Actual source code: dshep.c

slepc-3.13.2 2020-05-12
Report Typos and Errors
  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, 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: PetscErrorCode DSAllocate_HEP(DS ds,PetscInt ld)
 15: {

 19:   DSAllocateMat_Private(ds,DS_MAT_A);
 20:   DSAllocateMat_Private(ds,DS_MAT_Q);
 21:   DSAllocateMatReal_Private(ds,DS_MAT_T);
 22:   PetscFree(ds->perm);
 23:   PetscMalloc1(ld,&ds->perm);
 24:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 25:   return(0);
 26: }

 28: /*   0       l           k                 n-1
 29:     -----------------------------------------
 30:     |*       .           .                  |
 31:     |  *     .           .                  |
 32:     |    *   .           .                  |
 33:     |      * .           .                  |
 34:     |. . . . o           o                  |
 35:     |          o         o                  |
 36:     |            o       o                  |
 37:     |              o     o                  |
 38:     |                o   o                  |
 39:     |                  o o                  |
 40:     |. . . . o o o o o o o x                |
 41:     |                    x x x              |
 42:     |                      x x x            |
 43:     |                        x x x          |
 44:     |                          x x x        |
 45:     |                            x x x      |
 46:     |                              x x x    |
 47:     |                                x x x  |
 48:     |                                  x x x|
 49:     |                                    x x|
 50:     -----------------------------------------
 51: */

 53: static PetscErrorCode DSSwitchFormat_HEP(DS ds)
 54: {
 56:   PetscReal      *T = ds->rmat[DS_MAT_T];
 57:   PetscScalar    *A = ds->mat[DS_MAT_A];
 58:   PetscInt       i,n=ds->n,k=ds->k,ld=ds->ld;

 61:   /* switch from compact (arrow) to dense storage */
 62:   PetscArrayzero(A,ld*ld);
 63:   for (i=0;i<k;i++) {
 64:     A[i+i*ld] = T[i];
 65:     A[k+i*ld] = T[i+ld];
 66:     A[i+k*ld] = T[i+ld];
 67:   }
 68:   A[k+k*ld] = T[k];
 69:   for (i=k+1;i<n;i++) {
 70:     A[i+i*ld]     = T[i];
 71:     A[i-1+i*ld]   = T[i-1+ld];
 72:     A[i+(i-1)*ld] = T[i-1+ld];
 73:   }
 74:   if (ds->extrarow) A[n+(n-1)*ld] = T[n-1+ld];
 75:   return(0);
 76: }

 78: PetscErrorCode DSView_HEP(DS ds,PetscViewer viewer)
 79: {
 80:   PetscErrorCode    ierr;
 81:   PetscViewerFormat format;
 82:   PetscInt          i,j,r,c,rows;
 83:   PetscReal         value;
 84:   const char        *methodname[] = {
 85:                      "Implicit QR method (_steqr)",
 86:                      "Relatively Robust Representations (_stevr)",
 87:                      "Divide and Conquer method (_stedc)",
 88:                      "Block Divide and Conquer method (dsbtdc)"
 89:   };
 90:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

 93:   PetscViewerGetFormat(viewer,&format);
 94:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 95:     if (ds->bs>1) {
 96:       PetscViewerASCIIPrintf(viewer,"block size: %D\n",ds->bs);
 97:     }
 98:     if (ds->method<nmeth) {
 99:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
100:     }
101:     return(0);
102:   }
103:   if (ds->compact) {
104:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
105:     rows = ds->extrarow? ds->n+1: ds->n;
106:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
107:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",rows,ds->n);
108:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
109:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
110:       for (i=0;i<ds->n;i++) {
111:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
112:       }
113:       for (i=0;i<rows-1;i++) {
114:         r = PetscMax(i+2,ds->k+1);
115:         c = i+1;
116:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",r,c,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
117:         if (i<ds->n-1 && ds->k<ds->n) { /* do not print vertical arrow when k=n */
118:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",c,r,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
119:         }
120:       }
121:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
122:     } else {
123:       for (i=0;i<rows;i++) {
124:         for (j=0;j<ds->n;j++) {
125:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
126:           else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
127:           else if (i==j+1 && i>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+i-1);
128:           else if (i+1==j && j>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+j-1);
129:           else value = 0.0;
130:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
131:         }
132:         PetscViewerASCIIPrintf(viewer,"\n");
133:       }
134:     }
135:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
136:     PetscViewerFlush(viewer);
137:   } else {
138:     DSViewMat(ds,viewer,DS_MAT_A);
139:   }
140:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
141:   return(0);
142: }

