Date: 2015-09-03T15:05:19+00:00

Actual source code: svdsolve.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:       SVD routines related to the solution process.

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2015, 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: PetscErrorCode SVDComputeVectors(SVD svd)
     29: {
     31:   Vec            tl,uj,vj;
     32:   PetscInt       j,oldsize;
     33:   PetscReal      norm;

     36:   SVDCheckSolved(svd,1);
     37:   switch (svd->state) {
     38:   case SVD_STATE_SOLVED:
     39:     /* generate left singular vectors on U */
     40:     if (!svd->U) { SVDGetBV(svd,NULL,&svd->U); }
     41:     BVGetSizes(svd->U,NULL,NULL,&oldsize);
     42:     if (!oldsize) {
     43:       SVDMatCreateVecs(svd,NULL,&tl);
     44:       BVSetSizesFromVec(svd->U,tl,svd->ncv);
     45:       VecDestroy(&tl);
     46:     }
     47:     for (j=0;j<svd->nconv;j++) {
     48:       BVGetColumn(svd->V,j,&vj);
     49:       BVGetColumn(svd->U,j,&uj);
     50:       SVDMatMult(svd,PETSC_FALSE,vj,uj);
     51:       BVRestoreColumn(svd->V,j,&vj);
     52:       BVRestoreColumn(svd->U,j,&uj);
     53:       BVOrthogonalizeColumn(svd->U,j,NULL,&norm,NULL);
     54:       BVScaleColumn(svd->U,j,1.0/norm);
     55:     }
     56:     break;
     57:   default:
     58:     break;
     59:   }
     60:   svd->state = SVD_STATE_VECTORS;
     61:   return(0);
     62: }

     66: /*@
     67:    SVDSolve - Solves the singular value problem.

     69:    Collective on SVD

     71:    Input Parameter:
     72: .  svd - singular value solver context obtained from SVDCreate()

     74:    Options Database Keys:
     75: +  -svd_view - print information about the solver used
     76: .  -svd_view_mat binary - save the matrix to the default binary viewer
     77: .  -svd_view_vectors binary - save the computed singular vectors to the default binary viewer
     78: .  -svd_view_values - print computed singular values
     79: .  -svd_converged_reason - print reason for convergence, and number of iterations
     80: .  -svd_error_absolute - print absolute errors of each singular triplet
     81: -  -svd_error_relative - print relative errors of each singular triplet

     83:    Level: beginner

     85: .seealso: SVDCreate(), SVDSetUp(), SVDDestroy()
     86: @*/
     87: PetscErrorCode SVDSolve(SVD svd)
     88: {
     90:   PetscInt       i,*workperm;

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

     96:   /* call setup */
     97:   SVDSetUp(svd);
     98:   svd->its = 0;
     99:   svd->nconv = 0;
    100:   for (i=0;i<svd->ncv;i++) {
    101:     svd->sigma[i]  = 0.0;
    102:     svd->errest[i] = 0.0;
    103:     svd->perm[i]   = i;
    104:   }
    105:   SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv);
    106:   SVDViewFromOptions(svd,NULL,"-svd_view_pre");

    108:   (*svd->ops->solve)(svd);
    109:   svd->state = (svd->leftbasis)? SVD_STATE_VECTORS: SVD_STATE_SOLVED;

    111:   /* sort singular triplets */
    112:   if (svd->which == SVD_SMALLEST) {
    113:     PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm);
    114:   } else {
    115:     PetscMalloc(sizeof(PetscInt)*svd->nconv,&workperm);
    116:     for (i=0;i<svd->nconv;i++) workperm[i] = i;
    117:     PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm);
    118:     for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1];
    119:     PetscFree(workperm);
    120:   }
    121:   PetscLogEventEnd(SVD_Solve,svd,0,0,0);

    123:   /* various viewers */
    124:   SVDViewFromOptions(svd,NULL,"-svd_view");
    125:   SVDReasonViewFromOptions(svd);
    126:   SVDErrorViewFromOptions(svd);
    127:   SVDValuesViewFromOptions(svd);
    128:   SVDVectorsViewFromOptions(svd);
    129:   MatViewFromOptions(svd->OP,(PetscObject)svd,"-svd_view_mat");

    131:   /* Remove the initial subspaces */
    132:   svd->nini = 0;
    133:   svd->ninil = 0;
    134:   return(0);
    135: }

    139: /*@
    140:    SVDGetIterationNumber - Gets the current iteration number. If the
    141:    call to SVDSolve() is complete, then it returns the number of iterations
    142:    carried out by the solution method.

