GCC Code Coverage Report

Directory:	./
File:	src/svd/impls/randomized/rsvd.c
Date:	2025-11-19 04:19:03

	Exec	Total	Coverage
Lines:	98	98	100.0%
Functions:	5	5	100.0%
Branches:	258	408	63.2%

  
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      /*
    
         - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
         SLEPc - Scalable Library for Eigenvalue Problem Computations
    
         Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
    
         This file is part of SLEPc.
    
         SLEPc is distributed under a 2-clause BSD license (see LICENSE).
    
         - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
      */
    
      /*
    
         SLEPc singular value solver: "randomized"
    
         Method: RSVD
    
         Algorithm:
    
             Randomized singular value decomposition.
    
         References:
    
             [1] N. Halko, P.-G. Martinsson, and J. A. Tropp, "Finding
    
                 structure with randomness: Probabilistic algorithms for
    
                 constructing approximate matrix decompositions", SIAM Rev.,
    
                 53(2):217-288, 2011.
    
      */
    
      #include <slepc/private/svdimpl.h>                /*I "slepcsvd.h" I*/
    
      109
      static PetscErrorCode SVDSetUp_Randomized(SVD svd)
    
      {
    
      109
        PetscInt       N;
    
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      109
        PetscFunctionBegin;
    
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      109
        SVDCheckStandard(svd);
    
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      109
        SVDCheckDefinite(svd);
    
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      109
        SVDCheckUnsupported(svd,SVD_FEATURE_THRESHOLD);
    
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      109
        PetscCheck(svd->which==SVD_LARGEST,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"This solver supports only largest singular values");
    
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      109
        PetscCall(MatGetSize(svd->A,NULL,&N));
    
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      109
        PetscCall(SVDSetDimensions_Default(svd));
    
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      109
        PetscCheck(svd->ncv>=svd->nsv,PetscObjectComm((PetscObject)svd),PETSC_ERR_USER_INPUT,"The value of ncv must not be smaller than nsv");
    
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      109
        if (svd->max_it==PETSC_DETERMINE) svd->max_it = PetscMax(N/svd->ncv,100);
    
      109
        svd->leftbasis = PETSC_TRUE;
    
      109
        svd->mpd = svd->ncv;
    
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      109
        PetscCall(SVDAllocateSolution(svd,0));
    
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      109
        PetscCall(DSSetType(svd->ds,DSSVD));
    
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      109
        PetscCall(DSAllocate(svd->ds,svd->ncv));
    
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      109
        PetscCall(SVDSetWorkVecs(svd,1,1));
    
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      21
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      3756
      static PetscErrorCode SVDRandomizedResidualNorm(SVD svd,PetscInt i,PetscScalar sigma,PetscReal *res)
    
      {
    
      3756
        PetscReal      norm1,norm2;
    
      3756
        Vec            u,v,wu,wv;
    
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      3756
        PetscFunctionBegin;
    
      3756
        *res = 1.0;
    
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      3756
        if (svd->conv!=SVD_CONV_MAXIT) {
    
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      3738
          wu = svd->swapped? svd->workr[0]: svd->workl[0];
    
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      3738
          wv = svd->swapped? svd->workl[0]: svd->workr[0];
    
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      3738
          PetscCall(BVGetColumn(svd->V,i,&v));
    
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      3738
          PetscCall(BVGetColumn(svd->U,i,&u));
    
          /* norm1 = ||A*v-sigma*u||_2 */
    
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      3738
          PetscCall(MatMult(svd->A,v,wu));
    
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      3738
          PetscCall(VecAXPY(wu,-sigma,u));
    
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      3738
          PetscCall(VecNorm(wu,NORM_2,&norm1));
    
          /* norm2 = ||A^T*u-sigma*v||_2 */
    
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      3738
          PetscCall(MatMult(svd->AT,u,wv));
    
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      3738
          PetscCall(VecAXPY(wv,-sigma,v));
    
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      3738
          PetscCall(VecNorm(wv,NORM_2,&norm2));
    
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      3738
          PetscCall(BVRestoreColumn(svd->V,i,&v));
    
