Actual source code: dssvd.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: */

 11: #include <slepc/private/dsimpl.h>
 12: #include <slepcblaslapack.h>

 14: typedef struct {
 15:   PetscInt m;              /* number of columns */
 16:   PetscInt t;              /* number of rows of V after truncating */
 17: } DS_SVD;

 19: PetscErrorCode DSAllocate_SVD(DS ds,PetscInt ld)
 20: {
 21:   DSAllocateMat_Private(ds,DS_MAT_A);
 22:   DSAllocateMat_Private(ds,DS_MAT_U);
 23:   DSAllocateMat_Private(ds,DS_MAT_V);
 24:   DSAllocateMat_Private(ds,DS_MAT_T);
 25:   PetscFree(ds->perm);
 26:   PetscMalloc1(ld,&ds->perm);
 27:   return 0;
 28: }

 30: /*   0       l           k                 n-1
 31:     -----------------------------------------
 32:     |*       .           .                  |
 33:     |  *     .           .                  |
 34:     |    *   .           .                  |
 35:     |      * .           .                  |
 36:     |        o           o                  |
 37:     |          o         o                  |
 38:     |            o       o                  |
 39:     |              o     o                  |
 40:     |                o   o                  |
 41:     |                  o o                  |
 42:     |                    o x                |
 43:     |                      x x              |
 44:     |                        x x            |
 45:     |                          x x          |
 46:     |                            x x        |
 47:     |                              x x      |
 48:     |                                x x    |
 49:     |                                  x x  |
 50:     |                                    x x|
 51:     |                                      x|
 52:     -----------------------------------------
 53: */

 55: static PetscErrorCode DSSwitchFormat_SVD(DS ds)
 56: {
 57:   DS_SVD         *ctx = (DS_SVD*)ds->data;
 58:   PetscReal      *T;
 59:   PetscScalar    *A;
 60:   PetscInt       i,m=ctx->m,k=ds->k,ld=ds->ld;

 63:   /* switch from compact (arrow) to dense storage */
 64:   MatDenseGetArrayWrite(ds->omat[DS_MAT_A],&A);
 65:   DSGetArrayReal(ds,DS_MAT_T,&T);
 66:   PetscArrayzero(A,ld*ld);
 67:   for (i=0;i<k;i++) {
 68:     A[i+i*ld] = T[i];
 69:     A[i+k*ld] = T[i+ld];
 70:   }
 71:   A[k+k*ld] = T[k];
 72:   for (i=k+1;i<m;i++) {
 73:     A[i+i*ld]   = T[i];
 74:     A[i-1+i*ld] = T[i-1+ld];
 75:   }
 76:   MatDenseRestoreArrayWrite(ds->omat[DS_MAT_A],&A);
 77:   DSRestoreArrayReal(ds,DS_MAT_T,&T);
 78:   return 0;
 79: }

 81: PetscErrorCode DSView_SVD(DS ds,PetscViewer viewer)
 82: {
 83:   DS_SVD            *ctx = (DS_SVD*)ds->data;
 84:   PetscViewerFormat format;
 85:   PetscInt          i,j,r,c,m=ctx->m,rows,cols;
 86:   PetscReal         *T,value;

 88:   PetscViewerGetFormat(viewer,&format);
 89:   if (format == PETSC_VIEWER_ASCII_INFO) return 0;
 90:   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 91:     PetscViewerASCIIPrintf(viewer,"number of columns: %" PetscInt_FMT "\n",m);
 92:     return 0;
 93:   }
 95:   if (ds->compact) {
 96:     DSGetArrayReal(ds,DS_MAT_T,&T);
 97:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
 98:     rows = ds->n;
 99:     cols = ds->extrarow? m+1: m;
100:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
101:       PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,cols);
102:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",2*ds->n);
103:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
104:       for (i=0;i<PetscMin(ds->n,m);i++) PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)T[i]);
105:       for (i=0;i<cols-1;i++) {
106:         r = PetscMax(i+2,ds->k+1);
107:         c = i+1;
108:         PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",c,r,(double)T[i+ds->ld]);
109:       }
110:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
111:     } else {
112:       for (i=0;i<rows;i++) {
113:         for (j=0;j<cols;j++) {
114:           if (i==j) value = T[i];
115:           else if (i<ds->k && j==ds->k) value = T[PetscMin(i,j)+ds->ld];
116:           else if (i+1==j && i>=ds->k) value = T[i+ds->ld];
117:           else value = 0.0;
118:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
119:         }
120:         PetscViewerASCIIPrintf(viewer,"\n");
121:       }
122:     }
123:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
124:     PetscViewerFlush(viewer);
125:     DSRestoreArrayReal(ds,DS_MAT_T,&T);
126:   } else DSViewMat(ds,viewer,DS_MAT_A);
127:   if (ds->state>DS_STATE_INTERMEDIATE) {
128:     DSViewMat(ds,viewer,DS_MAT_U);
129:     DSViewMat(ds,viewer,DS_MAT_V);
130:   }
131:   return 0;
132: }

