Actual source code: dsgnhep.c

slepc-3.8.2 2017-12-01
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2017, 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,PetscBool doProd);

 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: {

 53:   DSViewMat(ds,viewer,DS_MAT_A);
 54:   DSViewMat(ds,viewer,DS_MAT_B);
 55:   if (ds->state>DS_STATE_INTERMEDIATE) {
 56:     DSViewMat(ds,viewer,DS_MAT_Z);
 57:     DSViewMat(ds,viewer,DS_MAT_Q);
 58:   }
 59:   if (ds->mat[DS_MAT_X]) {
 60:     DSViewMat(ds,viewer,DS_MAT_X);
 61:   }
 62:   if (ds->mat[DS_MAT_Y]) {
 63:     DSViewMat(ds,viewer,DS_MAT_Y);
 64:   }
 65:   return(0);
 66: }

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

 83:   PetscBLASIntCast(ds->n,&n);
 84:   PetscBLASIntCast(ds->ld,&ld);
 85:   if (left) {
 86:     X = NULL;
 87:     Y = &ds->mat[DS_MAT_Y][ld*(*k)];
 88:     side = "L";
 89:   } else {
 90:     X = &ds->mat[DS_MAT_X][ld*(*k)];
 91:     Y = NULL;
 92:     side = "R";
 93:   }
 94:   Z = left? Y: X;
 95:   DSAllocateWork_Private(ds,0,0,ld);
 96:   select = ds->iwork;
 97:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
 98:   if (ds->state <= DS_STATE_INTERMEDIATE) {
 99:     DSSetIdentity(ds,DS_MAT_Q);
100:     DSSetIdentity(ds,DS_MAT_Z);
101:   }
102:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
103:   if (ds->state < DS_STATE_CONDENSED) {
104:     DSSetState(ds,DS_STATE_CONDENSED);
105:   }

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

123:   /* accumulate and normalize eigenvectors */
124:   PetscMemcpy(ds->work,Z,mm*ld*sizeof(PetscScalar));
125:   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));
126:   norm = BLASnrm2_(&n,Z,&inc);
127: #if !defined(PETSC_USE_COMPLEX)
128:   if (iscomplex) {
129:     tmp = BLASnrm2_(&n,Z+ld,&inc);
130:     norm = SlepcAbsEigenvalue(norm,tmp);
131:   }
132: #endif
133:   tmp = 1.0 / norm;
134:   PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z,&inc));
135: #if !defined(PETSC_USE_COMPLEX)
136:   if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+ld,&inc));
137: #endif

139:   /* set output arguments */
140:   if (iscomplex) (*k)++;
141:   if (rnorm) {
142:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
143:     else *rnorm = PetscAbsScalar(Z[n-1]);
144:   }
145:   return(0);
146: #endif
147: }

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

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

198:   /* normalize eigenvectors */
199:   for (i=0;i<n;i++) {
200:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
201:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
202: #if !defined(PETSC_USE_COMPLEX)
203:     if (iscomplex) {
204:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
205:       norm = SlepcAbsEigenvalue(norm,tmp);
206:     }
207: #endif
208:     tmp = 1.0 / norm;
209:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
210: #if !defined(PETSC_USE_COMPLEX)
211:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
212: #endif
213:     if (iscomplex) i++;
214:   }
215:   return(0);
216: #endif
217: }

219: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
220: {

224:   switch (mat) {
225:     case DS_MAT_X:
226:     case DS_MAT_Y:
227:       if (k) {
228:         DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
229:       } else {
230:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
231:       }
232:       break;
233:     default:
234:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
235:   }
236:   return(0);
237: }

239: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
240: {
241: #if defined(PETSC_MISSING_LAPACK_TGSEN)
243:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
244: #else
246:   PetscInt       i;
247:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
248:   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;

251:   if (!ds->sc) return(0);
252:   PetscBLASIntCast(ds->n,&n);
253:   PetscBLASIntCast(ds->ld,&ld);
254: #if !defined(PETSC_USE_COMPLEX)
255:   lwork = 4*n+16;
256: #else
257:   lwork = 1;
258: #endif
259:   liwork = 1;
260:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
261:   beta      = ds->work;
262:   work      = ds->work + n;
263:   lwork     = ds->lwork - n;
264:   selection = ds->iwork;
265:   iwork     = ds->iwork + n;
266:   liwork    = ds->liwork - n;
267:   /* Compute the selected eigenvalue to be in the leading position */
268:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
269:   PetscMemzero(selection,n*sizeof(PetscBLASInt));
270:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
271: #if !defined(PETSC_USE_COMPLEX)
272:   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));
273: #else
274:   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));
275: #endif
276:   SlepcCheckLapackInfo("tgsen",info);
277:   *k = mout;
278:   for (i=0;i<n;i++) {
279:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
280:     else wr[i] /= beta[i];
281: #if !defined(PETSC_USE_COMPLEX)
282:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
283:     else wi[i] /= beta[i];
284: #endif
285:   }
286:   return(0);
287: #endif
288: }

