Actual source code: dsgnhep.c

slepc-3.12.0 2019-09-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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: /*
 15:   1) Patterns of A and B
 16:       DS_STATE_RAW:       DS_STATE_INTERM/CONDENSED
 17:        0       n-1              0       n-1
 18:       -------------            -------------
 19:     0 |* * * * * *|          0 |* * * * * *|
 20:       |* * * * * *|            |  * * * * *|
 21:       |* * * * * *|            |    * * * *|
 22:       |* * * * * *|            |    * * * *|
 23:       |* * * * * *|            |        * *|
 24:   n-1 |* * * * * *|        n-1 |          *|
 25:       -------------            -------------

 27:   2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
 28: */


 31: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY);

 33: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
 34: {

 38:   DSAllocateMat_Private(ds,DS_MAT_A);
 39:   DSAllocateMat_Private(ds,DS_MAT_B);
 40:   DSAllocateMat_Private(ds,DS_MAT_Z);
 41:   DSAllocateMat_Private(ds,DS_MAT_Q);
 42:   PetscFree(ds->perm);
 43:   PetscMalloc1(ld,&ds->perm);
 44:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 45:   return(0);
 46: }

 48: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
 49: {
 50:   PetscErrorCode    ierr;
 51:   PetscViewerFormat format;

 54:   PetscViewerGetFormat(viewer,&format);
 55:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
 56:   DSViewMat(ds,viewer,DS_MAT_A);
 57:   DSViewMat(ds,viewer,DS_MAT_B);
 58:   if (ds->state>DS_STATE_INTERMEDIATE) {
 59:     DSViewMat(ds,viewer,DS_MAT_Z);
 60:     DSViewMat(ds,viewer,DS_MAT_Q);
 61:   }
 62:   if (ds->mat[DS_MAT_X]) { DSViewMat(ds,viewer,DS_MAT_X); }
 63:   if (ds->mat[DS_MAT_Y]) { DSViewMat(ds,viewer,DS_MAT_Y); }
 64:   return(0);
 65: }

 67: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 68: {
 69: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
 71:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
 72: #else
 74:   PetscInt       i;
 75:   PetscBLASInt   n,ld,mout,info,*select,mm,inc = 1;
 76:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp,fone=1.0,fzero=0.0;
 77:   PetscReal      norm;
 78:   PetscBool      iscomplex = PETSC_FALSE;
 79:   const char     *side;

 82:   PetscBLASIntCast(ds->n,&n);
 83:   PetscBLASIntCast(ds->ld,&ld);
 84:   if (left) {
 85:     X = NULL;
 86:     Y = &ds->mat[DS_MAT_Y][ld*(*k)];
 87:     side = "L";
 88:   } else {
 89:     X = &ds->mat[DS_MAT_X][ld*(*k)];
 90:     Y = NULL;
 91:     side = "R";
 92:   }
 93:   Z = left? Y: X;
 94:   DSAllocateWork_Private(ds,0,0,ld);
 95:   select = ds->iwork;
 96:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
 97:   if (ds->state <= DS_STATE_INTERMEDIATE) {
 98:     DSSetIdentity(ds,DS_MAT_Q);
 99:     DSSetIdentity(ds,DS_MAT_Z);
100:   }
101:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
102:   if (ds->state < DS_STATE_CONDENSED) { DSSetState(ds,DS_STATE_CONDENSED); }

104:   /* compute k-th eigenvector */
105:   select[*k] = (PetscBLASInt)PETSC_TRUE;
106: #if defined(PETSC_USE_COMPLEX)
107:   mm = 1;
108:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
109:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
110: #else
111:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
112:   mm = iscomplex? 2: 1;
113:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
114:   DSAllocateWork_Private(ds,6*ld,0,0);
115:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
116: #endif
117:   SlepcCheckLapackInfo("tgevc",info);
118:   if (!select[*k] || mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");

120:   /* accumulate and normalize eigenvectors */
121:   PetscArraycpy(ds->work,Z,mm*ld);
122:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,Z,&ld));
123:   norm = BLASnrm2_(&n,Z,&inc);
124: #if !defined(PETSC_USE_COMPLEX)
125:   if (iscomplex) {
126:     tmp = BLASnrm2_(&n,Z+ld,&inc);
127:     norm = SlepcAbsEigenvalue(norm,tmp);
128:   }
129: #endif
130:   tmp = 1.0 / norm;
131:   PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z,&inc));
132: #if !defined(PETSC_USE_COMPLEX)
133:   if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+ld,&inc));
134: #endif