    144:    Not Collective

    146:    Input Parameter:
    147: .  svd - the singular value solver context

    149:    Output Parameter:
    150: .  its - number of iterations

    152:    Level: intermediate

    154:    Note:
    155:    During the i-th iteration this call returns i-1. If SVDSolve() is
    156:    complete, then parameter "its" contains either the iteration number at
    157:    which convergence was successfully reached, or failure was detected.
    158:    Call SVDGetConvergedReason() to determine if the solver converged or
    159:    failed and why.

    161: .seealso: SVDGetConvergedReason(), SVDSetTolerances()
    162: @*/
    163: PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its)
    164: {
    168:   *its = svd->its;
    169:   return(0);
    170: }

    174: /*@
    175:    SVDGetConvergedReason - Gets the reason why the SVDSolve() iteration was
    176:    stopped.

    178:    Not Collective

    180:    Input Parameter:
    181: .  svd - the singular value solver context

    183:    Output Parameter:
    184: .  reason - negative value indicates diverged, positive value converged
    185:    (see SVDConvergedReason)

    187:    Possible values for reason:
    188: +  SVD_CONVERGED_TOL - converged up to tolerance
    189: .  SVD_DIVERGED_ITS - required more than its to reach convergence
    190: -  SVD_DIVERGED_BREAKDOWN - generic breakdown in method

    192:    Level: intermediate

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

    196: .seealso: SVDSetTolerances(), SVDSolve(), SVDConvergedReason
    197: @*/
    198: PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason)
    199: {
    203:   SVDCheckSolved(svd,1);
    204:   *reason = svd->reason;
    205:   return(0);
    206: }

    210: /*@
    211:    SVDGetConverged - Gets the number of converged singular values.

    213:    Not Collective

    215:    Input Parameter:
    216: .  svd - the singular value solver context

    218:    Output Parameter:
    219: .  nconv - number of converged singular values

    221:    Note:
    222:    This function should be called after SVDSolve() has finished.

    224:    Level: beginner

    226: @*/
    227: PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv)
    228: {
    232:   SVDCheckSolved(svd,1);
    233:   *nconv = svd->nconv;
    234:   return(0);
    235: }

    239: /*@
    240:    SVDGetSingularTriplet - Gets the i-th triplet of the singular value decomposition
    241:    as computed by SVDSolve(). The solution consists in the singular value and its left
    242:    and right singular vectors.

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

    246:    Input Parameters:
    247: +  svd - singular value solver context
    248: -  i   - index of the solution

    250:    Output Parameters:
    251: +  sigma - singular value
    252: .  u     - left singular vector
    253: -  v     - right singular vector

    255:    Note:
    256:    Both U or V can be NULL if singular vectors are not required.
    257:    Otherwise, the caller must provide valid Vec objects, i.e.,
    258:    they must be created by the calling program with e.g. MatCreateVecs().

    260:    The index i should be a value between 0 and nconv-1 (see SVDGetConverged()).
    261:    Singular triplets are indexed according to the ordering criterion established
    262:    with SVDSetWhichSingularTriplets().