144: PetscErrorCode DSVectors_HEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
145: {
146:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
147:   PetscInt       ld = ds->ld,i;

151:   switch (mat) {
152:     case DS_MAT_X:
153:     case DS_MAT_Y:
154:       if (j) {
155:         if (ds->state>=DS_STATE_CONDENSED) {
156:           PetscArraycpy(ds->mat[mat]+(*j)*ld,Q+(*j)*ld,ld);
157:         } else {
158:           PetscArrayzero(ds->mat[mat]+(*j)*ld,ld);
159:           *(ds->mat[mat]+(*j)+(*j)*ld) = 1.0;
160:         }
161:       } else {
162:         if (ds->state>=DS_STATE_CONDENSED) {
163:           PetscArraycpy(ds->mat[mat],Q,ld*ld);
164:         } else {
165:           PetscArrayzero(ds->mat[mat],ld*ld);
166:           for (i=0;i<ds->n;i++) *(ds->mat[mat]+i+i*ld) = 1.0;
167:         }
168:       }
169:       if (rnorm && j) *rnorm = PetscAbsScalar(Q[ds->n-1+(*j)*ld]);
170:       break;
171:     case DS_MAT_U:
172:     case DS_MAT_VT:
173:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
174:     default:
175:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
176:   }
177:   return(0);
178: }

180: /*
181:   ARROWTRIDIAG reduces a symmetric arrowhead matrix of the form

183:                 [ d 0 0 0 e ]
184:                 [ 0 d 0 0 e ]
185:             A = [ 0 0 d 0 e ]
186:                 [ 0 0 0 d e ]
187:                 [ e e e e d ]

189:   to tridiagonal form

191:                 [ d e 0 0 0 ]
192:                 [ e d e 0 0 ]
193:    T = Q'*A*Q = [ 0 e d e 0 ],
194:                 [ 0 0 e d e ]
195:                 [ 0 0 0 e d ]

197:   where Q is an orthogonal matrix. Rutishauser's algorithm is used to
198:   perform the reduction, which requires O(n**2) flops. The accumulation
199:   of the orthogonal factor Q, however, requires O(n**3) flops.

201:   Arguments
202:   =========

204:   N       (input) INTEGER
205:           The order of the matrix A.  N >= 0.

207:   D       (input/output) DOUBLE PRECISION array, dimension (N)
208:           On entry, the diagonal entries of the matrix A to be
209:           reduced.
210:           On exit, the diagonal entries of the reduced matrix T.

212:   E       (input/output) DOUBLE PRECISION array, dimension (N-1)
213:           On entry, the off-diagonal entries of the matrix A to be
214:           reduced.
215:           On exit, the subdiagonal entries of the reduced matrix T.

217:   Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
218:           On exit, the orthogonal matrix Q.

220:   LDQ     (input) INTEGER
221:           The leading dimension of the array Q.

