Actual source code: dsghiep.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_GHIEP(DS ds,PetscInt ld)
 15: {
 16:   DSAllocateMat_Private(ds,DS_MAT_A);
 17:   DSAllocateMat_Private(ds,DS_MAT_B);
 18:   DSAllocateMat_Private(ds,DS_MAT_Q);
 19:   DSAllocateMatReal_Private(ds,DS_MAT_T);
 20:   DSAllocateMatReal_Private(ds,DS_MAT_D);
 21:   PetscFree(ds->perm);
 22:   PetscMalloc1(ld,&ds->perm);
 23:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 24:   PetscFunctionReturn(0);
 25: }

 27: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
 28: {
 29:   PetscReal      *T,*S;
 30:   PetscScalar    *A,*B;
 31:   PetscInt       i,n,ld;

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

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

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

111:       PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n);
112:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n);
113:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
114:       for (i=0;i<ds->n;i++) PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_D]+i));
115:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

117:     } else {
118:       PetscViewerASCIIPrintf(viewer,"T\n");
119:       for (i=0;i<ds->n;i++) {
120:         for (j=0;j<ds->n;j++) {
121:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
122:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
123:           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));
124:           else value = 0.0;
125:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
126:         }
127:         PetscViewerASCIIPrintf(viewer,"\n");
128:       }
129:       PetscViewerASCIIPrintf(viewer,"omega\n");
130:       for (i=0;i<ds->n;i++) {
131:         for (j=0;j<ds->n;j++) {
132:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
133:           else value = 0.0;
134:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
135:         }
136:         PetscViewerASCIIPrintf(viewer,"\n");
137:       }
138:     }
139:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
140:     PetscViewerFlush(viewer);
141:   } else {
142:     DSViewMat(ds,viewer,DS_MAT_A);
143:     DSViewMat(ds,viewer,DS_MAT_B);
144:   }
145:   if (ds->state>DS_STATE_INTERMEDIATE) DSViewMat(ds,viewer,DS_MAT_Q);
146:   PetscFunctionReturn(0);
147: }

149: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
150: {
151:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
152:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
153:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
154:   PetscInt       k;
155:   PetscBLASInt   two = 2,n_,ld,one=1;
156: #if !defined(PETSC_USE_COMPLEX)
157:   PetscBLASInt   four=4;
158: #endif

160:   X = ds->mat[DS_MAT_X];
161:   Q = ds->mat[DS_MAT_Q];
162:   k = *idx;
163:   PetscBLASIntCast(ds->n,&n_);
164:   PetscBLASIntCast(ds->ld,&ld);
165:   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));
166:   else e = 0.0;
167:   if (e == 0.0) { /* Real */
168:     if (ds->state>=DS_STATE_CONDENSED) PetscArraycpy(X+k*ld,Q+k*ld,ld);
169:     else {
170:       PetscArrayzero(X+k*ds->ld,ds->ld);
171:       X[k+k*ds->ld] = 1.0;
172:     }
173:     if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
174:   } else { /* 2x2 block */
175:     if (ds->compact) {
176:       s1 = *(ds->rmat[DS_MAT_D]+k);
177:       d1 = *(ds->rmat[DS_MAT_T]+k);
178:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
179:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
180:     } else {
181:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
182:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
183:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
184:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
185:     }
186:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
187:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
188:     ep = LAPACKlamch_("S");
189:     /* Compute eigenvalues of the block */
190:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
192:     else { /* Complex eigenvalues */
194:       wr1 /= scal1;
195:       wi  /= scal1;
196: #if !defined(PETSC_USE_COMPLEX)
197:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
198:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
199:       } else {
200:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
201:       }
202:       norm = BLASnrm2_(&four,Y,&one);
203:       norm = 1.0/norm;
204:       if (ds->state >= DS_STATE_CONDENSED) {
205:         alpha = norm;
206:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
207:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
208:       } else {
209:         PetscArrayzero(X+k*ld,2*ld);
210:         X[k*ld+k]       = Y[0]*norm;
211:         X[k*ld+k+1]     = Y[1]*norm;
212:         X[(k+1)*ld+k]   = Y[2]*norm;
213:         X[(k+1)*ld+k+1] = Y[3]*norm;
214:       }
215: #else
216:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
217:         Y[0] = PetscCMPLX(wr1-s2*d2,wi);
218:         Y[1] = s2*e;
219:       } else {
220:         Y[0] = s1*e;
221:         Y[1] = PetscCMPLX(wr1-s1*d1,wi);
222:       }
223:       norm = BLASnrm2_(&two,Y,&one);
224:       norm = 1.0/norm;
225:       if (ds->state >= DS_STATE_CONDENSED) {
226:         alpha = norm;
227:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
228:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
229:       } else {
230:         PetscArrayzero(X+k*ld,2*ld);
231:         X[k*ld+k]   = Y[0]*norm;
232:         X[k*ld+k+1] = Y[1]*norm;
233:       }
234:       X[(k+1)*ld+k]   = PetscConj(X[k*ld+k]);
235:       X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
236: #endif
237:       (*idx)++;
238:     }
239:   }
240:   PetscFunctionReturn(0);
241: }

