Actual source code: dspriv.c

  1: /*
  2:    Private DS routines

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

  8:    This file is part of SLEPc.

 10:    SLEPc is free software: you can redistribute it and/or modify it under  the
 11:    terms of version 3 of the GNU Lesser General Public License as published by
 12:    the Free Software Foundation.

 14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 17:    more details.

 19:    You  should have received a copy of the GNU Lesser General  Public  License
 20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 22: */

 24: #include <slepc-private/dsimpl.h>      /*I "slepcds.h" I*/
 25: #include <slepcblaslapack.h>

 29: PetscErrorCode DSAllocateMat_Private(DS ds,DSMatType m)
 30: {
 31:   PetscInt       sz;

 35:   if (m==DS_MAT_T) sz = 3*ds->ld*sizeof(PetscScalar);
 36:   else if (m==DS_MAT_D) sz = ds->ld*sizeof(PetscScalar);
 37:   else sz = ds->ld*ds->ld*sizeof(PetscScalar);
 38:   if (ds->mat[m]) {
 39:     PetscFree(ds->mat[m]);
 40:   } else {
 41:     PetscLogObjectMemory(ds,sz);
 42:   }
 43:   PetscMalloc(sz,&ds->mat[m]);
 44:   PetscMemzero(ds->mat[m],sz);
 45:   return(0);
 46: }

 50: PetscErrorCode DSAllocateMatReal_Private(DS ds,DSMatType m)
 51: {
 52:   PetscInt       sz;

 56:   if (m==DS_MAT_T) sz = 3*ds->ld*sizeof(PetscReal);
 57:   else if (m==DS_MAT_D) sz = ds->ld*sizeof(PetscReal);
 58:   else sz = ds->ld*ds->ld*sizeof(PetscReal);
 59:   if (!ds->rmat[m]) {
 60:     PetscLogObjectMemory(ds,sz);
 61:     PetscMalloc(sz,&ds->rmat[m]);
 62:   }
 63:   PetscMemzero(ds->rmat[m],sz);
 64:   return(0);
 65: }

 69: PetscErrorCode DSAllocateWork_Private(DS ds,PetscInt s,PetscInt r,PetscInt i)
 70: {

 74:   if (s>ds->lwork) {
 75:     PetscFree(ds->work);
 76:     PetscMalloc(s*sizeof(PetscScalar),&ds->work);
 77:     PetscLogObjectMemory(ds,(s-ds->lwork)*sizeof(PetscScalar));
 78:     ds->lwork = s;
 79:   }
 80:   if (r>ds->lrwork) {
 81:     PetscFree(ds->rwork);
 82:     PetscMalloc(r*sizeof(PetscReal),&ds->rwork);
 83:     PetscLogObjectMemory(ds,(r-ds->lrwork)*sizeof(PetscReal));
 84:     ds->lrwork = r;
 85:   }
 86:   if (i>ds->liwork) {
 87:     PetscFree(ds->iwork);
 88:     PetscMalloc(i*sizeof(PetscBLASInt),&ds->iwork);
 89:     PetscLogObjectMemory(ds,(i-ds->liwork)*sizeof(PetscBLASInt));
 90:     ds->liwork = i;
 91:   }
 92:   return(0);
 93: }

 97: PetscErrorCode DSViewMat_Private(DS ds,PetscViewer viewer,DSMatType m)
 98: {
 99:   PetscErrorCode    ierr;
100:   PetscInt          i,j,rows,cols;
101:   PetscScalar       *v;
102:   PetscViewerFormat format;
103: #if defined(PETSC_USE_COMPLEX)
104:   PetscBool         allreal = PETSC_TRUE;
105: #endif

108:   PetscViewerGetFormat(viewer,&format);
109:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
110:   PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
111:   if (ds->state==DS_STATE_TRUNCATED && m>=DS_MAT_Q) rows = ds->t;
112:   else rows = (m==DS_MAT_A && ds->extrarow)? ds->n+1: ds->n;
113:   cols = (ds->m!=0)? ds->m: ds->n;
114: #if defined(PETSC_USE_COMPLEX)
115:   /* determine if matrix has all real values */
116:   v = ds->mat[m];
117:   for (i=0;i<rows;i++)
118:     for (j=0;j<cols;j++)
119:       if (PetscImaginaryPart(v[i+j*ds->ld])) { allreal = PETSC_FALSE; break; }
120: #endif
121:   if (format == PETSC_VIEWER_ASCII_MATLAB) {
122:     PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",rows,cols);
123:     PetscViewerASCIIPrintf(viewer,"%s = [\n",DSMatName[m]);
124:   } else {
125:     PetscViewerASCIIPrintf(viewer,"Matrix %s =\n",DSMatName[m]);
126:   }