134: PetscErrorCode DSVectors_SVD(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
135: {
136:   switch (mat) {
137:     case DS_MAT_U:
138:     case DS_MAT_V:
139:       if (rnorm) *rnorm = 0.0;
140:       break;
141:     default:
142:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
143:   }
144:   return 0;
145: }

147: PetscErrorCode DSSort_SVD(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
148: {
149:   DS_SVD         *ctx = (DS_SVD*)ds->data;
150:   PetscInt       n,l,i,*perm,ld=ds->ld;
151:   PetscScalar    *A;
152:   PetscReal      *d;

154:   if (!ds->sc) return 0;
156:   l = ds->l;
157:   n = PetscMin(ds->n,ctx->m);
158:   DSGetArrayReal(ds,DS_MAT_T,&d);
159:   perm = ds->perm;
160:   if (!rr) DSSortEigenvaluesReal_Private(ds,d,perm);
161:   else DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
162:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
163:   DSPermuteBoth_Private(ds,l,n,ds->n,ctx->m,DS_MAT_U,DS_MAT_V,perm);
164:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
165:   if (!ds->compact) {
166:     MatDenseGetArray(ds->omat[DS_MAT_A],&A);
167:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
168:     MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
169:   }
170:   DSRestoreArrayReal(ds,DS_MAT_T,&d);
171:   return 0;
172: }

174: PetscErrorCode DSUpdateExtraRow_SVD(DS ds)
175: {
176:   DS_SVD            *ctx = (DS_SVD*)ds->data;
177:   PetscInt          i;
178:   PetscBLASInt      n=0,m=0,ld,incx=1;
179:   PetscScalar       *A,*x,*y,one=1.0,zero=0.0;
180:   PetscReal         *T,*e,beta;
181:   const PetscScalar *U;

184:   PetscBLASIntCast(ds->n,&n);
185:   PetscBLASIntCast(ctx->m,&m);
186:   PetscBLASIntCast(ds->ld,&ld);
187:   MatDenseGetArrayRead(ds->omat[DS_MAT_U],&U);
188:   if (ds->compact) {
189:     DSGetArrayReal(ds,DS_MAT_T,&T);
190:     e = T+ld;
191:     beta = e[m-1];   /* in compact, we assume all entries are zero except the last one */
192:     for (i=0;i<n;i++) e[i] = PetscRealPart(beta*U[n-1+i*ld]);
193:     ds->k = m;
194:     DSRestoreArrayReal(ds,DS_MAT_T,&T);
195:   } else {
196:     MatDenseGetArray(ds->omat[DS_MAT_A],&A);
197:     DSAllocateWork_Private(ds,2*ld,0,0);
198:     x = ds->work;
199:     y = ds->work+ld;
200:     for (i=0;i<n;i++) x[i] = PetscConj(A[i+m*ld]);
201:     PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,U,&ld,x,&incx,&zero,y,&incx));
202:     for (i=0;i<n;i++) A[i+m*ld] = PetscConj(y[i]);
203:     ds->k = m;
204:     MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
205:   }
206:   MatDenseRestoreArrayRead(ds->omat[DS_MAT_U],&U);
207:   return 0;
208: }

210: PetscErrorCode DSTruncate_SVD(DS ds,PetscInt n,PetscBool trim)
211: {
212:   PetscInt    i,ld=ds->ld,l=ds->l;
213:   PetscScalar *A;
214:   DS_SVD      *ctx = (DS_SVD*)ds->data;

