Actual source code: dshep.c

slepc-3.13.0 2020-03-31
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:       break;
175:     default:
176:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
177:   }
178:   return(0);
179: }

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

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

190:   to tridiagonal form

192:                 [ d e 0 0 0 ]
193:                 [ e d e 0 0 ]
194:    T = Q'*A*Q = [ 0 e d e 0 ],
195:                 [ 0 0 e d e ]
196:                 [ 0 0 0 e d ]

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

202:   Arguments
203:   =========

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

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

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

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

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

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

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

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

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

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

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

253:     /* Chase newly introduced off-diagonal entry to the top left corner */
254:     for (i=j-1;i>=0;i--) {
255:       off  = -s*e[i];
256:       e[i] = c*e[i];
257:       temp = e[i+1];
258:       PetscStackCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&off,&c,&s,&e[i+1]));
259:       s = -s;
260:       temp = (d[i]-d[i+1])*s - 2.0*c*e[i];
261:       p = s*temp;
262:       d[i+1] += p;
263:       d[i] -= p;
264:       e[i] = -e[i] - c*temp;
265:       j2 = j+2;
266:       PetscStackCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+i*ld,&one,Q+(i+1)*ld,&one,&c,&s));
267:     }
268:   }
269:   return(0);
270: }

272: /*
273:    Reduce to tridiagonal form by means of ArrowTridiag.
274: */
275: static PetscErrorCode DSIntermediate_HEP(DS ds)
276: {
278:   PetscInt       i;
279:   PetscBLASInt   n1,n2,n3,lwork,info,l,n,ld,off;
280:   PetscScalar    *A,*Q,*work,*tau;
281:   PetscReal      *d,*e;

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

298:   if (ds->compact) {

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

302:   } else {

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

306:     if (ds->state<DS_STATE_INTERMEDIATE) {
307:       DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
308:       DSAllocateWork_Private(ds,ld+ld*ld,0,0);
309:       tau  = ds->work;
310:       work = ds->work+ld;
311:       lwork = ld*ld;
312:       PetscStackCallBLAS("LAPACKsytrd",LAPACKsytrd_("L",&n3,Q+off,&ld,d+l,e+l,tau,work,&lwork,&info));
313:       SlepcCheckLapackInfo("sytrd",info);
314:       PetscStackCallBLAS("LAPACKorgtr",LAPACKorgtr_("L",&n3,Q+off,&ld,tau,work,&lwork,&info));
315:       SlepcCheckLapackInfo("orgtr",info);
316:     } else {
317:       /* copy tridiagonal to d,e */
318:       for (i=l;i<n;i++)   d[i] = PetscRealPart(A[i+i*ld]);
319:       for (i=l;i<n-1;i++) e[i] = PetscRealPart(A[(i+1)+i*ld]);
320:     }
321:   }
322:   return(0);
323: }

325: PetscErrorCode DSSort_HEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
326: {
328:   PetscInt       n,l,i,*perm,ld=ds->ld;
329:   PetscScalar    *A;
330:   PetscReal      *d;

333:   if (!ds->sc) return(0);
334:   n = ds->n;
335:   l = ds->l;
336:   A = ds->mat[DS_MAT_A];
337:   d = ds->rmat[DS_MAT_T];
338:   perm = ds->perm;
339:   if (!rr) {
340:     DSSortEigenvaluesReal_Private(ds,d,perm);
341:   } else {
342:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
343:   }
344:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
345:   DSPermuteColumns_Private(ds,l,n,DS_MAT_Q,perm);
346:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
347:   if (!ds->compact) {
348:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
349:   }
350:   return(0);
351: }

353: PetscErrorCode DSUpdateExtraRow_HEP(DS ds)
354: {
356:   PetscInt       i;
357:   PetscBLASInt   n,ld,incx=1;
358:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
359:   PetscReal      *e,beta;

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

368:   if (ds->compact) {
369:     beta = e[n-1];   /* in compact, we assume all entries are zero except the last one */
370:     for (i=0;i<n;i++) e[i] = PetscRealPart(beta*Q[n-1+i*ld]);
371:     ds->k = n;
372:   } else {
373:     DSAllocateWork_Private(ds,2*ld,0,0);
374:     x = ds->work;
375:     y = ds->work+ld;
376:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
377:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
378:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
379:     ds->k = n;
380:   }
381:   return(0);
382: }