243: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
244: {
245:   PetscInt       i;
246:   PetscReal      e;

248:   switch (mat) {
249:     case DS_MAT_X:
250:     case DS_MAT_Y:
251:       if (k) DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
252:       else {
253:         for (i=0; i<ds->n; i++) {
254:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
255:           if (e == 0.0) { /* real */
256:             if (ds->state >= DS_STATE_CONDENSED) PetscArraycpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld);
257:             else {
258:               PetscArrayzero(ds->mat[mat]+i*ds->ld,ds->ld);
259:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
260:             }
261:           } else DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
262:         }
263:       }
264:       break;
265:     case DS_MAT_U:
266:     case DS_MAT_V:
267:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
268:     default:
269:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
270:   }
271:   PetscFunctionReturn(0);
272: }

274: /*
275:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
276:   Only the index range n0..n1 is processed.
277: */
278: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
279: {
280:   PetscInt     k,ld;
281:   PetscBLASInt two=2;
282:   PetscScalar  *A,*B;
283:   PetscReal    *D,*T;
284:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
285:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

287:   ld = ds->ld;
288:   A = ds->mat[DS_MAT_A];
289:   B = ds->mat[DS_MAT_B];
290:   D = ds->rmat[DS_MAT_D];
291:   T = ds->rmat[DS_MAT_T];
292:   for (k=n0;k<n1;k++) {
293:     if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
294:     else e = 0.0;
295:     if (e==0.0) { /* real eigenvalue */
296:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
297: #if !defined(PETSC_USE_COMPLEX)
298:       wi[k] = 0.0 ;
299: #endif
300:     } else { /* diagonal block */
301:       if (ds->compact) {
302:         s1 = D[k];
303:         d1 = T[k];
304:         s2 = D[k+1];
305:         d2 = T[k+1];
306:       } else {
307:         s1 = PetscRealPart(B[k*ld+k]);
308:         d1 = PetscRealPart(A[k+k*ld]);
309:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
310:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
311:       }
312:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
313:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
314:       ep = LAPACKlamch_("S");
315:       /* Compute eigenvalues of the block */
316:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
318:       if (wi1==0.0) { /* Real eigenvalues */
320:         wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
321: #if !defined(PETSC_USE_COMPLEX)
322:         wi[k] = wi[k+1] = 0.0;
323: #endif
324:       } else { /* Complex eigenvalues */
325: #if !defined(PETSC_USE_COMPLEX)
326:         wr[k]   = wr1/scal1;
327:         wr[k+1] = wr[k];
328:         wi[k]   = wi1/scal1;
329:         wi[k+1] = -wi[k];
330: #else
331:         wr[k]   = PetscCMPLX(wr1,wi1)/scal1;
332:         wr[k+1] = PetscConj(wr[k]);
333: #endif
334:       }
335:       k++;
336:     }
337:   }
338: #if defined(PETSC_USE_COMPLEX)
339:   if (wi) {
340:     for (k=n0;k<n1;k++) wi[k] = 0.0;
341:   }
342: #endif
343:   PetscFunctionReturn(0);
344: }

346: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
347: {
348:   PetscInt       n,i,*perm;
349:   PetscReal      *d,*e,*s;

