

903: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
904: {
906:   ds->ops->allocate      = DSAllocate_GHIEP;
907:   ds->ops->view          = DSView_GHIEP;
908:   ds->ops->vectors       = DSVectors_GHIEP;
909:   ds->ops->solve[0]      = DSSolve_GHIEP_QR_II;
910:   ds->ops->solve[1]      = DSSolve_GHIEP_HZ;
911:   ds->ops->solve[2]      = DSSolve_GHIEP_QR;
912:   ds->ops->sort          = DSSort_GHIEP;
913:   ds->ops->synchronize   = DSSynchronize_GHIEP;
914:   ds->ops->hermitian     = DSHermitian_GHIEP;
915:   return(0);
916: }