Actual source code: svd.c

petsc-3.8.2 2017-11-09
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  2:  #include <petsc/private/pcimpl.h>
  3:  #include <petscblaslapack.h>

  5: /*
  6:    Private context (data structure) for the SVD preconditioner.
  7: */
  8: typedef struct {
  9:   Vec         diag,work;
 10:   Mat         A,U,Vt;
 11:   PetscInt    nzero;
 12:   PetscReal   zerosing;         /* measure of smallest singular value treated as nonzero */
 13:   PetscInt    essrank;          /* essential rank of operator */
 14:   VecScatter  left2red,right2red;
 15:   Vec         leftred,rightred;
 16:   PetscViewer monitor;
 17: } PC_SVD;

 19: typedef enum {READ=1, WRITE=2, READ_WRITE=3} AccessMode;

 21: /* -------------------------------------------------------------------------- */
 22: /*
 23:    PCSetUp_SVD - Prepares for the use of the SVD preconditioner
 24:                     by setting data structures and options.

 26:    Input Parameter:
 27: .  pc - the preconditioner context

 29:    Application Interface Routine: PCSetUp()

 31:    Notes:
 32:    The interface routine PCSetUp() is not usually called directly by
 33:    the user, but instead is called by PCApply() if necessary.
 34: */
 35: static PetscErrorCode PCSetUp_SVD(PC pc)
 36: {
 37: #if defined(PETSC_MISSING_LAPACK_GESVD)
 38:   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable\nNot able to provide singular value estimates.");
 39: #else
 40:   PC_SVD         *jac = (PC_SVD*)pc->data;
 42:   PetscScalar    *a,*u,*v,*d,*work;
 43:   PetscBLASInt   nb,lwork;
 44:   PetscInt       i,n;
 45:   PetscMPIInt    size;