351: #if !defined(PETSC_USE_COMPLEX)
353: #endif
354:   n = ds->n;
355:   d = ds->rmat[DS_MAT_T];
356:   e = d + ds->ld;
357:   s = ds->rmat[DS_MAT_D];
358:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
359:   perm = ds->perm;
360:   if (!rr) {
361:     rr = wr;
362:     ri = wi;
363:   }
364:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
365:   if (!ds->compact) DSSwitchFormat_GHIEP(ds,PETSC_TRUE);
366:   PetscArraycpy(ds->work,wr,n);
367:   for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
368: #if !defined(PETSC_USE_COMPLEX)
369:   PetscArraycpy(ds->work,wi,n);
370:   for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
371: #endif
372:   PetscArraycpy(ds->rwork,s,n);
373:   for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
374:   PetscArraycpy(ds->rwork,d,n);
375:   for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
376:   PetscArraycpy(ds->rwork,e,n-1);
377:   PetscArrayzero(e+ds->l,n-1-ds->l);
378:   for (i=ds->l;i<n-1;i++) {
379:     if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
380:   }
381:   if (!ds->compact) DSSwitchFormat_GHIEP(ds,PETSC_FALSE);
382:   DSPermuteColumns_Private(ds,ds->l,n,n,DS_MAT_Q,perm);
383:   PetscFunctionReturn(0);
384: }

386: PetscErrorCode DSUpdateExtraRow_GHIEP(DS ds)
387: {
388:   PetscInt       i;
389:   PetscBLASInt   n,ld,incx=1;
390:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
391:   PetscReal      *b,*r,beta;

393:   PetscBLASIntCast(ds->n,&n);
394:   PetscBLASIntCast(ds->ld,&ld);
395:   A  = ds->mat[DS_MAT_A];
396:   Q  = ds->mat[DS_MAT_Q];
397:   b  = ds->rmat[DS_MAT_T]+ld;
398:   r  = ds->rmat[DS_MAT_T]+2*ld;

400:   if (ds->compact) {
401:     beta = b[n-1];   /* in compact, we assume all entries are zero except the last one */
402:     for (i=0;i<n;i++) r[i] = PetscRealPart(beta*Q[n-1+i*ld]);
403:     ds->k = n;
404:   } else {
405:     DSAllocateWork_Private(ds,2*ld,0,0);
406:     x = ds->work;
407:     y = ds->work+ld;
408:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
409:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
410:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
411:     ds->k = n;
412:   }
413:   PetscFunctionReturn(0);
414: }

416: /*
417:   Get eigenvectors with inverse iteration.
418:   The system matrix is in Hessenberg form.
419: */
420: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
421: {
422:   PetscInt       i,off;
423:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
424:   PetscScalar    *A,*B,*H,*X;
425:   PetscReal      *s,*d,*e;
426: #if defined(PETSC_USE_COMPLEX)
427:   PetscInt       j;
428: #endif

430:   PetscBLASIntCast(ds->ld,&ld);
431:   PetscBLASIntCast(ds->n-ds->l,&n1);
432:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
433:   DSAllocateMat_Private(ds,DS_MAT_W);
434:   A = ds->mat[DS_MAT_A];
435:   B = ds->mat[DS_MAT_B];
436:   H = ds->mat[DS_MAT_W];
437:   s = ds->rmat[DS_MAT_D];
438:   d = ds->rmat[DS_MAT_T];
439:   e = d + ld;
440:   select = ds->iwork;
441:   infoC = ds->iwork + ld;
442:   off = ds->l+ds->l*ld;
443:   if (ds->compact) {
444:     H[off] = d[ds->l]*s[ds->l];
445:     H[off+ld] = e[ds->l]*s[ds->l];
446:     for (i=ds->l+1;i<ds->n-1;i++) {
447:       H[i+(i-1)*ld] = e[i-1]*s[i];
448:       H[i+i*ld] = d[i]*s[i];
449:       H[i+(i+1)*ld] = e[i]*s[i];
450:     }
451:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
452:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
453:   } else {
454:     s[ds->l]  = PetscRealPart(B[off]);
455:     H[off]    = A[off]*s[ds->l];
456:     H[off+ld] = A[off+ld]*s[ds->l];
457:     for (i=ds->l+1;i<ds->n-1;i++) {
458:       s[i] = PetscRealPart(B[i+i*ld]);
459:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
460:       H[i+i*ld]     = A[i+i*ld]*s[i];
461:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
462:     }
463:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
464:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
465:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
466:   }
467:   DSAllocateMat_Private(ds,DS_MAT_X);
468:   X = ds->mat[DS_MAT_X];
469:   for (i=0;i<n1;i++) select[i] = 1;
470: #if !defined(PETSC_USE_COMPLEX)
471:   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));
472: #else
473:   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));

