Actual source code: dspriv.c

slepc-3.18.3 2023-03-24
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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 DSAllocateMat_Private(DS ds,DSMatType m)
 18: {
 19:   PetscInt       n,d,rows=0,cols;
 20:   PetscBool      ispep,isnep;

 22:   n = ds->ld;
 23:   PetscObjectTypeCompare((PetscObject)ds,DSPEP,&ispep);
 24:   if (ispep) {
 25:     if (m==DS_MAT_A || m==DS_MAT_B || m==DS_MAT_W || m==DS_MAT_U || m==DS_MAT_X || m==DS_MAT_Y) {
 26:       DSPEPGetDegree(ds,&d);
 27:       n = d*ds->ld;
 28:     }
 29:   } else {
 30:     PetscObjectTypeCompare((PetscObject)ds,DSNEP,&isnep);
 31:     if (isnep) {
 32:       if (m==DS_MAT_Q || m==DS_MAT_Z || m==DS_MAT_U || m==DS_MAT_V || m==DS_MAT_X || m==DS_MAT_Y) {
 33:         DSNEPGetMinimality(ds,&d);
 34:         n = d*ds->ld;
 35:       }
 36:     }
 37:   }
 38:   cols = n;

 40:   switch (m) {
 41:     case DS_MAT_T:
 42:       cols = PetscDefined(USE_COMPLEX)? 2: 3;
 43:       rows = n;
 44:       break;
 45:     case DS_MAT_D:
 46:       cols = 1;
 47:       rows = n;
 48:       break;
 49:     case DS_MAT_X:
 50:       rows = ds->ld;
 51:       break;
 52:     case DS_MAT_Y:
 53:       rows = ds->ld;
 54:       break;
 55:     default:
 56:       rows = n;
 57:   }
 58:   if (ds->omat[m]) MatZeroEntries(ds->omat[m]);
 59:   else {
 60:     MatCreateSeqDense(PETSC_COMM_SELF,rows,cols,NULL,&ds->omat[m]);
 61:   }
 62:   return 0;
 63: }

 65: PetscErrorCode DSAllocateWork_Private(DS ds,PetscInt s,PetscInt r,PetscInt i)
 66: {
 67:   if (s>ds->lwork) {
 68:     PetscFree(ds->work);
 69:     PetscMalloc1(s,&ds->work);
 70:     ds->lwork = s;
 71:   }
 72:   if (r>ds->lrwork) {
 73:     PetscFree(ds->rwork);
 74:     PetscMalloc1(r,&ds->rwork);
 75:     ds->lrwork = r;
 76:   }
 77:   if (i>ds->liwork) {
 78:     PetscFree(ds->iwork);
 79:     PetscMalloc1(i,&ds->iwork);
 80:     ds->liwork = i;
 81:   }
 82:   return 0;
 83: }

 85: /*@C
 86:    DSViewMat - Prints one of the internal DS matrices.

 88:    Collective on ds

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

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

 99:    Level: developer

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

115:   DSCheckValidMat(ds,m,3);
116:   if (!viewer) PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ds),&viewer);
119:   PetscViewerGetFormat(viewer,&format);
120:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return 0;
121:   PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
122:   DSMatGetSize(ds,m,&rows,&cols);
123:   MatDenseGetArrayRead(ds->omat[m],&M);
124: #if defined(PETSC_USE_COMPLEX)
125:   /* determine if matrix has all real values */
126:   if (m!=DS_MAT_T && m!=DS_MAT_D) {
127:     /* determine if matrix has all real values */
128:     v = M;
129:     for (i=0;i<rows;i++)
130:       for (j=0;j<cols;j++)
131:         if (PetscImaginaryPart(v[i+j*ds->ld])) { allreal = PETSC_FALSE; break; }
132:   }
133:   if (m==DS_MAT_T) cols=3;
134: #endif
135:   if (format == PETSC_VIEWER_ASCII_MATLAB) {
136:     PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,cols);
137:     PetscViewerASCIIPrintf(viewer,"%s = [\n",DSMatName[m]);
138:   } else PetscViewerASCIIPrintf(viewer,"Matrix %s =\n",DSMatName[m]);