128:   for (i=0;i<rows;i++) {
129:     v = ds->mat[m]+i;
130:     for (j=0;j<cols;j++) {
131: #if defined(PETSC_USE_COMPLEX)
132:       if (allreal) {
133:         PetscViewerASCIIPrintf(viewer,"%18.16e ",PetscRealPart(*v));
134:       } else {
135:         PetscViewerASCIIPrintf(viewer,"%18.16e + %18.16ei ",PetscRealPart(*v),PetscImaginaryPart(*v));
136:       }
137: #else
138:       PetscViewerASCIIPrintf(viewer,"%18.16e ",*v);
139: #endif
140:       v += ds->ld;
141:     }
142:     PetscViewerASCIIPrintf(viewer,"\n");
143:   }

145:   if (format == PETSC_VIEWER_ASCII_MATLAB) {
146:     PetscViewerASCIIPrintf(viewer,"];\n");
147:   }
148:   PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
149:   PetscViewerFlush(viewer);
150:   return(0);
151: }

155: PetscErrorCode DSSortEigenvalues_Private(DS ds,PetscScalar *wr,PetscScalar *wi,PetscInt *perm,PetscBool isghiep)
156: {
158:   PetscScalar    re,im,wi0;
159:   PetscInt       n,i,j,result,tmp1,tmp2=0,d=1;

162:   n = ds->t;   /* sort only first t pairs if truncated */
163:   for (i=0;i<ds->n;i++) perm[i] = i;
164:   /* insertion sort */
165:   i=ds->l+1;
166: #if !defined(PETSC_USE_COMPLEX)
167:   if (wi && wi[perm[i-1]]!=0.0) i++; /* initial value is complex */
168: #else
169:   if (isghiep && PetscImaginaryPart(wr[perm[i-1]])!=0.0) i++;
170: #endif
171:   for (;i<n;i+=d) {
172:     re = wr[perm[i]];
173:     if (wi) im = wi[perm[i]];
174:     else im = 0.0;
175:     tmp1 = perm[i];
176: #if !defined(PETSC_USE_COMPLEX)
177:     if (im!=0.0) { d = 2; tmp2 = perm[i+1]; }
178:     else d = 1;
179: #else
180:     if (isghiep && PetscImaginaryPart(re)!=0.0) { d = 2; tmp2 = perm[i+1]; }
181:     else d = 1;
182: #endif
183:     j = i-1;
184:     if (wi) wi0 = wi[perm[j]];
185:     else wi0 = 0.0;
186:     (*ds->comparison)(re,im,wr[perm[j]],wi0,&result,ds->comparisonctx);
187:     while (result<0 && j>=ds->l) {
188:       perm[j+d] = perm[j];
189:       j--;
190: #if !defined(PETSC_USE_COMPLEX)
191:       if (wi && wi[perm[j+1]]!=0)
192: #else
193:       if (isghiep && PetscImaginaryPart(wr[perm[j+1]])!=0)
194: #endif
195:         { perm[j+d] = perm[j]; j--; }

197:       if (j>=ds->l) {
198:         if (wi) wi0 = wi[perm[j]];
199:         else wi0 = 0.0;
200:         (*ds->comparison)(re,im,wr[perm[j]],wi0,&result,ds->comparisonctx);
201:       }
202:     }
203:     perm[j+1] = tmp1;
204:     if (d==2) perm[j+2] = tmp2;
205:   }
206:   return(0);
207: }

211: PetscErrorCode DSSortEigenvaluesReal_Private(DS ds,PetscReal *eig,PetscInt *perm)
212: {
214:   PetscScalar    re;
215:   PetscInt       i,j,result,tmp,l,n;

