Actual source code: dsgnhep.c

slepc-3.7.4 2017-05-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: #include <slepc/private/dsimpl.h>
 23: #include <slepcblaslapack.h>

 25: /*
 26:   1) Patterns of A and B
 27:       DS_STATE_RAW:       DS_STATE_INTERM/CONDENSED
 28:        0       n-1              0       n-1
 29:       -------------            -------------
 30:     0 |* * * * * *|          0 |* * * * * *|
 31:       |* * * * * *|            |  * * * * *|
 32:       |* * * * * *|            |    * * * *|
 33:       |* * * * * *|            |    * * * *|
 34:       |* * * * * *|            |        * *|
 35:   n-1 |* * * * * *|        n-1 |          *|
 36:       -------------            -------------

 38:   2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
 39: */


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

 46: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
 47: {

 51:   DSAllocateMat_Private(ds,DS_MAT_A);
 52:   DSAllocateMat_Private(ds,DS_MAT_B);
 53:   DSAllocateMat_Private(ds,DS_MAT_Z);
 54:   DSAllocateMat_Private(ds,DS_MAT_Q);
 55:   PetscFree(ds->perm);
 56:   PetscMalloc1(ld,&ds->perm);
 57:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 58:   return(0);
 59: }

 63: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
 64: {

 68:   DSViewMat(ds,viewer,DS_MAT_A);
 69:   DSViewMat(ds,viewer,DS_MAT_B);
 70:   if (ds->state>DS_STATE_INTERMEDIATE) {
 71:     DSViewMat(ds,viewer,DS_MAT_Z);
 72:     DSViewMat(ds,viewer,DS_MAT_Q);
 73:   }
 74:   if (ds->mat[DS_MAT_X]) {
 75:     DSViewMat(ds,viewer,DS_MAT_X);
 76:   }
 77:   if (ds->mat[DS_MAT_Y]) {
 78:     DSViewMat(ds,viewer,DS_MAT_Y);
 79:   }
 80:   return(0);
 81: }

 85: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 86: {
 87: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
 89:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
 90: #else
 92:   PetscInt       i;
 93:   PetscBLASInt   n,ld,mout,info,*select,mm,inc = 1;
 94:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp,fone=1.0,fzero=0.0;
 95:   PetscReal      norm;
 96:   PetscBool      iscomplex = PETSC_FALSE;
 97:   const char     *side;

100:   PetscBLASIntCast(ds->n,&n);
101:   PetscBLASIntCast(ds->ld,&ld);
102:   if (left) {
103:     X = NULL;
104:     Y = &ds->mat[DS_MAT_Y][ld*(*k)];
105:     side = "L";
106:   } else {
107:     X = &ds->mat[DS_MAT_X][ld*(*k)];
108:     Y = NULL;
109:     side = "R";
110:   }
111:   Z = left? Y: X;
112:   DSAllocateWork_Private(ds,0,0,ld);
113:   select = ds->iwork;
114:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
115:   if (ds->state <= DS_STATE_INTERMEDIATE) {
116:     DSSetIdentity(ds,DS_MAT_Q);
117:     DSSetIdentity(ds,DS_MAT_Z);
118:   }
119:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
120:   if (ds->state < DS_STATE_CONDENSED) {
121:     DSSetState(ds,DS_STATE_CONDENSED);
122:   }

124:   /* compute k-th eigenvector */
125:   select[*k] = (PetscBLASInt)PETSC_TRUE;
126: #if defined(PETSC_USE_COMPLEX)
127:   mm = 1;
128:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
129:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
130: #else
131:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
132:   mm = iscomplex? 2: 1;
133:   DSAllocateWork_Private(ds,6*ld,0,0);
134:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
135: #endif
136:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);
137:   if (!select[*k] || mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");

139:   /* accumulate and normalize eigenvectors */
140:   PetscMemcpy(ds->work,Z,mm*ld*sizeof(PetscScalar));
141:   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));
142:   norm = BLASnrm2_(&n,Z,&inc);
143: #if !defined(PETSC_USE_COMPLEX)
144:   if (iscomplex) {
145:     tmp = BLASnrm2_(&n,Z+ld,&inc);
146:     norm = SlepcAbsEigenvalue(norm,tmp);
147:   }
148: #endif
149:   tmp = 1.0 / norm;
150:   PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z,&inc));
151: #if !defined(PETSC_USE_COMPLEX)
152:   if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+ld,&inc));
153: #endif