140:   for (i=0;i<rows;i++) {
141:     v = M+i;
142: #if defined(PETSC_USE_COMPLEX)
143:     vr = (const PetscReal*)M+i;   /* handle compact storage, 2nd column is in imaginary part of 1st column */
144: #endif
145:     for (j=0;j<cols;j++) {
146: #if defined(PETSC_USE_COMPLEX)
147:       if (m!=DS_MAT_T && m!=DS_MAT_D) {
148:         if (allreal) PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)PetscRealPart(*v));
149:         else PetscViewerASCIIPrintf(viewer,"%18.16e%+18.16ei ",(double)PetscRealPart(*v),(double)PetscImaginaryPart(*v));
150:       } else PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)*vr);
151: #else
152:       PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)*v);
153: #endif
154:       v += ds->ld;
155: #if defined(PETSC_USE_COMPLEX)
156:       if (m==DS_MAT_T) vr += ds->ld;
157: #endif
158:     }
159:     PetscViewerASCIIPrintf(viewer,"\n");
160:   }
161:   MatDenseRestoreArrayRead(ds->omat[m],&M);

163:   if (format == PETSC_VIEWER_ASCII_MATLAB) PetscViewerASCIIPrintf(viewer,"];\n");
164:   PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
165:   PetscViewerFlush(viewer);
166:   return 0;
167: }

169: PetscErrorCode DSSortEigenvalues_Private(DS ds,PetscScalar *wr,PetscScalar *wi,PetscInt *perm,PetscBool isghiep)
170: {
171:   PetscScalar    re,im,wi0;
172:   PetscInt       n,i,j,result,tmp1,tmp2=0,d=1;

174:   n = ds->t;   /* sort only first t pairs if truncated */
175:   /* insertion sort */
176:   i=ds->l+1;
177: #if !defined(PETSC_USE_COMPLEX)
178:   if (wi && wi[perm[i-1]]!=0.0) i++; /* initial value is complex */
179: #else
180:   if (isghiep && PetscImaginaryPart(wr[perm[i-1]])!=0.0) i++;
181: #endif
182:   for (;i<n;i+=d) {
183:     re = wr[perm[i]];
184:     if (wi) im = wi[perm[i]];
185:     else im = 0.0;
186:     tmp1 = perm[i];
187: #if !defined(PETSC_USE_COMPLEX)
188:     if (im!=0.0) { d = 2; tmp2 = perm[i+1]; }
189:     else d = 1;
190: #else
191:     if (isghiep && PetscImaginaryPart(re)!=0.0) { d = 2; tmp2 = perm[i+1]; }
192:     else d = 1;
193: #endif
194:     j = i-1;
195:     if (wi) wi0 = wi[perm[j]];
196:     else wi0 = 0.0;
197:     SlepcSCCompare(ds->sc,re,im,wr[perm[j]],wi0,&result);
198:     while (result<0 && j>=ds->l) {
199:       perm[j+d] = perm[j];
200:       j--;
201: #if !defined(PETSC_USE_COMPLEX)
202:       if (wi && wi[perm[j+1]]!=0)
203: #else
204:       if (isghiep && PetscImaginaryPart(wr[perm[j+1]])!=0)
205: #endif
206:         { perm[j+d] = perm[j]; j--; }

208:       if (j>=ds->l) {
209:         if (wi) wi0 = wi[perm[j]];
210:         else wi0 = 0.0;
211:         SlepcSCCompare(ds->sc,re,im,wr[perm[j]],wi0,&result);
212:       }
213:     }
214:     perm[j+1] = tmp1;
215:     if (d==2) perm[j+2] = tmp2;
216:   }
217:   return 0;
218: }

220: PetscErrorCode DSSortEigenvaluesReal_Private(DS ds,PetscReal *eig,PetscInt *perm)
221: {
222:   PetscScalar    re;
223:   PetscInt       i,j,result,tmp,l,n;

225:   n = ds->t;   /* sort only first t pairs if truncated */
226:   l = ds->l;
227:   /* insertion sort */
228:   for (i=l+1;i<n;i++) {
229:     re = eig[perm[i]];
230:     j = i-1;
231:     SlepcSCCompare(ds->sc,re,0.0,eig[perm[j]],0.0,&result);
232:     while (result<0 && j>=l) {
233:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
234:       if (j>=l) SlepcSCCompare(ds->sc,re,0.0,eig[perm[j]],0.0,&result);
235:     }
236:   }
237:   return 0;
238: }