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      3738
          PetscCall(BVRestoreColumn(svd->U,i,&u));
    
      3738
          *res = SlepcAbs(norm1,norm2);
    
        }
    
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      696
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      /* If A is a virtual Hermitian transpose, then BVMatMult will fail if PRODUCT_AhB is not implemented */
    
      6744
      static PetscErrorCode BlockMatMult(BV V,Mat A,BV Y,Mat AT)
    
      {
    
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      6744
        PetscFunctionBegin;
    
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      6744
        if (!PetscDefined(USE_COMPLEX)) PetscCall(BVMatMult(V,A,Y));
    
        else {
    
      3066
          PetscBool flg=PETSC_FALSE;
    
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      3066
          PetscCall(PetscObjectTypeCompare((PetscObject)A,MATHERMITIANTRANSPOSEVIRTUAL,&flg));
    
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      3066
          if (flg) PetscCall(BVMatMultHermitianTranspose(V,AT,Y));
    
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      2961
          else PetscCall(BVMatMult(V,A,Y));
    
        }
    
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      3754
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      109
      static PetscErrorCode SVDSolve_Randomized(SVD svd)
    
      {
    
      109
        PetscScalar    *w;
    
      109
        PetscReal      res=1.0;
    
      109
        PetscInt       i,k=0;
    
      109
        Mat            A,U,V;
    
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      109
        PetscFunctionBegin;
    
        /* Form random matrix, G. Complete the initial basis with random vectors */
    
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      109
        PetscCall(BVSetActiveColumns(svd->V,svd->nini,svd->ncv));
    
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      109
        PetscCall(BVSetRandomNormal(svd->V));
    
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      109
        PetscCall(PetscCalloc1(svd->ncv,&w));
    
        /* Subspace Iteration */
    
      3372
        do {
    
      3372
          svd->its++;
    
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      3372
          PetscCall(BVSetActiveColumns(svd->V,svd->nconv,svd->ncv));
    
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      3372
          PetscCall(BVSetActiveColumns(svd->U,svd->nconv,svd->ncv));
    
          /* Form AG */
    
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      3372
          PetscCall(BlockMatMult(svd->V,svd->A,svd->U,svd->AT));
    
          /* Orthogonalization Q=qr(AG)*/
    
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      3372
          PetscCall(BVOrthogonalize(svd->U,NULL));
    
          /* Form B^*= AQ */
    
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      3372
          PetscCall(BlockMatMult(svd->U,svd->AT,svd->V,svd->A));
    
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      3372
          PetscCall(DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv));
    
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      3372
          PetscCall(DSSVDSetDimensions(svd->ds,svd->ncv));
    
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      3372
          PetscCall(DSGetMat(svd->ds,DS_MAT_A,&A));
    
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      3372
          PetscCall(MatZeroEntries(A));
    
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      3372
          PetscCall(BVOrthogonalize(svd->V,A));
    
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      3372
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_A,&A));
    
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      3372
          PetscCall(DSSetState(svd->ds,DS_STATE_RAW));
    
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      3372
          PetscCall(DSSolve(svd->ds,w,NULL));
    
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      3372
          PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
    
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      3372
          PetscCall(DSSynchronize(svd->ds,w,NULL));
    
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      3372
          PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
    
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      3372
          PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
    
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      3372
          PetscCall(BVMultInPlace(svd->U,V,svd->nconv,svd->ncv));
    
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      3372
          PetscCall(BVMultInPlace(svd->V,U,svd->nconv,svd->ncv));
    
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      3372
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
    
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      3372
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
    
          /* Check convergence */
    
      3372
          k = 0;
    
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      3762
          for (i=svd->nconv;i<svd->ncv;i++) {
    
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      3756
            PetscCall(SVDRandomizedResidualNorm(svd,i,w[i],&res));
    
      3756
            svd->sigma[i] = PetscRealPart(w[i]);
    
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      3756
            PetscCall((*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx));
    
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      3756
            if (svd->errest[i] < svd->tol) k++;
    
            else break;
    
          }
    
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      3372
          if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
    
      18
            k = svd->nsv;
    
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      198
            for (i=0;i<svd->ncv;i++) svd->sigma[i] = PetscRealPart(w[i]);
    
          }
    
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      3372
          PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx));
    
      3372
          svd->nconv += k;
    
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      3372
          PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv));
    
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      3372
        } while (svd->reason == SVD_CONVERGED_ITERATING);
    
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      109
        PetscCall(PetscFree(w));
    
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      21
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      /*MC
    
         SVDRANDOMIZED - SVDRANDOMIZED = "randomized" - A basic randomization-based
    
         singular value solver.
    
