Actual source code: dsgnhep.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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: {

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

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

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

 66: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
 67: {
 69:   PetscInt       i;
 70:   PetscBLASInt   n,ld,mout,info,*select,mm,inc=1,cols=1,zero=0;
 71:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],fone=1.0,fzero=0.0;
 72:   PetscReal      norm,done=1.0;
 73:   PetscBool      iscomplex = PETSC_FALSE;
 74:   const char     *side;

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

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

115:   /* accumulate and normalize eigenvectors */
116:   PetscArraycpy(ds->work,Z,mm*ld);
117:   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));
118:   norm = BLASnrm2_(&n,Z,&inc);
119: #if !defined(PETSC_USE_COMPLEX)
120:   if (iscomplex) {
121:     norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+ld,&inc));
122:     cols = 2;
123:   }
124: #endif
125:   PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z,&ld,&info));
126:   SlepcCheckLapackInfo("lascl",info);

128:   /* set output arguments */
129:   if (iscomplex) (*k)++;
130:   if (rnorm) {
131:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
132:     else *rnorm = PetscAbsScalar(Z[n-1]);
133:   }
134:   return(0);
135: }

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

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

182:   /* normalize eigenvectors */
183:   for (i=0;i<n;i++) {
184:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
185:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
186: #if !defined(PETSC_USE_COMPLEX)
187:     if (iscomplex) {
188:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
189:       norm = SlepcAbsEigenvalue(norm,tmp);
190:     }
191: #endif
192:     tmp = 1.0 / norm;
193:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
194: #if !defined(PETSC_USE_COMPLEX)
195:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
196: #endif
197:     if (iscomplex) i++;
198:   }
199:   return(0);
200: }

202: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
203: {

207:   switch (mat) {
208:     case DS_MAT_X:
209:     case DS_MAT_Y:
210:       if (k) {
211:         DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
212:       } else {
213:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
214:       }
215:       break;
216:     default:
217:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
218:   }
219:   return(0);
220: }

222: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
223: {
225:   PetscInt       i;
226:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
227:   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;

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: #if !defined(PETSC_USE_COMPLEX)
251:   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));
252: #else
253:   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));
254: #endif
255:   SlepcCheckLapackInfo("tgsen",info);
256:   *k = mout;
257:   for (i=0;i<n;i++) {
258:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
259:     else wr[i] /= beta[i];
260: #if !defined(PETSC_USE_COMPLEX)
261:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
262:     else wi[i] /= beta[i];
263: #endif
264:   }
265:   return(0);
266: }

268: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
269: {
271:   PetscScalar    re;
272:   PetscInt       i,j,pos,result;
273:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
274:   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];
275: #if !defined(PETSC_USE_COMPLEX)
276:   PetscBLASInt   lwork;
277:   PetscScalar    *work,a,safmin,scale1,scale2,im;
278: #endif

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

361: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
362: {

366:   if (!rr || wr == rr) {
367:     DSSort_GNHEP_Total(ds,wr,wi);
368:   } else {
369:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
370:   }
371:   return(0);
372: }

374: PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
375: {
377:   PetscInt       i;
378:   PetscBLASInt   n,ld,incx=1;
379:   PetscScalar    *A,*B,*Q,*x,*y,one=1.0,zero=0.0;

382:   PetscBLASIntCast(ds->n,&n);
383:   PetscBLASIntCast(ds->ld,&ld);
384:   A  = ds->mat[DS_MAT_A];
385:   B  = ds->mat[DS_MAT_B];
386:   Q  = ds->mat[DS_MAT_Q];
387:   DSAllocateWork_Private(ds,2*ld,0,0);
388:   x = ds->work;
389:   y = ds->work+ld;
390:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
391:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
392:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
393:   for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
394:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
395:   for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
396:   ds->k = n;
397:   return(0);
398: }

400: /*
401:    Write zeros from the column k to n in the lower triangular part of the
402:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
403:    make (S,T) a valid Schur decompositon.
404: */
405: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
406: {
407:   PetscInt       i;
408: #if defined(PETSC_USE_COMPLEX)
409:   PetscInt       j;
410:   PetscScalar    s;
411: #else
413:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
414:   PetscScalar    b11,b22,sr,cr,sl,cl;
415: #endif

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

480: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
481: {
483:   PetscScalar    *work,*beta,a;
484:   PetscInt       i;
485:   PetscBLASInt   lwork,info,n,ld,iaux;
486:   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];

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

526: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
527: {
529:   PetscInt       ld=ds->ld,l=ds->l,k;
530:   PetscMPIInt    n,rank,off=0,size,ldn;

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

578: PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
579: {
580:   PetscInt    i,ld=ds->ld,l=ds->l;
581:   PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];

584: #if defined(PETSC_USE_DEBUG)
585:   /* make sure diagonal 2x2 block is not broken */
586:   if (ds->state>=DS_STATE_CONDENSED && n>0 && n<ds->n && (A[n+(n-1)*ld]!=0.0 || B[n+(n-1)*ld]!=0.0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
587: #endif
588:   if (trim) {
589:     if (ds->extrarow) {   /* clean extra row */
590:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
591:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
592:     }
593:     ds->l = 0;
594:     ds->k = 0;
595:     ds->n = n;
596:     ds->t = ds->n;   /* truncated length equal to the new dimension */
597:   } else {
598:     if (ds->extrarow && ds->k==ds->n) {
599:       /* copy entries of extra row to the new position, then clean last row */
600:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
601:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
602:       for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
603:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
604:     }
605:     ds->k = (ds->extrarow)? n: 0;
606:     ds->t = ds->n;   /* truncated length equal to previous dimension */
607:     ds->n = n;
608:   }
609:   return(0);
610: }

612: /*MC
613:    DSGNHEP - Dense Generalized Non-Hermitian Eigenvalue Problem.

615:    Level: beginner

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

624:    Used DS matrices:
625: +  DS_MAT_A - first problem matrix
626: .  DS_MAT_B - second problem matrix
627: .  DS_MAT_Q - first orthogonal/unitary transformation that reduces to
628:    generalized (real) Schur form
629: -  DS_MAT_Z - second orthogonal/unitary transformation that reduces to
630:    generalized (real) Schur form

632:    Implemented methods:
633: .  0 - QZ iteration (_gges)

635: .seealso: DSCreate(), DSSetType(), DSType
636: M*/
637: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
638: {
640:   ds->ops->allocate        = DSAllocate_GNHEP;
641:   ds->ops->view            = DSView_GNHEP;
642:   ds->ops->vectors         = DSVectors_GNHEP;
643:   ds->ops->solve[0]        = DSSolve_GNHEP;
644:   ds->ops->sort            = DSSort_GNHEP;
645:   ds->ops->synchronize     = DSSynchronize_GNHEP;
646:   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
647:   ds->ops->truncate        = DSTruncate_GNHEP;
648:   ds->ops->update          = DSUpdateExtraRow_GNHEP;
649:   return(0);
650: }