240: /*
241:   Permute comumns [istart..iend-1] of [mat] according to perm. Columns have length n
242:  */
243: PetscErrorCode DSPermuteColumns_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt n,DSMatType mat,PetscInt *perm)
244: {
245:   PetscInt    i,j,k,p,ld;
246:   PetscScalar *Q,rtmp;

248:   ld = ds->ld;
249:   MatDenseGetArray(ds->omat[mat],&Q);
250:   for (i=istart;i<iend;i++) {
251:     p = perm[i];
252:     if (p != i) {
253:       j = i + 1;
254:       while (perm[j] != i) j++;
255:       perm[j] = p; perm[i] = i;
256:       /* swap columns i and j */
257:       for (k=0;k<n;k++) {
258:         rtmp = Q[k+p*ld]; Q[k+p*ld] = Q[k+i*ld]; Q[k+i*ld] = rtmp;
259:       }
260:     }
261:   }
262:   MatDenseRestoreArray(ds->omat[mat],&Q);
263:   return 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:   MatDenseGetArray(ds->omat[mat1],&Q);
276:   MatDenseGetArray(ds->omat[mat2],&Z);
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:   MatDenseRestoreArray(ds->omat[mat1],&Q);
291:   MatDenseRestoreArray(ds->omat[mat2],&Z);
292:   return 0;
293: }

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

303:   ld = ds->ld;
304:   MatDenseGetArray(ds->omat[mat],&Q);
305:   for (i=istart;i<iend;i++) {
306:     p = perm[i];
307:     if (p != i) {
308:       j = i + 1;
309:       while (perm[j] != i) j++;
310:       perm[j] = p; perm[i] = i;
311:       /* swap rows i and j */
312:       for (k=0;k<m;k++) {
313:         rtmp = Q[p+k*ld]; Q[p+k*ld] = Q[i+k*ld]; Q[i+k*ld] = rtmp;
314:       }
315:     }
316:   }
317:   MatDenseRestoreArray(ds->omat[mat],&Q);
318:   return 0;
319: }

321: /*
322:   Permute columns [istart..iend-1] of [mat1] and [mat2] according to perm.
323:   Columns of [mat1] have length n, columns of [mat2] have length m
324:  */
325: PetscErrorCode DSPermuteBoth_Private(DS ds,PetscInt istart,PetscInt iend,PetscInt n,PetscInt m,DSMatType mat1,DSMatType mat2,PetscInt *perm)
326: {
327:   PetscInt    i,j,k,p,ld;
328:   PetscScalar *U,*V,rtmp;

330:   ld = ds->ld;
331:   MatDenseGetArray(ds->omat[mat1],&U);
332:   MatDenseGetArray(ds->omat[mat2],&V);
333:   for (i=istart;i<iend;i++) {
334:     p = perm[i];
335:     if (p != i) {
336:       j = i + 1;
337:       while (perm[j] != i) j++;
338:       perm[j] = p; perm[i] = i;
339:       /* swap columns i and j of U */
340:       for (k=0;k<n;k++) {
341:         rtmp = U[k+p*ld]; U[k+p*ld] = U[k+i*ld]; U[k+i*ld] = rtmp;
342:       }
343:       /* swap columns i and j of V */
344:       for (k=0;k<m;k++) {
345:         rtmp = V[k+p*ld]; V[k+p*ld] = V[k+i*ld]; V[k+i*ld] = rtmp;
346:       }
347:     }
348:   }
349:   MatDenseRestoreArray(ds->omat[mat1],&U);
350:   MatDenseRestoreArray(ds->omat[mat2],&V);
351:   return 0;
352: }

354: /*@
355:    DSSetIdentity - Copy the identity (a diagonal matrix with ones) on the
356:    active part of a matrix.