         Notes:
    
         Only available for standard SVD problems.
    
         This solver relies on randomization techniques described in {cite:p}`Hal11`.
    
         It is different from other solvers in the sense that it assumes that the
    
         input matrix has low rank, in which case the computation will be very fast.
    
         Otherwise, the solver will proceed iteratively as a subspace iteration
    
         solver (which may have slow convergence), until the required accuracy is reached.
    
         Alternatively, it is possible to set a limited number of iterations (e.g., 1)
    
         and the solver will return approximate bases of the dominant singular spaces.
    
         Note that in this latter case, the individual singular vectors are not good
    
         approximations, so residuals are expected to be large.
    
         Level: beginner
    
      .seealso: [](ch:svd), [](#sec:svdback), `SVD`, `SVDType`, `SVDSetType()`, `SVDSetProblemType()`, `SVDTRLANCZOS`
    
      M*/
    
      89
      SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
    
      {
    
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      89
        PetscFunctionBegin;
    
      89
        svd->ops->setup          = SVDSetUp_Randomized;
    
      89
        svd->ops->solve          = SVDSolve_Randomized;
    
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      89
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }

Line	Branch	Exec	Source
1			/*
2			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3			SLEPc - Scalable Library for Eigenvalue Problem Computations
4			Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
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"
12
13			Method: RSVD
14
15			Algorithm:
16
17			Randomized singular value decomposition.
18
19			References:
20
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			*/
26
27			#include <slepc/private/svdimpl.h> /I "slepcsvd.h" I/
28
29		109	static PetscErrorCode SVDSetUp_Randomized(SVD svd)
30			{
31		109	PetscInt N;
32
33	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	109	PetscFunctionBegin;
34	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	109	SVDCheckStandard(svd);
35	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	109	SVDCheckDefinite(svd);
36	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	109	SVDCheckUnsupported(svd,SVD_FEATURE_THRESHOLD);
37	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	109	PetscCheck(svd->which==SVD_LARGEST,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"This solver supports only largest singular values");
38	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(MatGetSize(svd->A,NULL,&N));
39	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(SVDSetDimensions_Default(svd));
40	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	109	PetscCheck(svd->ncv>=svd->nsv,PetscObjectComm((PetscObject)svd),PETSC_ERR_USER_INPUT,"The value of ncv must not be smaller than nsv");
41	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	109	if (svd->max_it==PETSC_DETERMINE) svd->max_it = PetscMax(N/svd->ncv,100);
42		109	svd->leftbasis = PETSC_TRUE;
43		109	svd->mpd = svd->ncv;
44	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(SVDAllocateSolution(svd,0));
45	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(DSSetType(svd->ds,DSSVD));
46	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(DSAllocate(svd->ds,svd->ncv));
47	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(SVDSetWorkVecs(svd,1,1));
48	6/12 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken. ✗ Branch 2 not taken. ✓ Branch 3 taken 2 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken. ✓ Branch 8 taken 2 times. ✗ Branch 9 not taken. ✗ Branch 10 not taken. ✓ Branch 11 taken 2 times.	21	PetscFunctionReturn(PETSC_SUCCESS);
49			}
50
51		3756	static PetscErrorCode SVDRandomizedResidualNorm(SVD svd,PetscInt i,PetscScalar sigma,PetscReal *res)
52			{
53		3756	PetscReal norm1,norm2;
54		3756	Vec u,v,wu,wv;
55
56	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	3756	PetscFunctionBegin;
57		3756	*res = 1.0;
58	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3756	if (svd->conv!=SVD_CONV_MAXIT) {
59	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3738	wu = svd->swapped? svd->workr[0]: svd->workl[0];
60	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3738	wv = svd->swapped? svd->workl[0]: svd->workr[0];
