Actual source code: dsghiep.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2013, 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: */
 21: #include <slepc-private/dsimpl.h>      /*I "slepcds.h" I*/
 22: #include <slepcblaslapack.h>

 26: PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
 27: {

 31:   DSAllocateMat_Private(ds,DS_MAT_A);
 32:   DSAllocateMat_Private(ds,DS_MAT_B);
 33:   DSAllocateMat_Private(ds,DS_MAT_Q);
 34:   DSAllocateMatReal_Private(ds,DS_MAT_T);
 35:   DSAllocateMatReal_Private(ds,DS_MAT_D);
 36:   PetscFree(ds->perm);
 37:   PetscMalloc(ld*sizeof(PetscInt),&ds->perm);
 38:   PetscLogObjectMemory(ds,ld*sizeof(PetscInt));
 39:   return(0);
 40: }

 44: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
 45: {
 47:   PetscReal      *T,*S;
 48:   PetscScalar    *A,*B;
 49:   PetscInt       i,n,ld;

 52:   A = ds->mat[DS_MAT_A];
 53:   B = ds->mat[DS_MAT_B];
 54:   T = ds->rmat[DS_MAT_T];
 55:   S = ds->rmat[DS_MAT_D];
 56:   n = ds->n;
 57:   ld = ds->ld;
 58:   if (tocompact) { /* switch from dense (arrow) to compact storage */
 59:     PetscMemzero(T,3*ld*sizeof(PetscReal));
 60:     PetscMemzero(S,ld*sizeof(PetscReal));
 61:     for (i=0;i<n-1;i++) {
 62:       T[i] = PetscRealPart(A[i+i*ld]);
 63:       T[ld+i] = PetscRealPart(A[i+1+i*ld]);
 64:       S[i] = PetscRealPart(B[i+i*ld]);
 65:     }
 66:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
 67:     S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
 68:     for (i=ds->l;i< ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
 69:   } else { /* switch from compact (arrow) to dense storage */
 70:     PetscMemzero(A,ld*ld*sizeof(PetscScalar));
 71:     PetscMemzero(B,ld*ld*sizeof(PetscScalar));
 72:     for (i=0;i<n-1;i++) {
 73:       A[i+i*ld] = T[i];
 74:       A[i+1+i*ld] = T[ld+i];
 75:       A[i+(i+1)*ld] = T[ld+i];
 76:       B[i+i*ld] = S[i];
 77:     }
 78:     A[n-1+(n-1)*ld] = T[n-1];
 79:     B[n-1+(n-1)*ld] = S[n-1];
 80:     for (i=ds->l;i<ds->k;i++) {
 81:       A[ds->k+i*ld] = T[2*ld+i];
 82:       A[i+ds->k*ld] = T[2*ld+i];
 83:     }
 84:   }
 85:   return(0);
 86: }

 90: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
 91: {
 92:   PetscErrorCode    ierr;
 93:   PetscViewerFormat format;
 94:   PetscInt          i,j;
 95:   PetscReal         value;
 96:   const char        *methodname[] = {
 97:                      "HR method",
 98:                      "QR + Inverse Iteration",
 99:                      "QR",
100:                      "DQDS + Inverse Iteration "
101:   };
102:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

105:   PetscViewerGetFormat(viewer,&format);
106:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
107:     if (ds->method>=nmeth) {
108:       PetscViewerASCIIPrintf(viewer,"solving the problem with: INVALID METHOD\n");
109:     } else {
110:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
111:     }
112:     return(0);
113:   }
114:   if (ds->compact) {
115:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
116:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
117:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
118:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
119:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
120:       for (i=0;i<ds->n;i++) {
121:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_T]+i));
122:       }
123:       for (i=0;i<ds->n-1;i++) {
124:         if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
125:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+2,i+1,*(ds->rmat[DS_MAT_T]+ds->ld+i));
126:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+2,*(ds->rmat[DS_MAT_T]+ds->ld+i));
127:         }
128:       }
129:       for (i = ds->l;i<ds->k;i++) {
130:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",ds->k+1,i+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
131:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,ds->k+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
132:       }
133:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);

135:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
136:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
137:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
138:       for (i=0;i<ds->n;i++) {
139:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_D]+i));
140:       }
141:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

