Actual source code: dsgnhep.c

slepc-3.6.1 2015-09-03
Report Typos and Errors
  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2015, 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: PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,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;
 94:   PetscScalar    *X,*Y,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],fone=1.0,fzero=0.0;
 95:   PetscBool      iscomplex = PETSC_FALSE;
 96:   const char     *side;

 99:   PetscBLASIntCast(ds->n,&n);
100:   PetscBLASIntCast(ds->ld,&ld);
101:   if (left) {
102:     X = NULL;
103:     Y = &ds->mat[DS_MAT_Y][ld*(*k)];
104:     side = "L";
105:   } else {
106:     X = &ds->mat[DS_MAT_X][ld*(*k)];
107:     Y = NULL;
108:     side = "R";
109:   }
110:   DSAllocateWork_Private(ds,0,0,ld);
111:   select = ds->iwork;
112:   for (i=0;i<n;i++) select[i] = 0;
113:   select[*k] = 1;
114:   if (ds->state <= DS_STATE_INTERMEDIATE) {
115:     DSSetIdentity(ds,DS_MAT_Q);
116:     DSSetIdentity(ds,DS_MAT_Z);
117:   }
118:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
119:   if (ds->state < DS_STATE_CONDENSED) {
120:     DSSetState(ds,DS_STATE_CONDENSED);
121:   }
122: #if defined(PETSC_USE_COMPLEX)
123:   mm = 1;
124:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
125:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
126: #else
127:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
128:   mm = iscomplex ? 2 : 1;
129:   DSAllocateWork_Private(ds,6*ld,0,0);
130:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
131: #endif
132:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);
133:   if (select[(*k)] == 0 || mout != mm) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Unsupported the computation of the second vector in a complex pair");
134:   /* Backtransform: (X/Y) <- (Q/Z) * (X/Y) */
135:   PetscMemcpy(ds->work,left?Y:X,mm*ld*sizeof(PetscScalar));
136:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,left?Y:X,&ld));
137:   /* Update k to the last vector index in the conjugate pair */
138:   if (iscomplex) (*k)++;
139:   return(0);
140: #endif
141: }

145: PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
146: {
147: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
149:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
150: #else
152:   PetscBLASInt   n,ld,mout,info;
153:   PetscScalar    *X,*Y,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];
154:   const char     *side,*back;

157:   PetscBLASIntCast(ds->n,&n);
158:   PetscBLASIntCast(ds->ld,&ld);
159:   if (left) {
160:     X = NULL;
161:     Y = ds->mat[DS_MAT_Y];
162:     side = "L";
163:   } else {
164:     X = ds->mat[DS_MAT_X];
165:     Y = NULL;
166:     side = "R";
167:   }
168:   if (ds->state <= DS_STATE_INTERMEDIATE) {
169:     DSSetIdentity(ds,DS_MAT_Q);
170:     DSSetIdentity(ds,DS_MAT_Z);
171:   }
172:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
173:   if (ds->state>=DS_STATE_CONDENSED) {
174:     /* DSSolve() has been called, backtransform with matrix Q */
175:     back = "B";
176:     PetscMemcpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld*sizeof(PetscScalar));
177:   } else {
178:     back = "A";
179:     DSSetState(ds,DS_STATE_CONDENSED);
180:   }
181: #if defined(PETSC_USE_COMPLEX)
182:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
183:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
184: #else
185:   DSAllocateWork_Private(ds,6*ld,0,0);
186:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
187: #endif
188:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);
189:   return(0);
190: #endif
191: }

195: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
196: {

200:   if (rnorm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
201:   switch (mat) {
202:     case DS_MAT_X:
203:     case DS_MAT_Y:
204:       if (k) {
205:         DSVectors_GNHEP_Eigen_Some(ds,k,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
206:       } else {
207:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
208:       }
209:       break;
210:     default:
211:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
212:   }
213:   return(0);
214: }

218: PetscErrorCode DSNormalize_GNHEP(DS ds,DSMatType mat,PetscInt col)
219: {
221:   PetscInt       i,i0,i1;
222:   PetscBLASInt   ld,n,one = 1;
223:   PetscScalar    *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],norm,*x;
224: #if !defined(PETSC_USE_COMPLEX)
225:   PetscScalar    norm0;
226: #endif

229:   switch (mat) {
230:     case DS_MAT_X:
231:     case DS_MAT_Y:
232:     case DS_MAT_Q:
233:     case DS_MAT_Z:
234:       /* Supported matrices */
235:       break;
236:     case DS_MAT_U:
237:     case DS_MAT_VT:
238:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
239:       break;
240:     default:
241:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
242:   }