223:   Note
224:   ====
225:   Based on Fortran code contributed by Daniel Kressner
226: */
227: static PetscErrorCode ArrowTridiag(PetscBLASInt n,PetscReal *d,PetscReal *e,PetscScalar *Q,PetscBLASInt ld)
228: {
229:   PetscBLASInt i,j,j2,one=1;
230:   PetscReal    c,s,p,off,temp;

233:   if (n<=2) return(0);

235:   for (j=0;j<n-2;j++) {

237:     /* Eliminate entry e(j) by a rotation in the planes (j,j+1) */
238:     temp = e[j+1];
239:     PetscStackCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&e[j],&c,&s,&e[j+1]));
240:     s = -s;

242:     /* Apply rotation to diagonal elements */
243:     temp   = d[j+1];
244:     e[j]   = c*s*(temp-d[j]);
245:     d[j+1] = s*s*d[j] + c*c*temp;
246:     d[j]   = c*c*d[j] + s*s*temp;

248:     /* Apply rotation to Q */
249:     j2 = j+2;
250:     PetscStackCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+j*ld,&one,Q+(j+1)*ld,&one,&c,&s));

252:     /* Chase newly introduced off-diagonal entry to the top left corner */
253:     for (i=j-1;i>=0;i--) {
254:       off  = -s*e[i];
255:       e[i] = c*e[i];
256:       temp = e[i+1];
257:       PetscStackCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&off,&c,&s,&e[i+1]));
258:       s = -s;
259:       temp = (d[i]-d[i+1])*s - 2.0*c*e[i];
260:       p = s*temp;
261:       d[i+1] += p;
262:       d[i] -= p;
263:       e[i] = -e[i] - c*temp;
264:       j2 = j+2;
265:       PetscStackCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+i*ld,&one,Q+(i+1)*ld,&one,&c,&s));
266:     }
267:   }
268:   return(0);
269: }

271: /*
272:    Reduce to tridiagonal form by means of ArrowTridiag.
273: */
274: static PetscErrorCode DSIntermediate_HEP(DS ds)
275: {
277:   PetscInt       i;
278:   PetscBLASInt   n1,n2,n3,lwork,info,l,n,ld,off;
279:   PetscScalar    *A,*Q,*work,*tau;
280:   PetscReal      *d,*e;

283:   PetscBLASIntCast(ds->n,&n);
284:   PetscBLASIntCast(ds->l,&l);
285:   PetscBLASIntCast(ds->ld,&ld);
286:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
287:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
288:   n3 = n1+n2;
289:   off = l+l*ld;
290:   A  = ds->mat[DS_MAT_A];
291:   Q  = ds->mat[DS_MAT_Q];
292:   d  = ds->rmat[DS_MAT_T];
293:   e  = ds->rmat[DS_MAT_T]+ld;
294:   PetscArrayzero(Q,ld*ld);
295:   for (i=0;i<n;i++) Q[i+i*ld] = 1.0;

297:   if (ds->compact) {

299:     if (ds->state<DS_STATE_INTERMEDIATE) ArrowTridiag(n1,d+l,e+l,Q+off,ld);

301:   } else {

303:     for (i=0;i<l;i++) { d[i] = PetscRealPart(A[i+i*ld]); e[i] = 0.0; }

305:     if (ds->state<DS_STATE_INTERMEDIATE) {
306:       DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
307:       DSAllocateWork_Private(ds,ld+ld*ld,0,0);
308:       tau  = ds->work;
309:       work = ds->work+ld;
310:       lwork = ld*ld;
311:       PetscStackCallBLAS("LAPACKsytrd",LAPACKsytrd_("L",&n3,Q+off,&ld,d+l,e+l,tau,work,&lwork,&info));
312:       SlepcCheckLapackInfo("sytrd",info);
313:       PetscStackCallBLAS("LAPACKorgtr",LAPACKorgtr_("L",&n3,Q+off,&ld,tau,work,&lwork,&info));
314:       SlepcCheckLapackInfo("orgtr",info);
315:     } else {
316:       /* copy tridiagonal to d,e */
317:       for (i=l;i<n;i++)   d[i] = PetscRealPart(A[i+i*ld]);
318:       for (i=l;i<n-1;i++) e[i] = PetscRealPart(A[(i+1)+i*ld]);
319:     }
320:   }
321:   return(0);
322: }