216:   if (!ds->compact && ds->extrarow) MatDenseGetArray(ds->omat[DS_MAT_A],&A);
217:   if (trim) {
218:     if (!ds->compact && ds->extrarow) {   /* clean extra column */
219:       for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
220:     }
221:     ds->l  = 0;
222:     ds->k  = 0;
223:     ds->n  = n;
224:     ctx->m = n;
225:     ds->t  = ds->n;   /* truncated length equal to the new dimension */
226:     ctx->t = ctx->m;  /* must also keep the previous dimension of V */
227:   } else {
228:     if (!ds->compact && ds->extrarow && ds->k==ds->n) {
229:       /* copy entries of extra column to the new position, then clean last row */
230:       for (i=l;i<n;i++) A[i+n*ld] = A[i+ctx->m*ld];
231:       for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
232:     }
233:     ds->k  = (ds->extrarow)? n: 0;
234:     ds->t  = ds->n;   /* truncated length equal to previous dimension */
235:     ctx->t = ctx->m;  /* must also keep the previous dimension of V */
236:     ds->n  = n;
237:     ctx->m = n;
238:   }
239:   if (!ds->compact && ds->extrarow) MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
240:   return 0;
241: }

243: PetscErrorCode DSSolve_SVD_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
244: {
245:   DS_SVD         *ctx = (DS_SVD*)ds->data;
246:   PetscInt       i,j;
247:   PetscBLASInt   n1,m1,info,l = 0,n = 0,m = 0,nm,ld,off,lwork;
248:   PetscScalar    *A,*U,*V,*W,qwork;
249:   PetscReal      *d,*e,*Ur,*Vr;

252:   PetscBLASIntCast(ds->n,&n);
253:   PetscBLASIntCast(ctx->m,&m);
254:   PetscBLASIntCast(ds->l,&l);
255:   PetscBLASIntCast(ds->ld,&ld);
256:   n1 = n-l;     /* n1 = size of leading block, excl. locked + size of trailing block */
257:   m1 = m-l;
258:   off = l+l*ld;
259:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
260:   MatDenseGetArrayWrite(ds->omat[DS_MAT_U],&U);
261:   MatDenseGetArrayWrite(ds->omat[DS_MAT_V],&V);
262:   DSGetArrayReal(ds,DS_MAT_T,&d);
263:   e = d+ld;
264:   PetscArrayzero(U,ld*ld);
265:   for (i=0;i<l;i++) U[i+i*ld] = 1.0;
266:   PetscArrayzero(V,ld*ld);
267:   for (i=0;i<l;i++) V[i+i*ld] = 1.0;

269:   if (ds->state>DS_STATE_RAW) {
270:     /* solve bidiagonal SVD problem */
271:     for (i=0;i<l;i++) wr[i] = d[i];
272: #if defined(PETSC_USE_COMPLEX)
273:     DSAllocateWork_Private(ds,0,3*n1*n1+4*n1+2*ld*ld,8*n1);
274:     Ur = ds->rwork+3*n1*n1+4*n1;
275:     Vr = ds->rwork+3*n1*n1+4*n1+ld*ld;
276: #else
277:     DSAllocateWork_Private(ds,0,3*n1*n1+4*n1+ld*ld,8*n1);
278:     Ur = U;
279:     Vr = ds->rwork+3*n1*n1+4*n1;
280: #endif
281:     PetscCallBLAS("LAPACKbdsdc",LAPACKbdsdc_("U","I",&n1,d+l,e+l,Ur+off,&ld,Vr+off,&ld,NULL,NULL,ds->rwork,ds->iwork,&info));
282:     SlepcCheckLapackInfo("bdsdc",info);
283:     for (i=l;i<n;i++) {
284:       for (j=l;j<n;j++) {
285: #if defined(PETSC_USE_COMPLEX)
286:         U[i+j*ld] = Ur[i+j*ld];
287: #endif
288:         V[i+j*ld] = PetscConj(Vr[j+i*ld]);  /* transpose VT returned by Lapack */
289:       }
290:     }
291:   } else {
292:     /* solve general rectangular SVD problem */
293:     DSAllocateMat_Private(ds,DS_MAT_W);
294:     MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&W);
295:     if (ds->compact) DSSwitchFormat_SVD(ds);
296:     for (i=0;i<l;i++) wr[i] = d[i];
297:     nm = PetscMin(n,m);
298:     DSAllocateWork_Private(ds,0,0,8*nm);
299:     lwork = -1;
300: #if defined(PETSC_USE_COMPLEX)
301:     DSAllocateWork_Private(ds,0,5*nm*nm+7*nm,0);
302:     PetscCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,W+off,&ld,&qwork,&lwork,ds->rwork,ds->iwork,&info));
303: #else
304:     PetscCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,W+off,&ld,&qwork,&lwork,ds->iwork,&info));
305: #endif
306:     SlepcCheckLapackInfo("gesdd",info);
307:     PetscBLASIntCast((PetscInt)PetscRealPart(qwork),&lwork);
308:     DSAllocateWork_Private(ds,lwork,0,0);
309: #if defined(PETSC_USE_COMPLEX)
310:     PetscCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,W+off,&ld,ds->work,&lwork,ds->rwork,ds->iwork,&info));
311: #else
312:     PetscCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,W+off,&ld,ds->work,&lwork,ds->iwork,&info));
313: #endif
314:     SlepcCheckLapackInfo("gesdd",info);
315:     for (i=l;i<m;i++) {
316:       for (j=l;j<m;j++) V[i+j*ld] = PetscConj(W[j+i*ld]);  /* transpose VT returned by Lapack */
317:     }
318:     MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&W);
319:   }
320:   for (i=l;i<PetscMin(ds->n,ctx->m);i++) wr[i] = d[i];

