Actual source code: dssvd.c

slepc-3.10.1 2018-10-23
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2018, 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_SVD(DS ds,PetscInt ld)
 15: {

 19:   DSAllocateMat_Private(ds,DS_MAT_A);
 20:   DSAllocateMat_Private(ds,DS_MAT_U);
 21:   DSAllocateMat_Private(ds,DS_MAT_VT);
 22:   DSAllocateMatReal_Private(ds,DS_MAT_T);
 23:   PetscFree(ds->perm);
 24:   PetscMalloc1(ld,&ds->perm);
 25:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
 26:   return(0);
 27: }

 29: /*   0       l           k                 n-1
 30:     -----------------------------------------
 31:     |*       .           .                  |
 32:     |  *     .           .                  |
 33:     |    *   .           .                  |
 34:     |      * .           .                  |
 35:     |        o           o                  |
 36:     |          o         o                  |
 37:     |            o       o                  |
 38:     |              o     o                  |
 39:     |                o   o                  |
 40:     |                  o o                  |
 41:     |                    o x                |
 42:     |                      x x              |
 43:     |                        x x            |
 44:     |                          x x          |
 45:     |                            x x        |
 46:     |                              x x      |
 47:     |                                x x    |
 48:     |                                  x x  |
 49:     |                                    x x|
 50:     |                                      x|
 51:     -----------------------------------------
 52: */

 54: static PetscErrorCode DSSwitchFormat_SVD(DS ds,PetscBool tocompact)
 55: {
 57:   PetscReal      *T = ds->rmat[DS_MAT_T];
 58:   PetscScalar    *A = ds->mat[DS_MAT_A];
 59:   PetscInt       i,m=ds->m,k=ds->k,ld=ds->ld;

 62:   if (!m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
 63:   if (tocompact) { /* switch from dense (arrow) to compact storage */
 64:     PetscMemzero(T,3*ld*sizeof(PetscReal));
 65:     for (i=0;i<k;i++) {
 66:       T[i]    = PetscRealPart(A[i+i*ld]);
 67:       T[i+ld] = PetscRealPart(A[i+k*ld]);
 68:     }
 69:     for (i=k;i<m-1;i++) {
 70:       T[i]    = PetscRealPart(A[i+i*ld]);
 71:       T[i+ld] = PetscRealPart(A[i+(i+1)*ld]);
 72:     }
 73:     T[m-1] = PetscRealPart(A[m-1+(m-1)*ld]);
 74:   } else { /* switch from compact (arrow) to dense storage */
 75:     PetscMemzero(A,ld*ld*sizeof(PetscScalar));
 76:     for (i=0;i<k;i++) {
 77:       A[i+i*ld] = T[i];
 78:       A[i+k*ld] = T[i+ld];
 79:     }
 80:     A[k+k*ld] = T[k];
 81:     for (i=k+1;i<m;i++) {
 82:       A[i+i*ld]   = T[i];
 83:       A[i-1+i*ld] = T[i-1+ld];
 84:     }
 85:   }
 86:   return(0);
 87: }

 89: PetscErrorCode DSView_SVD(DS ds,PetscViewer viewer)
 90: {
 91:   PetscErrorCode    ierr;
 92:   PetscViewerFormat format;
 93:   PetscInt          i,j,r,c;
 94:   PetscReal         value;

 97:   PetscViewerGetFormat(viewer,&format);
 98:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 99:     return(0);
100:   }
101:   if (ds->compact) {
102:     if (!ds->m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
103:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
104:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
105:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->m);
106:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",2*ds->n);
107:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
108:       for (i=0;i<PetscMin(ds->n,ds->m);i++) {
109:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
110:       }
111:       for (i=0;i<PetscMin(ds->n,ds->m)-1;i++) {
112:         r = PetscMax(i+2,ds->k+1);
113:         c = i+1;
114:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",c,r,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
115:       }
116:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
117:     } else {
118:       for (i=0;i<ds->n;i++) {
119:         for (j=0;j<ds->m;j++) {
120:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
121:           else if (i<ds->k && j==ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
122:           else if (i==j+1 && i>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+i-1);
123:           else value = 0.0;
124:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
125:         }
126:         PetscViewerASCIIPrintf(viewer,"\n");
127:       }
128:     }
129:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
130:     PetscViewerFlush(viewer);
131:   } else {
132:     DSViewMat(ds,viewer,DS_MAT_A);
133:   }
134:   if (ds->state>DS_STATE_INTERMEDIATE) {
135:     DSViewMat(ds,viewer,DS_MAT_U);
136:     DSViewMat(ds,viewer,DS_MAT_VT);
137:   }
138:   return(0);
139: }