475:   /* Separate real and imaginary part of complex eigenvectors */
476:   for (j=ds->l;j<ds->n;j++) {
477:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
478:       for (i=ds->l;i<ds->n;i++) {
479:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
480:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
481:       }
482:       j++;
483:     }
484:   }
485: #endif
486:   SlepcCheckLapackInfo("hsein",info);
487:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
488:   PetscFunctionReturn(0);
489: }

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

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

547:         /* Compute eigenvalues of the block */
548:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
549:         if (wi==0.0) { /* Real eigenvalues */
550:           isreal = PETSC_TRUE;
552:           wr1 /= scal1;
553:           wr2 /= scal2;
554:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
555:             Y[0] = wr1-s2*d2;
556:             Y[1] = s2*e;
557:           } else {
558:             Y[0] = s1*e;
559:             Y[1] = wr1-s1*d1;
560:           }
561:           /* normalize with a signature*/
562:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
563:           scal1 = PetscRealPart(Y[0])/maxy;
564:           scal2 = PetscRealPart(Y[1])/maxy;
565:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
566:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
567:           snorm = maxy*PetscSqrtReal(snorm);
568:           Y[0] = Y[0]/snorm;
569:           Y[1] = Y[1]/snorm;
570:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
571:             Y[2] = wr2-s2*d2;
572:             Y[3] = s2*e;
573:           } else {
574:             Y[2] = s1*e;
575:             Y[3] = wr2-s1*d1;
576:           }
577:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
578:           scal1 = PetscRealPart(Y[2])/maxy;
579:           scal2 = PetscRealPart(Y[3])/maxy;
580:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
581:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
582:           snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
583:         }
584:         wr1 *= ss1; wr2 *= ss2;
585:       }
586:       if (isreal) {
587:         if (ds->compact) {
588:           D[i]    = ss1;
589:           T[i]    = wr1;
590:           D[i+1]  = ss2;
591:           T[i+1]  = wr2;
592:           T[ld+i] = 0.0;
593:         } else {
594:           B[i*ld+i]       = ss1;
595:           A[i*ld+i]       = wr1;
596:           B[(i+1)*ld+i+1] = ss2;
597:           A[(i+1)*ld+i+1] = wr2;
598:           A[(i+1)+ld*i]   = 0.0;
599:           A[i+ld*(i+1)]   = 0.0;
600:         }
601:         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));
602:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
603:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
604:       }
605:       i++;
606:     }
607:   }
608:   PetscFunctionReturn(0);
609: }

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

621: #if !defined(PETSC_USE_COMPLEX)
623: #endif
624:   one = 1;
625:   PetscBLASIntCast(ds->n-ds->l,&n1);
626:   PetscBLASIntCast(ds->ld,&ld);
627:   off = ds->l + ds->l*ld;
628:   A = ds->mat[DS_MAT_A];
629:   B = ds->mat[DS_MAT_B];
630:   Q = ds->mat[DS_MAT_Q];
631:   d = ds->rmat[DS_MAT_T];
632:   e = ds->rmat[DS_MAT_T] + ld;
633:   s = ds->rmat[DS_MAT_D];
634: #if defined(PETSC_USE_DEBUG)
635:   /* Check signature */
636:   for (i=0;i<ds->n;i++) {
637:     PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
639:   }
640: #endif
641:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
642:   lwork = ld*ld;

644:   /* Quick return if possible */
645:   if (n1 == 1) {
646:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
647:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
648:     if (!ds->compact) {
649:       d[ds->l] = PetscRealPart(A[off]);
650:       s[ds->l] = PetscRealPart(B[off]);
651:     }
652:     wr[ds->l] = d[ds->l]/s[ds->l];
653:     if (wi) wi[ds->l] = 0.0;
654:     PetscFunctionReturn(0);
655:   }
656:   /* Reduce to pseudotriadiagonal form */
657:   DSIntermediate_GHIEP(ds);

