Actual source code: dsgnhep.c

slepc-3.18.1 2022-11-02
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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: /*
 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: */

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

 32: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
 33: {
 34:   DSAllocateMat_Private(ds,DS_MAT_A);
 35:   DSAllocateMat_Private(ds,DS_MAT_B);
 36:   DSAllocateMat_Private(ds,DS_MAT_Z);
 37:   DSAllocateMat_Private(ds,DS_MAT_Q);
 38:   PetscFree(ds->perm);
 39:   PetscMalloc1(ld,&ds->perm);
 40:   return 0;
 41: }

 43: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
 44: {
 45:   PetscViewerFormat format;

 47:   PetscViewerGetFormat(viewer,&format);
 48:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return 0;
 49:   DSViewMat(ds,viewer,DS_MAT_A);
 50:   DSViewMat(ds,viewer,DS_MAT_B);
 51:   if (ds->state>DS_STATE_INTERMEDIATE) {
 52:     DSViewMat(ds,viewer,DS_MAT_Z);
 53:     DSViewMat(ds,viewer,DS_MAT_Q);
 54:   }
 55:   if (ds->omat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
 56:   if (ds->omat[DS_MAT_Y]) DSViewMat(ds,viewer,DS_MAT_Y);
 57:   return 0;
 58: }

 60: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 61: {
 62:   PetscInt       i;
 63:   PetscBLASInt   n,ld,mout,info,*select,mm,inc=1,cols=1,zero=0;
 64:   PetscScalar    *X,*Y,*XY,*Z,*Q,*A,*B,fone=1.0,fzero=0.0;
 65:   PetscReal      norm,done=1.0;
 66:   PetscBool      iscomplex = PETSC_FALSE;
 67:   const char     *side;

 69:   PetscBLASIntCast(ds->n,&n);
 70:   PetscBLASIntCast(ds->ld,&ld);
 71:   if (left) {
 72:     X = NULL;
 73:     MatDenseGetArray(ds->omat[DS_MAT_Y],&Y);
 74:     side = "L";
 75:   } else {
 76:     MatDenseGetArray(ds->omat[DS_MAT_X],&X);
 77:     Y = NULL;
 78:     side = "R";
 79:   }
 80:   XY = left? Y: X;
 81:   DSAllocateWork_Private(ds,0,0,ld);
 82:   select = ds->iwork;
 83:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
 84:   if (ds->state <= DS_STATE_INTERMEDIATE) {
 85:     DSSetIdentity(ds,DS_MAT_Q);
 86:     DSSetIdentity(ds,DS_MAT_Z);
 87:   }
 88:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
 89:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
 90:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
 91:   MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
 92:   CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld);
 93:   if (ds->state < DS_STATE_CONDENSED) DSSetState(ds,DS_STATE_CONDENSED);

 95:   /* compute k-th eigenvector */
 96:   select[*k] = (PetscBLASInt)PETSC_TRUE;
 97: #if defined(PETSC_USE_COMPLEX)
 98:   mm = 1;
 99:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
100:   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y+(*k)*ld,&ld,X+(*k)*ld,&ld,&mm,&mout,ds->work,ds->rwork,&info));
101: #else
102:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
103:   mm = iscomplex? 2: 1;
104:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
105:   DSAllocateWork_Private(ds,6*ld,0,0);
106:   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y+(*k)*ld,&ld,X+(*k)*ld,&ld,&mm,&mout,ds->work,&info));
107: #endif
108:   SlepcCheckLapackInfo("tgevc",info);
110:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
111:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);

113:   /* accumulate and normalize eigenvectors */
114:   PetscArraycpy(ds->work,XY+(*k)*ld,mm*ld);
115:   PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,left?Z:Q,&ld,ds->work,&ld,&fzero,XY+(*k)*ld,&ld));
116:   norm = BLASnrm2_(&n,XY+(*k)*ld,&inc);
117: #if !defined(PETSC_USE_COMPLEX)
118:   if (iscomplex) {
119:     norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,XY+(*k+1)*ld,&inc));
120:     cols = 2;
121:   }
122: #endif
123:   PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,XY+(*k)*ld,&ld,&info));
124:   SlepcCheckLapackInfo("lascl",info);
125:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
126:   MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);

128:   /* set output arguments */
129:   if (rnorm) {
130:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(XY[n-1+(*k)*ld],XY[n-1+(*k+1)*ld]);
131:     else *rnorm = PetscAbsScalar(XY[n-1+(*k)*ld]);
132:   }
133:   if (iscomplex) (*k)++;
134:   MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY);
135:   return 0;
136: }