136:   /* set output arguments */
137:   if (iscomplex) (*k)++;
138:   if (rnorm) {
139:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
140:     else *rnorm = PetscAbsScalar(Z[n-1]);
141:   }
142:   return(0);
143: #endif
144: }

146: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
147: {
148: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
150:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
151: #else
153:   PetscInt       i;
154:   PetscBLASInt   n,ld,mout,info,inc = 1;
155:   PetscBool      iscomplex;
156:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
157:   PetscReal      norm;
158:   const char     *side,*back;

161:   PetscBLASIntCast(ds->n,&n);
162:   PetscBLASIntCast(ds->ld,&ld);
163:   if (left) {
164:     X = NULL;
165:     Y = ds->mat[DS_MAT_Y];
166:     side = "L";
167:   } else {
168:     X = ds->mat[DS_MAT_X];
169:     Y = NULL;
170:     side = "R";
171:   }
172:   Z = left? Y: X;
173:   if (ds->state <= DS_STATE_INTERMEDIATE) {
174:     DSSetIdentity(ds,DS_MAT_Q);
175:     DSSetIdentity(ds,DS_MAT_Z);
176:   }
177:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
178:   if (ds->state>=DS_STATE_CONDENSED) {
179:     /* DSSolve() has been called, backtransform with matrix Q */
180:     back = "B";
181:     PetscArraycpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld);
182:   } else {
183:     back = "A";
184:     DSSetState(ds,DS_STATE_CONDENSED);
185:   }
186: #if defined(PETSC_USE_COMPLEX)
187:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
188:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
189: #else
190:   DSAllocateWork_Private(ds,6*ld,0,0);
191:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
192: #endif
193:   SlepcCheckLapackInfo("tgevc",info);

195:   /* normalize eigenvectors */
196:   for (i=0;i<n;i++) {
197:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
198:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
199: #if !defined(PETSC_USE_COMPLEX)
200:     if (iscomplex) {
201:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
202:       norm = SlepcAbsEigenvalue(norm,tmp);
203:     }
204: #endif
205:     tmp = 1.0 / norm;
206:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
207: #if !defined(PETSC_USE_COMPLEX)
208:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
209: #endif
210:     if (iscomplex) i++;
211:   }
212:   return(0);
213: #endif
214: }

216: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
217: {

221:   switch (mat) {
222:     case DS_MAT_X:
223:     case DS_MAT_Y:
224:       if (k) {
225:         DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
226:       } else {
227:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
228:       }
229:       break;
230:     default:
231:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
232:   }
233:   return(0);
234: }

236: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
237: {
238: #if defined(PETSC_MISSING_LAPACK_TGSEN)
240:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
241: #else
243:   PetscInt       i;
244:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
245:   PetscScalar    *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Q = ds->mat[DS_MAT_Q],*Z = ds->mat[DS_MAT_Z],*work,*beta;

248:   if (!ds->sc) return(0);
249:   PetscBLASIntCast(ds->n,&n);
250:   PetscBLASIntCast(ds->ld,&ld);
251: #if !defined(PETSC_USE_COMPLEX)
252:   lwork = 4*n+16;
253: #else
254:   lwork = 1;
255: #endif
256:   liwork = 1;
257:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
258:   beta      = ds->work;
259:   work      = ds->work + n;
260:   lwork     = ds->lwork - n;
261:   selection = ds->iwork;
262:   iwork     = ds->iwork + n;
263:   liwork    = ds->liwork - n;
264:   /* Compute the selected eigenvalue to be in the leading position */
265:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
266:   PetscArrayzero(selection,n);
267:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
268: #if !defined(PETSC_USE_COMPLEX)
269:   PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,wi,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
270: #else
271:   PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
272: #endif
273:   SlepcCheckLapackInfo("tgsen",info);
274:   *k = mout;
275:   for (i=0;i<n;i++) {
276:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
277:     else wr[i] /= beta[i];
278: #if !defined(PETSC_USE_COMPLEX)
279:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
280:     else wi[i] /= beta[i];
281: #endif
282:   }
283:   return(0);
284: #endif
285: }

