Actual source code: svdsolve.c

  1: /*
  2:       SVD routines related to the solution process.

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

  8:    This file is part of SLEPc.

 10:    SLEPc is free software: you can redistribute it and/or modify it under  the
 11:    terms of version 3 of the GNU Lesser General Public License as published by
 12:    the Free Software Foundation.

 14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 17:    more details.

 19:    You  should have received a copy of the GNU Lesser General  Public  License
 20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 22: */

 24: #include <slepc-private/svdimpl.h>   /*I "slepcsvd.h" I*/

 28: /*@
 29:    SVDSolve - Solves the singular value problem.

 31:    Collective on SVD

 33:    Input Parameter:
 34: .  svd - singular value solver context obtained from SVDCreate()

 36:    Options Database Keys:
 37: +  -svd_view - print information about the solver used
 38: -  -svd_view_mat binary - save the matrix to the default binary viewer

 40:    Level: beginner

 42: .seealso: SVDCreate(), SVDSetUp(), SVDDestroy()
 43: @*/
 44: PetscErrorCode SVDSolve(SVD svd)
 45: {
 46:   PetscErrorCode    ierr;
 47:   PetscBool         flg;
 48:   PetscInt          i,*workperm;
 49:   PetscViewer       viewer;
 50:   PetscViewerFormat format;
 51:   PetscErrorCode    (*which_func)(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);

 55:   PetscLogEventBegin(SVD_Solve,svd,0,0,0);

 57:   /* call setup */
 58:   SVDSetUp(svd);
 59:   svd->its = 0;
 60:   svd->nconv = 0;
 61:   for (i=0;i<svd->ncv;i++) {
 62:     svd->sigma[i]  = 0.0;
 63:     svd->errest[i] = 0.0;
 64:   }
 65:   SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv);

 67:   which_func = (svd->which==SVD_LARGEST)? SlepcCompareLargestReal: SlepcCompareSmallestReal;
 68:   DSSetEigenvalueComparison(svd->ds,which_func,NULL);

 70:   (*svd->ops->solve)(svd);

 72:   /* sort singular triplets */
 73:   if (svd->which == SVD_SMALLEST) {
 74:     for (i=0;i<svd->nconv;i++) svd->perm[i] = i;
 75:     PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm);
 76:   } else {
 77:     PetscMalloc(sizeof(PetscInt)*svd->nconv,&workperm);
 78:     for (i=0;i<svd->nconv;i++) workperm[i] = i;
 79:     PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm);
 80:     for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1];
 81:     PetscFree(workperm);
 82:   }

 84:   PetscLogEventEnd(SVD_Solve,svd,0,0,0);

 86:   /* various viewers */
 87:   MatViewFromOptions(svd->OP,((PetscObject)svd)->prefix,"-svd_view_mat");

 89:   PetscOptionsGetViewer(PetscObjectComm((PetscObject)svd),((PetscObject)svd)->prefix,"-svd_view",&viewer,&format,&flg);
 90:   if (flg && !PetscPreLoadingOn) {
 91:     PetscViewerPushFormat(viewer,format);
 92:     SVDView(svd,viewer);
 93:     PetscViewerPopFormat(viewer);
 94:     PetscViewerDestroy(&viewer);
 95:   }

 97:   /* Remove the initial subspace */
 98:   svd->nini = 0;
 99:   return(0);
100: }

104: /*@
105:    SVDGetIterationNumber - Gets the current iteration number. If the
106:    call to SVDSolve() is complete, then it returns the number of iterations
107:    carried out by the solution method.

109:    Not Collective

111:    Input Parameter:
112: .  svd - the singular value solver context

114:    Output Parameter:
115: .  its - number of iterations

117:    Level: intermediate

119:    Notes:
120:       During the i-th iteration this call returns i-1. If SVDSolve() is
121:       complete, then parameter "its" contains either the iteration number at
122:       which convergence was successfully reached, or failure was detected.
123:       Call SVDGetConvergedReason() to determine if the solver converged or
124:       failed and why.