218:   n = ds->t;   /* sort only first t pairs if truncated */
219:   l = ds->l;
220:   for (i=0;i<n;i++) perm[i] = i;
221:   /* insertion sort */
222:   for (i=l+1;i<n;i++) {
223:     re = eig[perm[i]];
224:     j = i-1;
225:     (*ds->comparison)(re,0.0,eig[perm[j]],0.0,&result,ds->comparisonctx);
226:     while (result<0 && j>=l) {
227:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
228:       if (j>=l) {
229:         (*ds->comparison)(re,0.0,eig[perm[j]],0.0,&result,ds->comparisonctx);
230:       }
231:     }
232:   }
233:   return(0);
234: }

238: /*
239:   DSCopyMatrix_Private - Copies the trailing block of a matrix (from
240:   rows/columns l to n).
241: */
242: PetscErrorCode DSCopyMatrix_Private(DS ds,DSMatType dst,DSMatType src)
243: {
245:   PetscInt    j,m,off,ld;
246:   PetscScalar *S,*D;

249:   ld  = ds->ld;
250:   m   = ds->n-ds->l;
251:   off = ds->l+ds->l*ld;
252:   S   = ds->mat[src];
253:   D   = ds->mat[dst];
254:   for (j=0;j<m;j++) {
255:     PetscMemcpy(D+off+j*ld,S+off+j*ld,m*sizeof(PetscScalar));
256:   }
257:   return(0);
258: }

262: PetscErrorCode DSPermuteColumns_Private(DS ds,PetscInt l,PetscInt n,DSMatType mat,PetscInt *perm)
263: {
264:   PetscInt    i,j,k,p,ld;
265:   PetscScalar *Q,rtmp;

268:   ld = ds->ld;
269:   Q  = ds->mat[mat];
270:   for (i=l;i<n;i++) {
271:     p = perm[i];
272:     if (p != i) {
273:       j = i + 1;
274:       while (perm[j] != i) j++;
275:       perm[j] = p; perm[i] = i;
276:       /* swap columns i and j */
277:       for (k=0;k<n;k++) {
278:         rtmp = Q[k+p*ld]; Q[k+p*ld] = Q[k+i*ld]; Q[k+i*ld] = rtmp;
279:       }
280:     }
281:   }
282:   return(0);
283: }

287: PetscErrorCode DSPermuteRows_Private(DS ds,PetscInt l,PetscInt n,DSMatType mat,PetscInt *perm)
288: {
289:   PetscInt    i,j,m=ds->m,k,p,ld;
290:   PetscScalar *Q,rtmp;

293:   if (!m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
294:   ld = ds->ld;
295:   Q  = ds->mat[mat];
296:   for (i=l;i<n;i++) {
297:     p = perm[i];
298:     if (p != i) {
299:       j = i + 1;
300:       while (perm[j] != i) j++;
301:       perm[j] = p; perm[i] = i;
302:       /* swap rows i and j */
303:       for (k=0;k<m;k++) {
304:         rtmp = Q[p+k*ld]; Q[p+k*ld] = Q[i+k*ld]; Q[i+k*ld] = rtmp;
305:       }
306:     }
307:   }
308:   return(0);
309: }

313: PetscErrorCode DSPermuteBoth_Private(DS ds,PetscInt l,PetscInt n,DSMatType mat1,DSMatType mat2,PetscInt *perm)
314: {
315:   PetscInt    i,j,m=ds->m,k,p,ld;
316:   PetscScalar *U,*VT,rtmp;

319:   if (!m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
320:   ld = ds->ld;
321:   U  = ds->mat[mat1];
322:   VT = ds->mat[mat2];
323:   for (i=l;i<n;i++) {
324:     p = perm[i];
325:     if (p != i) {
326:       j = i + 1;
327:       while (perm[j] != i) j++;
328:       perm[j] = p; perm[i] = i;
329:       /* swap columns i and j of U */
330:       for (k=0;k<n;k++) {
331:         rtmp = U[k+p*ld]; U[k+p*ld] = U[k+i*ld]; U[k+i*ld] = rtmp;
332:       }
333:       /* swap rows i and j of VT */
334:       for (k=0;k<m;k++) {
335:         rtmp = VT[p+k*ld]; VT[p+k*ld] = VT[i+k*ld]; VT[i+k*ld] = rtmp;
336:       }
337:     }
338:   }
339:   return(0);
340: }