244:   PetscBLASIntCast(ds->n,&n);
245:   PetscBLASIntCast(ds->ld,&ld);
246:   DSGetArray(ds,mat,&x);
247:   if (col < 0) {
248:     i0 = 0; i1 = ds->n;
249:   } else if (col>0 && (A[ds->ld*(col-1)+col] != 0.0 || (B && B[ds->ld*(col-1)+col] != 0.0))) {
250:     i0 = col-1; i1 = col+1;
251:   } else {
252:     i0 = col; i1 = col+1;
253:   }
254:   for (i=i0;i<i1;i++) {
255: #if !defined(PETSC_USE_COMPLEX)
256:     if (i<n-1 && (A[ds->ld*i+i+1] != 0.0 || (B && B[ds->ld*i+i+1] != 0.0))) {
257:       norm = BLASnrm2_(&n,&x[ld*i],&one);
258:       norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
259:       norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
260:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
261:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
262:       i++;
263:     } else
264: #endif
265:     {
266:       norm = BLASnrm2_(&n,&x[ld*i],&one);
267:       norm = 1.0/norm;
268:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
269:     }
270:   }
271:   return(0);
272: }

276: PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
277: {
278: #if defined(SLEPC_MISSING_LAPACK_TGSEN)
280:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
281: #else
283:   PetscInt       i;
284:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
285:   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;

288:   if (!ds->sc) return(0);
289:   PetscBLASIntCast(ds->n,&n);
290:   PetscBLASIntCast(ds->ld,&ld);
291: #if !defined(PETSC_USE_COMPLEX)
292:   lwork = 4*n+16;
293: #else
294:   lwork = 1;
295: #endif
296:   liwork = 1;
297:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
298:   beta      = ds->work;
299:   work      = ds->work + n;
300:   lwork     = ds->lwork - n;
301:   selection = ds->iwork;
302:   iwork     = ds->iwork + n;
303:   liwork    = ds->liwork - n;
304:   /* Compute the selected eigenvalue to be in the leading position */
305:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
306:   PetscMemzero(selection,n*sizeof(PetscBLASInt));
307:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
308: #if !defined(PETSC_USE_COMPLEX)
309:   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));
310: #else
311:   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));
312: #endif
313:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGSEN %d",info);
314:   *k = mout;
315:   for (i=0;i<n;i++) {
316:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
317:     else wr[i] /= beta[i];
318: #if !defined(PETSC_USE_COMPLEX)
319:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
320:     else wi[i] /= beta[i];
321: #endif
322:   }
323:   return(0);
324: #endif
325: }

329: PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
330: {
331: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
333:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
334: #else
336:   PetscScalar    re;
337:   PetscInt       i,j,pos,result;
338:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
339:   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];
340: #if !defined(PETSC_USE_COMPLEX)
341:   PetscBLASInt   lwork;
342:   PetscScalar    *work,a,safmin,scale1,scale2,im;
343: #endif

346:   if (!ds->sc) return(0);
347:   PetscBLASIntCast(ds->n,&n);
348:   PetscBLASIntCast(ds->ld,&ld);
349: #if !defined(PETSC_USE_COMPLEX)
350:   lwork = -1;
351:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
352:   safmin = LAPACKlamch_("S");
353:   PetscBLASIntCast((PetscInt)a,&lwork);
354:   DSAllocateWork_Private(ds,lwork,0,0);
355:   work = ds->work;
356: #endif
357:   /* selection sort */
358:   for (i=ds->l;i<n-1;i++) {
359:     re = wr[i];
360: #if !defined(PETSC_USE_COMPLEX)
361:     im = wi[i];
362: #endif
363:     pos = 0;
364:     j = i+1; /* j points to the next eigenvalue */
365: #if !defined(PETSC_USE_COMPLEX)
366:     if (im != 0) j=i+2;
367: #endif
368:     /* find minimum eigenvalue */
369:     for (;j<n;j++) {
370: #if !defined(PETSC_USE_COMPLEX)
371:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
372: #else
373:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
374: #endif
375:       if (result > 0) {
376:         re = wr[j];
377: #if !defined(PETSC_USE_COMPLEX)
378:         im = wi[j];
379: #endif
380:         pos = j;
381:       }
382: #if !defined(PETSC_USE_COMPLEX)
383:       if (wi[j] != 0) j++;
384: #endif
385:     }
386:     if (pos) {
387:       /* interchange blocks */
388:       PetscBLASIntCast(pos+1,&ifst);
389:       PetscBLASIntCast(i+1,&ilst);
390: #if !defined(PETSC_USE_COMPLEX)
391:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
392: #else
393:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
394: #endif
395:       if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEXC %i",info);
396:       /* recover original eigenvalues from T and S matrices */
397:       for (j=i;j<n;j++) {
398: #if !defined(PETSC_USE_COMPLEX)
399:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
400:           /* complex conjugate eigenvalue */
401:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
402:           wr[j] = re / scale1;
403:           wi[j] = im / scale1;
404:           wr[j+1] = a / scale2;
405:           wi[j+1] = -wi[j];
406:           j++;
407:         } else
408: #endif
409:         {
410:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
411:           else wr[j] = S[j*ld+j] / T[j*ld+j];
412: #if !defined(PETSC_USE_COMPLEX)
413:           wi[j] = 0.0;
414: #endif
415:         }
416:       }
417:     }
418: #if !defined(PETSC_USE_COMPLEX)
419:     if (wi[i] != 0.0) i++;
420: #endif
421:   }
422:   return(0);
423: #endif
424: }