126: @*/
127: PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its)
128: {
132:   *its = svd->its;
133:   return(0);
134: }

138: /*@C
139:    SVDGetConvergedReason - Gets the reason why the SVDSolve() iteration was
140:    stopped.

142:    Not Collective

144:    Input Parameter:
145: .  svd - the singular value solver context

147:    Output Parameter:
148: .  reason - negative value indicates diverged, positive value converged
149:    (see SVDConvergedReason)

151:    Possible values for reason:
152: +  SVD_CONVERGED_TOL - converged up to tolerance
153: .  SVD_DIVERGED_ITS - required more than its to reach convergence
154: -  SVD_DIVERGED_BREAKDOWN - generic breakdown in method

156:    Level: intermediate

158:    Notes: Can only be called after the call to SVDSolve() is complete.

160: .seealso: SVDSetTolerances(), SVDSolve(), SVDConvergedReason
161: @*/
162: PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason)
163: {
167:   *reason = svd->reason;
168:   return(0);
169: }

173: /*@
174:    SVDGetConverged - Gets the number of converged singular values.

176:    Not Collective

178:    Input Parameter:
179: .  svd - the singular value solver context

181:    Output Parameter:
182: .  nconv - number of converged singular values

184:    Note:
185:    This function should be called after SVDSolve() has finished.

187:    Level: beginner

189: @*/
190: PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv)
191: {
195:   *nconv = svd->nconv;
196:   return(0);
197: }

201: /*@
202:    SVDGetSingularTriplet - Gets the i-th triplet of the singular value decomposition
203:    as computed by SVDSolve(). The solution consists in the singular value and its left
204:    and right singular vectors.

206:    Not Collective, but vectors are shared by all processors that share the SVD

208:    Input Parameters:
209: +  svd - singular value solver context
210: -  i   - index of the solution

212:    Output Parameters:
213: +  sigma - singular value
214: .  u     - left singular vector
215: -  v     - right singular vector

217:    Note:
218:    The index i should be a value between 0 and nconv-1 (see SVDGetConverged()).
219:    Both U or V can be NULL if singular vectors are not required.

221:    Level: beginner

223: .seealso: SVDSolve(),  SVDGetConverged()
224: @*/
225: PetscErrorCode SVDGetSingularTriplet(SVD svd,PetscInt i,PetscReal *sigma,Vec u,Vec v)
226: {
228:   PetscReal      norm;
229:   PetscInt       j,M,N;
230:   Vec            w;

236:   if (svd->reason == SVD_CONVERGED_ITERATING) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_WRONGSTATE,"SVDSolve must be called first");
237:   if (i<0 || i>=svd->nconv) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
238:   *sigma = svd->sigma[svd->perm[i]];
239:   MatGetSize(svd->OP,&M,&N);
240:   if (M<N) { w = u; u = v; v = w; }
241:   if (u) {
242:     if (!svd->U) {
243:       VecDuplicateVecs(svd->tl,svd->ncv,&svd->U);
244:       PetscLogObjectParents(svd,svd->ncv,svd->U);
245:       for (j=0;j<svd->nconv;j++) {
246:         SVDMatMult(svd,PETSC_FALSE,svd->V[j],svd->U[j]);
247:         IPOrthogonalize(svd->ip,0,NULL,j,NULL,svd->U,svd->U[j],NULL,&norm,NULL);
248:         VecScale(svd->U[j],1.0/norm);
249:       }
250:     }
251:     VecCopy(svd->U[svd->perm[i]],u);
252:   }
253:   if (v) {
254:     VecCopy(svd->V[svd->perm[i]],v);
255:   }
256:   return(0);
257: }

261: /*@
262:    SVDComputeResidualNorms - Computes the norms of the residual vectors associated with
263:    the i-th computed singular triplet.

265:    Collective on SVD

267:    Input Parameters:
268: +  svd  - the singular value solver context
269: -  i    - the solution index

271:    Output Parameters:
272: +  norm1 - the norm ||A*v-sigma*u||_2 where sigma is the
273:            singular value, u and v are the left and right singular vectors.
274: -  norm2 - the norm ||A^T*u-sigma*v||_2 with the same sigma, u and v

276:    Note:
277:    The index i should be a value between 0 and nconv-1 (see SVDGetConverged()).
278:    Both output parameters can be NULL on input if not needed.