 48:   MatDestroy(&jac->A);
 49:   MPI_Comm_size(((PetscObject)pc->pmat)->comm,&size);
 50:   if (size > 1) {
 51:     Mat          redmat;
 52:     MatCreateRedundantMatrix(pc->pmat,size,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&redmat);
 53:     MatConvert(redmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
 54:     MatDestroy(&redmat);
 55:   } else {
 56:     MatConvert(pc->pmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
 57:   }
 58:   if (!jac->diag) {    /* assume square matrices */
 59:     MatCreateVecs(jac->A,&jac->diag,&jac->work);
 60:   }
 61:   if (!jac->U) {
 62:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->U);
 63:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->Vt);
 64:   }
 65:   MatGetSize(jac->A,&n,NULL);
 66:   if (!n) {
 67:     PetscInfo(pc,"Matrix has zero rows, skipping svd\n");
 68:     return(0);
 69:   }
 70:   PetscBLASIntCast(n,&nb);
 71:   lwork = 5*nb;
 72:   PetscMalloc1(lwork,&work);
 73:   MatDenseGetArray(jac->A,&a);
 74:   MatDenseGetArray(jac->U,&u);
 75:   MatDenseGetArray(jac->Vt,&v);
 76:   VecGetArray(jac->diag,&d);
 77: #if !defined(PETSC_USE_COMPLEX)
 78:   {
 79:     PetscBLASInt lierr;
 80:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
 81:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,d,u,&nb,v,&nb,work,&lwork,&lierr));
 82:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
 83:     PetscFPTrapPop();
 84:   }
 85: #else
 86:   {
 87:     PetscBLASInt lierr;
 88:     PetscReal    *rwork,*dd;
 89:     PetscMalloc1(5*nb,&rwork);
 90:     PetscMalloc1(nb,&dd);
 91:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
 92:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,dd,u,&nb,v,&nb,work,&lwork,rwork,&lierr));
 93:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
 94:     PetscFree(rwork);
 95:     for (i=0; i<n; i++) d[i] = dd[i];
 96:     PetscFree(dd);
 97:     PetscFPTrapPop();
 98:   }
 99: #endif
100:   MatDenseRestoreArray(jac->A,&a);
101:   MatDenseRestoreArray(jac->U,&u);
102:   MatDenseRestoreArray(jac->Vt,&v);
103:   for (i=n-1; i>=0; i--) if (PetscRealPart(d[i]) > jac->zerosing) break;
104:   jac->nzero = n-1-i;
105:   if (jac->monitor) {
106:     PetscViewerASCIIAddTab(jac->monitor,((PetscObject)pc)->tablevel);
107:     PetscViewerASCIIPrintf(jac->monitor,"    SVD: condition number %14.12e, %D of %D singular values are (nearly) zero\n",(double)PetscRealPart(d[0]/d[n-1]),jac->nzero,n);
108:     if (n >= 10) {              /* print 5 smallest and 5 largest */
109:       PetscViewerASCIIPrintf(jac->monitor,"    SVD: smallest singular values: %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[n-1]),(double)PetscRealPart(d[n-2]),(double)PetscRealPart(d[n-3]),(double)PetscRealPart(d[n-4]),(double)PetscRealPart(d[n-5]));
110:       PetscViewerASCIIPrintf(jac->monitor,"    SVD: largest singular values : %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[4]),(double)PetscRealPart(d[3]),(double)PetscRealPart(d[2]),(double)PetscRealPart(d[1]),(double)PetscRealPart(d[0]));
111:     } else {                    /* print all singular values */
112:       char     buf[256],*p;
113:       size_t   left = sizeof(buf),used;
114:       PetscInt thisline;
115:       for (p=buf,i=n-1,thisline=1; i>=0; i--,thisline++) {
116:         PetscSNPrintfCount(p,left," %14.12e",&used,(double)PetscRealPart(d[i]));
117:         left -= used;
118:         p    += used;
119:         if (thisline > 4 || i==0) {
120:           PetscViewerASCIIPrintf(jac->monitor,"    SVD: singular values:%s\n",buf);
121:           p        = buf;
122:           thisline = 0;
123:         }
124:       }
125:     }
126:     PetscViewerASCIISubtractTab(jac->monitor,((PetscObject)pc)->tablevel);
127:   }
128:   PetscInfo2(pc,"Largest and smallest singular values %14.12e %14.12e\n",(double)PetscRealPart(d[0]),(double)PetscRealPart(d[n-1]));
129:   for (i=0; i<n-jac->nzero; i++) d[i] = 1.0/d[i];
130:   for (; i<n; i++) d[i] = 0.0;
131:   if (jac->essrank > 0) for (i=0; i<n-jac->nzero-jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
132:   PetscInfo1(pc,"Number of zero or nearly singular values %D\n",jac->nzero);
133:   VecRestoreArray(jac->diag,&d);
134: #if defined(foo)
135:   {
136:     PetscViewer viewer;
137:     PetscViewerBinaryOpen(PETSC_COMM_SELF,"joe",FILE_MODE_WRITE,&viewer);
138:     MatView(jac->A,viewer);
139:     MatView(jac->U,viewer);
140:     MatView(jac->Vt,viewer);
141:     VecView(jac->diag,viewer);
142:     PetscViewerDestroy(viewer);
143:   }
144: #endif
145:   PetscFree(work);
146:   return(0);
147: #endif
148: }

150: static PetscErrorCode PCSVDGetVec(PC pc,PCSide side,AccessMode amode,Vec x,Vec *xred)
151: {
152:   PC_SVD         *jac = (PC_SVD*)pc->data;
154:   PetscMPIInt    size;

157:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
158:   *xred = NULL;
159:   switch (side) {
160:   case PC_LEFT:
161:     if (size == 1) *xred = x;
162:     else {
163:       if (!jac->left2red) {VecScatterCreateToAll(x,&jac->left2red,&jac->leftred);}
164:       if (amode & READ) {
165:         VecScatterBegin(jac->left2red,x,jac->leftred,INSERT_VALUES,SCATTER_FORWARD);
166:         VecScatterEnd(jac->left2red,x,jac->leftred,INSERT_VALUES,SCATTER_FORWARD);
167:       }
168:       *xred = jac->leftred;
169:     }
170:     break;
171:   case PC_RIGHT:
172:     if (size == 1) *xred = x;
173:     else {
174:       if (!jac->right2red) {VecScatterCreateToAll(x,&jac->right2red,&jac->rightred);}
175:       if (amode & READ) {
176:         VecScatterBegin(jac->right2red,x,jac->rightred,INSERT_VALUES,SCATTER_FORWARD);
177:         VecScatterEnd(jac->right2red,x,jac->rightred,INSERT_VALUES,SCATTER_FORWARD);
178:       }
179:       *xred = jac->rightred;
180:     }
181:     break;
182:   default: SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Side must be LEFT or RIGHT");
183:   }
184:   return(0);
185: }