143:     } else {
144:       PetscViewerASCIIPrintf(viewer,"T\n");
145:       for (i=0;i<ds->n;i++) {
146:         for (j=0;j<ds->n;j++) {
147:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
148:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
149:           else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+2*ds->ld+PetscMin(i,j));
150:           else value = 0.0;
151:           PetscViewerASCIIPrintf(viewer," %18.16e ",value);
152:         }
153:         PetscViewerASCIIPrintf(viewer,"\n");
154:       }
155:       PetscViewerASCIIPrintf(viewer,"omega\n");
156:       for (i=0;i<ds->n;i++) {
157:         for (j=0;j<ds->n;j++) {
158:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
159:           else value = 0.0;
160:           PetscViewerASCIIPrintf(viewer," %18.16e ",value);
161:         }
162:         PetscViewerASCIIPrintf(viewer,"\n");
163:       }
164:     }
165:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
166:     PetscViewerFlush(viewer);
167:   } else {
168:     DSViewMat_Private(ds,viewer,DS_MAT_A);
169:     DSViewMat_Private(ds,viewer,DS_MAT_B);
170:   }
171:   if (ds->state>DS_STATE_INTERMEDIATE) {
172:     DSViewMat_Private(ds,viewer,DS_MAT_Q);
173:   }
174:   return(0);
175: }

179: PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
180: {
182:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
183:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
184:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
185:   PetscInt       k;
186:   PetscBLASInt   two = 2,n_,ld,one=1;
187: #if !defined(PETSC_USE_COMPLEX)
188:   PetscBLASInt   four=4;
189: #endif

192:   X = ds->mat[DS_MAT_X];
193:   Q = ds->mat[DS_MAT_Q];
194:   k = *idx;
195:   PetscBLASIntCast(ds->n,&n_);
196:   PetscBLASIntCast(ds->ld,&ld);
197:   if (k < ds->n-1) {
198:     e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
199:   } else e = 0.0;
200:   if (e == 0.0) {/* Real */
201:     if (ds->state>=DS_STATE_CONDENSED) {
202:       PetscMemcpy(X+k*ld,Q+k*ld,ld*sizeof(PetscScalar));
203:     } else {
204:       PetscMemzero(X+k*ds->ld,ds->ld*sizeof(PetscScalar));
205:       X[k+k*ds->ld] = 1.0;
206:     }
207:     if (rnorm) {
208:       *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
209:     }
210:   } else { /* 2x2 block */
211:     if (ds->compact) {
212:       s1 = *(ds->rmat[DS_MAT_D]+k);
213:       d1 = *(ds->rmat[DS_MAT_T]+k);
214:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
215:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
216:     } else {
217:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
218:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
219:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
220:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
221:     }
222:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
223:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
224:     ep = LAPACKlamch_("S");
225:     /* Compute eigenvalues of the block */
226:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
227:     if (wi==0.0)  /* Real eigenvalues */
228:       SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
229:     else { /* Complex eigenvalues */
230:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
231:       wr1 /= scal1; wi /= scal1;
232: #if !defined(PETSC_USE_COMPLEX)
233:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
234:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
235:       } else {
236:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
237:       }
238:       norm = BLASnrm2_(&four,Y,&one);
239:       norm = 1/norm;
240:       if (ds->state >= DS_STATE_CONDENSED) {
241:         alpha = norm;
242:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
243:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
244:       } else {
245:         PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
246:         X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
247:         X[(k+1)*ld+k] = Y[2]*norm; X[(k+1)*ld+k+1] = Y[3]*norm;
248:       }
249: #else
250:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
251:         Y[0] = wr1-s2*d2+PETSC_i*wi; Y[1] = s2*e;
252:       } else {
253:         Y[0] = s1*e; Y[1] = wr1-s1*d1+PETSC_i*wi;
254:       }
255:       norm = BLASnrm2_(&two,Y,&one);
256:       norm = 1/norm;
257:       if (ds->state >= DS_STATE_CONDENSED) {
258:         alpha = norm;
259:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
260:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
261:       } else {
262:         PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
263:         X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
264:       }
265:       X[(k+1)*ld+k] = PetscConj(X[k*ld+k]); X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
266: #endif
267:       (*idx)++;
268:     }
269:   }
270:   return(0);
271: }

275: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
276: {
277:   PetscInt       i;
278:   PetscReal      e;