290: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
291: {
292: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
294:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
295: #else
297:   PetscScalar    re;
298:   PetscInt       i,j,pos,result;
299:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
300:   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];
301: #if !defined(PETSC_USE_COMPLEX)
302:   PetscBLASInt   lwork;
303:   PetscScalar    *work,a,safmin,scale1,scale2,im;
304: #endif

307:   if (!ds->sc) return(0);
308:   PetscBLASIntCast(ds->n,&n);
309:   PetscBLASIntCast(ds->ld,&ld);
310: #if !defined(PETSC_USE_COMPLEX)
311:   lwork = -1;
312:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
313:   SlepcCheckLapackInfo("tgexc",info);
314:   safmin = LAPACKlamch_("S");
315:   PetscBLASIntCast((PetscInt)a,&lwork);
316:   DSAllocateWork_Private(ds,lwork,0,0);
317:   work = ds->work;
318: #endif
319:   /* selection sort */
320:   for (i=ds->l;i<n-1;i++) {
321:     re = wr[i];
322: #if !defined(PETSC_USE_COMPLEX)
323:     im = wi[i];
324: #endif
325:     pos = 0;
326:     j = i+1; /* j points to the next eigenvalue */
327: #if !defined(PETSC_USE_COMPLEX)
328:     if (im != 0) j=i+2;
329: #endif
330:     /* find minimum eigenvalue */
331:     for (;j<n;j++) {
332: #if !defined(PETSC_USE_COMPLEX)
333:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
334: #else
335:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
336: #endif
337:       if (result > 0) {
338:         re = wr[j];
339: #if !defined(PETSC_USE_COMPLEX)
340:         im = wi[j];
341: #endif
342:         pos = j;
343:       }
344: #if !defined(PETSC_USE_COMPLEX)
345:       if (wi[j] != 0) j++;
346: #endif
347:     }
348:     if (pos) {
349:       /* interchange blocks */
350:       PetscBLASIntCast(pos+1,&ifst);
351:       PetscBLASIntCast(i+1,&ilst);
352: #if !defined(PETSC_USE_COMPLEX)
353:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
354: #else
355:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
356: #endif
357:       SlepcCheckLapackInfo("tgexc",info);
358:       /* recover original eigenvalues from T and S matrices */
359:       for (j=i;j<n;j++) {
360: #if !defined(PETSC_USE_COMPLEX)
361:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
362:           /* complex conjugate eigenvalue */
363:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
364:           wr[j] = re / scale1;
365:           wi[j] = im / scale1;
366:           wr[j+1] = a / scale2;
367:           wi[j+1] = -wi[j];
368:           j++;
369:         } else
370: #endif
371:         {
372:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
373:           else wr[j] = S[j*ld+j] / T[j*ld+j];
374: #if !defined(PETSC_USE_COMPLEX)
375:           wi[j] = 0.0;
376: #endif
377:         }
378:       }
379:     }
380: #if !defined(PETSC_USE_COMPLEX)
381:     if (wi[i] != 0.0) i++;
382: #endif
383:   }
384:   return(0);
385: #endif
386: }

388: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
389: {

393:   if (!rr || wr == rr) {
394:     DSSort_GNHEP_Total(ds,wr,wi);
395:   } else {
396:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
397:   }
398:   return(0);
399: }

401: /*
402:    Write zeros from the column k to n in the lower triangular part of the
403:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
404:    make (S,T) a valid Schur decompositon.
405: */
406: 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)
407: {
408: #if defined(SLEPC_MISSING_LAPACK_LASV2)
410:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
411: #else
412:   PetscInt       i,j;
413: #if defined(PETSC_USE_COMPLEX)
414:   PetscScalar    s;
415: #else
417:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
418:   PetscScalar    b11,b22,sr,cr,sl,cl;
419: #endif

422:   if (!doProd && X) {
423:     for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
424:     for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
425:   }
426:   if (!doProd && Y) {
427:     for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
428:     for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
429:   }