155:   /* set output arguments */
156:   if (iscomplex) (*k)++;
157:   if (rnorm) {
158:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
159:     else *rnorm = PetscAbsScalar(Z[n-1]);
160:   }
161:   return(0);
162: #endif
163: }

167: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
168: {
169: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
171:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
172: #else
174:   PetscInt       i;
175:   PetscBLASInt   n,ld,mout,info,inc = 1;
176:   PetscBool      iscomplex;
177:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
178:   PetscReal      norm;
179:   const char     *side,*back;

182:   PetscBLASIntCast(ds->n,&n);
183:   PetscBLASIntCast(ds->ld,&ld);
184:   if (left) {
185:     X = NULL;
186:     Y = ds->mat[DS_MAT_Y];
187:     side = "L";
188:   } else {
189:     X = ds->mat[DS_MAT_X];
190:     Y = NULL;
191:     side = "R";
192:   }
193:   Z = left? Y: X;
194:   if (ds->state <= DS_STATE_INTERMEDIATE) {
195:     DSSetIdentity(ds,DS_MAT_Q);
196:     DSSetIdentity(ds,DS_MAT_Z);
197:   }
198:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
199:   if (ds->state>=DS_STATE_CONDENSED) {
200:     /* DSSolve() has been called, backtransform with matrix Q */
201:     back = "B";
202:     PetscMemcpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld*sizeof(PetscScalar));
203:   } else {
204:     back = "A";
205:     DSSetState(ds,DS_STATE_CONDENSED);
206:   }
207: #if defined(PETSC_USE_COMPLEX)
208:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
209:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
210: #else
211:   DSAllocateWork_Private(ds,6*ld,0,0);
212:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
213: #endif
214:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);

216:   /* normalize eigenvectors */
217:   for (i=0;i<n;i++) {
218:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
219:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
220: #if !defined(PETSC_USE_COMPLEX)
221:     if (iscomplex) {
222:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
223:       norm = SlepcAbsEigenvalue(norm,tmp);
224:     }
225: #endif
226:     tmp = 1.0 / norm;
227:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
228: #if !defined(PETSC_USE_COMPLEX)
229:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
230: #endif
231:     if (iscomplex) i++;
232:   }
233:   return(0);
234: #endif
235: }

239: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
240: {

244:   switch (mat) {
245:     case DS_MAT_X:
246:     case DS_MAT_Y:
247:       if (k) {
248:         DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
249:       } else {
250:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
251:       }
252:       break;
253:     default:
254:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
255:   }
256:   return(0);
257: }

261: PetscErrorCode DSNormalize_GNHEP(DS ds,DSMatType mat,PetscInt col)
262: {
264:   PetscInt       i,i0,i1;
265:   PetscBLASInt   ld,n,one = 1;
266:   PetscScalar    *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],norm,*x;
267: #if !defined(PETSC_USE_COMPLEX)
268:   PetscScalar    norm0;
269: #endif

272:   switch (mat) {
273:     case DS_MAT_X:
274:     case DS_MAT_Y:
275:     case DS_MAT_Q:
276:     case DS_MAT_Z:
277:       /* Supported matrices */
278:       break;
279:     case DS_MAT_U:
280:     case DS_MAT_VT:
281:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
282:       break;
283:     default:
284:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
285:   }

287:   PetscBLASIntCast(ds->n,&n);
288:   PetscBLASIntCast(ds->ld,&ld);
289:   DSGetArray(ds,mat,&x);
290:   if (col < 0) {
291:     i0 = 0; i1 = ds->n;
292:   } else if (col>0 && (A[ds->ld*(col-1)+col] != 0.0 || (B && B[ds->ld*(col-1)+col] != 0.0))) {
293:     i0 = col-1; i1 = col+1;
294:   } else {
295:     i0 = col; i1 = col+1;
296:   }
297:   for (i=i0;i<i1;i++) {
298: #if !defined(PETSC_USE_COMPLEX)
299:     if (i<n-1 && (A[ds->ld*i+i+1] != 0.0 || (B && B[ds->ld*i+i+1] != 0.0))) {
300:       norm = BLASnrm2_(&n,&x[ld*i],&one);
301:       norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
302:       norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
303:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
304:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
305:       i++;
306:     } else
307: #endif
308:     {
309:       norm = BLASnrm2_(&n,&x[ld*i],&one);
310:       norm = 1.0/norm;
311:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
312:     }
313:   }
314:   return(0);
315: }

319: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
320: {
321: #if defined(PETSC_MISSING_LAPACK_TGSEN)
323:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
324: #else
326:   PetscInt       i;
327:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
328:   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;