    264:    Level: beginner

    266: .seealso: SVDSolve(), SVDGetConverged(), SVDSetWhichSingularTriplets()
    267: @*/
    268: PetscErrorCode SVDGetSingularTriplet(SVD svd,PetscInt i,PetscReal *sigma,Vec u,Vec v)
    269: {
    271:   PetscInt       M,N;
    272:   Vec            w;

    277:   SVDCheckSolved(svd,1);
    280:   if (i<0 || i>=svd->nconv) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
    281:   *sigma = svd->sigma[svd->perm[i]];
    282:   MatGetSize(svd->OP,&M,&N);
    283:   if (M<N) { w = u; u = v; v = w; }
    284:   if (u) {
    285:     SVDComputeVectors(svd);
    286:     BVCopyVec(svd->U,svd->perm[i],u);
    287:   }
    288:   if (v) {
    289:     BVCopyVec(svd->V,svd->perm[i],v);
    290:   }
    291:   return(0);
    292: }

    296: /*
    297:    SVDComputeResidualNorms_Private - Computes the norms of the left and
    298:    right residuals associated with the i-th computed singular triplet.
    299: @*/
    300: static PetscErrorCode SVDComputeResidualNorms_Private(SVD svd,PetscInt i,PetscReal *norm1,PetscReal *norm2)
    301: {
    303:   Vec            u,v,x = NULL,y = NULL;
    304:   PetscReal      sigma;
    305:   PetscInt       M,N;

    308:   MatCreateVecs(svd->OP,&v,&u);
    309:   SVDGetSingularTriplet(svd,i,&sigma,u,v);
    310:   /* norm1 = ||A*v-sigma*u||_2 */
    311:   if (norm1) {
    312:     VecDuplicate(u,&x);
    313:     MatMult(svd->OP,v,x);
    314:     VecAXPY(x,-sigma,u);
    315:     VecNorm(x,NORM_2,norm1);
    316:   }
    317:   /* norm2 = ||A^T*u-sigma*v||_2 */
    318:   if (norm2) {
    319:     VecDuplicate(v,&y);
    320:     if (svd->A && svd->AT) {
    321:       MatGetSize(svd->OP,&M,&N);
    322:       if (M<N) {
    323:         MatMult(svd->A,u,y);
    324:       } else {
    325:         MatMult(svd->AT,u,y);
    326:       }
    327:     } else {
    328: #if defined(PETSC_USE_COMPLEX)
    329:       MatMultHermitianTranspose(svd->OP,u,y);
    330: #else
    331:       MatMultTranspose(svd->OP,u,y);
    332: #endif
    333:     }
    334:     VecAXPY(y,-sigma,v);
    335:     VecNorm(y,NORM_2,norm2);
    336:   }

    338:   VecDestroy(&v);
    339:   VecDestroy(&u);
    340:   VecDestroy(&x);
    341:   VecDestroy(&y);
    342:   return(0);
    343: }

    347: /*@
    348:    SVDComputeError - Computes the error (based on the residual norm) associated
    349:    with the i-th singular triplet.

    351:    Collective on SVD

    353:    Input Parameter:
    354: +  svd  - the singular value solver context
    355: .  i    - the solution index
    356: -  type - the type of error to compute

    358:    Output Parameter:
    359: .  error - the error

    361:    Notes:
    362:    The error can be computed in various ways, all of them based on the residual
    363:    norm obtained as sqrt(n1^2+n2^2) with n1 = ||A*v-sigma*u||_2 and
    364:    n2 = ||A^T*u-sigma*v||_2, where sigma is the singular value, u is the left
    365:    singular vector and v is the right singular vector.

    367:    Level: beginner

    369: .seealso: SVDErrorType, SVDSolve()
    370: @*/
    371: PetscErrorCode SVDComputeError(SVD svd,PetscInt i,SVDErrorType type,PetscReal *error)
    372: {
    374:   PetscReal      sigma,norm1,norm2;

    381:   SVDCheckSolved(svd,1);
    382:   SVDGetSingularTriplet(svd,i,&sigma,NULL,NULL);
    383:   SVDComputeResidualNorms_Private(svd,i,&norm1,&norm2);
    384:   *error = PetscSqrtReal(norm1*norm1+norm2*norm2);
    385:   switch (type) {
    386:     case SVD_ERROR_ABSOLUTE:
    387:       break;
    388:     case SVD_ERROR_RELATIVE:
    389:       *error /= sigma;
    390:       break;
    391:     default:
    392:       SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
    393:   }
    394:   return(0);
    395: }