Actual source code: dspriv.c

slepc-3.17.1 2022-04-11
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, 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: */
 10: /*
 11:    Private DS routines
 12: */

 14: #include <slepc/private/dsimpl.h>
 15: #include <slepcblaslapack.h>

 17: PetscErrorCode DSAllocateMatrix_Private(DS ds,DSMatType m,PetscBool isreal)
 18: {
 19:   size_t         sz;
 20:   PetscInt       n,d,nelem;
 21:   PetscBool      ispep,isnep;

 23:   PetscObjectTypeCompare((PetscObject)ds,DSPEP,&ispep);
 24:   PetscObjectTypeCompare((PetscObject)ds,DSNEP,&isnep);
 25:   if (ispep) DSPEPGetDegree(ds,&d);
 26:   if (isnep) DSNEPGetMinimality(ds,&d);
 27:   if ((ispep || isnep) && (m==DS_MAT_A || m==DS_MAT_B || m==DS_MAT_W || m==DS_MAT_U || m==DS_MAT_X || m==DS_MAT_Y)) n = d*ds->ld;
 28:   else n = ds->ld;

 30:   switch (m) {
 31:     case DS_MAT_T:
 32:       nelem = 3*ds->ld;
 33:       break;
 34:     case DS_MAT_D:
 35:       nelem = ds->ld;
 36:       break;
 37:     case DS_MAT_X:
 38:       nelem = ds->ld*n;
 39:       break;
 40:     case DS_MAT_Y:
 41:       nelem = ds->ld*n;
 42:       break;
 43:     default:
 44:       nelem = n*n;
 45:   }
 46:   if (isreal) {
 47:     sz = nelem*sizeof(PetscReal);
 48:     if (ds->rmat[m]) PetscFree(ds->rmat[m]);
 49:     else PetscLogObjectMemory((PetscObject)ds,sz);
 50:     PetscCalloc1(nelem,&ds->rmat[m]);
 51:   } else {
 52:     sz = nelem*sizeof(PetscScalar);
 53:     if (ds->mat[m]) PetscFree(ds->mat[m]);
 54:     else PetscLogObjectMemory((PetscObject)ds,sz);
 55:     PetscCalloc1(nelem,&ds->mat[m]);
 56:   }
 57:   PetscFunctionReturn(0);
 58: }

 60: PetscErrorCode DSAllocateWork_Private(DS ds,PetscInt s,PetscInt r,PetscInt i)
 61: {
 62:   if (s>ds->lwork) {
 63:     PetscFree(ds->work);
 64:     PetscMalloc1(s,&ds->work);
 65:     PetscLogObjectMemory((PetscObject)ds,(s-ds->lwork)*sizeof(PetscScalar));
 66:     ds->lwork = s;
 67:   }
 68:   if (r>ds->lrwork) {
 69:     PetscFree(ds->rwork);
 70:     PetscMalloc1(r,&ds->rwork);
 71:     PetscLogObjectMemory((PetscObject)ds,(r-ds->lrwork)*sizeof(PetscReal));
 72:     ds->lrwork = r;
 73:   }
 74:   if (i>ds->liwork) {
 75:     PetscFree(ds->iwork);
 76:     PetscMalloc1(i,&ds->iwork);
 77:     PetscLogObjectMemory((PetscObject)ds,(i-ds->liwork)*sizeof(PetscBLASInt));
 78:     ds->liwork = i;
 79:   }
 80:   PetscFunctionReturn(0);
 81: }

 83: /*@C
 84:    DSViewMat - Prints one of the internal DS matrices.

 86:    Collective on ds

 88:    Input Parameters:
 89: +  ds     - the direct solver context
 90: .  viewer - visualization context
 91: -  m      - matrix to display

 93:    Note:
 94:    Works only for ascii viewers. Set the viewer in Matlab format if
 95:    want to paste into Matlab.