358:    Logically Collective on ds

360:    Input Parameters:
361: +  ds  - the direct solver context
362: -  mat - the matrix to modify

364:    Level: intermediate

366: .seealso: DSGetMat()
367: @*/
368: PetscErrorCode DSSetIdentity(DS ds,DSMatType mat)
369: {
370:   PetscScalar    *A;
371:   PetscInt       i,ld,n,l;

375:   DSCheckValidMat(ds,mat,2);

377:   DSGetDimensions(ds,&n,&l,NULL,NULL);
378:   DSGetLeadingDimension(ds,&ld);
379:   PetscLogEventBegin(DS_Other,ds,0,0,0);
380:   MatDenseGetArray(ds->omat[mat],&A);
381:   PetscArrayzero(A+l*ld,ld*(n-l));
382:   for (i=l;i<n;i++) A[i+i*ld] = 1.0;
383:   MatDenseRestoreArray(ds->omat[mat],&A);
384:   PetscLogEventEnd(DS_Other,ds,0,0,0);
385:   return 0;
386: }

388: /*@C
389:    DSOrthogonalize - Orthogonalize the columns of a matrix.

391:    Logically Collective on ds

393:    Input Parameters:
394: +  ds   - the direct solver context
395: .  mat  - a matrix
396: -  cols - number of columns to orthogonalize (starting from column zero)

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

401:    Level: developer

403: .seealso: DSPseudoOrthogonalize()
404: @*/
405: PetscErrorCode DSOrthogonalize(DS ds,DSMatType mat,PetscInt cols,PetscInt *lindcols)
406: {
407:   PetscInt       n,l,ld;
408:   PetscBLASInt   ld_,rA,cA,info,ltau,lw;
409:   PetscScalar    *A,*tau,*w,saux,dummy;

412:   DSCheckAlloc(ds,1);
414:   DSCheckValidMat(ds,mat,2);

417:   DSGetDimensions(ds,&n,&l,NULL,NULL);
418:   DSGetLeadingDimension(ds,&ld);
419:   n = n - l;
421:   if (n == 0 || cols == 0) return 0;

423:   PetscLogEventBegin(DS_Other,ds,0,0,0);
424:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
425:   MatDenseGetArray(ds->omat[mat],&A);
426:   PetscBLASIntCast(PetscMin(cols,n),&ltau);
427:   PetscBLASIntCast(ld,&ld_);
428:   PetscBLASIntCast(n,&rA);
429:   PetscBLASIntCast(cols,&cA);
430:   lw = -1;
431:   PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,A,&ld_,&dummy,&saux,&lw,&info));
432:   SlepcCheckLapackInfo("geqrf",info);
433:   lw = (PetscBLASInt)PetscRealPart(saux);
434:   DSAllocateWork_Private(ds,lw+ltau,0,0);
435:   tau = ds->work;
436:   w = &tau[ltau];
437:   PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rA,&cA,&A[ld*l+l],&ld_,tau,w,&lw,&info));
438:   SlepcCheckLapackInfo("geqrf",info);
439:   PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&rA,&ltau,&ltau,&A[ld*l+l],&ld_,tau,w,&lw,&info));
440:   SlepcCheckLapackInfo("orgqr",info);
441:   if (lindcols) *lindcols = ltau;
442:   PetscFPTrapPop();
443:   MatDenseRestoreArray(ds->omat[mat],&A);
444:   PetscLogEventEnd(DS_Other,ds,0,0,0);
445:   PetscObjectStateIncrease((PetscObject)ds);
446:   return 0;
447: }

449: /*
450:   Compute C <- a*A*B + b*C, where
451:     ldC, the leading dimension of C,
452:     ldA, the leading dimension of A,
453:     rA, cA, rows and columns of A,
454:     At, if true use the transpose of A instead,
455:     ldB, the leading dimension of B,
456:     rB, cB, rows and columns of B,
457:     Bt, if true use the transpose of B instead
458: */
459: 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)
460: {
461:   PetscInt       tmp;
462:   PetscBLASInt   m, n, k, ldA = _ldA, ldB = _ldB, ldC = _ldC;
463:   const char     *N = "N", *T = "C", *qA = N, *qB = N;

465:   if ((rA == 0) || (cB == 0)) return 0;

470:   /* Transpose if needed */
471:   if (At) tmp = rA, rA = cA, cA = tmp, qA = T;
472:   if (Bt) tmp = rB, rB = cB, cB = tmp, qB = T;