331:   if (!ds->sc) return(0);
332:   PetscBLASIntCast(ds->n,&n);
333:   PetscBLASIntCast(ds->ld,&ld);
334: #if !defined(PETSC_USE_COMPLEX)
335:   lwork = 4*n+16;
336: #else
337:   lwork = 1;
338: #endif
339:   liwork = 1;
340:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
341:   beta      = ds->work;
342:   work      = ds->work + n;
343:   lwork     = ds->lwork - n;
344:   selection = ds->iwork;
345:   iwork     = ds->iwork + n;
346:   liwork    = ds->liwork - n;
347:   /* Compute the selected eigenvalue to be in the leading position */
348:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
349:   PetscMemzero(selection,n*sizeof(PetscBLASInt));
350:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
351: #if !defined(PETSC_USE_COMPLEX)
352:   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));
353: #else
354:   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));
355: #endif
356:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGSEN %d",info);
357:   *k = mout;
358:   for (i=0;i<n;i++) {
359:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
360:     else wr[i] /= beta[i];
361: #if !defined(PETSC_USE_COMPLEX)
362:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
363:     else wi[i] /= beta[i];
364: #endif
365:   }
366:   return(0);
367: #endif
368: }

372: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
373: {
374: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
376:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
377: #else
379:   PetscScalar    re;
380:   PetscInt       i,j,pos,result;
381:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
382:   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];
383: #if !defined(PETSC_USE_COMPLEX)
384:   PetscBLASInt   lwork;
385:   PetscScalar    *work,a,safmin,scale1,scale2,im;
386: #endif

389:   if (!ds->sc) return(0);
390:   PetscBLASIntCast(ds->n,&n);
391:   PetscBLASIntCast(ds->ld,&ld);
392: #if !defined(PETSC_USE_COMPLEX)
393:   lwork = -1;
394:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
395:   safmin = LAPACKlamch_("S");
396:   PetscBLASIntCast((PetscInt)a,&lwork);
397:   DSAllocateWork_Private(ds,lwork,0,0);
398:   work = ds->work;
399: #endif
400:   /* selection sort */
401:   for (i=ds->l;i<n-1;i++) {
402:     re = wr[i];
403: #if !defined(PETSC_USE_COMPLEX)
404:     im = wi[i];
405: #endif
406:     pos = 0;
407:     j = i+1; /* j points to the next eigenvalue */
408: #if !defined(PETSC_USE_COMPLEX)
409:     if (im != 0) j=i+2;
410: #endif
411:     /* find minimum eigenvalue */
412:     for (;j<n;j++) {
413: #if !defined(PETSC_USE_COMPLEX)
414:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
415: #else
416:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
417: #endif
418:       if (result > 0) {
419:         re = wr[j];
420: #if !defined(PETSC_USE_COMPLEX)
421:         im = wi[j];
422: #endif
423:         pos = j;
424:       }
425: #if !defined(PETSC_USE_COMPLEX)
426:       if (wi[j] != 0) j++;
427: #endif
428:     }
429:     if (pos) {
430:       /* interchange blocks */
431:       PetscBLASIntCast(pos+1,&ifst);
432:       PetscBLASIntCast(i+1,&ilst);
433: #if !defined(PETSC_USE_COMPLEX)
434:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
435: #else
436:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
437: #endif
438:       if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEXC %i",info);
439:       /* recover original eigenvalues from T and S matrices */
440:       for (j=i;j<n;j++) {
441: #if !defined(PETSC_USE_COMPLEX)
442:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
443:           /* complex conjugate eigenvalue */
444:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
445:           wr[j] = re / scale1;
446:           wi[j] = im / scale1;
447:           wr[j+1] = a / scale2;
448:           wi[j+1] = -wi[j];
449:           j++;
450:         } else
451: #endif
452:         {
453:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
454:           else wr[j] = S[j*ld+j] / T[j*ld+j];
455: #if !defined(PETSC_USE_COMPLEX)
456:           wi[j] = 0.0;
457: #endif
458:         }
459:       }
460:     }
461: #if !defined(PETSC_USE_COMPLEX)
462:     if (wi[i] != 0.0) i++;
463: #endif
464:   }
465:   return(0);
466: #endif
467: }

471: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
472: {

476:   if (!rr || wr == rr) {
477:     DSSort_GNHEP_Total(ds,wr,wi);
478:   } else {
479:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
480:   }
481:   return(0);
482: }