141: PetscErrorCode DSVectors_SVD(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
142: {
144:   switch (mat) {
145:     case DS_MAT_U:
146:     case DS_MAT_VT:
147:       if (rnorm) *rnorm = 0.0;
148:       break;
149:     default:
150:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
151:   }
152:   return(0);
153: }

155: PetscErrorCode DSSort_SVD(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
156: {
158:   PetscInt       n,l,i,*perm,ld=ds->ld;
159:   PetscScalar    *A;
160:   PetscReal      *d;

163:   if (!ds->sc) return(0);
164:   l = ds->l;
165:   n = PetscMin(ds->n,ds->m);
166:   A = ds->mat[DS_MAT_A];
167:   d = ds->rmat[DS_MAT_T];
168:   perm = ds->perm;
169:   if (!rr) {
170:     DSSortEigenvaluesReal_Private(ds,d,perm);
171:   } else {
172:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
173:   }
174:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
175:   DSPermuteBoth_Private(ds,l,n,DS_MAT_U,DS_MAT_VT,perm);
176:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
177:   if (!ds->compact) {
178:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
179:   }
180:   return(0);
181: }

183: PetscErrorCode DSSolve_SVD_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
184: {
185: #if defined(SLEPC_MISSING_LAPACK_GESDD) || defined(SLEPC_MISSING_LAPACK_BDSDC)
187:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESDD/BDSDC - Lapack routines are unavailable");
188: #else
190:   PetscInt       i;
191:   PetscBLASInt   n1,n2,n3,m2,m3,info,l,n,m,nm,ld,off,lwork;
192:   PetscScalar    *A,*U,*VT,qwork;
193:   PetscReal      *d,*e,*Ur,*VTr;
194: #if defined(PETSC_USE_COMPLEX)
195:   PetscInt       j;
196: #endif

199:   PetscBLASIntCast(ds->n,&n);
200:   PetscBLASIntCast(ds->m,&m);
201:   PetscBLASIntCast(ds->l,&l);
202:   PetscBLASIntCast(ds->ld,&ld);
203:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
204:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
205:   PetscBLASIntCast(m-ds->k-1,&m2);
206:   n3 = n1+n2;
207:   m3 = n1+m2;
208:   off = l+l*ld;
209:   A  = ds->mat[DS_MAT_A];
210:   U  = ds->mat[DS_MAT_U];
211:   VT = ds->mat[DS_MAT_VT];
212:   d  = ds->rmat[DS_MAT_T];
213:   e  = ds->rmat[DS_MAT_T]+ld;
214:   PetscMemzero(U,ld*ld*sizeof(PetscScalar));
215:   for (i=0;i<l;i++) U[i+i*ld] = 1.0;
216:   PetscMemzero(VT,ld*ld*sizeof(PetscScalar));
217:   for (i=0;i<l;i++) VT[i+i*ld] = 1.0;

