Actual source code: rsvd.c
slepc-3.16.2 2022-02-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: {
32: PetscInt N;
35: if (svd->which!=SVD_LARGEST) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"This solver supports only largest singular values");
36: MatGetSize(svd->A,NULL,&N);
37: SVDSetDimensions_Default(svd);
38: if (svd->ncv<svd->nsv) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_USER_INPUT,"The value of ncv must not be smaller than nsv");
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: {
52: PetscReal norm1,norm2;
53: Vec u,v,wu,wv;
56: wu = svd->swapped? svd->workr[0]: svd->workl[0];
57: wv = svd->swapped? svd->workl[0]: svd->workr[0];
58: if (svd->conv!=SVD_CONV_MAXIT) {
59: BVGetColumn(svd->V,i,&v);
60: BVGetColumn(svd->U,i,&u);
61: /* norm1 = ||A*v-sigma*u||_2 */
62: MatMult(svd->A,v,wu);
63: VecAXPY(wu,-sigma,u);
64: VecNorm(wu,NORM_2,&norm1);
65: /* norm2 = ||A^T*u-sigma*v||_2 */
66: MatMult(svd->AT,u,wv);
67: VecAXPY(wv,-sigma,v);
68: VecNorm(wv,NORM_2,&norm2);
69: BVRestoreColumn(svd->V,i,&v);
70: BVRestoreColumn(svd->U,i,&u);
71: *res = PetscSqrtReal(norm1*norm1+norm2*norm2);
72: } else {
73: *res = 1.0;
74: }
75: return(0);
76: }
78: PetscErrorCode SVDSolve_Randomized(SVD svd)
79: {
81: PetscScalar *w;
82: PetscReal res=1.0;
83: PetscInt i,k=0;
84: Mat A,U,V;
87: /* Form random matrix, G. Complete the initial basis with random vectors */
88: BVSetActiveColumns(svd->V,svd->nini,svd->ncv);
89: BVSetRandomNormal(svd->V);
90: PetscCalloc1(svd->ncv,&w);
92: /* Subspace Iteration */
93: do {
94: svd->its++;
95: BVSetActiveColumns(svd->V,svd->nconv,svd->ncv);
96: BVSetActiveColumns(svd->U,svd->nconv,svd->ncv);
97: /* Form AG */
98: BVMatMult(svd->V,svd->A,svd->U);
99: /* Orthogonalization Q=qr(AG)*/
100: BVOrthogonalize(svd->U,NULL);
101: /* Form B^*= AQ */
102: BVMatMult(svd->U,svd->AT,svd->V);
104: DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv);
105: DSSVDSetDimensions(svd->ds,svd->ncv);
106: DSGetMat(svd->ds,DS_MAT_A,&A);
107: MatZeroEntries(A);
108: BVOrthogonalize(svd->V,A);
109: DSRestoreMat(svd->ds,DS_MAT_A,&A);
110: DSSetState(svd->ds,DS_STATE_RAW);
111: DSSolve(svd->ds,w,NULL);
112: DSSort(svd->ds,w,NULL,NULL,NULL,NULL);
113: DSSynchronize(svd->ds,w,NULL);
114: DSGetMat(svd->ds,DS_MAT_U,&U);
115: DSGetMat(svd->ds,DS_MAT_V,&V);
116: BVMultInPlace(svd->U,V,svd->nconv,svd->ncv);
117: BVMultInPlace(svd->V,U,svd->nconv,svd->ncv);
118: MatDestroy(&U);
119: MatDestroy(&V);
120: /* Check convergence */
121: k = 0;
122: for (i=svd->nconv;i<svd->ncv;i++) {
123: SVDRandomizedResidualNorm(svd,i,w[i],&res);
124: svd->sigma[i] = PetscRealPart(w[i]);
125: (*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx);
126: if (svd->errest[i] < svd->tol) k++;
127: else break;
128: }
129: if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
130: k = svd->nsv;
131: for (i=0;i<svd->ncv;i++) svd->sigma[i] = PetscRealPart(w[i]);
132: }
133: (*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx);
134: svd->nconv += k;
135: SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv);
136: } while (svd->reason == SVD_CONVERGED_ITERATING);
137: PetscFree(w);
138: return(0);
139: }
141: SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
142: {
144: svd->ops->setup = SVDSetUp_Randomized;
145: svd->ops->solve = SVDSolve_Randomized;
146: return(0);
147: }