324: PetscErrorCode DSSort_HEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
325: {
327:   PetscInt       n,l,i,*perm,ld=ds->ld;
328:   PetscScalar    *A;
329:   PetscReal      *d;

332:   if (!ds->sc) return(0);
333:   n = ds->n;
334:   l = ds->l;
335:   A = ds->mat[DS_MAT_A];
336:   d = ds->rmat[DS_MAT_T];
337:   perm = ds->perm;
338:   if (!rr) {
339:     DSSortEigenvaluesReal_Private(ds,d,perm);
340:   } else {
341:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
342:   }
343:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
344:   DSPermuteColumns_Private(ds,l,n,DS_MAT_Q,perm);
345:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
346:   if (!ds->compact) {
347:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
348:   }
349:   return(0);
350: }

352: PetscErrorCode DSUpdateExtraRow_HEP(DS ds)
353: {
355:   PetscInt       i;
356:   PetscBLASInt   n,ld,incx=1;
357:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
358:   PetscReal      *e,beta;

361:   PetscBLASIntCast(ds->n,&n);
362:   PetscBLASIntCast(ds->ld,&ld);
363:   A  = ds->mat[DS_MAT_A];
364:   Q  = ds->mat[DS_MAT_Q];
365:   e  = ds->rmat[DS_MAT_T]+ld;

367:   if (ds->compact) {
368:     beta = e[n-1];   /* in compact, we assume all entries are zero except the last one */
369:     for (i=0;i<n;i++) e[i] = PetscRealPart(beta*Q[n-1+i*ld]);
370:     ds->k = n;
371:   } else {
372:     DSAllocateWork_Private(ds,2*ld,0,0);
373:     x = ds->work;
374:     y = ds->work+ld;
375:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
376:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
377:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
378:     ds->k = n;
379:   }
380:   return(0);
381: }

383: PetscErrorCode DSSolve_HEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
384: {
386:   PetscInt       i;
387:   PetscBLASInt   n1,n2,n3,info,l,n,ld,off;
388:   PetscScalar    *Q,*A;
389:   PetscReal      *d,*e;

392:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
393:   PetscBLASIntCast(ds->n,&n);
394:   PetscBLASIntCast(ds->l,&l);
395:   PetscBLASIntCast(ds->ld,&ld);
396:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
397:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
398:   n3 = n1+n2;
399:   off = l+l*ld;
400:   Q  = ds->mat[DS_MAT_Q];
401:   A  = ds->mat[DS_MAT_A];
402:   d  = ds->rmat[DS_MAT_T];
403:   e  = ds->rmat[DS_MAT_T]+ld;

405:   /* Reduce to tridiagonal form */
406:   DSIntermediate_HEP(ds);

408:   /* Solve the tridiagonal eigenproblem */
409:   for (i=0;i<l;i++) wr[i] = d[i];

411:   DSAllocateWork_Private(ds,0,2*ld,0);
412:   PetscStackCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n3,d+l,e+l,Q+off,&ld,ds->rwork,&info));
413:   SlepcCheckLapackInfo("steqr",info);
414:   for (i=l;i<n;i++) wr[i] = d[i];

416:   /* Create diagonal matrix as a result */
417:   if (ds->compact) {
418:     PetscArrayzero(e,n-1);
419:   } else {
420:     for (i=l;i<n;i++) {
421:       PetscArrayzero(A+l+i*ld,n-l);
422:     }
423:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
424:   }

426:   /* Set zero wi */
427:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
428:   return(0);
429: }