282:   switch (mat) {
283:     case DS_MAT_X:
284:       if (k) {
285:         DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
286:       } else {
287:         for (i=0; i<ds->n; i++) {
288:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
289:           if (e == 0.0) {/* real */
290:             if (ds->state >= DS_STATE_CONDENSED) {
291:               PetscMemcpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld*sizeof(PetscScalar));
292:             } else {
293:               PetscMemzero(ds->mat[mat]+i*ds->ld,ds->ld*sizeof(PetscScalar));
294:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
295:             }
296:           } else {
297:             DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
298:           }
299:         }
300:       }
301:       break;
302:     case DS_MAT_Y:
303:     case DS_MAT_U:
304:     case DS_MAT_VT:
305:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
306:       break;
307:     default:
308:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
309:   }
310:   return(0);
311: }

315: /*
316:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
317:   Only the index range n0..n1 is processed.
318: */
319: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
320: {
321:   PetscInt     k,ld;
322:   PetscBLASInt two=2;
323:   PetscScalar  *A,*B;
324:   PetscReal    *D,*T;
325:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
326:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

329:   ld = ds->ld;
330:   A = ds->mat[DS_MAT_A];
331:   B = ds->mat[DS_MAT_B];
332:   D = ds->rmat[DS_MAT_D];
333:   T = ds->rmat[DS_MAT_T];
334:   for (k=n0;k<n1;k++) {
335:     if (k < n1-1) {
336:       e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
337:     } else {
338:       e = 0.0;
339:     }
340:     if (e==0.0) {
341:       /* real eigenvalue */
342:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
343: #if !defined(PETSC_USE_COMPLEX)
344:       wi[k] = 0.0 ;
345: #endif
346:     } else {
347:       /* diagonal block */
348:       if (ds->compact) {
349:         s1 = D[k];
350:         d1 = T[k];
351:         s2 = D[k+1];
352:         d2 = T[k+1];
353:       } else {
354:         s1 = PetscRealPart(B[k*ld+k]);
355:         d1 = PetscRealPart(A[k+k*ld]);
356:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
357:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
358:       }
359:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
360:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
361:       ep = LAPACKlamch_("S");
362:       /* Compute eigenvalues of the block */
363:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
364:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
365:       wr[k] = wr1/scal1;
366:       if (wi1==0.0) { /* Real eigenvalues */
367:         if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
368:         wr[k+1] = wr2/scal2;
369: #if !defined(PETSC_USE_COMPLEX)
370:         wi[k] = 0.0;
371:         wi[k+1] = 0.0;
372: #endif
373:       } else { /* Complex eigenvalues */
374: #if !defined(PETSC_USE_COMPLEX)
375:         wr[k+1] = wr[k];
376:         wi[k] = wi1/scal1;
377:         wi[k+1] = -wi[k];
378: #else
379:         wr[k] += PETSC_i*wi1/scal1;
380:         wr[k+1] = PetscConj(wr[k]);
381: #endif
382:       }
383:       k++;
384:     }
385:   }
386: #if defined(PETSC_USE_COMPLEX)
387:   if (wi) {
388:     for (k=n0;k<n1;k++) wi[k] = 0.0;
389:   }
390: #endif
391:   return(0);
392: }

396: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
397: {
399:   PetscInt       n,i,*perm;
400:   PetscReal      *d,*e,*s;

403: #if !defined(PETSC_USE_COMPLEX)
405: #endif
406:   n = ds->n;
407:   d = ds->rmat[DS_MAT_T];
408:   e = d + ds->ld;
409:   s = ds->rmat[DS_MAT_D];
410:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
411:   perm = ds->perm;
412:   if (!rr) {
413:     rr = wr;
414:     ri = wi;
415:   }
416:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
417:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
418:   PetscMemcpy(ds->work,wr,n*sizeof(PetscScalar));
419:   for (i=ds->l;i<n;i++) {
420:     wr[i] = *(ds->work + perm[i]);
421:   }
422: #if !defined(PETSC_USE_COMPLEX)
423:   PetscMemcpy(ds->work,wi,n*sizeof(PetscScalar));
424:   for (i=ds->l;i<n;i++) {
425:     wi[i] = *(ds->work + perm[i]);
426:   }
427: #endif
428:   PetscMemcpy(ds->rwork,s,n*sizeof(PetscReal));
429:   for (i=ds->l;i<n;i++) {
430:     s[i] = *(ds->rwork+perm[i]);
431:   }
432:   PetscMemcpy(ds->rwork,d,n*sizeof(PetscReal));
433:   for (i=ds->l;i<n;i++) {
434:     d[i] = *(ds->rwork  + perm[i]);
435:   }
436:   PetscMemcpy(ds->rwork,e,(n-1)*sizeof(PetscReal));
437:   PetscMemzero(e+ds->l,(n-1-ds->l)*sizeof(PetscScalar));
438:   for (i=ds->l;i<n-1;i++) {
439:     if (perm[i]<n-1) e[i] = *(ds->rwork + perm[i]);
440:   }
441:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
442:   DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
443:   return(0);
444: }