61	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(BVGetColumn(svd->V,i,&v));
62	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(BVGetColumn(svd->U,i,&u));
63			/* norm1 = \|\|Av-sigmau\|\|_2 */
64	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(MatMult(svd->A,v,wu));
65	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(VecAXPY(wu,-sigma,u));
66	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(VecNorm(wu,NORM_2,&norm1));
67			/* norm2 = \|\|A^Tu-sigmav\|\|_2 */
68	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(MatMult(svd->AT,u,wv));
69	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(VecAXPY(wv,-sigma,v));
70	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(VecNorm(wv,NORM_2,&norm2));
71	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(BVRestoreColumn(svd->V,i,&v));
72	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3738	PetscCall(BVRestoreColumn(svd->U,i,&u));
73		3738	*res = SlepcAbs(norm1,norm2);
74			}
75	6/12 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken. ✗ Branch 2 not taken. ✓ Branch 3 taken 2 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken. ✓ Branch 8 taken 2 times. ✗ Branch 9 not taken. ✗ Branch 10 not taken. ✓ Branch 11 taken 2 times.	696	PetscFunctionReturn(PETSC_SUCCESS);
76			}
77
78			/* If A is a virtual Hermitian transpose, then BVMatMult will fail if PRODUCT_AhB is not implemented */
79		6744	static PetscErrorCode BlockMatMult(BV V,Mat A,BV Y,Mat AT)
80			{
81	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	6744	PetscFunctionBegin;
82	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 4 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	6744	if (!PetscDefined(USE_COMPLEX)) PetscCall(BVMatMult(V,A,Y));
83			else {
84		3066	PetscBool flg=PETSC_FALSE;
85	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 4 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	3066	PetscCall(PetscObjectTypeCompare((PetscObject)A,MATHERMITIANTRANSPOSEVIRTUAL,&flg));
86	6/8 ✓ Branch 0 taken 5 times. ✓ Branch 1 taken 5 times. ✓ Branch 2 taken 1 times. ✓ Branch 3 taken 4 times. ✓ Branch 4 taken 1 times. ✗ Branch 5 not taken. ✗ Branch 6 not taken. ✓ Branch 7 taken 1 times.	3066	if (flg) PetscCall(BVMatMultHermitianTranspose(V,AT,Y));
87	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 4 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	2961	else PetscCall(BVMatMult(V,A,Y));
88			}
89	6/12 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken. ✗ Branch 2 not taken. ✓ Branch 3 taken 2 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken. ✓ Branch 8 taken 2 times. ✗ Branch 9 not taken. ✗ Branch 10 not taken. ✓ Branch 11 taken 2 times.	3754	PetscFunctionReturn(PETSC_SUCCESS);
90			}
91
92		109	static PetscErrorCode SVDSolve_Randomized(SVD svd)
93			{
94		109	PetscScalar *w;
95		109	PetscReal res=1.0;
96		109	PetscInt i,k=0;
97		109	Mat A,U,V;
98
99	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	109	PetscFunctionBegin;
100			/* Form random matrix, G. Complete the initial basis with random vectors */
101	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(BVSetActiveColumns(svd->V,svd->nini,svd->ncv));
102	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(BVSetRandomNormal(svd->V));
103	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	109	PetscCall(PetscCalloc1(svd->ncv,&w));
104
105			/* Subspace Iteration */
106		3372	do {
107		3372	svd->its++;
108	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVSetActiveColumns(svd->V,svd->nconv,svd->ncv));
109	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVSetActiveColumns(svd->U,svd->nconv,svd->ncv));
110			/* Form AG */
111	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BlockMatMult(svd->V,svd->A,svd->U,svd->AT));
112			/* Orthogonalization Q=qr(AG)*/
113	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVOrthogonalize(svd->U,NULL));
114			/* Form B^= AQ /
115	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BlockMatMult(svd->U,svd->AT,svd->V,svd->A));
116
117	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv));
118	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSVDSetDimensions(svd->ds,svd->ncv));
119	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSGetMat(svd->ds,DS_MAT_A,&A));
120	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(MatZeroEntries(A));
121	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVOrthogonalize(svd->V,A));