344: /*
345:    DSSetIdentity - Copy the identity (a diagonal matrix with ones) on the
346:    active part of a matrix.
347: */
348: PetscErrorCode DSSetIdentity(DS ds,DSMatType mat)
349: {
351:   PetscScalar    *x;
352:   PetscInt       i,ld,n,l;

355:   DSGetDimensions(ds,&n,NULL,&l,NULL,NULL);
356:   DSGetLeadingDimension(ds,&ld);
357:   PetscLogEventBegin(DS_Other,ds,0,0,0);
358:   DSGetArray(ds,mat,&x);
359:   PetscMemzero(&x[ld*l],ld*(n-l)*sizeof(PetscScalar));
360:   for (i=l;i<n;i++) {
361:     x[ld*i+i] = 1.0;
362:   }
363:   DSRestoreArray(ds,mat,&x);
364:   PetscLogEventEnd(DS_Other,ds,0,0,0);
365:   return(0);
366: }

370: /*
371:    DSComputeMatrix - Build the matrix associated to a nonlinear operator
372:    T(lambda) or its derivative T'(lambda), given the parameter lambda, where
373:    T(lambda) = sum_i E_i*f_i(lambda). The result is written in mat.
374: */
375: PetscErrorCode DSComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat)
376: {
378:   PetscScalar    *T,*E,alpha;
379:   PetscInt       i,ld,n;
380:   PetscBLASInt   k,inc=1;

383:   DSGetDimensions(ds,&n,NULL,NULL,NULL,NULL);
384:   DSGetLeadingDimension(ds,&ld);
385:   PetscBLASIntCast(ld*n,&k);
386:   PetscLogEventBegin(DS_Other,ds,0,0,0);
387:   DSGetArray(ds,mat,&T);
388:   PetscMemzero(T,k*sizeof(PetscScalar));
389:   for (i=0;i<ds->nf;i++) {
390:     if (deriv) {
391:       FNEvaluateDerivative(ds->f[i],lambda,&alpha);
392:     } else {
393:       FNEvaluateFunction(ds->f[i],lambda,&alpha);
394:     }
395:     E = ds->mat[DSMatExtra[i]];
396:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&k,&alpha,E,&inc,T,&inc));
397:   }
398:   DSRestoreArray(ds,mat,&T);
399:   PetscLogEventEnd(DS_Other,ds,0,0,0);
400:   return(0);
401: }

405: /*
406:    DSOrthogonalize - Orthogonalize the columns of a matrix.

408:    Input Parameters:
409: +  ds   - the direct solver context
410: .  mat  - a matrix
411: -  cols - number of columns to orthogonalize (starting from the column zero)

413:    Output Parameter:
414: .  lindcols - number of linearly independent columns of the matrix (can be NULL)
415: */
416: PetscErrorCode DSOrthogonalize(DS ds,DSMatType mat,PetscInt cols,PetscInt *lindcols)
417: {
418: #if defined(PETSC_MISSING_LAPACK_GEQRF) || defined(SLEPC_MISSING_LAPACK_ORGQR)
420:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEQRF/ORGQR - Lapack routine is unavailable");
421: #else
422:   PetscErrorCode  ierr;
423:   PetscInt        n,l,ld;
424:   PetscBLASInt    ld_,rA,cA,info,ltau,lw;
425:   PetscScalar     *A,*tau,*w,saux;

431:   DSGetDimensions(ds,&n,NULL,&l,NULL,NULL);
432:   DSGetLeadingDimension(ds,&ld);
433:   n = n - l;
434:   if (cols > n) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Invalid number of columns");
435:   if (n == 0 || cols == 0) return(0);
436:   DSGetArray(ds,mat,&A);
437:   PetscBLASIntCast(PetscMin(cols,n),&ltau);
438:   PetscBLASIntCast(ld,&ld_);
439:   PetscBLASIntCast(n,&rA);
440:   PetscBLASIntCast(cols,&cA);
441:   lw = -1;
442:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,A,&ld_,NULL,&saux,&lw,&info));
443:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
444:   lw = (PetscBLASInt)PetscRealPart(saux);
445:   DSAllocateWork_Private(ds,lw+ltau,0,0);
446:   tau = ds->work;
447:   w = &tau[ltau];
448:   PetscLogEventBegin(DS_Other,ds,0,0,0);
449:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
450:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,&A[ld*l+l],&ld_,tau,w,&lw,&info));
451:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
452:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&rA,&ltau,&ltau,&A[ld*l+l],&ld_,tau,w,&lw,&info));
453:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGQR %d",info);
454:   PetscFPTrapPop();
455:   PetscLogEventEnd(DS_Other,ds,0,0,0);
456:   DSRestoreArray(ds,mat,&A);
457:   PetscObjectStateIncrease((PetscObject)ds);
458:   if (lindcols) *lindcols = ltau;
459:   return(0);
460: #endif
461: }