138: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
139: {
140:   PetscInt       i;
141:   PetscBLASInt   n,ld,mout,info,inc = 1;
142:   PetscBool      iscomplex;
143:   PetscScalar    *X,*Y,*XY,*Q,*Z,*A,*B,tmp;
144:   PetscReal      norm;
145:   const char     *side,*back;

147:   PetscBLASIntCast(ds->n,&n);
148:   PetscBLASIntCast(ds->ld,&ld);
149:   if (left) {
150:     X = NULL;
151:     MatDenseGetArray(ds->omat[DS_MAT_Y],&Y);
152:     side = "L";
153:   } else {
154:     MatDenseGetArray(ds->omat[DS_MAT_X],&X);
155:     Y = NULL;
156:     side = "R";
157:   }
158:   XY = left? Y: X;
159:   if (ds->state <= DS_STATE_INTERMEDIATE) {
160:     DSSetIdentity(ds,DS_MAT_Q);
161:     DSSetIdentity(ds,DS_MAT_Z);
162:   }
163:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
164:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
165:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
166:   MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
167:   CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld);
168:   if (ds->state>=DS_STATE_CONDENSED) {
169:     /* DSSolve() has been called, backtransform with matrix Q */
170:     back = "B";
171:     PetscArraycpy(left?Y:X,left?Z:Q,ld*ld);
172:   } else {
173:     back = "A";
174:     DSSetState(ds,DS_STATE_CONDENSED);
175:   }
176: #if defined(PETSC_USE_COMPLEX)
177:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
178:   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
179: #else
180:   DSAllocateWork_Private(ds,6*ld,0,0);
181:   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
182: #endif
183:   SlepcCheckLapackInfo("tgevc",info);
184:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
185:   MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);

187:   /* normalize eigenvectors */
188:   for (i=0;i<n;i++) {
189:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
190:     norm = BLASnrm2_(&n,XY+i*ld,&inc);
191: #if !defined(PETSC_USE_COMPLEX)
192:     if (iscomplex) {
193:       tmp = BLASnrm2_(&n,XY+(i+1)*ld,&inc);
194:       norm = SlepcAbsEigenvalue(norm,tmp);
195:     }
196: #endif
197:     tmp = 1.0 / norm;
198:     PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+i*ld,&inc));
199: #if !defined(PETSC_USE_COMPLEX)
200:     if (iscomplex) PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+(i+1)*ld,&inc));
201: #endif
202:     if (iscomplex) i++;
203:   }
204:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
205:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
206:   MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY);
207:   return 0;
208: }

210: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
211: {
212:   switch (mat) {
213:     case DS_MAT_X:
214:     case DS_MAT_Y:
215:       if (k) DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
216:       else DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
217:       break;
218:     default:
219:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
220:   }
221:   return 0;
222: }

224: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
225: {
226:   PetscInt       i;
227:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
228:   PetscScalar    *S,*T,*Q,*Z,*work,*beta;

230:   if (!ds->sc) return 0;
231:   PetscBLASIntCast(ds->n,&n);
232:   PetscBLASIntCast(ds->ld,&ld);
233: #if !defined(PETSC_USE_COMPLEX)
234:   lwork = 4*n+16;
235: #else
236:   lwork = 1;
237: #endif
238:   liwork = 1;
239:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
240:   beta      = ds->work;
241:   work      = ds->work + n;
242:   lwork     = ds->lwork - n;
243:   selection = ds->iwork;
244:   iwork     = ds->iwork + n;
245:   liwork    = ds->liwork - n;
246:   /* Compute the selected eigenvalue to be in the leading position */
247:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
248:   PetscArrayzero(selection,n);
249:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
250:   MatDenseGetArray(ds->omat[DS_MAT_A],&S);
251:   MatDenseGetArray(ds->omat[DS_MAT_B],&T);
252:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
253:   MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
254: #if !defined(PETSC_USE_COMPLEX)
255:   PetscCallBLAS("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));
256: #else
257:   PetscCallBLAS("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));
258: #endif
259:   SlepcCheckLapackInfo("tgsen",info);
260:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&S);
261:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&T);
262:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
263:   MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);
264:   *k = mout;
265:   for (i=0;i<n;i++) {
266:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
267:     else wr[i] /= beta[i];
268: #if !defined(PETSC_USE_COMPLEX)
269:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
270:     else wi[i] /= beta[i];
271: #endif
272:   }
273:   return 0;
274: }