280:    Level: beginner

282: .seealso: SVDSolve(), SVDGetConverged(), SVDComputeRelativeError()
283: @*/
284: PetscErrorCode SVDComputeResidualNorms(SVD svd,PetscInt i,PetscReal *norm1,PetscReal *norm2)
285: {
287:   Vec            u,v,x = NULL,y = NULL;
288:   PetscReal      sigma;
289:   PetscInt       M,N;

294:   if (svd->reason == SVD_CONVERGED_ITERATING) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_WRONGSTATE,"SVDSolve must be called first");
295:   if (i<0 || i>=svd->nconv) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");

297:   MatGetVecs(svd->OP,&v,&u);
298:   SVDGetSingularTriplet(svd,i,&sigma,u,v);
299:   if (norm1) {
300:     VecDuplicate(u,&x);
301:     MatMult(svd->OP,v,x);
302:     VecAXPY(x,-sigma,u);
303:     VecNorm(x,NORM_2,norm1);
304:   }
305:   if (norm2) {
306:     VecDuplicate(v,&y);
307:     if (svd->A && svd->AT) {
308:       MatGetSize(svd->OP,&M,&N);
309:       if (M<N) {
310:         MatMult(svd->A,u,y);
311:       } else {
312:         MatMult(svd->AT,u,y);
313:       }
314:     } else {
315: #if defined(PETSC_USE_COMPLEX)
316:       MatMultHermitianTranspose(svd->OP,u,y);
317: #else
318:       MatMultTranspose(svd->OP,u,y);
319: #endif
320:     }
321:     VecAXPY(y,-sigma,v);
322:     VecNorm(y,NORM_2,norm2);
323:   }

325:   VecDestroy(&v);
326:   VecDestroy(&u);
327:   VecDestroy(&x);
328:   VecDestroy(&y);
329:   return(0);
330: }

334: /*@
335:    SVDComputeRelativeError - Computes the relative error bound associated
336:    with the i-th singular triplet.

338:    Collective on SVD

340:    Input Parameter:
341: +  svd - the singular value solver context
342: -  i   - the solution index

344:    Output Parameter:
345: .  error - the relative error bound, computed as sqrt(n1^2+n2^2)/sigma
346:    where n1 = ||A*v-sigma*u||_2 , n2 = ||A^T*u-sigma*v||_2 , sigma is the singular value,
347:    u and v are the left and right singular vectors.
348:    If sigma is too small the relative error is computed as sqrt(n1^2+n2^2).

350:    Level: beginner

352: .seealso: SVDSolve(), SVDComputeResidualNorms()
353: @*/
354: PetscErrorCode SVDComputeRelativeError(SVD svd,PetscInt i,PetscReal *error)
355: {
357:   PetscReal      sigma,norm1,norm2;

363:   SVDGetSingularTriplet(svd,i,&sigma,NULL,NULL);
364:   SVDComputeResidualNorms(svd,i,&norm1,&norm2);
365:   *error = PetscSqrtReal(norm1*norm1+norm2*norm2);
366:   if (sigma>*error) *error /= sigma;
367:   return(0);
368: }

372: /*@
373:    SVDGetOperationCounters - Gets the total number of matrix vector and dot
374:    products used by the SVD object during the last SVDSolve() call.

376:    Not Collective

378:    Input Parameter:
379: .  svd - SVD context

381:    Output Parameter:
382: +  matvecs - number of matrix vector product operations
383: -  dots    - number of dot product operations

385:    Notes:
386:    These counters are reset to zero at each successive call to SVDSolve().

388:    Level: intermediate

390: @*/
391: PetscErrorCode SVDGetOperationCounters(SVD svd,PetscInt* matvecs,PetscInt* dots)
392: {

397:   if (matvecs) *matvecs = svd->matvecs;
398:   if (dots) {
399:     if (!svd->ip) { SVDGetIP(svd,&svd->ip); }
400:     IPGetOperationCounters(svd->ip,dots);
401:   }
402:   return(0);
403: }