431: PetscErrorCode DSSolve_HEP_MRRR(DS ds,PetscScalar *wr,PetscScalar *wi)
432: {
434:   PetscInt       i;
435:   PetscBLASInt   n1,n2,n3,lwork,liwork,info,l,n,m,ld,off,il,iu,*isuppz;
436:   PetscScalar    *A,*Q,*W=NULL,one=1.0,zero=0.0;
437:   PetscReal      *d,*e,abstol=0.0,vl,vu;
438: #if defined(PETSC_USE_COMPLEX)
439:   PetscInt       j;
440:   PetscReal      *ritz;
441: #endif

444:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
445:   PetscBLASIntCast(ds->n,&n);
446:   PetscBLASIntCast(ds->l,&l);
447:   PetscBLASIntCast(ds->ld,&ld);
448:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
449:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
450:   n3 = n1+n2;
451:   off = l+l*ld;
452:   A  = ds->mat[DS_MAT_A];
453:   Q  = ds->mat[DS_MAT_Q];
454:   d  = ds->rmat[DS_MAT_T];
455:   e  = ds->rmat[DS_MAT_T]+ld;

457:   /* Reduce to tridiagonal form */
458:   DSIntermediate_HEP(ds);

460:   /* Solve the tridiagonal eigenproblem */
461:   for (i=0;i<l;i++) wr[i] = d[i];

463:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* Q contains useful info */
464:     DSAllocateMat_Private(ds,DS_MAT_W);
465:     DSCopyMatrix_Private(ds,DS_MAT_W,DS_MAT_Q);
466:     W = ds->mat[DS_MAT_W];
467:   }
468: #if defined(PETSC_USE_COMPLEX)
469:   DSAllocateMatReal_Private(ds,DS_MAT_Q);
470: #endif
471:   lwork = 20*ld;
472:   liwork = 10*ld;
473:   DSAllocateWork_Private(ds,0,lwork+ld,liwork+2*ld);
474:   isuppz = ds->iwork+liwork;
475: #if defined(PETSC_USE_COMPLEX)
476:   ritz = ds->rwork+lwork;
477:   PetscStackCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,ritz+l,ds->rmat[DS_MAT_Q]+off,&ld,isuppz,ds->rwork,&lwork,ds->iwork,&liwork,&info));
478:   for (i=l;i<n;i++) wr[i] = ritz[i];
479: #else
480:   PetscStackCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,wr+l,Q+off,&ld,isuppz,ds->rwork,&lwork,ds->iwork,&liwork,&info));
481: #endif
482:   SlepcCheckLapackInfo("stevr",info);
483: #if defined(PETSC_USE_COMPLEX)
484:   for (i=l;i<n;i++)
485:     for (j=l;j<n;j++)
486:       Q[i+j*ld] = (ds->rmat[DS_MAT_Q])[i+j*ld];
487: #endif
488:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* accumulate previous Q */
489:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n3,&n3,&n3,&one,W+off,&ld,Q+off,&ld,&zero,A+off,&ld));
490:     DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
491:   }
492:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);

494:   /* Create diagonal matrix as a result */
495:   if (ds->compact) {
496:     PetscArrayzero(e,n-1);
497:   } else {
498:     for (i=l;i<n;i++) {
499:       PetscArrayzero(A+l+i*ld,n-l);
500:     }
501:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
502:   }

504:   /* Set zero wi */
505:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
506:   return(0);
507: }

509: PetscErrorCode DSSolve_HEP_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
510: {
512:   PetscInt       i;
513:   PetscBLASInt   n1,info,l,ld,off,lrwork,liwork;
514:   PetscScalar    *Q,*A;
515:   PetscReal      *d,*e;
516: #if defined(PETSC_USE_COMPLEX)
517:   PetscBLASInt   lwork;
518:   PetscInt       j;
519: #endif

522:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
523:   PetscBLASIntCast(ds->l,&l);
524:   PetscBLASIntCast(ds->ld,&ld);
525:   PetscBLASIntCast(ds->n-ds->l,&n1);
526:   off = l+l*ld;
527:   Q  = ds->mat[DS_MAT_Q];
528:   A  = ds->mat[DS_MAT_A];
529:   d  = ds->rmat[DS_MAT_T];
530:   e  = ds->rmat[DS_MAT_T]+ld;