276: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
277: {
278:   PetscScalar    re;
279:   PetscInt       i,j,pos,result;
280:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
281:   PetscScalar    *S,*T,*Z,*Q;
282: #if !defined(PETSC_USE_COMPLEX)
283:   PetscBLASInt   lwork;
284:   PetscScalar    *work,a,safmin,scale1,scale2,im;
285: #endif

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

375: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
376: {
377:   if (!rr || wr == rr) DSSort_GNHEP_Total(ds,wr,wi);
378:   else DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
379:   return 0;
380: }

382: PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
383: {
384:   PetscInt          i;
385:   PetscBLASInt      n,ld,incx=1;
386:   PetscScalar       *A,*B,*x,*y,one=1.0,zero=0.0;
387:   const PetscScalar *Q;

389:   PetscBLASIntCast(ds->n,&n);
390:   PetscBLASIntCast(ds->ld,&ld);
391:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
392:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
393:   MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q);
394:   DSAllocateWork_Private(ds,2*ld,0,0);
395:   x = ds->work;
396:   y = ds->work+ld;
397:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
398:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
399:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
400:   for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
401:   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
402:   for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
403:   ds->k = n;
404:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
405:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
406:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q);
407:   return 0;
408: }

410: /*
411:    Write zeros from the column k to n in the lower triangular part of the
412:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
413:    make (S,T) a valid Schur decompositon.
414: */
415: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
416: {
417:   PetscInt       i;
418: #if defined(PETSC_USE_COMPLEX)
419:   PetscInt       j;
420:   PetscScalar    s;
421: #else
422:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
423:   PetscScalar    b11,b22,sr,cr,sl,cl;
424: #endif

426: #if defined(PETSC_USE_COMPLEX)
427:   for (i=k; i<n; i++) {
428:     /* Some functions need the diagonal elements in T be real */
429:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
430:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
431:       for (j=0;j<=i;j++) {
432:         T[ldT*i+j] *= s;
433:         S[ldS*i+j] *= s;
434:       }
435:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
436:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
437:     }
438:     j = i+1;
439:     if (j<n) {
440:       S[ldS*i+j] = 0.0;
441:       if (T) T[ldT*i+j] = 0.0;
442:     }
443:   }
444: #else
445:   PetscBLASIntCast(ldS,&ldS_);
446:   PetscBLASIntCast(ldT,&ldT_);
447:   PetscBLASIntCast(n,&n_);
448:   for (i=k;i<n-1;i++) {
449:     if (S[ldS*i+i+1] != 0.0) {
450:       /* Check if T(i+1,i) and T(i,i+1) are zero */
451:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
452:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
453:         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) {
454:           T[ldT*i+i+1] = 0.0;
455:           T[ldT*(i+1)+i] = 0.0;
456:         } else {
457:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
458:           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) {
459:             PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
460:           } 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) {
461:             PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
462:           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
463:           PetscBLASIntCast(n-i,&n_i);
464:           n_i_2 = n_i - 2;
465:           PetscBLASIntCast(i+2,&i_2);
466:           PetscBLASIntCast(i,&i_);
467:           if (b11 < 0.0) {
468:             cr = -cr; sr = -sr;
469:             b11 = -b11; b22 = -b22;
470:           }
471:           PetscCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
472:           PetscCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
473:           PetscCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
474:           PetscCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
475:           if (X) PetscCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
476:           if (Y) PetscCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
477:           T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
478:           T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
479:         }
480:       }
481:       i++;
482:     }
483:   }
484: #endif
485:   return 0;
486: }

488: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
489: {
490:   PetscScalar    *work,*beta,a;
491:   PetscInt       i;
492:   PetscBLASInt   lwork,info,n,ld,iaux;
493:   PetscScalar    *A,*B,*Z,*Q;

495: #if !defined(PETSC_USE_COMPLEX)
497: #endif
498:   PetscBLASIntCast(ds->n,&n);
499:   PetscBLASIntCast(ds->ld,&ld);
500:   lwork = -1;
501:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
502:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
503:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
504:   MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
505: #if !defined(PETSC_USE_COMPLEX)
506:   PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
507:   PetscBLASIntCast((PetscInt)a,&lwork);
508:   DSAllocateWork_Private(ds,lwork+ld,0,0);
509:   beta = ds->work;
510:   work = beta+ds->n;
511:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
512:   PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
513: #else
514:   PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
515:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
516:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
517:   beta = ds->work;
518:   work = beta+ds->n;
519:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
520:   PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
521: #endif
522:   SlepcCheckLapackInfo("gges",info);
523:   for (i=0;i<n;i++) {
524:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
525:     else wr[i] /= beta[i];
526: #if !defined(PETSC_USE_COMPLEX)
527:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
528:     else wi[i] /= beta[i];
529: #else
530:     if (wi) wi[i] = 0.0;
531: #endif
532:   }
533:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
534:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
535:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
536:   MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);
537:   return 0;
538: }