 97:    Level: developer

 99: .seealso: DSView()
100: @*/
101: PetscErrorCode DSViewMat(DS ds,PetscViewer viewer,DSMatType m)
102: {
103:   PetscInt          i,j,rows,cols;
104:   PetscScalar       *v;
105:   PetscViewerFormat format;
106: #if defined(PETSC_USE_COMPLEX)
107:   PetscBool         allreal = PETSC_TRUE;
108: #endif

112:   DSCheckValidMat(ds,m,3);
113:   if (!viewer) PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ds),&viewer);
116:   PetscViewerGetFormat(viewer,&format);
117:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);
118:   PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
119:   DSMatGetSize(ds,m,&rows,&cols);
120: #if defined(PETSC_USE_COMPLEX)
121:   /* determine if matrix has all real values */
122:   v = ds->mat[m];
123:   for (i=0;i<rows;i++)
124:     for (j=0;j<cols;j++)
125:       if (PetscImaginaryPart(v[i+j*ds->ld])) { allreal = PETSC_FALSE; break; }
126: #endif
127:   if (format == PETSC_VIEWER_ASCII_MATLAB) {
128:     PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,cols);
129:     PetscViewerASCIIPrintf(viewer,"%s = [\n",DSMatName[m]);
130:   } else PetscViewerASCIIPrintf(viewer,"Matrix %s =\n",DSMatName[m]);

132:   for (i=0;i<rows;i++) {
133:     v = ds->mat[m]+i;
134:     for (j=0;j<cols;j++) {
135: #if defined(PETSC_USE_COMPLEX)
136:       if (allreal) PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)PetscRealPart(*v));
137:       else PetscViewerASCIIPrintf(viewer,"%18.16e%+18.16ei ",(double)PetscRealPart(*v),(double)PetscImaginaryPart(*v));
138: #else
139:       PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)*v);
140: #endif
141:       v += ds->ld;
142:     }
143:     PetscViewerASCIIPrintf(viewer,"\n");
144:   }

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

152: PetscErrorCode DSSortEigenvalues_Private(DS ds,PetscScalar *wr,PetscScalar *wi,PetscInt *perm,PetscBool isghiep)
153: {
154:   PetscScalar    re,im,wi0;
155:   PetscInt       n,i,j,result,tmp1,tmp2=0,d=1;

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

191:       if (j>=ds->l) {
192:         if (wi) wi0 = wi[perm[j]];
193:         else wi0 = 0.0;
194:         SlepcSCCompare(ds->sc,re,im,wr[perm[j]],wi0,&result);
195:       }
196:     }
197:     perm[j+1] = tmp1;
198:     if (d==2) perm[j+2] = tmp2;
199:   }
200:   PetscFunctionReturn(0);
201: }

203: PetscErrorCode DSSortEigenvaluesReal_Private(DS ds,PetscReal *eig,PetscInt *perm)
204: {
205:   PetscScalar    re;
206:   PetscInt       i,j,result,tmp,l,n;

208:   n = ds->t;   /* sort only first t pairs if truncated */
209:   l = ds->l;
210:   /* insertion sort */
211:   for (i=l+1;i<n;i++) {
212:     re = eig[perm[i]];
213:     j = i-1;
214:     SlepcSCCompare(ds->sc,re,0.0,eig[perm[j]],0.0,&result);
215:     while (result<0 && j>=l) {
216:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
217:       if (j>=l) SlepcSCCompare(ds->sc,re,0.0,eig[perm[j]],0.0,&result);
218:     }
219:   }
220:   PetscFunctionReturn(0);
221: }

223: /*
224:   DSCopyMatrix_Private - Copies the trailing block of a matrix (from
225:   rows/columns l to n).
226: */
227: PetscErrorCode DSCopyMatrix_Private(DS ds,DSMatType dst,DSMatType src)
228: {
229:   PetscInt    j,m,off,ld;
230:   PetscScalar *S,*D;

232:   ld  = ds->ld;
233:   m   = ds->n-ds->l;
234:   off = ds->l+ds->l*ld;
235:   S   = ds->mat[src];
236:   D   = ds->mat[dst];
237:   for (j=0;j<m;j++) PetscArraycpy(D+off+j*ld,S+off+j*ld,m);
238:   PetscFunctionReturn(0);
239: }

241: /*
242:   Permute comumns [istart..iend-1] of [mat] according to perm. Columns have length n
243:  */
244: PetscErrorCode DSPermuteColumns_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt n,DSMatType mat,PetscInt *perm)
245: {
246:   PetscInt    i,j,k,p,ld;
247:   PetscScalar *Q,rtmp;

249:   ld = ds->ld;
250:   Q  = ds->mat[mat];
251:   for (i=istart;i<iend;i++) {
252:     p = perm[i];
253:     if (p != i) {
254:       j = i + 1;
255:       while (perm[j] != i) j++;
256:       perm[j] = p; perm[i] = i;
257:       /* swap columns i and j */
258:       for (k=0;k<n;k++) {
259:         rtmp = Q[k+p*ld]; Q[k+p*ld] = Q[k+i*ld]; Q[k+i*ld] = rtmp;
260:       }
261:     }
262:   }
263:   PetscFunctionReturn(0);
264: }