486: /*
487:    Write zeros from the column k to n in the lower triangular part of the
488:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
489:    make (S,T) a valid Schur decompositon.
490: */
491: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY,PetscBool doProd)
492: {
493: #if defined(SLEPC_MISSING_LAPACK_LASV2)
495:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
496: #else
497:   PetscInt       i,j;
498: #if defined(PETSC_USE_COMPLEX)
499:   PetscScalar    s;
500: #else
502:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
503:   PetscScalar    b11,b22,sr,cr,sl,cl;
504: #endif

507:   if (!doProd && X) {
508:     for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
509:     for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
510:   }
511:   if (!doProd && Y) {
512:     for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
513:     for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
514:   }

516: #if defined(PETSC_USE_COMPLEX)
517:   for (i=k; i<n; i++) {
518:     /* Some functions need the diagonal elements in T be real */
519:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
520:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
521:       for (j=0;j<=i;j++) {
522:         T[ldT*i+j] *= s;
523:         S[ldS*i+j] *= s;
524:       }
525:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
526:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
527:     }
528:     j = i+1;
529:     if (j<n) {
530:       S[ldS*i+j] = 0.0;
531:       if (T) T[ldT*i+j] = 0.0;
532:     }
533:   }
534: #else
535:   PetscBLASIntCast(ldS,&ldS_);
536:   PetscBLASIntCast(ldT,&ldT_);
537:   PetscBLASIntCast(n,&n_);
538:   for (i=k;i<n-1;i++) {
539:     if (S[ldS*i+i+1] != 0.0) {
540:       /* Check if T(i+1,i) and T(i,i+1) are zero */
541:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
542:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
543:         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) {
544:           T[ldT*i+i+1] = 0.0;
545:           T[ldT*(i+1)+i] = 0.0;

547:         } else {
548:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
549:           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) {
550:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
551:           } 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) {
552:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
553:           } else {
554:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
555:           }
556:           PetscBLASIntCast(n-i,&n_i);
557:           n_i_2 = n_i - 2;
558:           PetscBLASIntCast(i+2,&i_2);
559:           PetscBLASIntCast(i,&i_);
560:           if (b11 < 0.0) {
561:             cr  = -cr;
562:             sr  = -sr;
563:             b11 = -b11;
564:             b22 = -b22;
565:           }
566:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
567:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
568:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
569:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
570:           if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
571:           if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
572:           T[ldT*i+i] = b11;
573:           T[ldT*i+i+1] = 0.0;
574:           T[ldT*(i+1)+i] = 0.0;
575:           T[ldT*(i+1)+i+1] = b22;
576:         }
577:       }
578:     i++;
579:     }
580:   }
581: #endif
582:   return(0);
583: #endif
584: }

588: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
589: {
590: #if defined(PETSC_MISSING_LAPACK_GGES)
592:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
593: #else
595:   PetscScalar    *work,*beta,a;
596:   PetscInt       i;
597:   PetscBLASInt   lwork,info,n,ld,iaux;
598:   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];

601: #if !defined(PETSC_USE_COMPLEX)
603: #endif
604:   PetscBLASIntCast(ds->n,&n);
605:   PetscBLASIntCast(ds->ld,&ld);
606:   lwork = -1;
607: #if !defined(PETSC_USE_COMPLEX)
608:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
609:   PetscBLASIntCast((PetscInt)a,&lwork);
610:   DSAllocateWork_Private(ds,lwork+ld,0,0);
611:   beta = ds->work;
612:   work = beta+ds->n;
613:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
614:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
615: #else
616:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
617:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
618:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
619:   beta = ds->work;
620:   work = beta+ds->n;
621:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
622:   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));
623: #endif
624:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xGGES %i",info);
625:   for (i=0;i<n;i++) {
626:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
627:     else wr[i] /= beta[i];
628: #if !defined(PETSC_USE_COMPLEX)
629:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
630:     else wi[i] /= beta[i];
631: #else
632:     if (wi) wi[i] = 0.0;
633: #endif
634:   }
635:   return(0);
636: #endif
637: }

641: PETSC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
642: {
644:   ds->ops->allocate      = DSAllocate_GNHEP;
645:   ds->ops->view          = DSView_GNHEP;
646:   ds->ops->vectors       = DSVectors_GNHEP;
647:   ds->ops->solve[0]      = DSSolve_GNHEP;
648:   ds->ops->sort          = DSSort_GNHEP;
649:   ds->ops->normalize     = DSNormalize_GNHEP;
650:   return(0);
651: }