540: #if !defined(PETSC_HAVE_MPIUNI)
541: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
542: {
543:   PetscInt       ld=ds->ld,l=ds->l,k;
544:   PetscMPIInt    n,rank,off=0,size,ldn;
545:   PetscScalar    *A,*B,*Q,*Z;

547:   k = 2*(ds->n-l)*ld;
548:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
549:   if (eigr) k += (ds->n-l);
550:   if (eigi) k += (ds->n-l);
551:   DSAllocateWork_Private(ds,k,0,0);
552:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
553:   PetscMPIIntCast(ds->n-l,&n);
554:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
555:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
556:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
557:   if (ds->state>DS_STATE_RAW) {
558:     MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
559:     MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
560:   }
561:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
562:   if (!rank) {
563:     MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
564:     MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
565:     if (ds->state>DS_STATE_RAW) {
566:       MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
567:       MPI_Pack(Z+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
568:     }
569:     if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
570: #if !defined(PETSC_USE_COMPLEX)
571:     if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
572: #endif
573:   }
574:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
575:   if (rank) {
576:     MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
577:     MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
578:     if (ds->state>DS_STATE_RAW) {
579:       MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
580:       MPI_Unpack(ds->work,size,&off,Z+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
581:     }
582:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
583: #if !defined(PETSC_USE_COMPLEX)
584:     if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
585: #endif
586:   }
587:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
588:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
589:   if (ds->state>DS_STATE_RAW) {
590:     MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
591:     MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);
592:   }
593:   return 0;
594: }
595: #endif

597: PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
598: {
599:   PetscInt    i,ld=ds->ld,l=ds->l;
600:   PetscScalar *A,*B;

602:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
603:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
604: #if defined(PETSC_USE_DEBUG)
605:   /* make sure diagonal 2x2 block is not broken */
607: #endif
608:   if (trim) {
609:     if (ds->extrarow) {   /* clean extra row */
610:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
611:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
612:     }
613:     ds->l = 0;
614:     ds->k = 0;
615:     ds->n = n;
616:     ds->t = ds->n;   /* truncated length equal to the new dimension */
617:   } else {
618:     if (ds->extrarow && ds->k==ds->n) {
619:       /* copy entries of extra row to the new position, then clean last row */
620:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
621:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
622:       for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
623:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
624:     }
625:     ds->k = (ds->extrarow)? n: 0;
626:     ds->t = ds->n;   /* truncated length equal to previous dimension */
627:     ds->n = n;
628:   }
629:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
630:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
631:   return 0;
632: }

634: /*MC
635:    DSGNHEP - Dense Generalized Non-Hermitian Eigenvalue Problem.

637:    Level: beginner

639:    Notes:
640:    The problem is expressed as A*X = B*X*Lambda, where (A,B) is the input
641:    matrix pencil. Lambda is a diagonal matrix whose diagonal elements are the
642:    arguments of DSSolve(). After solve, (A,B) is overwritten with the
643:    generalized (real) Schur form (S,T) = (Z'*A*Q,Z'*B*Q), with the first
644:    matrix being upper quasi-triangular and the second one triangular.

646:    Used DS matrices:
647: +  DS_MAT_A - first problem matrix
648: .  DS_MAT_B - second problem matrix
649: .  DS_MAT_Q - first orthogonal/unitary transformation that reduces to
650:    generalized (real) Schur form
651: -  DS_MAT_Z - second orthogonal/unitary transformation that reduces to
652:    generalized (real) Schur form

654:    Implemented methods:
655: .  0 - QZ iteration (_gges)

657: .seealso: DSCreate(), DSSetType(), DSType
658: M*/
659: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
660: {
661:   ds->ops->allocate        = DSAllocate_GNHEP;
662:   ds->ops->view            = DSView_GNHEP;
663:   ds->ops->vectors         = DSVectors_GNHEP;
664:   ds->ops->solve[0]        = DSSolve_GNHEP;
665:   ds->ops->sort            = DSSort_GNHEP;
666: #if !defined(PETSC_HAVE_MPIUNI)
667:   ds->ops->synchronize     = DSSynchronize_GNHEP;
668: #endif
669:   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
670:   ds->ops->truncate        = DSTruncate_GNHEP;
671:   ds->ops->update          = DSUpdateExtraRow_GNHEP;
672:   return 0;
673: }