659:   /* Compute Eigenvalues (QR) */
660:   DSAllocateMat_Private(ds,DS_MAT_W);
661:   H = ds->mat[DS_MAT_W];
662:   if (ds->compact) {
663:     H[off]    = d[ds->l]*s[ds->l];
664:     H[off+ld] = e[ds->l]*s[ds->l];
665:     for (i=ds->l+1;i<ds->n-1;i++) {
666:       H[i+(i-1)*ld] = e[i-1]*s[i];
667:       H[i+i*ld]     = d[i]*s[i];
668:       H[i+(i+1)*ld] = e[i]*s[i];
669:     }
670:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
671:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
672:   } else {
673:     s[ds->l]  = PetscRealPart(B[off]);
674:     H[off]    = A[off]*s[ds->l];
675:     H[off+ld] = A[off+ld]*s[ds->l];
676:     for (i=ds->l+1;i<ds->n-1;i++) {
677:       s[i] = PetscRealPart(B[i+i*ld]);
678:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
679:       H[i+i*ld]     = A[i+i*ld]*s[i];
680:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
681:     }
682:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
683:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
684:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
685:   }

687: #if !defined(PETSC_USE_COMPLEX)
688:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
689: #else
690:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
691:   for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
692:   /* Sort to have consecutive conjugate pairs */
693:   for (i=ds->l;i<ds->n;i++) {
694:       j=i+1;
695:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
696:       if (j==ds->n) {
698:         wr[i]=PetscRealPart(wr[i]);
699:       } else { /* complex eigenvalue */
700:         wr[j] = wr[i+1];
701:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
702:         wr[i+1] = PetscConj(wr[i]);
703:         i++;
704:       }
705:   }
706: #endif
707:   SlepcCheckLapackInfo("hseqr",info);
708:   /* Compute Eigenvectors with Inverse Iteration */
709:   DSGHIEPInverseIteration(ds,wr,wi);

711:   /* Recover eigenvalues from diagonal */
712:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
713: #if defined(PETSC_USE_COMPLEX)
714:   if (wi) {
715:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
716:   }
717: #endif
718:   PetscFunctionReturn(0);
719: }

721: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
722: {
723:   PetscInt       i,j,off,nwu=0,n,lw,lwr,nwru=0;
724:   PetscBLASInt   n_,ld,info,lwork,ilo,ihi;
725:   PetscScalar    *H,*A,*B,*Q,*X;
726:   PetscReal      *d,*s,*scale,nrm,*rcde,*rcdv;
727: #if defined(PETSC_USE_COMPLEX)
728:   PetscInt       k;
729: #endif

731: #if !defined(PETSC_USE_COMPLEX)
733: #endif
734:   n = ds->n-ds->l;
735:   PetscBLASIntCast(n,&n_);
736:   PetscBLASIntCast(ds->ld,&ld);
737:   off = ds->l + ds->l*ld;
738:   A = ds->mat[DS_MAT_A];
739:   B = ds->mat[DS_MAT_B];
740:   Q = ds->mat[DS_MAT_Q];
741:   d = ds->rmat[DS_MAT_T];
742:   s = ds->rmat[DS_MAT_D];
743: #if defined(PETSC_USE_DEBUG)
744:   /* Check signature */
745:   for (i=0;i<ds->n;i++) {
746:     PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
748:   }
749: #endif
750:   lw = 14*ld+ld*ld;
751:   lwr = 7*ld;
752:   DSAllocateWork_Private(ds,lw,lwr,0);
753:   scale = ds->rwork+nwru;
754:   nwru += ld;
755:   rcde = ds->rwork+nwru;
756:   nwru += ld;
757:   rcdv = ds->rwork+nwru;
758:   /* Quick return if possible */
759:   if (n_ == 1) {
760:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
761:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
762:     if (!ds->compact) {
763:       d[ds->l] = PetscRealPart(A[off]);
764:       s[ds->l] = PetscRealPart(B[off]);
765:     }
766:     wr[ds->l] = d[ds->l]/s[ds->l];
767:     if (wi) wi[ds->l] = 0.0;
768:     PetscFunctionReturn(0);
769:   }