428: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
429: {

433:   if (!rr || wr == rr) {
434:     DSSort_GNHEP_Total(ds,wr,wi);
435:   } else {
436:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
437:   }
438:   return(0);
439: }

443: /*
444:    Write zeros from the column k to n in the lower triangular part of the
445:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
446:    make (S,T) a valid Schur decompositon.
447: */
448: 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)
449: {
450: #if defined(SLEPC_MISSING_LAPACK_LASV2)
452:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
453: #else
454:   PetscInt       i,j;
455: #if defined(PETSC_USE_COMPLEX)
456:   PetscScalar    s;
457: #else
459:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
460:   PetscScalar    b11,b22,sr,cr,sl,cl;
461: #endif

464:   if (!doProd && X) {
465:     for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
466:     for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
467:   }
468:   if (!doProd && Y) {
469:     for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
470:     for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
471:   }

473: #if defined(PETSC_USE_COMPLEX)
474:   for (i=k; i<n; i++) {
475:     /* Some functions need the diagonal elements in T be real */
476:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
477:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
478:       for (j=0;j<=i;j++) {
479:         T[ldT*i+j] *= s;
480:         S[ldS*i+j] *= s;
481:       }
482:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
483:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
484:     }
485:     j = i+1;
486:     if (j<n) {
487:       S[ldS*i+j] = 0.0;
488:       if (T) T[ldT*i+j] = 0.0;
489:     }
490:   }
491: #else
492:   PetscBLASIntCast(ldS,&ldS_);
493:   PetscBLASIntCast(ldT,&ldT_);
494:   PetscBLASIntCast(n,&n_);
495:   for (i=k;i<n-1;i++) {
496:     if (S[ldS*i+i+1] != 0.0) {
497:       /* Check if T(i+1,i) and T(i,i+1) are zero */
498:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
499:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
500:         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) {
501:           T[ldT*i+i+1] = 0.0;
502:           T[ldT*(i+1)+i] = 0.0;

504:         } else {
505:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
506:           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) {
507:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
508:           } 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) {
509:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
510:           } else {
511:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
512:           }
513:           PetscBLASIntCast(n-i,&n_i);
514:           n_i_2 = n_i - 2;
515:           PetscBLASIntCast(i+2,&i_2);
516:           PetscBLASIntCast(i,&i_);
517:           if (b11 < 0.0) {
518:             cr  = -cr;
519:             sr  = -sr;
520:             b11 = -b11;
521:             b22 = -b22;
522:           }
523:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
524:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
525:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
526:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
527:           if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
528:           if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
529:           T[ldT*i+i] = b11;
530:           T[ldT*i+i+1] = 0.0;
531:           T[ldT*(i+1)+i] = 0.0;
532:           T[ldT*(i+1)+i+1] = b22;
533:         }
534:       }
535:     i++;
536:     }
537:   }
538: #endif
539:   return(0);
540: #endif
541: }

545: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
546: {
547: #if defined(PETSC_MISSING_LAPACK_GGES)
549:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
550: #else
552:   PetscScalar    *work,*beta,a;
553:   PetscInt       i;
554:   PetscBLASInt   lwork,info,n,ld,iaux;
555:   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];

558: #if !defined(PETSC_USE_COMPLEX)
560: #endif
561:   PetscBLASIntCast(ds->n,&n);
562:   PetscBLASIntCast(ds->ld,&ld);
563:   lwork = -1;
564: #if !defined(PETSC_USE_COMPLEX)
565:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
566:   PetscBLASIntCast((PetscInt)a,&lwork);
567:   DSAllocateWork_Private(ds,lwork+ld,0,0);
568:   beta = ds->work;
569:   work = beta+ds->n;
570:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
571:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
572: #else
573:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
574:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
575:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
576:   beta = ds->work;
577:   work = beta+ds->n;
578:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
579:   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));
580: #endif
581:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xGGES %i",info);
582:   for (i=0;i<n;i++) {
583:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
584:     else wr[i] /= beta[i];
585: #if !defined(PETSC_USE_COMPLEX)
586:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
587:     else wi[i] /= beta[i];
588: #else
589:     if (wi) wi[i] = 0.0;
590: #endif
591:   }
592:   return(0);
593: #endif
594: }

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->normalize     = DSNormalize_GNHEP;
607:   return(0);
608: }