322:   /* create diagonal matrix as a result */
323:   if (ds->compact) PetscArrayzero(e,n-1);
324:   else {
325:     for (i=l;i<m;i++) PetscArrayzero(A+l+i*ld,n-l);
326:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
327:   }
328:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
329:   MatDenseRestoreArrayWrite(ds->omat[DS_MAT_U],&U);
330:   MatDenseRestoreArrayWrite(ds->omat[DS_MAT_V],&V);
331:   DSRestoreArrayReal(ds,DS_MAT_T,&d);
332:   return 0;
333: }

335: #if !defined(PETSC_HAVE_MPIUNI)
336: PetscErrorCode DSSynchronize_SVD(DS ds,PetscScalar eigr[],PetscScalar eigi[])
337: {
338:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
339:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;
340:   PetscScalar    *A,*U,*V;
341:   PetscReal      *T;

343:   if (ds->compact) kr = 3*ld;
344:   else k = (ds->n-l)*ld;
345:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
346:   if (eigr) k += ds->n-l;
347:   DSAllocateWork_Private(ds,k+kr,0,0);
348:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
349:   PetscMPIIntCast(ds->n-l,&n);
350:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
351:   PetscMPIIntCast(3*ld,&ld3);
352:   if (ds->compact) DSGetArrayReal(ds,DS_MAT_T,&T);
353:   else MatDenseGetArray(ds->omat[DS_MAT_A],&A);
354:   if (ds->state>DS_STATE_RAW) {
355:     MatDenseGetArray(ds->omat[DS_MAT_U],&U);
356:     MatDenseGetArray(ds->omat[DS_MAT_V],&V);
357:   }
358:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
359:   if (!rank) {
360:     if (ds->compact) MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
361:     else MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
362:     if (ds->state>DS_STATE_RAW) {
363:       MPI_Pack(U+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
364:       MPI_Pack(V+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
365:     }
366:     if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
367:   }
368:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
369:   if (rank) {
370:     if (ds->compact) MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
371:     else MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
372:     if (ds->state>DS_STATE_RAW) {
373:       MPI_Unpack(ds->work,size,&off,U+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
374:       MPI_Unpack(ds->work,size,&off,V+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
375:     }
376:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
377:   }
378:   if (ds->compact) DSRestoreArrayReal(ds,DS_MAT_T,&T);
379:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
380:   if (ds->state>DS_STATE_RAW) {
381:     MatDenseRestoreArray(ds->omat[DS_MAT_U],&U);
382:     MatDenseRestoreArray(ds->omat[DS_MAT_V],&V);
383:   }
384:   return 0;
385: }
386: #endif

388: PetscErrorCode DSMatGetSize_SVD(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
389: {
390:   DS_SVD *ctx = (DS_SVD*)ds->data;

393:   switch (t) {
394:     case DS_MAT_A:
395:       *rows = ds->n;
396:       *cols = ds->extrarow? ctx->m+1: ctx->m;
397:       break;
398:     case DS_MAT_T:
399:       *rows = ds->n;
400:       *cols = PetscDefined(USE_COMPLEX)? 2: 3;
401:       break;
402:     case DS_MAT_U:
403:       *rows = ds->state==DS_STATE_TRUNCATED? ds->t: ds->n;
404:       *cols = ds->n;
405:       break;
406:     case DS_MAT_V:
407:       *rows = ds->state==DS_STATE_TRUNCATED? ctx->t: ctx->m;
408:       *cols = ctx->m;
409:       break;
410:     default:
411:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid t parameter");
412:   }
413:   return 0;
414: }

416: static PetscErrorCode DSSVDSetDimensions_SVD(DS ds,PetscInt m)
417: {
418:   DS_SVD *ctx = (DS_SVD*)ds->data;

420:   DSCheckAlloc(ds,1);
421:   if (m==PETSC_DECIDE || m==PETSC_DEFAULT) {
422:     ctx->m = ds->ld;
423:   } else {
425:     ctx->m = m;
426:   }
427:   return 0;
428: }

430: /*@
431:    DSSVDSetDimensions - Sets the number of columns for a DSSVD.