771:   /* Form pseudo-symmetric matrix */
772:   H =  ds->work+nwu;
773:   nwu += n*n;
774:   PetscArrayzero(H,n*n);
775:   if (ds->compact) {
776:     for (i=0;i<n-1;i++) {
777:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
778:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
779:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
780:     }
781:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
782:     for (i=0;i<ds->k-ds->l;i++) {
783:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
784:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
785:     }
786:   } else {
787:     for (j=0;j<n;j++) {
788:       for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
789:     }
790:   }

792:   /* Compute eigenpairs */
793:   PetscBLASIntCast(lw-nwu,&lwork);
794:   DSAllocateMat_Private(ds,DS_MAT_X);
795:   X = ds->mat[DS_MAT_X];
796: #if !defined(PETSC_USE_COMPLEX)
797:   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));
798: #else
799:   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));

801:   /* Sort to have consecutive conjugate pairs
802:      Separate real and imaginary part of complex eigenvectors*/
803:   for (i=ds->l;i<ds->n;i++) {
804:     j=i+1;
805:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
806:     if (j==ds->n) {
808:       wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
809:       for (k=ds->l;k<ds->n;k++) {
810:         X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
811:       }
812:     } else { /* complex eigenvalue */
813:       if (j!=i+1) {
814:         wr[j] = wr[i+1];
815:         PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
816:       }
817:       if (PetscImaginaryPart(wr[i])<0) {
818:         wr[i] = PetscConj(wr[i]);
819:         for (k=ds->l;k<ds->n;k++) {
820:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
821:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
822:         }
823:       } else {
824:         for (k=ds->l;k<ds->n;k++) {
825:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
826:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
827:         }
828:       }
829:       wr[i+1] = PetscConj(wr[i]);
830:       i++;
831:     }
832:   }
833: #endif
834:   SlepcCheckLapackInfo("geevx",info);

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

839:   /* Recover eigenvalues from diagonal */
840:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
841: #if defined(PETSC_USE_COMPLEX)
842:   if (wi) {
843:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
844:   }
845: #endif
846:   PetscFunctionReturn(0);
847: }

849: PetscErrorCode DSGetTruncateSize_GHIEP(DS ds,PetscInt l,PetscInt n,PetscInt *k)
850: {
851:   PetscReal *T = ds->rmat[DS_MAT_T];

853:   if (T[l+(*k)-1+ds->ld] !=0.0) {
854:     if (l+(*k)<n-1) (*k)++;
855:     else (*k)--;
856:   }
857:   PetscFunctionReturn(0);
858: }

860: PetscErrorCode DSTruncate_GHIEP(DS ds,PetscInt n,PetscBool trim)
861: {
862:   PetscInt    i,ld=ds->ld,l=ds->l;
863:   PetscScalar *A = ds->mat[DS_MAT_A];
864:   PetscReal   *T = ds->rmat[DS_MAT_T],*b,*r,*omega;

866: #if defined(PETSC_USE_DEBUG)
867:   /* make sure diagonal 2x2 block is not broken */
869: #endif
870:   if (trim) {
871:     if (!ds->compact && ds->extrarow) {   /* clean extra row */
872:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
873:     }
874:     ds->l = 0;
875:     ds->k = 0;
876:     ds->n = n;
877:     ds->t = ds->n;   /* truncated length equal to the new dimension */
878:   } else {
879:     if (!ds->compact && ds->extrarow && ds->k==ds->n) {
880:       /* copy entries of extra row to the new position, then clean last row */
881:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
882:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
883:     }
884:     if (ds->compact) {
885:       b = T+ld;
886:       r = T+2*ld;
887:       omega = ds->rmat[DS_MAT_D];
888:       b[n-1] = r[n-1];
889:       b[n] = b[ds->n];
890:       omega[n] = omega[ds->n];
891:     }
892:     ds->k = (ds->extrarow)? n: 0;
893:     ds->t = ds->n;   /* truncated length equal to previous dimension */
894:     ds->n = n;
895:   }
896:   PetscFunctionReturn(0);
897: }