532:   /* Reduce to tridiagonal form */
533:   DSIntermediate_HEP(ds);

535:   /* Solve the tridiagonal eigenproblem */
536:   for (i=0;i<l;i++) wr[i] = d[i];

538:   lrwork = 5*n1*n1+3*n1+1;
539:   liwork = 5*n1*n1+6*n1+6;
540: #if !defined(PETSC_USE_COMPLEX)
541:   DSAllocateWork_Private(ds,0,lrwork,liwork);
542:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
543: #else
544:   lwork = ld*ld;
545:   DSAllocateWork_Private(ds,lwork,lrwork,liwork);
546:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->work,&lwork,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
547:   /* Fixing Lapack bug*/
548:   for (j=ds->l;j<ds->n;j++)
549:     for (i=0;i<ds->l;i++) Q[i+j*ld] = 0.0;
550: #endif
551:   SlepcCheckLapackInfo("stedc",info);
552:   for (i=l;i<ds->n;i++) wr[i] = d[i];

554:   /* Create diagonal matrix as a result */
555:   if (ds->compact) {
556:     PetscArrayzero(e,ds->n-1);
557:   } else {
558:     for (i=l;i<ds->n;i++) {
559:       PetscArrayzero(A+l+i*ld,ds->n-l);
560:     }
561:     for (i=l;i<ds->n;i++) A[i+i*ld] = d[i];
562:   }

564:   /* Set zero wi */
565:   if (wi) for (i=l;i<ds->n;i++) wi[i] = 0.0;
566:   return(0);
567: }

569: #if !defined(PETSC_USE_COMPLEX)
570: PetscErrorCode DSSolve_HEP_BDC(DS ds,PetscScalar *wr,PetscScalar *wi)
571: {
573:   PetscBLASInt   i,j,k,m,n,info,nblks,bs,ld,lde,lrwork,liwork,*ksizes,*iwork,mingapi;
574:   PetscScalar    *Q,*A;
575:   PetscReal      *D,*E,*d,*e,tol=PETSC_MACHINE_EPSILON/2,tau1=1e-16,tau2=1e-18,*rwork,mingap;

578:   if (ds->l>0) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for l>1");
579:   if (ds->compact) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for compact storage");
580:   PetscBLASIntCast(ds->ld,&ld);
581:   PetscBLASIntCast(ds->bs,&bs);
582:   PetscBLASIntCast(ds->n,&n);
583:   nblks = n/bs;
584:   Q  = ds->mat[DS_MAT_Q];
585:   A  = ds->mat[DS_MAT_A];
586:   d  = ds->rmat[DS_MAT_T];
587:   e  = ds->rmat[DS_MAT_T]+ld;
588:   lrwork = 4*n*n+60*n+1;
589:   liwork = 5*n+5*nblks-1;
590:   lde = 2*bs+1;
591:   DSAllocateWork_Private(ds,bs*n+lde*lde*(nblks-1),lrwork,nblks+liwork);
592:   D      = ds->work;
593:   E      = ds->work+bs*n;
594:   rwork  = ds->rwork;
595:   ksizes = ds->iwork;
596:   iwork  = ds->iwork+nblks;
597:   PetscArrayzero(iwork,liwork);

599:   /* Copy matrix to block tridiagonal format */
600:   j=0;
601:   for (i=0;i<nblks;i++) {
602:     ksizes[i]=bs;
603:     for (k=0;k<bs;k++)
604:       for (m=0;m<bs;m++)
605:         D[k+m*bs+i*bs*bs] = PetscRealPart(A[j+k+(j+m)*n]);
606:     j = j + bs;
607:   }
608:   j=0;
609:   for (i=0;i<nblks-1;i++) {
610:     for (k=0;k<bs;k++)
611:       for (m=0;m<bs;m++)
612:         E[k+m*lde+i*lde*lde] = PetscRealPart(A[j+bs+k+(j+m)*n]);
613:     j = j + bs;
614:   }