287: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
288: {
289: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
291:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
292: #else
294:   PetscScalar    re;
295:   PetscInt       i,j,pos,result;
296:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
297:   PetscScalar    *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
298: #if !defined(PETSC_USE_COMPLEX)
299:   PetscBLASInt   lwork;
300:   PetscScalar    *work,a,safmin,scale1,scale2,im;
301: #endif

304:   if (!ds->sc) return(0);
305:   PetscBLASIntCast(ds->n,&n);
306:   PetscBLASIntCast(ds->ld,&ld);
307: #if !defined(PETSC_USE_COMPLEX)
308:   lwork = -1;
309:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
310:   SlepcCheckLapackInfo("tgexc",info);
311:   safmin = LAPACKlamch_("S");
312:   PetscBLASIntCast((PetscInt)a,&lwork);
313:   DSAllocateWork_Private(ds,lwork,0,0);
314:   work = ds->work;
315: #endif
316:   /* selection sort */
317:   for (i=ds->l;i<n-1;i++) {
318:     re = wr[i];
319: #if !defined(PETSC_USE_COMPLEX)
320:     im = wi[i];
321: #endif
322:     pos = 0;
323:     j = i+1; /* j points to the next eigenvalue */
324: #if !defined(PETSC_USE_COMPLEX)
325:     if (im != 0) j=i+2;
326: #endif
327:     /* find minimum eigenvalue */
328:     for (;j<n;j++) {
329: #if !defined(PETSC_USE_COMPLEX)
330:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
331: #else
332:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
333: #endif
334:       if (result > 0) {
335:         re = wr[j];
336: #if !defined(PETSC_USE_COMPLEX)
337:         im = wi[j];
338: #endif
339:         pos = j;
340:       }
341: #if !defined(PETSC_USE_COMPLEX)
342:       if (wi[j] != 0) j++;
343: #endif
344:     }
345:     if (pos) {
346:       /* interchange blocks */
347:       PetscBLASIntCast(pos+1,&ifst);
348:       PetscBLASIntCast(i+1,&ilst);
349: #if !defined(PETSC_USE_COMPLEX)
350:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
351: #else
352:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
353: #endif
354:       SlepcCheckLapackInfo("tgexc",info);
355:       /* recover original eigenvalues from T and S matrices */
356:       for (j=i;j<n;j++) {
357: #if !defined(PETSC_USE_COMPLEX)
358:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
359:           /* complex conjugate eigenvalue */
360:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
361:           wr[j] = re / scale1;
362:           wi[j] = im / scale1;
363:           wr[j+1] = a / scale2;
364:           wi[j+1] = -wi[j];
365:           j++;
366:         } else
367: #endif
368:         {
369:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
370:           else wr[j] = S[j*ld+j] / T[j*ld+j];
371: #if !defined(PETSC_USE_COMPLEX)
372:           wi[j] = 0.0;
373: #endif
374:         }
375:       }
376:     }
377: #if !defined(PETSC_USE_COMPLEX)
378:     if (wi[i] != 0.0) i++;
379: #endif
380:   }
381:   return(0);
382: #endif
383: }

385: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
386: {

390:   if (!rr || wr == rr) {
391:     DSSort_GNHEP_Total(ds,wr,wi);
392:   } else {
393:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
394:   }
395:   return(0);
396: }

398: /*
399:    Write zeros from the column k to n in the lower triangular part of the
400:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
401:    make (S,T) a valid Schur decompositon.
402: */
403: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
404: {
405: #if defined(SLEPC_MISSING_LAPACK_LASV2)
407:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
408: #else
409:   PetscInt       i;
410: #if defined(PETSC_USE_COMPLEX)
411:   PetscInt       j;
412:   PetscScalar    s;
413: #else
415:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
416:   PetscScalar    b11,b22,sr,cr,sl,cl;
417: #endif