474:   /* Check size */

477:   /* Do stub */
478:   if ((rA == 1) && (cA == 1) && (cB == 1)) {
479:     if (!At && !Bt) *C = *A * *B;
480:     else if (At && !Bt) *C = PetscConj(*A) * *B;
481:     else if (!At && Bt) *C = *A * PetscConj(*B);
482:     else *C = PetscConj(*A) * PetscConj(*B);
483:     m = n = k = 1;
484:   } else {
485:     m = rA; n = cB; k = cA;
486:     PetscCallBLAS("BLASgemm",BLASgemm_(qA,qB,&m,&n,&k,&a,(PetscScalar*)A,&ldA,(PetscScalar*)B,&ldB,&b,C,&ldC));
487:   }

489:   PetscLogFlops(2.0*m*n*k);
490:   return 0;
491: }

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

497:    Logically Collective on ds

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

505:    Output Parameters:
506: +  lindcols - (optional) linearly independent columns of the matrix
507: -  ns   - (optional) the new signature of the vectors

509:    Note:
510:    After the call the matrix satisfies A'*s*A = ns.

512:    Level: developer

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

524:   DSCheckAlloc(ds,1);
526:   DSCheckValidMat(ds,mat,2);
529:   DSGetDimensions(ds,&n,&l,NULL,NULL);
530:   DSGetLeadingDimension(ds,&ld);
531:   n = n - l;
533:   if (n == 0 || cols == 0) return 0;
534:   PetscLogEventBegin(DS_Other,ds,0,0,0);
535:   PetscBLASIntCast(n,&rA_);
536:   PetscBLASIntCast(ld,&ld_);
537:   MatDenseGetArray(ds->omat[mat],&A_);
538:   A = &A_[ld*l+l];
539:   DSAllocateWork_Private(ds,n+cols,ns?0:cols,0);
540:   m = ds->work;
541:   h = &m[n];
542:   ns_ = ns ? ns : ds->rwork;
543:   for (i=0; i<cols; i++) {
544:     /* m <- diag(s)*A[i] */
545:     for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
546:     /* nr_o <- mynorm(A[i]'*m), mynorm(x) = sign(x)*sqrt(|x|) */
547:     SlepcMatDenseMult(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
548:     nr = nr_o = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
549:     for (j=0; j<3 && i>0; j++) {
550:       /* h <- A[0:i-1]'*m */
551:       SlepcMatDenseMult(h,i,0.0,1.0,A,ld,n,i,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
552:       /* h <- diag(ns)*h */
553:       for (k=0; k<i; k++) h[k] *= ns_[k];
554:       /* A[i] <- A[i] - A[0:i-1]*h */
555:       SlepcMatDenseMult(&A[ld*i],ld,1.0,-1.0,A,ld,n,i,PETSC_FALSE,h,i,i,1,PETSC_FALSE);
556:       /* m <- diag(s)*A[i] */
557:       for (k=0; k<n; k++) m[k] = s[k]*A[k+i*ld];
558:       /* nr_o <- mynorm(A[i]'*m) */
559:       SlepcMatDenseMult(&nr0,1,0.0,1.0,&A[ld*i],ld,n,1,PETSC_TRUE,m,n,n,1,PETSC_FALSE);
560:       nr = PetscSign(PetscRealPart(nr0))*PetscSqrtReal(PetscAbsScalar(nr0));
562:       if (PetscAbs(nr) > 0.7*PetscAbs(nr_o)) break;
563:       nr_o = nr;
564:     }
565:     ns_[i] = PetscSign(nr);
566:     /* A[i] <- A[i]/|nr| */
567:     nr_abs = PetscAbs(nr);
568:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&nr_abs,&done,&rA_,&one,A+i*ld,&ld_,&info));
569:     SlepcCheckLapackInfo("lascl",info);
570:   }
571:   MatDenseRestoreArray(ds->omat[mat],&A_);
572:   PetscLogEventEnd(DS_Other,ds,0,0,0);
573:   PetscObjectStateIncrease((PetscObject)ds);
574:   if (lindcols) *lindcols = cols;
575:   return 0;
576: }