431: #if defined(PETSC_USE_COMPLEX)
432:   for (i=k; i<n; i++) {
433:     /* Some functions need the diagonal elements in T be real */
434:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
435:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
436:       for (j=0;j<=i;j++) {
437:         T[ldT*i+j] *= s;
438:         S[ldS*i+j] *= s;
439:       }
440:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
441:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
442:     }
443:     j = i+1;
444:     if (j<n) {
445:       S[ldS*i+j] = 0.0;
446:       if (T) T[ldT*i+j] = 0.0;
447:     }
448:   }
449: #else
450:   PetscBLASIntCast(ldS,&ldS_);
451:   PetscBLASIntCast(ldT,&ldT_);
452:   PetscBLASIntCast(n,&n_);
453:   for (i=k;i<n-1;i++) {
454:     if (S[ldS*i+i+1] != 0.0) {
455:       /* Check if T(i+1,i) and T(i,i+1) are zero */
456:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
457:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
458:         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) {
459:           T[ldT*i+i+1] = 0.0;
460:           T[ldT*(i+1)+i] = 0.0;

462:         } else {
463:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
464:           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) {
465:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
466:           } 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) {
467:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
468:           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
469:           PetscBLASIntCast(n-i,&n_i);
470:           n_i_2 = n_i - 2;
471:           PetscBLASIntCast(i+2,&i_2);
472:           PetscBLASIntCast(i,&i_);
473:           if (b11 < 0.0) {
474:             cr  = -cr;
475:             sr  = -sr;
476:             b11 = -b11;
477:             b22 = -b22;
478:           }
479:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
480:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
481:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
482:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
483:           if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
484:           if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
485:           T[ldT*i+i] = b11;
486:           T[ldT*i+i+1] = 0.0;
487:           T[ldT*(i+1)+i] = 0.0;
488:           T[ldT*(i+1)+i+1] = b22;
489:         }
490:       }
491:     i++;
492:     }
493:   }
494: #endif
495:   return(0);
496: #endif
497: }

499: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
500: {
501: #if defined(PETSC_MISSING_LAPACK_GGES)
503:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
504: #else
506:   PetscScalar    *work,*beta,a;
507:   PetscInt       i;
508:   PetscBLASInt   lwork,info,n,ld,iaux;
509:   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];

512: #if !defined(PETSC_USE_COMPLEX)
514: #endif
515:   PetscBLASIntCast(ds->n,&n);
516:   PetscBLASIntCast(ds->ld,&ld);
517:   lwork = -1;
518: #if !defined(PETSC_USE_COMPLEX)
519:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
520:   PetscBLASIntCast((PetscInt)a,&lwork);
521:   DSAllocateWork_Private(ds,lwork+ld,0,0);
522:   beta = ds->work;
523:   work = beta+ds->n;
524:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
525:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
526: #else
527:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
528:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
529:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
530:   beta = ds->work;
531:   work = beta+ds->n;
532:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
533:   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));
534: #endif
535:   SlepcCheckLapackInfo("gges",info);
536:   for (i=0;i<n;i++) {
537:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
538:     else wr[i] /= beta[i];
539: #if !defined(PETSC_USE_COMPLEX)
540:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
541:     else wi[i] /= beta[i];
542: #else
543:     if (wi) wi[i] = 0.0;
544: #endif
545:   }
546:   return(0);
547: #endif
548: }

550: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
551: {
553:   PetscInt       ld=ds->ld,l=ds->l,k;
554:   PetscMPIInt    n,rank,off=0,size,ldn;

557:   k = 2*(ds->n-l)*ld;
558:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
559:   if (eigr) k += (ds->n-l); 
560:   if (eigi) k += (ds->n-l); 
561:   DSAllocateWork_Private(ds,k,0,0);
562:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
563:   PetscMPIIntCast(ds->n-l,&n);
564:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
565:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
566:   if (!rank) {
567:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
568:     MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
569:     if (ds->state>DS_STATE_RAW) {
570:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
571:       MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
572:     }
573:     if (eigr) {
574:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
575:     }
576:     if (eigi) {
577:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
578:     }
579:   }
580:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
581:   if (rank) {
582:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
583:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
584:     if (ds->state>DS_STATE_RAW) {
585:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
586:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
587:     }
588:     if (eigr) {
589:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
590:     }
591:     if (eigi) {
592:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
593:     }
594:   }
595:   return(0);
596: }

598: PETSC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
599: {
601:   ds->ops->allocate      = DSAllocate_GNHEP;
602:   ds->ops->view          = DSView_GNHEP;
603:   ds->ops->vectors       = DSVectors_GNHEP;
604:   ds->ops->solve[0]      = DSSolve_GNHEP;
605:   ds->ops->sort          = DSSort_GNHEP;
606:   ds->ops->synchronize   = DSSynchronize_GNHEP;
607:   return(0);
608: }