187: static PetscErrorCode PCSVDRestoreVec(PC pc,PCSide side,AccessMode amode,Vec x,Vec *xred)
188: {
189:   PC_SVD         *jac = (PC_SVD*)pc->data;
191:   PetscMPIInt    size;

194:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
195:   switch (side) {
196:   case PC_LEFT:
197:     if (size != 1 && amode & WRITE) {
198:       VecScatterBegin(jac->left2red,jac->leftred,x,INSERT_VALUES,SCATTER_REVERSE);
199:       VecScatterEnd(jac->left2red,jac->leftred,x,INSERT_VALUES,SCATTER_REVERSE);
200:     }
201:     break;
202:   case PC_RIGHT:
203:     if (size != 1 && amode & WRITE) {
204:       VecScatterBegin(jac->right2red,jac->rightred,x,INSERT_VALUES,SCATTER_REVERSE);
205:       VecScatterEnd(jac->right2red,jac->rightred,x,INSERT_VALUES,SCATTER_REVERSE);
206:     }
207:     break;
208:   default: SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Side must be LEFT or RIGHT");
209:   }
210:   *xred = NULL;
211:   return(0);
212: }

214: /* -------------------------------------------------------------------------- */
215: /*
216:    PCApply_SVD - Applies the SVD preconditioner to a vector.

218:    Input Parameters:
219: .  pc - the preconditioner context
220: .  x - input vector

222:    Output Parameter:
223: .  y - output vector

225:    Application Interface Routine: PCApply()
226:  */
227: static PetscErrorCode PCApply_SVD(PC pc,Vec x,Vec y)
228: {
229:   PC_SVD         *jac = (PC_SVD*)pc->data;
230:   Vec            work = jac->work,xred,yred;

234:   PCSVDGetVec(pc,PC_RIGHT,READ,x,&xred);
235:   PCSVDGetVec(pc,PC_LEFT,WRITE,y,&yred);
236: #if !defined(PETSC_USE_COMPLEX)
237:   MatMultTranspose(jac->U,xred,work);
238: #else
239:   MatMultHermitianTranspose(jac->U,xred,work);
240: #endif
241:   VecPointwiseMult(work,work,jac->diag);
242: #if !defined(PETSC_USE_COMPLEX)
243:   MatMultTranspose(jac->Vt,work,yred);
244: #else
245:   MatMultHermitianTranspose(jac->Vt,work,yred);
246: #endif
247:   PCSVDRestoreVec(pc,PC_RIGHT,READ,x,&xred);
248:   PCSVDRestoreVec(pc,PC_LEFT,WRITE,y,&yred);
249:   return(0);
250: }

252: static PetscErrorCode PCApplyTranspose_SVD(PC pc,Vec x,Vec y)
253: {
254:   PC_SVD         *jac = (PC_SVD*)pc->data;
255:   Vec            work = jac->work,xred,yred;

259:   PCSVDGetVec(pc,PC_LEFT,READ,x,&xred);
260:   PCSVDGetVec(pc,PC_RIGHT,WRITE,y,&yred);
261: #if !defined(PETSC_USE_COMPLEX)
262:   MatMultTranspose(jac->Vt,work,yred);
263: #else
264:   MatMultHermitianTranspose(jac->Vt,work,yred);
265: #endif
266:   VecPointwiseMult(work,work,jac->diag);
267: #if !defined(PETSC_USE_COMPLEX)
268:   MatMultTranspose(jac->U,xred,work);
269: #else
270:   MatMultHermitianTranspose(jac->U,xred,work);
271: #endif
272:   PCSVDRestoreVec(pc,PC_LEFT,READ,x,&xred);
273:   PCSVDRestoreVec(pc,PC_RIGHT,WRITE,y,&yred);
274:   return(0);
275: }

277: static PetscErrorCode PCReset_SVD(PC pc)
278: {
279:   PC_SVD         *jac = (PC_SVD*)pc->data;

283:   MatDestroy(&jac->A);
284:   MatDestroy(&jac->U);
285:   MatDestroy(&jac->Vt);
286:   VecDestroy(&jac->diag);
287:   VecDestroy(&jac->work);
288:   VecScatterDestroy(&jac->right2red);
289:   VecScatterDestroy(&jac->left2red);
290:   VecDestroy(&jac->rightred);
291:   VecDestroy(&jac->leftred);
292:   return(0);
293: }

295: /* -------------------------------------------------------------------------- */
296: /*
297:    PCDestroy_SVD - Destroys the private context for the SVD preconditioner
298:    that was created with PCCreate_SVD().