616:   /* Solve the block tridiagonal eigenproblem */
617:   BDC_dsbtdc_("D","A",n,nblks,ksizes,D,bs,bs,E,lde,lde,tol,tau1,tau2,d,
618:            Q,n,rwork,lrwork,iwork,liwork,&mingap,&mingapi,&info,1,1);
619:   for (i=0;i<ds->n;i++) wr[i] = d[i];

621:   /* Create diagonal matrix as a result */
622:   if (ds->compact) {
623:     PetscArrayzero(e,ds->n-1);
624:   } else {
625:     for (i=0;i<ds->n;i++) {
626:       PetscArrayzero(A+i*ld,ds->n);
627:     }
628:     for (i=0;i<ds->n;i++) A[i+i*ld] = wr[i];
629:   }

631:   /* Set zero wi */
632:   if (wi) for (i=0;i<ds->n;i++) wi[i] = 0.0;
633:   return(0);
634: }
635: #endif

637: PetscErrorCode DSTruncate_HEP(DS ds,PetscInt n)
638: {
639:   PetscInt    i,ld=ds->ld,l=ds->l;
640:   PetscScalar *A;

643:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
644:   A = ds->mat[DS_MAT_A];
645:   if (!ds->compact && ds->extrarow && ds->k==ds->n) {
646:     for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
647:   }
648:   if (ds->extrarow) ds->k = n;
649:   else ds->k = 0;
650:   ds->n = n;
651:   return(0);
652: }

654: PetscErrorCode DSSynchronize_HEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
655: {
657:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
658:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;

661:   if (ds->compact) kr = 3*ld;
662:   else k = (ds->n-l)*ld;
663:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
664:   if (eigr) k += (ds->n-l);
665:   DSAllocateWork_Private(ds,k+kr,0,0);
666:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
667:   PetscMPIIntCast(ds->n-l,&n);
668:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
669:   PetscMPIIntCast(ld*3,&ld3);
670:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
671:   if (!rank) {
672:     if (ds->compact) {
673:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
674:     } else {
675:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
676:     }
677:     if (ds->state>DS_STATE_RAW) {
678:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
679:     }
680:     if (eigr) {
681:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
682:     }
683:   }
684:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
685:   if (rank) {
686:     if (ds->compact) {
687:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
688:     } else {
689:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
690:     }
691:     if (ds->state>DS_STATE_RAW) {
692:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
693:     }
694:     if (eigr) {
695:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
696:     }
697:   }
698:   return(0);
699: }

701: PetscErrorCode DSCond_HEP(DS ds,PetscReal *cond)
702: {
704:   PetscScalar    *work;
705:   PetscReal      *rwork;
706:   PetscBLASInt   *ipiv;
707:   PetscBLASInt   lwork,info,n,ld;
708:   PetscReal      hn,hin;
709:   PetscScalar    *A;

712:   PetscBLASIntCast(ds->n,&n);
713:   PetscBLASIntCast(ds->ld,&ld);
714:   lwork = 8*ld;
715:   DSAllocateWork_Private(ds,lwork,ld,ld);
716:   work  = ds->work;
717:   rwork = ds->rwork;
718:   ipiv  = ds->iwork;
719:   DSSwitchFormat_HEP(ds);

721:   /* use workspace matrix W to avoid overwriting A */
722:   DSAllocateMat_Private(ds,DS_MAT_W);
723:   A = ds->mat[DS_MAT_W];
724:   PetscArraycpy(A,ds->mat[DS_MAT_A],ds->ld*ds->ld);

726:   /* norm of A */
727:   hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);

729:   /* norm of inv(A) */
730:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
731:   SlepcCheckLapackInfo("getrf",info);
732:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
733:   SlepcCheckLapackInfo("getri",info);
734:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