449: /*
450:   Get eigenvectors with inverse iteration.
451:   The system matrix is in Hessenberg form.
452: */
453: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
454: {
455: #if defined(PETSC_MISSING_LAPACK_HSEIN)
457:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEIN - Lapack routine is unavailable");
458: #else
460:   PetscInt       i,off;
461:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
462:   PetscScalar    *A,*B,*H,*X;
463:   PetscReal      *s,*d,*e;

466:   PetscBLASIntCast(ds->ld,&ld);
467:   PetscBLASIntCast(ds->n-ds->l,&n1);
468:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
469:   DSAllocateMat_Private(ds,DS_MAT_W);
470:   A = ds->mat[DS_MAT_A];
471:   B = ds->mat[DS_MAT_B];
472:   H = ds->mat[DS_MAT_W];
473:   s = ds->rmat[DS_MAT_D];
474:   d = ds->rmat[DS_MAT_T];
475:   e = d + ld;
476:   select = ds->iwork;
477:   infoC = ds->iwork + ld;
478:   off = ds->l+ds->l*ld;
479:   if (ds->compact) {
480:     H[off] = d[ds->l]*s[ds->l];
481:     H[off+ld] = e[ds->l]*s[ds->l];
482:     for (i=ds->l+1;i<ds->n-1;i++) {
483:       H[i+(i-1)*ld] = e[i-1]*s[i];
484:       H[i+i*ld] = d[i]*s[i];
485:       H[i+(i+1)*ld] = e[i]*s[i];
486:     }
487:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
488:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
489:   } else {
490:     s[ds->l] = PetscRealPart(B[off]);
491:     H[off] = A[off]*s[ds->l];
492:     H[off+ld] = A[off+ld]*s[ds->l];
493:     for (i=ds->l+1;i<ds->n-1;i++) {
494:       s[i] = PetscRealPart(B[i+i*ld]);
495:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
496:       H[i+i*ld]     = A[i+i*ld]*s[i];
497:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
498:     }
499:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
500:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
501:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
502:   }
503:   DSAllocateMat_Private(ds,DS_MAT_X);
504:   X = ds->mat[DS_MAT_X];
505:   for (i=0;i<n1;i++)select[i]=1;
506: #if !defined(PETSC_USE_COMPLEX)
507:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,NULL,infoC,&info));
508: #else
509:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,ds->rwork,NULL,infoC,&info));
510: #endif
511:   if (info<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in hsein routine %d",-i);
512:   if (info>0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Convergence error in hsein routine %d",i);
513:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
514:   return(0);
515: #endif
516: }


521: /*
522:    Undo 2x2 blocks that have real eigenvalues.
523: */
524: PetscErrorCode DSGHIEPRealBlocks(DS ds)
525: {
527:   PetscInt       i;
528:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
529:   PetscReal      maxy,ep,scal1,scal2,snorm;
530:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
531:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
532:   PetscBLASInt   m,two=2,ld;
533:   PetscBool      isreal;