219:   if (ds->state>DS_STATE_RAW) {
220:     /* solve bidiagonal SVD problem */
221:     for (i=0;i<l;i++) wr[i] = d[i];
222:     DSAllocateWork_Private(ds,0,3*ld*ld+4*ld,8*ld);
223: #if defined(PETSC_USE_COMPLEX)
224:     DSAllocateMatReal_Private(ds,DS_MAT_U);
225:     DSAllocateMatReal_Private(ds,DS_MAT_VT);
226:     Ur  = ds->rmat[DS_MAT_U];
227:     VTr = ds->rmat[DS_MAT_VT];
228: #else
229:     Ur  = U;
230:     VTr = VT;
231: #endif
232:     PetscStackCallBLAS("LAPACKbdsdc",LAPACKbdsdc_("U","I",&n3,d+l,e+l,Ur+off,&ld,VTr+off,&ld,NULL,NULL,ds->rwork,ds->iwork,&info));
233:     SlepcCheckLapackInfo("bdsdc",info);
234: #if defined(PETSC_USE_COMPLEX)
235:     for (i=l;i<n;i++) {
236:       for (j=0;j<n;j++) {
237:         U[i+j*ld] = Ur[i+j*ld];
238:         VT[i+j*ld] = VTr[i+j*ld];
239:       }
240:     }
241: #endif
242:   } else {
243:     /* solve general rectangular SVD problem */
244:     if (ds->compact) { DSSwitchFormat_SVD(ds,PETSC_FALSE); }
245:     for (i=0;i<l;i++) wr[i] = d[i];
246:     nm = PetscMin(n,m);
247:     DSAllocateWork_Private(ds,0,0,8*nm);
248:     lwork = -1;
249: #if defined(PETSC_USE_COMPLEX)
250:     DSAllocateWork_Private(ds,0,5*nm*nm+7*nm,0);
251:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n3,&m3,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,&qwork,&lwork,ds->rwork,ds->iwork,&info));
252: #else
253:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n3,&m3,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,&qwork,&lwork,ds->iwork,&info));
254: #endif
255:     SlepcCheckLapackInfo("gesdd",info);
256:     PetscBLASIntCast((PetscInt)PetscRealPart(qwork),&lwork);
257:     DSAllocateWork_Private(ds,lwork,0,0);
258: #if defined(PETSC_USE_COMPLEX)
259:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n3,&m3,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,ds->work,&lwork,ds->rwork,ds->iwork,&info));
260: #else
261:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n3,&m3,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,ds->work,&lwork,ds->iwork,&info));
262: #endif
263:     SlepcCheckLapackInfo("gesdd",info);
264:   }
265:   for (i=l;i<PetscMin(ds->n,ds->m);i++) wr[i] = d[i];

267:   /* create diagonal matrix as a result */
268:   if (ds->compact) {
269:     PetscMemzero(e,(n-1)*sizeof(PetscReal));
270:   } else {
271:     for (i=l;i<n;i++) {
272:       PetscMemzero(A+l+i*ld,(n-l)*sizeof(PetscScalar));
273:     }
274:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
275:   }
276:   return(0);
277: #endif
278: }

280: PetscErrorCode DSSynchronize_SVD(DS ds,PetscScalar eigr[],PetscScalar eigi[])
281: {
283:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
284:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;

287:   if (ds->compact) kr = 3*ld;
288:   else k = (ds->n-l)*ld;
289:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
290:   if (eigr) k += ds->n-l; 
291:   if (eigi) k += ds->n-l; 
292:   DSAllocateWork_Private(ds,k+kr,0,0);
293:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
294:   PetscMPIIntCast(ds->n-l,&n);
295:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
296:   PetscMPIIntCast(3*ld,&ld3);
297:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
298:   if (!rank) {
299:     if (ds->compact) {
300:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
301:     } else {
302:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
303:     }
304:     if (ds->state>DS_STATE_RAW) {
305:       MPI_Pack(ds->mat[DS_MAT_U]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
306:       MPI_Pack(ds->mat[DS_MAT_VT]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
307:     }
308:     if (eigr) {
309:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
310:     }
311:     if (eigi) {
312:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
313:     }
314:   }
315:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
316:   if (rank) {
317:     if (ds->compact) {
318:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
319:     } else {
320:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
321:     }
322:     if (ds->state>DS_STATE_RAW) {
323:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_U]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
324:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_VT]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
325:     }
326:     if (eigr) {
327:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
328:     }
329:     if (eigi) {
330:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
331:     }
332:   }
333:   return(0);
334: }

336: PetscErrorCode DSMatGetSize_SVD(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
337: {
339:   switch (t) {
340:     case DS_MAT_A:
341:     case DS_MAT_T:
342:       *rows = ds->n;
343:       *cols = ds->m;
344:       break;
345:     case DS_MAT_U:
346:       *rows = ds->n;
347:       *cols = ds->n;
348:       break;
349:     case DS_MAT_VT:
350:       *rows = ds->m;
351:       *cols = ds->m;
352:       break;
353:     default:
354:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid t parameter");
355:   }
356:   return(0);
357: }

359: PETSC_EXTERN PetscErrorCode DSCreate_SVD(DS ds)
360: {
362:   ds->ops->allocate      = DSAllocate_SVD;
363:   ds->ops->view          = DSView_SVD;
364:   ds->ops->vectors       = DSVectors_SVD;
365:   ds->ops->solve[0]      = DSSolve_SVD_DC;
366:   ds->ops->sort          = DSSort_SVD;
367:   ds->ops->synchronize   = DSSynchronize_SVD;
368:   ds->ops->matgetsize    = DSMatGetSize_SVD;
369:   return(0);
370: }