384: PetscErrorCode DSSolve_HEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
385: {
387:   PetscInt       i;
388:   PetscBLASInt   n1,n2,n3,info,l,n,ld,off;
389:   PetscScalar    *Q,*A;
390:   PetscReal      *d,*e;

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

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

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

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

417:   /* Create diagonal matrix as a result */
418:   if (ds->compact) {
419:     PetscArrayzero(e,n-1);
420:   } else {
421:     for (i=l;i<n;i++) {
422:       PetscArrayzero(A+l+i*ld,n-l);
423:     }
424:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
425:   }

427:   /* Set zero wi */
428:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
429:   return(0);
430: }

432: PetscErrorCode DSSolve_HEP_MRRR(DS ds,PetscScalar *wr,PetscScalar *wi)
433: {
435:   PetscInt       i;
436:   PetscBLASInt   n1,n2,n3,lwork,liwork,info,l,n,m,ld,off,il,iu,*isuppz;
437:   PetscScalar    *A,*Q,*W=NULL,one=1.0,zero=0.0;
438:   PetscReal      *d,*e,abstol=0.0,vl,vu;
439: #if defined(PETSC_USE_COMPLEX)
440:   PetscInt       j;
441:   PetscReal      *ritz;
442: #endif

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

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

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

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

495:   /* Create diagonal matrix as a result */
496:   if (ds->compact) {
497:     PetscArrayzero(e,n-1);
498:   } else {
499:     for (i=l;i<n;i++) {
500:       PetscArrayzero(A+l+i*ld,n-l);
501:     }
502:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
503:   }

505:   /* Set zero wi */
506:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
507:   return(0);
508: }

510: PetscErrorCode DSSolve_HEP_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
511: {
513:   PetscInt       i;
514:   PetscBLASInt   n1,info,l,ld,off,lrwork,liwork;
515:   PetscScalar    *Q,*A;
516:   PetscReal      *d,*e;
517: #if defined(PETSC_USE_COMPLEX)
518:   PetscBLASInt   lwork;
519:   PetscInt       j;
520: #endif

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

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

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

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

555:   /* Create diagonal matrix as a result */
556:   if (ds->compact) {
557:     PetscArrayzero(e,ds->n-1);
558:   } else {
559:     for (i=l;i<ds->n;i++) {
560:       PetscArrayzero(A+l+i*ld,ds->n-l);
561:     }
562:     for (i=l;i<ds->n;i++) A[i+i*ld] = d[i];
563:   }

565:   /* Set zero wi */
566:   if (wi) for (i=l;i<ds->n;i++) wi[i] = 0.0;
567:   return(0);
568: }

570: #if !defined(PETSC_USE_COMPLEX)
571: PetscErrorCode DSSolve_HEP_BDC(DS ds,PetscScalar *wr,PetscScalar *wi)
572: {
574:   PetscBLASInt   i,j,k,m,n,info,nblks,bs,ld,lde,lrwork,liwork,*ksizes,*iwork,mingapi;
575:   PetscScalar    *Q,*A;
576:   PetscReal      *D,*E,*d,*e,tol=PETSC_MACHINE_EPSILON/2,tau1=1e-16,tau2=1e-18,*rwork,mingap;

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

600:   /* Copy matrix to block tridiagonal format */
601:   j=0;
602:   for (i=0;i<nblks;i++) {
603:     ksizes[i]=bs;
604:     for (k=0;k<bs;k++)
605:       for (m=0;m<bs;m++)
606:         D[k+m*bs+i*bs*bs] = PetscRealPart(A[j+k+(j+m)*n]);
607:     j = j + bs;
608:   }
609:   j=0;
610:   for (i=0;i<nblks-1;i++) {
611:     for (k=0;k<bs;k++)
612:       for (m=0;m<bs;m++)
613:         E[k+m*lde+i*lde*lde] = PetscRealPart(A[j+bs+k+(j+m)*n]);
614:     j = j + bs;
615:   }

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

622:   /* Create diagonal matrix as a result */
623:   if (ds->compact) {
624:     PetscArrayzero(e,ds->n-1);
625:   } else {
626:     for (i=0;i<ds->n;i++) {
627:       PetscArrayzero(A+i*ld,ds->n);
628:     }
629:     for (i=0;i<ds->n;i++) A[i+i*ld] = wr[i];
630:   }