536:   PetscBLASIntCast(ds->ld,&ld);
537:   PetscBLASIntCast(ds->n-ds->l,&m);
538:   A = ds->mat[DS_MAT_A];
539:   B = ds->mat[DS_MAT_B];
540:   T = ds->rmat[DS_MAT_T];
541:   D = ds->rmat[DS_MAT_D];
542:   DSAllocateWork_Private(ds,2*m,0,0);
543:   for (i=ds->l;i<ds->n-1;i++) {
544:     e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
545:     if (e != 0.0) { /* 2x2 block */
546:       if (ds->compact) {
547:         s1 = D[i];
548:         d1 = T[i];
549:         s2 = D[i+1];
550:         d2 = T[i+1];
551:       } else {
552:         s1 = PetscRealPart(B[i*ld+i]);
553:         d1 = PetscRealPart(A[i*ld+i]);
554:         s2 = PetscRealPart(B[(i+1)*ld+i+1]);
555:         d2 = PetscRealPart(A[(i+1)*ld+i+1]);
556:       }
557:       isreal = PETSC_FALSE;
558:       if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
559:         dd = d1-d2;
560:         if (2*PetscAbsReal(e) <= dd) {
561:           t = 2*e/dd;
562:           t = t/(1 + PetscSqrtReal(1+t*t));
563:         } else {
564:           t = dd/(2*e);
565:           ss = (t>=0)?1.0:-1.0;
566:           t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
567:         }
568:         Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
569:         Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
570:         wr1 = d1+t*e;
571:         wr2 = d2-t*e;
572:         ss1 = s1; ss2 = s2;
573:         isreal = PETSC_TRUE;
574:       } else {
575:         ss1 = 1.0; ss2 = 1.0,
576:         M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
577:         b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
578:         ep = LAPACKlamch_("S");
579:         /* Compute eigenvalues of the block */
580:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
581:         if (wi==0.0) { /* Real eigenvalues */
582:           isreal = PETSC_TRUE;
583:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
584:           wr1 /= scal1; wr2 /= scal2;
585:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
586:             Y[0] = wr1-s2*d2;
587:             Y[1] = s2*e;
588:           } else {
589:             Y[0] = s1*e;
590:             Y[1] = wr1-s1*d1;
591:           }
592:           /* normalize with a signature*/
593:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
594:           scal1 = PetscRealPart(Y[0])/maxy; scal2 = PetscRealPart(Y[1])/maxy;
595:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
596:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
597:           snorm = maxy*PetscSqrtReal(snorm); Y[0] = Y[0]/snorm; Y[1] = Y[1]/snorm;
598:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
599:             Y[2] = wr2-s2*d2;
600:             Y[3] = s2*e;
601:           } else {
602:             Y[2] = s1*e;
603:             Y[3] = wr2-s1*d1;
604:           }
605:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
606:           scal1 = PetscRealPart(Y[2])/maxy; scal2 = PetscRealPart(Y[3])/maxy;
607:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
608:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
609:           snorm = maxy*PetscSqrtReal(snorm);Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
610:         }
611:         wr1 *= ss1; wr2 *= ss2;
612:       }
613:       if (isreal) {
614:         if (ds->compact) {
615:           D[i] = ss1;;
616:           T[i] = wr1;
617:           D[i+1] = ss2;
618:           T[i+1] = wr2;
619:           T[ld+i] = 0.0;
620:         } else {
621:           B[i*ld+i] = ss1;
622:           A[i*ld+i] = wr1;
623:           B[(i+1)*ld+i+1] = ss2;
624:           A[(i+1)*ld+i+1] = wr2;
625:           A[(i+1)+ld*i] = 0.0;
626:           A[i+ld*(i+1)] = 0.0;
627:         }
628:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&oneS,ds->mat[DS_MAT_Q]+ds->l+i*ld,&ld,Y,&two,&zeroS,ds->work,&m));
629:         PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m*sizeof(PetscScalar));
630:         PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m*sizeof(PetscScalar));
631:       }
632:       i++;
633:     }
634:   }
635:   return(0);
636: }

640: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
641: {
642: #if defined(PETSC_MISSING_LAPACK_HSEQR)
644:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable");
645: #else
647:   PetscInt       i,off;
648:   PetscBLASInt   n1,ld,one,info,lwork;
649:   PetscScalar    *H,*A,*B,*Q;
650:   PetscReal      *d,*e,*s;

653: #if !defined(PETSC_USE_COMPLEX)
655: #endif
656:   one = 1;
657:   PetscBLASIntCast(ds->n-ds->l,&n1);
658:   PetscBLASIntCast(ds->ld,&ld);
659:   off = ds->l + ds->l*ld;
660:   A = ds->mat[DS_MAT_A];
661:   B = ds->mat[DS_MAT_B];
662:   Q = ds->mat[DS_MAT_Q];
663:   d = ds->rmat[DS_MAT_T];
664:   e = ds->rmat[DS_MAT_T] + ld;
665:   s = ds->rmat[DS_MAT_D];
666:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
667:   lwork = ld*ld;