433:    Logically Collective on ds

435:    Input Parameters:
436: +  ds - the direct solver context
437: -  m  - the number of columns

439:    Notes:
440:    This call is complementary to DSSetDimensions(), to provide a dimension
441:    that is specific to this DS type.

443:    Level: intermediate

445: .seealso: DSSVDGetDimensions(), DSSetDimensions()
446: @*/
447: PetscErrorCode DSSVDSetDimensions(DS ds,PetscInt m)
448: {
451:   PetscTryMethod(ds,"DSSVDSetDimensions_C",(DS,PetscInt),(ds,m));
452:   return 0;
453: }

455: static PetscErrorCode DSSVDGetDimensions_SVD(DS ds,PetscInt *m)
456: {
457:   DS_SVD *ctx = (DS_SVD*)ds->data;

459:   *m = ctx->m;
460:   return 0;
461: }

463: /*@
464:    DSSVDGetDimensions - Returns the number of columns for a DSSVD.

466:    Not collective

468:    Input Parameter:
469: .  ds - the direct solver context

471:    Output Parameters:
472: .  m - the number of columns

474:    Level: intermediate

476: .seealso: DSSVDSetDimensions()
477: @*/
478: PetscErrorCode DSSVDGetDimensions(DS ds,PetscInt *m)
479: {
482:   PetscUseMethod(ds,"DSSVDGetDimensions_C",(DS,PetscInt*),(ds,m));
483:   return 0;
484: }

486: PetscErrorCode DSDestroy_SVD(DS ds)
487: {
488:   PetscFree(ds->data);
489:   PetscObjectComposeFunction((PetscObject)ds,"DSSVDSetDimensions_C",NULL);
490:   PetscObjectComposeFunction((PetscObject)ds,"DSSVDGetDimensions_C",NULL);
491:   return 0;
492: }

494: /*MC
495:    DSSVD - Dense Singular Value Decomposition.

497:    Level: beginner

499:    Notes:
500:    The problem is expressed as A = U*Sigma*V', where A is rectangular in
501:    general, with n rows and m columns. Sigma is a diagonal matrix whose diagonal
502:    elements are the arguments of DSSolve(). After solve, A is overwritten
503:    with Sigma.

505:    The orthogonal (or unitary) matrices of left and right singular vectors, U
506:    and V, have size n and m, respectively. The number of columns m must
507:    be specified via DSSVDSetDimensions().

509:    If the DS object is in the intermediate state, A is assumed to be in upper
510:    bidiagonal form (possibly with an arrow) and is stored in compact format
511:    on matrix T. Otherwise, no particular structure is assumed. The compact
512:    storage is implemented for the square case only, m=n. The extra row should
513:    be interpreted in this case as an extra column.

515:    Used DS matrices:
516: +  DS_MAT_A - problem matrix
517: -  DS_MAT_T - upper bidiagonal matrix

519:    Implemented methods:
520: .  0 - Divide and Conquer (_bdsdc or _gesdd)

522: .seealso: DSCreate(), DSSetType(), DSType, DSSVDSetDimensions()
523: M*/
524: SLEPC_EXTERN PetscErrorCode DSCreate_SVD(DS ds)
525: {
526:   DS_SVD         *ctx;

528:   PetscNew(&ctx);
529:   ds->data = (void*)ctx;

531:   ds->ops->allocate      = DSAllocate_SVD;
532:   ds->ops->view          = DSView_SVD;
533:   ds->ops->vectors       = DSVectors_SVD;
534:   ds->ops->solve[0]      = DSSolve_SVD_DC;
535:   ds->ops->sort          = DSSort_SVD;
536: #if !defined(PETSC_HAVE_MPIUNI)
537:   ds->ops->synchronize   = DSSynchronize_SVD;
538: #endif
539:   ds->ops->truncate      = DSTruncate_SVD;
540:   ds->ops->update        = DSUpdateExtraRow_SVD;
541:   ds->ops->destroy       = DSDestroy_SVD;
542:   ds->ops->matgetsize    = DSMatGetSize_SVD;
543:   PetscObjectComposeFunction((PetscObject)ds,"DSSVDSetDimensions_C",DSSVDSetDimensions_SVD);
544:   PetscObjectComposeFunction((PetscObject)ds,"DSSVDGetDimensions_C",DSSVDGetDimensions_SVD);
545:   return 0;
546: }