899: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
900: {
901:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
902:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;

904:   if (ds->compact) kr = 4*ld;
905:   else k = 2*(ds->n-l)*ld;
906:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
907:   if (eigr) k += (ds->n-l);
908:   if (eigi) k += (ds->n-l);
909:   DSAllocateWork_Private(ds,k+kr,0,0);
910:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
911:   PetscMPIIntCast(ds->n-l,&n);
912:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
913:   PetscMPIIntCast(ld*3,&ld3);
914:   PetscMPIIntCast(ld,&ld_);
915:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
916:   if (!rank) {
917:     if (ds->compact) {
918:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
919:       MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
920:     } else {
921:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
922:       MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
923:     }
924:     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));
925:     if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
926: #if !defined(PETSC_USE_COMPLEX)
927:     if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
928: #endif
929:   }
930:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
931:   if (rank) {
932:     if (ds->compact) {
933:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
934:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));
935:     } else {
936:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
937:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
938:     }
939:     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));
940:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
941: #if !defined(PETSC_USE_COMPLEX)
942:     if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
943: #endif
944:   }
945:   PetscFunctionReturn(0);
946: }

948: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
949: {
950:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
951:   else *flg = PETSC_FALSE;
952:   PetscFunctionReturn(0);
953: }

955: /*MC
956:    DSGHIEP - Dense Generalized Hermitian Indefinite Eigenvalue Problem.

958:    Level: beginner

960:    Notes:
961:    The problem is expressed as A*X = B*X*Lambda, where both A and B are
962:    real symmetric (or complex Hermitian) and possibly indefinite. Lambda
963:    is a diagonal matrix whose diagonal elements are the arguments of DSSolve().
964:    After solve, A is overwritten with Lambda. Note that in the case of real
965:    scalars, A is overwritten with a real representation of Lambda, i.e.,
966:    complex conjugate eigenvalue pairs are stored as a 2x2 block in the
967:    quasi-diagonal matrix.

969:    In the intermediate state A is reduced to tridiagonal form and B is
970:    transformed into a signature matrix. In compact storage format, these
971:    matrices are stored in T and D, respectively.

973:    Used DS matrices:
974: +  DS_MAT_A - first problem matrix
975: .  DS_MAT_B - second problem matrix
976: .  DS_MAT_T - symmetric tridiagonal matrix of the reduced pencil
977: .  DS_MAT_D - diagonal matrix (signature) of the reduced pencil
978: -  DS_MAT_Q - pseudo-orthogonal transformation that reduces (A,B) to
979:    tridiagonal-diagonal form (intermediate step) or a real basis of eigenvectors

981:    Implemented methods:
982: +  0 - QR iteration plus inverse iteration for the eigenvectors
983: .  1 - HZ iteration
984: -  2 - QR iteration plus pseudo-orthogonalization for the eigenvectors

986:    References:
987: .  1. - C. Campos and J. E. Roman, "Restarted Q-Arnoldi-type methods exploiting
988:    symmetry in quadratic eigenvalue problems", BIT Numer. Math. 56(4):1213-1236, 2016.

990: .seealso: DSCreate(), DSSetType(), DSType
991: M*/
992: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
993: {
994:   ds->ops->allocate        = DSAllocate_GHIEP;
995:   ds->ops->view            = DSView_GHIEP;
996:   ds->ops->vectors         = DSVectors_GHIEP;
997:   ds->ops->solve[0]        = DSSolve_GHIEP_QR_II;
998:   ds->ops->solve[1]        = DSSolve_GHIEP_HZ;
999:   ds->ops->solve[2]        = DSSolve_GHIEP_QR;
1000:   ds->ops->sort            = DSSort_GHIEP;
1001:   ds->ops->synchronize     = DSSynchronize_GHIEP;
1002:   ds->ops->gettruncatesize = DSGetTruncateSize_GHIEP;
1003:   ds->ops->truncate        = DSTruncate_GHIEP;
1004:   ds->ops->update          = DSUpdateExtraRow_GHIEP;
1005:   ds->ops->hermitian       = DSHermitian_GHIEP;
1006:   PetscFunctionReturn(0);
1007: }