669:   /* Quick return if possible */
670:   if (n1 == 1) {
671:     *(Q+off) = 1;
672:     if (!ds->compact) {
673:       d[ds->l] = PetscRealPart(A[off]);
674:       s[ds->l] = PetscRealPart(B[off]);
675:     }
676:     wr[ds->l] = d[ds->l]/s[ds->l];
677:     if (wi) wi[ds->l] = 0.0;
678:     return(0);
679:   }
680:   /* Reduce to pseudotriadiagonal form */
681:   DSIntermediate_GHIEP(ds);

683:   /* Compute Eigenvalues (QR)*/
684:   DSAllocateMat_Private(ds,DS_MAT_W);
685:   H = ds->mat[DS_MAT_W];
686:   if (ds->compact) {
687:     H[off] = d[ds->l]*s[ds->l];
688:     H[off+ld] = e[ds->l]*s[ds->l];
689:     for (i=ds->l+1;i<ds->n-1;i++) {
690:       H[i+(i-1)*ld] = e[i-1]*s[i];
691:       H[i+i*ld]     = d[i]*s[i];
692:       H[i+(i+1)*ld] = e[i]*s[i];
693:     }
694:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
695:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
696:   } else {
697:     s[ds->l] = PetscRealPart(B[off]);
698:     H[off] = A[off]*s[ds->l];
699:     H[off+ld] = A[off+ld]*s[ds->l];
700:     for (i=ds->l+1;i<ds->n-1;i++) {
701:       s[i] = PetscRealPart(B[i+i*ld]);
702:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
703:       H[i+i*ld]     = A[i+i*ld]*s[i];
704:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
705:     }
706:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
707:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
708:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
709:   }

711: #if !defined(PETSC_USE_COMPLEX)
712:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
713: #else
714:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
715: #endif
716:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);

718:   /* Compute Eigenvectors with Inverse Iteration */
719:   DSGHIEPInverseIteration(ds,wr,wi);

721:   /* Recover eigenvalues from diagonal */
722:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
723: #if defined(PETSC_USE_COMPLEX)
724:   if (wi) {
725:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
726:   }
727: #endif
728:   return(0);
729: #endif
730: }

734: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
735: {
736: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
738:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
739: #else
741:   PetscInt       i,off;
742:   PetscBLASInt   n1,ld,one,info,lwork,mout;
743:   PetscScalar    *H,*A,*B,*Q,*X;
744:   PetscReal      *d,*e,*s;

747: #if !defined(PETSC_USE_COMPLEX)
749: #endif
750:   one = 1;
751:   PetscBLASIntCast(ds->n-ds->l,&n1);
752:   PetscBLASIntCast(ds->ld,&ld);
753:   off = ds->l + ds->l*ld;
754:   A = ds->mat[DS_MAT_A];
755:   B = ds->mat[DS_MAT_B];
756:   Q = ds->mat[DS_MAT_Q];
757:   d = ds->rmat[DS_MAT_T];
758:   e = ds->rmat[DS_MAT_T] + ld;
759:   s = ds->rmat[DS_MAT_D];
760:   DSAllocateWork_Private(ds,ld+ld*ld,2*ld,ld*2);
761:   lwork = ld*ld;

763:   /* Quick return if possible */
764:   if (n1 == 1) {
765:     *(Q+off) = 1;
766:     if (!ds->compact) {
767:       d[ds->l] = PetscRealPart(A[off]);
768:       s[ds->l] = PetscRealPart(B[off]);
769:     }
770:     wr[ds->l] = d[ds->l]/s[ds->l];
771:     if (wi) wi[ds->l] = 0.0;
772:     return(0);
773:   }
774:   /* Reduce to pseudotriadiagonal form */
775:   DSIntermediate_GHIEP(ds);