266: /*
267:   The same as DSPermuteColumns_Private but for two matrices [mat1] and [mat2]
268:  */
269: PetscErrorCode DSPermuteColumnsTwo_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt n,DSMatType mat1,DSMatType mat2,PetscInt *perm)
270: {
271:   PetscInt    i,j,k,p,ld;
272:   PetscScalar *Q,*Z,rtmp,rtmp2;

274:   ld = ds->ld;
275:   Q  = ds->mat[mat1];
276:   Z  = ds->mat[mat2];
277:   for (i=istart;i<iend;i++) {
278:     p = perm[i];
279:     if (p != i) {
280:       j = i + 1;
281:       while (perm[j] != i) j++;
282:       perm[j] = p; perm[i] = i;
283:       /* swap columns i and j */
284:       for (k=0;k<n;k++) {
285:         rtmp  = Q[k+p*ld]; Q[k+p*ld] = Q[k+i*ld]; Q[k+i*ld] = rtmp;
286:         rtmp2 = Z[k+p*ld]; Z[k+p*ld] = Z[k+i*ld]; Z[k+i*ld] = rtmp2;
287:       }
288:     }
289:   }
290:   PetscFunctionReturn(0);
291: }

293: /*
294:   Permute rows [istart..iend-1] of [mat] according to perm. Rows have length m
295:  */
296: PetscErrorCode DSPermuteRows_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt m,DSMatType mat,PetscInt *perm)
297: {
298:   PetscInt    i,j,k,p,ld;
299:   PetscScalar *Q,rtmp;

301:   ld = ds->ld;
302:   Q  = ds->mat[mat];
303:   for (i=istart;i<iend;i++) {
304:     p = perm[i];
305:     if (p != i) {
306:       j = i + 1;
307:       while (perm[j] != i) j++;
308:       perm[j] = p; perm[i] = i;
309:       /* swap rows i and j */
310:       for (k=0;k<m;k++) {
311:         rtmp = Q[p+k*ld]; Q[p+k*ld] = Q[i+k*ld]; Q[i+k*ld] = rtmp;
312:       }
313:     }
314:   }
315:   PetscFunctionReturn(0);
316: }

318: /*
319:   Permute columns [istart..iend-1] of [mat1] and [mat2] according to perm.
320:   Columns of [mat1] have length n, columns of [mat2] have length m
321:  */
322: PetscErrorCode DSPermuteBoth_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt n,PetscInt m,DSMatType mat1,DSMatType mat2,PetscInt *perm)
323: {
324:   PetscInt    i,j,k,p,ld;
325:   PetscScalar *U,*V,rtmp;

327:   ld = ds->ld;
328:   U  = ds->mat[mat1];
329:   V  = ds->mat[mat2];
330:   for (i=istart;i<iend;i++) {
331:     p = perm[i];
332:     if (p != i) {
333:       j = i + 1;
334:       while (perm[j] != i) j++;
335:       perm[j] = p; perm[i] = i;
336:       /* swap columns i and j of U */
337:       for (k=0;k<n;k++) {
338:         rtmp = U[k+p*ld]; U[k+p*ld] = U[k+i*ld]; U[k+i*ld] = rtmp;
339:       }
340:       /* swap columns i and j of V */
341:       for (k=0;k<m;k++) {
342:         rtmp = V[k+p*ld]; V[k+p*ld] = V[k+i*ld]; V[k+i*ld] = rtmp;
343:       }
344:     }
345:   }
346:   PetscFunctionReturn(0);
347: }

349: /*@
350:    DSSetIdentity - Copy the identity (a diagonal matrix with ones) on the
351:    active part of a matrix.

353:    Logically Collective on ds

355:    Input Parameters:
356: +  ds  - the direct solver context
357: -  mat - the matrix to modify

359:    Level: intermediate

361: .seealso: DSGetMat()
362: @*/
363: PetscErrorCode DSSetIdentity(DS ds,DSMatType mat)
364: {
365:   PetscScalar    *x;
366:   PetscInt       i,ld,n,l;

370:   DSCheckValidMat(ds,mat,2);

372:   DSGetDimensions(ds,&n,&l,NULL,NULL);
373:   DSGetLeadingDimension(ds,&ld);
374:   PetscLogEventBegin(DS_Other,ds,0,0,0);
375:   DSGetArray(ds,mat,&x);
376:   PetscArrayzero(&x[ld*l],ld*(n-l));
377:   for (i=l;i<n;i++) x[i+i*ld] = 1.0;
378:   DSRestoreArray(ds,mat,&x);
379:   PetscLogEventEnd(DS_Other,ds,0,0,0);
380:   PetscFunctionReturn(0);
381: }

383: /*@C
384:    DSOrthogonalize - Orthogonalize the columns of a matrix.