736:   *cond = hn*hin;
737:   return(0);
738: }

740: PetscErrorCode DSTranslateRKS_HEP(DS ds,PetscScalar alpha)
741: {
743:   PetscInt       i,j,k=ds->k;
744:   PetscScalar    *Q,*A,*R,*tau,*work;
745:   PetscBLASInt   ld,n1,n0,lwork,info;

748:   PetscBLASIntCast(ds->ld,&ld);
749:   DSAllocateWork_Private(ds,ld*ld,0,0);
750:   tau = ds->work;
751:   work = ds->work+ld;
752:   PetscBLASIntCast(ld*(ld-1),&lwork);
753:   DSAllocateMat_Private(ds,DS_MAT_W);
754:   A  = ds->mat[DS_MAT_A];
755:   Q  = ds->mat[DS_MAT_Q];
756:   R  = ds->mat[DS_MAT_W];

758:   /* copy I+alpha*A */
759:   PetscArrayzero(Q,ld*ld);
760:   PetscArrayzero(R,ld*ld);
761:   for (i=0;i<k;i++) {
762:     Q[i+i*ld] = 1.0 + alpha*A[i+i*ld];
763:     Q[k+i*ld] = alpha*A[k+i*ld];
764:   }

766:   /* compute qr */
767:   PetscBLASIntCast(k+1,&n1);
768:   PetscBLASIntCast(k,&n0);
769:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&n1,&n0,Q,&ld,tau,work,&lwork,&info));
770:   SlepcCheckLapackInfo("geqrf",info);

772:   /* copy R from Q */
773:   for (j=0;j<k;j++)
774:     for (i=0;i<=j;i++)
775:       R[i+j*ld] = Q[i+j*ld];

777:   /* compute orthogonal matrix in Q */
778:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&n1,&n1,&n0,Q,&ld,tau,work,&lwork,&info));
779:   SlepcCheckLapackInfo("orgqr",info);

781:   /* compute the updated matrix of projected problem */
782:   for (j=0;j<k;j++)
783:     for (i=0;i<k+1;i++)
784:       A[j*ld+i] = Q[i*ld+j];
785:   alpha = -1.0/alpha;
786:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&n1,&n0,&alpha,R,&ld,A,&ld));
787:   for (i=0;i<k;i++)
788:     A[ld*i+i] -= alpha;
789:   return(0);
790: }

792: PetscErrorCode DSHermitian_HEP(DS ds,DSMatType m,PetscBool *flg)
793: {
795:   if (m==DS_MAT_A && !ds->extrarow) *flg = PETSC_TRUE;
796:   else *flg = PETSC_FALSE;
797:   return(0);
798: }

800: SLEPC_EXTERN PetscErrorCode DSCreate_HEP(DS ds)
801: {
803:   ds->ops->allocate      = DSAllocate_HEP;
804:   ds->ops->view          = DSView_HEP;
805:   ds->ops->vectors       = DSVectors_HEP;
806:   ds->ops->solve[0]      = DSSolve_HEP_QR;
807:   ds->ops->solve[1]      = DSSolve_HEP_MRRR;
808:   ds->ops->solve[2]      = DSSolve_HEP_DC;
809: #if !defined(PETSC_USE_COMPLEX)
810:   ds->ops->solve[3]      = DSSolve_HEP_BDC;
811: #endif
812:   ds->ops->sort          = DSSort_HEP;
813:   ds->ops->synchronize   = DSSynchronize_HEP;
814:   ds->ops->truncate      = DSTruncate_HEP;
815:   ds->ops->update        = DSUpdateExtraRow_HEP;
816:   ds->ops->cond          = DSCond_HEP;
817:   ds->ops->transrks      = DSTranslateRKS_HEP;
818:   ds->ops->hermitian     = DSHermitian_HEP;
819:   return(0);
820: }