300:    Input Parameter:
301: .  pc - the preconditioner context

303:    Application Interface Routine: PCDestroy()
304: */
305: static PetscErrorCode PCDestroy_SVD(PC pc)
306: {
307:   PC_SVD         *jac = (PC_SVD*)pc->data;

311:   PCReset_SVD(pc);
312:   PetscViewerDestroy(&jac->monitor);
313:   PetscFree(pc->data);
314:   return(0);
315: }

317: static PetscErrorCode PCSetFromOptions_SVD(PetscOptionItems *PetscOptionsObject,PC pc)
318: {
320:   PC_SVD         *jac = (PC_SVD*)pc->data;
321:   PetscBool      flg,set;

324:   PetscOptionsHead(PetscOptionsObject,"SVD options");
325:   PetscOptionsReal("-pc_svd_zero_sing","Singular values smaller than this treated as zero","None",jac->zerosing,&jac->zerosing,NULL);
326:   PetscOptionsInt("-pc_svd_ess_rank","Essential rank of operator (0 to use entire operator)","None",jac->essrank,&jac->essrank,NULL);
327:   PetscOptionsBool("-pc_svd_monitor","Monitor the conditioning, and extremal singular values","None",jac->monitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);
328:   if (set) {                    /* Should make PCSVDSetMonitor() */
329:     if (flg && !jac->monitor) {
330:       PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),"stdout",&jac->monitor);
331:     } else if (!flg) {
332:       PetscViewerDestroy(&jac->monitor);
333:     }
334:   }
335:   PetscOptionsTail();
336:   return(0);
337: }

339: static PetscErrorCode PCView_SVD(PC pc,PetscViewer viewer)
340: {
341:   PC_SVD         *svd = (PC_SVD*)pc->data;
343:   PetscBool      iascii;

346:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
347:   if (iascii) {
348:     PetscViewerASCIIPrintf(viewer,"  All singular values smaller than %g treated as zero\n",(double)svd->zerosing);
349:     PetscViewerASCIIPrintf(viewer,"  Provided essential rank of the matrix %D (all other eigenvalues are zeroed)\n",svd->essrank);
350:   }
351:   return(0);
352: }
353: /* -------------------------------------------------------------------------- */
354: /*
355:    PCCreate_SVD - Creates a SVD preconditioner context, PC_SVD,
356:    and sets this as the private data within the generic preconditioning
357:    context, PC, that was created within PCCreate().

359:    Input Parameter:
360: .  pc - the preconditioner context

362:    Application Interface Routine: PCCreate()
363: */

365: /*MC
366:      PCSVD - Use pseudo inverse defined by SVD of operator

368:    Level: advanced

370:   Concepts: SVD

372:   Options Database:
373: -  -pc_svd_zero_sing <rtol> Singular values smaller than this are treated as zero
374: +  -pc_svd_monitor  Print information on the extreme singular values of the operator

376:   Developer Note: This implementation automatically creates a redundant copy of the
377:    matrix on each process and uses a sequential SVD solve. Why does it do this instead
378:    of using the composable PCREDUNDANT object?

380: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC
381: M*/

383: PETSC_EXTERN PetscErrorCode PCCreate_SVD(PC pc)
384: {
385:   PC_SVD         *jac;

389:   /*
390:      Creates the private data structure for this preconditioner and
391:      attach it to the PC object.
392:   */
393:   PetscNewLog(pc,&jac);
394:   jac->zerosing = 1.e-12;
395:   pc->data      = (void*)jac;

397:   /*
398:       Set the pointers for the functions that are provided above.
399:       Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
400:       are called, they will automatically call these functions.  Note we
401:       choose not to provide a couple of these functions since they are
402:       not needed.
403:   */
404:   pc->ops->apply           = PCApply_SVD;
405:   pc->ops->applytranspose  = PCApplyTranspose_SVD;
406:   pc->ops->setup           = PCSetUp_SVD;
407:   pc->ops->reset           = PCReset_SVD;
408:   pc->ops->destroy         = PCDestroy_SVD;
409:   pc->ops->setfromoptions  = PCSetFromOptions_SVD;
410:   pc->ops->view            = PCView_SVD;
411:   pc->ops->applyrichardson = 0;
412:   return(0);
413: }