386:    Logically Collective on ds

388:    Input Parameters:
389: +  ds   - the direct solver context
390: .  mat  - a matrix
391: -  cols - number of columns to orthogonalize (starting from column zero)

393:    Output Parameter:
394: .  lindcols - (optional) number of linearly independent columns of the matrix

396:    Level: developer

398: .seealso: DSPseudoOrthogonalize()
399: @*/
400: PetscErrorCode DSOrthogonalize(DS ds,DSMatType mat,PetscInt cols,PetscInt *lindcols)
401: {
402:   PetscInt       n,l,ld;
403:   PetscBLASInt   ld_,rA,cA,info,ltau,lw;
404:   PetscScalar    *A,*tau,*w,saux,dummy;

407:   DSCheckAlloc(ds,1);
409:   DSCheckValidMat(ds,mat,2);

412:   DSGetDimensions(ds,&n,&l,NULL,NULL);
413:   DSGetLeadingDimension(ds,&ld);
414:   n = n - l;
416:   if (n == 0 || cols == 0) PetscFunctionReturn(0);

418:   PetscLogEventBegin(DS_Other,ds,0,0,0);
419:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
420:   DSGetArray(ds,mat,&A);
421:   PetscBLASIntCast(PetscMin(cols,n),&ltau);
422:   PetscBLASIntCast(ld,&ld_);
423:   PetscBLASIntCast(n,&rA);
424:   PetscBLASIntCast(cols,&cA);
425:   lw = -1;
426:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,A,&ld_,&dummy,&saux,&lw,&info));
427:   SlepcCheckLapackInfo("geqrf",info);
428:   lw = (PetscBLASInt)PetscRealPart(saux);
429:   DSAllocateWork_Private(ds,lw+ltau,0,0);
430:   tau = ds->work;
431:   w = &tau[ltau];
432:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,&A[ld*l+l],&ld_,tau,w,&lw,&info));
433:   SlepcCheckLapackInfo("geqrf",info);
434:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&rA,&ltau,&ltau,&A[ld*l+l],&ld_,tau,w,&lw,&info));
435:   SlepcCheckLapackInfo("orgqr",info);
436:   if (lindcols) *lindcols = ltau;

438:   PetscFPTrapPop();
439:   PetscLogEventEnd(DS_Other,ds,0,0,0);
440:   DSRestoreArray(ds,mat,&A);
441:   PetscObjectStateIncrease((PetscObject)ds);
442:   PetscFunctionReturn(0);
443: }

445: /*
446:   Compute C <- a*A*B + b*C, where
447:     ldC, the leading dimension of C,
448:     ldA, the leading dimension of A,
449:     rA, cA, rows and columns of A,
450:     At, if true use the transpose of A instead,
451:     ldB, the leading dimension of B,
452:     rB, cB, rows and columns of B,
453:     Bt, if true use the transpose of B instead
454: */
455: static PetscErrorCode SlepcMatDenseMult(PetscScalar *C,PetscInt _ldC,PetscScalar b,PetscScalar a,const PetscScalar *A,PetscInt _ldA,PetscInt rA,PetscInt cA,PetscBool At,const PetscScalar *B,PetscInt _ldB,PetscInt rB,PetscInt cB,PetscBool Bt)
456: {
457:   PetscInt       tmp;
458:   PetscBLASInt   m, n, k, ldA = _ldA, ldB = _ldB, ldC = _ldC;
459:   const char     *N = "N", *T = "C", *qA = N, *qB = N;

461:   if ((rA == 0) || (cB == 0)) PetscFunctionReturn(0);

466:   /* Transpose if needed */
467:   if (At) tmp = rA, rA = cA, cA = tmp, qA = T;
468:   if (Bt) tmp = rB, rB = cB, cB = tmp, qB = T;