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

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

644:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
645:   A = ds->mat[DS_MAT_A];
646:   if (!ds->compact && ds->extrarow && ds->k==ds->n) {
647:     for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
648:   }
649:   if (ds->extrarow) ds->k = n;
650:   else ds->k = 0;
651:   ds->n = n;
652:   return(0);
653: }

655: PetscErrorCode DSSynchronize_HEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
656: {
658:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
659:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;

662:   if (ds->compact) kr = 3*ld;
663:   else k = (ds->n-l)*ld;
664:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
665:   if (eigr) k += (ds->n-l);
666:   DSAllocateWork_Private(ds,k+kr,0,0);
667:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
668:   PetscMPIIntCast(ds->n-l,&n);
669:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
670:   PetscMPIIntCast(ld*3,&ld3);
671:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
672:   if (!rank) {
673:     if (ds->compact) {
674:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
675:     } else {
676:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
677:     }
678:     if (ds->state>DS_STATE_RAW) {
679:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
680:     }
681:     if (eigr) {
682:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
683:     }
684:   }
685:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
686:   if (rank) {
687:     if (ds->compact) {
688:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
689:     } else {
690:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
691:     }
692:     if (ds->state>DS_STATE_RAW) {
693:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
694:     }
695:     if (eigr) {
696:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
697:     }
698:   }
699:   return(0);
700: }

702: PetscErrorCode DSCond_HEP(DS ds,PetscReal *cond)
703: {
705:   PetscScalar    *work;
706:   PetscReal      *rwork;
707:   PetscBLASInt   *ipiv;
708:   PetscBLASInt   lwork,info,n,ld;
709:   PetscReal      hn,hin;
710:   PetscScalar    *A;

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

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

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

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

737:   *cond = hn*hin;
738:   return(0);
739: }

741: PetscErrorCode DSTranslateRKS_HEP(DS ds,PetscScalar alpha)
742: {
744:   PetscInt       i,j,k=ds->k;
745:   PetscScalar    *Q,*A,*R,*tau,*work;
746:   PetscBLASInt   ld,n1,n0,lwork,info;

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

759:   /* copy I+alpha*A */
760:   PetscArrayzero(Q,ld*ld);
761:   PetscArrayzero(R,ld*ld);
762:   for (i=0;i<k;i++) {
763:     Q[i+i*ld] = 1.0 + alpha*A[i+i*ld];
764:     Q[k+i*ld] = alpha*A[k+i*ld];
765:   }

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

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

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

782:   /* compute the updated matrix of projected problem */
783:   for (j=0;j<k;j++)
784:     for (i=0;i<k+1;i++)
785:       A[j*ld+i] = Q[i*ld+j];
786:   alpha = -1.0/alpha;
787:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&n1,&n0,&alpha,R,&ld,A,&ld));
788:   for (i=0;i<k;i++)
789:     A[ld*i+i] -= alpha;
790:   return(0);
791: }

793: PetscErrorCode DSHermitian_HEP(DS ds,DSMatType m,PetscBool *flg)
794: {
796:   if (m==DS_MAT_A && !ds->extrarow) *flg = PETSC_TRUE;
797:   else *flg = PETSC_FALSE;
798:   return(0);
799: }

801: SLEPC_EXTERN PetscErrorCode DSCreate_HEP(DS ds)
802: {
804:   ds->ops->allocate      = DSAllocate_HEP;
805:   ds->ops->view          = DSView_HEP;
806:   ds->ops->vectors       = DSVectors_HEP;
807:   ds->ops->solve[0]      = DSSolve_HEP_QR;
808:   ds->ops->solve[1]      = DSSolve_HEP_MRRR;
809:   ds->ops->solve[2]      = DSSolve_HEP_DC;
810: #if !defined(PETSC_USE_COMPLEX)
811:   ds->ops->solve[3]      = DSSolve_HEP_BDC;
812: #endif
813:   ds->ops->sort          = DSSort_HEP;
814:   ds->ops->synchronize   = DSSynchronize_HEP;
815:   ds->ops->truncate      = DSTruncate_HEP;
816:   ds->ops->update        = DSUpdateExtraRow_HEP;
817:   ds->ops->cond          = DSCond_HEP;
818:   ds->ops->transrks      = DSTranslateRKS_HEP;
819:   ds->ops->hermitian     = DSHermitian_HEP;
820:   return(0);
821: }