Date: 2022-10-01T06:40:12+00:00

Actual source code: rsvd.c
slepc-3.18.0 2022-10-01
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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: */
     10: /*
     11:    SLEPc singular value solver: "randomized"

     13:    Method: RSVD

     15:    Algorithm:

     17:        Randomized singular value decomposition.

     19:    References:

     21:        [1] N. Halko, P.-G. Martinsson, and J. A. Tropp, "Finding
     22:            structure with randomness: Probabilistic algorithms for
     23:            constructing approximate matrix decompositions", SIAM Rev.,
     24:            53(2):217-288, 2011.
     25: */

     27: #include <slepc/private/svdimpl.h>

     29: PetscErrorCode SVDSetUp_Randomized(SVD svd)
     30: {
     31:   PetscInt       N;

     33:   SVDCheckStandard(svd);
     34:   SVDCheckDefinite(svd);
     36:   MatGetSize(svd->A,NULL,&N);
     37:   SVDSetDimensions_Default(svd);
     39:   if (svd->max_it==PETSC_DEFAULT) svd->max_it = PetscMax(N/svd->ncv,100);
     40:   svd->leftbasis = PETSC_TRUE;
     41:   svd->mpd = svd->ncv;
     42:   SVDAllocateSolution(svd,0);
     43:   DSSetType(svd->ds,DSSVD);
     44:   DSAllocate(svd->ds,svd->ncv);
     45:   SVDSetWorkVecs(svd,1,1);
     46:   return 0;
     47: }

     49: static PetscErrorCode SVDRandomizedResidualNorm(SVD svd,PetscInt i,PetscScalar sigma,PetscReal *res)
     50: {
     51:   PetscReal      norm1,norm2;
     52:   Vec            u,v,wu,wv;

     54:   *res = 1.0;
     55:   if (svd->conv!=SVD_CONV_MAXIT) {
     56:     wu = svd->swapped? svd->workr[0]: svd->workl[0];
     57:     wv = svd->swapped? svd->workl[0]: svd->workr[0];
     58:     BVGetColumn(svd->V,i,&v);
     59:     BVGetColumn(svd->U,i,&u);
     60:     /* norm1 = ||A*v-sigma*u||_2 */
     61:     MatMult(svd->A,v,wu);
     62:     VecAXPY(wu,-sigma,u);
     63:     VecNorm(wu,NORM_2,&norm1);
     64:     /* norm2 = ||A^T*u-sigma*v||_2 */
     65:     MatMult(svd->AT,u,wv);
     66:     VecAXPY(wv,-sigma,v);
     67:     VecNorm(wv,NORM_2,&norm2);
     68:     BVRestoreColumn(svd->V,i,&v);
     69:     BVRestoreColumn(svd->U,i,&u);
     70:     *res = SlepcAbs(norm1,norm2);
     71:   }
     72:   return 0;
     73: }

     75: /* If A is a virtual Hermitian transpose, then BVMatMult will fail if PRODUCT_AhB is not implemented */
     76: static PetscErrorCode BlockMatMult(BV V,Mat A,BV Y,Mat AT)
     77: {
     78:   if (!PetscDefined(USE_COMPLEX)) BVMatMult(V,A,Y);
     79:   else {
     80:     PetscBool flg=PETSC_FALSE;
     81:     PetscObjectTypeCompare((PetscObject)A,MATHERMITIANTRANSPOSEVIRTUAL,&flg);
     82:     if (flg) BVMatMultHermitianTranspose(V,AT,Y);
     83:     else BVMatMult(V,A,Y);
     84:   }
     85:   return 0;
     86: }

     88: PetscErrorCode SVDSolve_Randomized(SVD svd)
     89: {
     90:   PetscScalar    *w;
     91:   PetscReal      res=1.0;
     92:   PetscInt       i,k=0;
     93:   Mat            A,U,V;

     95:   /* Form random matrix, G. Complete the initial basis with random vectors */
     96:   BVSetActiveColumns(svd->V,svd->nini,svd->ncv);
     97:   BVSetRandomNormal(svd->V);
     98:   PetscCalloc1(svd->ncv,&w);

    100:   /* Subspace Iteration */
    101:   do {
    102:     svd->its++;
    103:     BVSetActiveColumns(svd->V,svd->nconv,svd->ncv);
    104:     BVSetActiveColumns(svd->U,svd->nconv,svd->ncv);
    105:     /* Form AG */
    106:     BlockMatMult(svd->V,svd->A,svd->U,svd->AT);
    107:     /* Orthogonalization Q=qr(AG)*/
    108:     BVOrthogonalize(svd->U,NULL);
    109:     /* Form B^*= AQ */
    110:     BlockMatMult(svd->U,svd->AT,svd->V,svd->A);

    112:     DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv);
    113:     DSSVDSetDimensions(svd->ds,svd->ncv);
    114:     DSGetMat(svd->ds,DS_MAT_A,&A);
    115:     MatZeroEntries(A);
    116:     BVOrthogonalize(svd->V,A);
    117:     DSRestoreMat(svd->ds,DS_MAT_A,&A);
    118:     DSSetState(svd->ds,DS_STATE_RAW);
    119:     DSSolve(svd->ds,w,NULL);
    120:     DSSort(svd->ds,w,NULL,NULL,NULL,NULL);
    121:     DSSynchronize(svd->ds,w,NULL);
    122:     DSGetMat(svd->ds,DS_MAT_U,&U);
    123:     DSGetMat(svd->ds,DS_MAT_V,&V);
    124:     BVMultInPlace(svd->U,V,svd->nconv,svd->ncv);
    125:     BVMultInPlace(svd->V,U,svd->nconv,svd->ncv);
    126:     DSRestoreMat(svd->ds,DS_MAT_U,&U);
    127:     DSRestoreMat(svd->ds,DS_MAT_V,&V);
    128:     /* Check convergence */
    129:     k = 0;
    130:     for (i=svd->nconv;i<svd->ncv;i++) {
    131:       SVDRandomizedResidualNorm(svd,i,w[i],&res);
    132:       svd->sigma[i] = PetscRealPart(w[i]);
    133:       (*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx);
    134:       if (svd->errest[i] < svd->tol) k++;
    135:       else break;
    136:     }
    137:     if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
    138:       k = svd->nsv;
    139:       for (i=0;i<svd->ncv;i++) svd->sigma[i] = PetscRealPart(w[i]);
    140:     }
    141:     (*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx);
    142:     svd->nconv += k;
    143:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv);
    144:   } while (svd->reason == SVD_CONVERGED_ITERATING);
    145:   PetscFree(w);
    146:   return 0;
    147: }

    149: SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
    150: {
    151:   svd->ops->setup          = SVDSetUp_Randomized;
    152:   svd->ops->solve          = SVDSolve_Randomized;
    153:   return 0;
    154: }