470:   /* Check size */

473:   /* Do stub */
474:   if ((rA == 1) && (cA == 1) && (cB == 1)) {
475:     if (!At && !Bt) *C = *A * *B;
476:     else if (At && !Bt) *C = PetscConj(*A) * *B;
477:     else if (!At && Bt) *C = *A * PetscConj(*B);
478:     else *C = PetscConj(*A) * PetscConj(*B);
479:     m = n = k = 1;
480:   } else {
481:     m = rA; n = cB; k = cA;
482:     PetscStackCallBLAS("BLASgemm",BLASgemm_(qA,qB,&m,&n,&k,&a,(PetscScalar*)A,&ldA,(PetscScalar*)B,&ldB,&b,C,&ldC));
483:   }

485:   PetscLogFlops(2.0*m*n*k);
486:   PetscFunctionReturn(0);
487: }

489: /*@C
490:    DSPseudoOrthogonalize - Orthogonalize the columns of a matrix with Modified
491:    Gram-Schmidt in an indefinite inner product space defined by a signature.

493:    Logically Collective on ds

495:    Input Parameters:
496: +  ds   - the direct solver context
497: .  mat  - the matrix
498: .  cols - number of columns to orthogonalize (starting from column zero)
499: -  s    - the signature that defines the inner product

501:    Output Parameters:
502: +  lindcols - (optional) linearly independent columns of the matrix
503: -  ns   - (optional) the new signature of the vectors

505:    Note:
506:    After the call the matrix satisfies A'*s*A = ns.

508:    Level: developer

510: .seealso: DSOrthogonalize()
511: @*/
512: PetscErrorCode DSPseudoOrthogonalize(DS ds,DSMatType mat,PetscInt cols,PetscReal *s,PetscInt *lindcols,PetscReal *ns)
513: {
514:   PetscInt       i,j,k,l,n,ld;
515:   PetscBLASInt   info,one=1,zero=0,rA_,ld_;
516:   PetscScalar    *A,*A_,*m,*h,nr0;
517:   PetscReal      nr_o,nr,nr_abs,*ns_,done=1.0;

520:   DSCheckAlloc(ds,1);
522:   DSCheckValidMat(ds,mat,2);
525:   DSGetDimensions(ds,&n,&l,NULL,NULL);
526:   DSGetLeadingDimension(ds,&ld);
527:   n = n - l;
529:   if (n == 0 || cols == 0) PetscFunctionReturn(0);
530:   PetscBLASIntCast(n,&rA_);
531:   PetscBLASIntCast(ld,&ld_);
532:   DSGetArray(ds,mat,&A_);
533:   A = &A_[ld*l+l];
534:   DSAllocateWork_Private(ds,n+cols,ns?0:cols,0);
535:   m = ds->work;
536:   h = &m[n];
537:   ns_ = ns ? ns : ds->rwork;
538:   PetscLogEventBegin(DS_Other,ds,0,0,0);
539:   for (i=0; i<cols; i++) {
540:     /* m <- diag(s)*A[i] */
541:     for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
542:     /* nr_o <- mynorm(A[i]'*m), mynorm(x) = sign(x)*sqrt(|x|) */
543:     SlepcMatDenseMult(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
544:     nr = nr_o = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
545:     for (j=0; j<3 && i>0; j++) {
546:       /* h <- A[0:i-1]'*m */
547:       SlepcMatDenseMult(h,i,0.0,1.0,A,ld,n,i,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
548:       /* h <- diag(ns)*h */
549:       for (k=0; k<i; k++) h[k] *= ns_[k];
550:       /* A[i] <- A[i] - A[0:i-1]*h */
551:       SlepcMatDenseMult(&A[ld*i],ld,1.0,-1.0,A,ld,n,i,PETSC_FALSE,h,i,i,1,PETSC_FALSE);
552:       /* m <- diag(s)*A[i] */
553:       for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
554:       /* nr_o <- mynorm(A[i]'*m) */
555:       SlepcMatDenseMult(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
556:       nr = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
558:       if (PetscAbs(nr) > 0.7*PetscAbs(nr_o)) break;
559:       nr_o = nr;
560:     }
561:     ns_[i] = PetscSign(nr);
562:     /* A[i] <- A[i]/|nr| */
563:     nr_abs = PetscAbs(nr);
564:     PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&nr_abs,&done,&rA_,&one,A+i*ld,&ld_,&info));
565:     SlepcCheckLapackInfo("lascl",info);
566:   }
567:   PetscLogEventEnd(DS_Other,ds,0,0,0);
568:   DSRestoreArray(ds,mat,&A_);
569:   PetscObjectStateIncrease((PetscObject)ds);
570:   if (lindcols) *lindcols = cols;
571:   PetscFunctionReturn(0);
572: }