420: #if defined(PETSC_USE_COMPLEX)
421:   for (i=k; i<n; i++) {
422:     /* Some functions need the diagonal elements in T be real */
423:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
424:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
425:       for (j=0;j<=i;j++) {
426:         T[ldT*i+j] *= s;
427:         S[ldS*i+j] *= s;
428:       }
429:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
430:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
431:     }
432:     j = i+1;
433:     if (j<n) {
434:       S[ldS*i+j] = 0.0;
435:       if (T) T[ldT*i+j] = 0.0;
436:     }
437:   }
438: #else
439:   PetscBLASIntCast(ldS,&ldS_);
440:   PetscBLASIntCast(ldT,&ldT_);
441:   PetscBLASIntCast(n,&n_);
442:   for (i=k;i<n-1;i++) {
443:     if (S[ldS*i+i+1] != 0.0) {
444:       /* Check if T(i+1,i) and T(i,i+1) are zero */
445:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
446:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
447:         if (PetscAbs(T[ldT*(i+1)+i])+PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1]))*PETSC_MACHINE_EPSILON) {
448:           T[ldT*i+i+1] = 0.0;
449:           T[ldT*(i+1)+i] = 0.0;
450:         } else {
451:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
452:           if (PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*(i+1)+i]))*PETSC_MACHINE_EPSILON) {
453:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
454:           } else if (PetscAbs(T[ldT*(i+1)+i]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*i+i+1]))*PETSC_MACHINE_EPSILON) {
455:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
456:           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
457:           PetscBLASIntCast(n-i,&n_i);
458:           n_i_2 = n_i - 2;
459:           PetscBLASIntCast(i+2,&i_2);
460:           PetscBLASIntCast(i,&i_);
461:           if (b11 < 0.0) {
462:             cr = -cr; sr = -sr;
463:             b11 = -b11; b22 = -b22;
464:           }
465:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
466:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
467:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
468:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
469:           if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
470:           if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
471:           T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
472:           T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
473:         }
474:       }
475:       i++;
476:     }
477:   }
478: #endif
479:   return(0);
480: #endif
481: }

483: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
484: {
485: #if defined(PETSC_MISSING_LAPACK_GGES)
487:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
488: #else
490:   PetscScalar    *work,*beta,a;
491:   PetscInt       i;
492:   PetscBLASInt   lwork,info,n,ld,iaux;
493:   PetscScalar    *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];

496: #if !defined(PETSC_USE_COMPLEX)
498: #endif
499:   PetscBLASIntCast(ds->n,&n);
500:   PetscBLASIntCast(ds->ld,&ld);
501:   lwork = -1;
502: #if !defined(PETSC_USE_COMPLEX)
503:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
504:   PetscBLASIntCast((PetscInt)a,&lwork);
505:   DSAllocateWork_Private(ds,lwork+ld,0,0);
506:   beta = ds->work;
507:   work = beta+ds->n;
508:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
509:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
510: #else
511:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
512:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
513:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
514:   beta = ds->work;
515:   work = beta+ds->n;
516:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
517:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
518: #endif
519:   SlepcCheckLapackInfo("gges",info);
520:   for (i=0;i<n;i++) {
521:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
522:     else wr[i] /= beta[i];
523: #if !defined(PETSC_USE_COMPLEX)
524:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
525:     else wi[i] /= beta[i];
526: #else
527:     if (wi) wi[i] = 0.0;
528: #endif
529:   }
530:   return(0);
531: #endif
532: }

534: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
535: {
537:   PetscInt       ld=ds->ld,l=ds->l,k;
538:   PetscMPIInt    n,rank,off=0,size,ldn;

541:   k = 2*(ds->n-l)*ld;
542:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
543:   if (eigr) k += (ds->n-l);
544:   if (eigi) k += (ds->n-l);
545:   DSAllocateWork_Private(ds,k,0,0);
546:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
547:   PetscMPIIntCast(ds->n-l,&n);
548:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
549:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
550:   if (!rank) {
551:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
552:     MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
553:     if (ds->state>DS_STATE_RAW) {
554:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
555:       MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
556:     }
557:     if (eigr) {
558:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
559:     }
560:     if (eigi) {
561:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
562:     }
563:   }
564:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
565:   if (rank) {
566:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
567:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
568:     if (ds->state>DS_STATE_RAW) {
569:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
570:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
571:     }
572:     if (eigr) {
573:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
574:     }
575:     if (eigi) {
576:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
577:     }
578:   }
579:   return(0);
580: }

582: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
583: {
585:   ds->ops->allocate      = DSAllocate_GNHEP;
586:   ds->ops->view          = DSView_GNHEP;
587:   ds->ops->vectors       = DSVectors_GNHEP;
588:   ds->ops->solve[0]      = DSSolve_GNHEP;
589:   ds->ops->sort          = DSSort_GNHEP;
590:   ds->ops->synchronize   = DSSynchronize_GNHEP;
591:   return(0);
592: }