465: /*
466:    DSPseudoOrthogonalize - Orthogonalize the columns of a matrix with Modified
467:    Gram-Schmidt in an indefinite inner product space defined by a signature.

469:    Input Parameters:
470: +  ds   - the direct solver context
471: .  mat  - the matrix
472: .  cols - number of columns to orthogonalize (starting from the column zero)
473: -  s    - the signature that defines the inner product

475:    Output Parameter:
476: +  lindcols - linear independent columns of the matrix (can be NULL)
477: -  ns - the new norm of the vectors (can be NULL)
478: */
479: PetscErrorCode DSPseudoOrthogonalize(DS ds,DSMatType mat,PetscInt cols,PetscReal *s,PetscInt *lindcols,PetscReal *ns)
480: {
481:   PetscErrorCode  ierr;
482:   PetscInt        i,j,k,l,n,ld;
483:   PetscBLASInt    one=1,rA_;
484:   PetscScalar     alpha,*A,*A_,*m,*h,nr0;
485:   PetscReal       nr_o,nr,*ns_;

493:   DSGetDimensions(ds,&n,NULL,&l,NULL,NULL);
494:   DSGetLeadingDimension(ds,&ld);
495:   n = n - l;
496:   if (cols > n) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Invalid number of columns");
497:   if (n == 0 || cols == 0) return(0);
498:   PetscBLASIntCast(n,&rA_);
499:   DSGetArray(ds,mat,&A_);
500:   A = &A_[ld*l+l];
501:   DSAllocateWork_Private(ds,n+cols,ns?0:cols,0);
502:   m = ds->work;
503:   h = &m[n];
504:   ns_ = ns ? ns : ds->rwork;
505:   PetscLogEventBegin(DS_Other,ds,0,0,0);
506:   for (i=0; i<cols; i++) {
507:     /* m <- diag(s)*A[i] */
508:     for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
509:     /* nr_o <- mynorm(A[i]'*m), mynorm(x) = sign(x)*sqrt(|x|) */
510:     SlepcDenseMatProd(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
511:     nr = nr_o = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
512:     for (j=0; j<3 && i>0; j++) {
513:       /* h <- A[0:i-1]'*m */
514:       SlepcDenseMatProd(h,i,0.0,1.0,A,ld,n,i,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
515:       /* h <- diag(ns)*h */
516:       for (k=0; k<i; k++) h[k] *= ns_[k];
517:       /* A[i] <- A[i] - A[0:i-1]*h */
518:       SlepcDenseMatProd(&A[ld*i],ld,1.0,-1.0,A,ld,n,i,PETSC_FALSE,h,i,i,1,PETSC_FALSE);
519:       /* m <- diag(s)*A[i] */
520:       for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
521:       /* nr_o <- mynorm(A[i]'*m) */
522:       SlepcDenseMatProd(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
523:       nr = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
524:       if (PetscAbs(nr) < PETSC_MACHINE_EPSILON) SETERRQ(PETSC_COMM_SELF,1,"Linear dependency detected");
525:       if (PetscAbs(nr) > 0.7*PetscAbs(nr_o)) break;
526:       nr_o = nr;
527:     }
528:     ns_[i] = PetscSign(nr);
529:     /* A[i] <- A[i]/|nr| */
530:     alpha = 1.0/PetscAbs(nr);
531:     PetscStackCallBLAS("BLASscal",BLASscal_(&rA_,&alpha,&A[i*ld],&one));
532:   }
533:   PetscLogEventEnd(DS_Other,ds,0,0,0);
534:   DSRestoreArray(ds,mat,&A_);
535:   PetscObjectStateIncrease((PetscObject)ds);
536:   if (lindcols) *lindcols = cols;
537:   return(0);
538: }