777:   /* form standard problem in H */
778:   DSAllocateMat_Private(ds,DS_MAT_W);
779:   H = ds->mat[DS_MAT_W];
780:   if (ds->compact) {
781:     H[off] = d[ds->l]*s[ds->l];
782:     H[off+ld] = e[ds->l]*s[ds->l];
783:     for (i=ds->l+1;i<ds->n-1;i++) {
784:       H[i+(i-1)*ld] = e[i-1]*s[i];
785:       H[i+i*ld]     = d[i]*s[i];
786:       H[i+(i+1)*ld] = e[i]*s[i];
787:     }
788:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
789:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
790:   } else {
791:     s[ds->l] = PetscRealPart(B[off]);
792:     H[off] = A[off]*s[ds->l];
793:     H[off+ld] = A[off+ld]*s[ds->l];
794:     for (i=ds->l+1;i<ds->n-1;i++) {
795:       s[i] = PetscRealPart(B[i+i*ld]);
796:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
797:       H[i+i*ld]     = A[i+i*ld]*s[i];
798:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
799:     }
800:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
801:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
802:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
803:   }
804:   /* Compute the real Schur form */
805:   DSAllocateMat_Private(ds,DS_MAT_X);
806:   X = ds->mat[DS_MAT_X];
807: #if !defined(PETSC_USE_COMPLEX)
808:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","I",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,X+off,&ld,ds->work,&lwork,&info));
809: #else
810:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","I",&n1,&one,&n1,H+off,&ld,wr+ds->l,X+off,&ld,ds->work,&lwork,&info));
811: #endif
812:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);

814:   /* Compute eigenvectors */
815: #if !defined(PETSC_USE_COMPLEX)
816:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","B",NULL,&n1,H+off,&ld,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,&info));
817: #else
818:   PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","B",NULL,&n1,H+off,&ld,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,ds->rwork,&info));
819: #endif
820:   if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTREVC %i",&info);

822:   /* Compute real s-orthonormal basis */
823:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);

825:   /* Recover eigenvalues from diagonal */
826:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
827: #if defined(PETSC_USE_COMPLEX)
828:   if (wi) {
829:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
830:   }
831: #endif
832:   return(0);
833: #endif
834: }

838: PetscErrorCode DSNormalize_GHIEP(DS ds,DSMatType mat,PetscInt col)
839: {
841:   PetscInt       i,i0,i1;
842:   PetscBLASInt   ld,n,one = 1;
843:   PetscScalar    *A = ds->mat[DS_MAT_A],norm,*x;
844: #if !defined(PETSC_USE_COMPLEX)
845:   PetscScalar    norm0;
846: #endif

849:   switch (mat) {
850:     case DS_MAT_X:
851:     case DS_MAT_Y:
852:     case DS_MAT_Q:
853:       /* Supported matrices */
854:       break;
855:     case DS_MAT_U:
856:     case DS_MAT_VT:
857:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
858:       break;
859:     default:
860:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
861:   }

863:   PetscBLASIntCast(ds->n,&n);
864:   PetscBLASIntCast(ds->ld,&ld);
865:   DSGetArray(ds,mat,&x);
866:   if (col < 0) {
867:     i0 = 0; i1 = ds->n;
868:   } else if (col>0 && A[ds->ld*(col-1)+col] != 0.0) {
869:     i0 = col-1; i1 = col+1;
870:   } else {
871:     i0 = col; i1 = col+1;
872:   }
873:   for (i=i0; i<i1; i++) {
874: #if !defined(PETSC_USE_COMPLEX)
875:     if (i<n-1 && A[ds->ld*i+i+1] != 0.0) {
876:       norm = BLASnrm2_(&n,&x[ld*i],&one);
877:       norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
878:       norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
879:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
880:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
881:       i++;
882:     } else
883: #endif
884:     {
885:       norm = BLASnrm2_(&n,&x[ld*i],&one);
886:       norm = 1.0/norm;
887:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
888:      }
889:   }
890:   return(0);
891: }

895: PETSC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
896: {
898:   ds->ops->allocate      = DSAllocate_GHIEP;
899:   ds->ops->view          = DSView_GHIEP;
900:   ds->ops->vectors       = DSVectors_GHIEP;
901:   ds->ops->solve[0]      = DSSolve_GHIEP_HZ;
902:   ds->ops->solve[1]      = DSSolve_GHIEP_QR_II;
903:   ds->ops->solve[2]      = DSSolve_GHIEP_QR;
904:   ds->ops->solve[3]      = DSSolve_GHIEP_DQDS_II;
905:   ds->ops->sort          = DSSort_GHIEP;
906:   ds->ops->normalize     = DSNormalize_GHIEP;
907:   return(0);
908: }