122	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSRestoreMat(svd->ds,DS_MAT_A,&A));
123	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSetState(svd->ds,DS_STATE_RAW));
124	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSolve(svd->ds,w,NULL));
125	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
126	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSSynchronize(svd->ds,w,NULL));
127	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
128	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
129	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVMultInPlace(svd->U,V,svd->nconv,svd->ncv));
130	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(BVMultInPlace(svd->V,U,svd->nconv,svd->ncv));
131	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
132	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
133			/* Check convergence */
134		3372	k = 0;
135	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 6 times.	3762	for (i=svd->nconv;i<svd->ncv;i++) {
136	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3756	PetscCall(SVDRandomizedResidualNorm(svd,i,w[i],&res));
137		3756	svd->sigma[i] = PetscRealPart(w[i]);
138	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3756	PetscCall((*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx));
139	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3756	if (svd->errest[i] < svd->tol) k++;
140			else break;
141			}
142	3/4 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times. ✓ Branch 2 taken 10 times. ✗ Branch 3 not taken.	3372	if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
143		18	k = svd->nsv;
144	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	198	for (i=0;i<svd->ncv;i++) svd->sigma[i] = PetscRealPart(w[i]);
145			}
146	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx));
147		3372	svd->nconv += k;
148	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	3372	PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv));
149	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3372	} while (svd->reason == SVD_CONVERGED_ITERATING);
150	5/8 ✓ Branch 0 taken 10 times. ✗ Branch 1 not taken. ✓ Branch 2 taken 2 times. ✓ Branch 3 taken 8 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✗ Branch 6 not taken. ✓ Branch 7 taken 2 times.	109	PetscCall(PetscFree(w));
151	6/12 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken. ✗ Branch 2 not taken. ✓ Branch 3 taken 2 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken. ✓ Branch 8 taken 2 times. ✗ Branch 9 not taken. ✗ Branch 10 not taken. ✓ Branch 11 taken 2 times.	21	PetscFunctionReturn(PETSC_SUCCESS);
152			}
153
154			/*MC
155			SVDRANDOMIZED - SVDRANDOMIZED = "randomized" - A basic randomization-based
156			singular value solver.
157
158			Notes:
159			Only available for standard SVD problems.
160
161			This solver relies on randomization techniques described in {cite:p}`Hal11`.
162			It is different from other solvers in the sense that it assumes that the
163			input matrix has low rank, in which case the computation will be very fast.
164			Otherwise, the solver will proceed iteratively as a subspace iteration
165			solver (which may have slow convergence), until the required accuracy is reached.
166			Alternatively, it is possible to set a limited number of iterations (e.g., 1)
167			and the solver will return approximate bases of the dominant singular spaces.
168			Note that in this latter case, the individual singular vectors are not good
169			approximations, so residuals are expected to be large.
170
171			Level: beginner
172
173			.seealso: [](ch:svd), [](#sec:svdback), `SVD`, `SVDType`, `SVDSetType()`, `SVDSetProblemType()`, `SVDTRLANCZOS`
174			M*/
175		89	SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
176			{
177	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	89	PetscFunctionBegin;
178		89	svd->ops->setup = SVDSetUp_Randomized;
179		89	svd->ops->solve = SVDSolve_Randomized;
180	6/12 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken. ✗ Branch 2 not taken. ✓ Branch 3 taken 2 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken. ✓ Branch 8 taken 2 times. ✗ Branch 9 not taken. ✗ Branch 10 not taken. ✓ Branch 11 taken 2 times.	89	PetscFunctionReturn(PETSC_SUCCESS);
181			}
182

Function (Line)	Call count	Block coverage
BlockMatMult (line 79)	called 6744 times	77.0%
SVDCreate_Randomized (line 175)	called 89 times	100.0%
SVDRandomizedResidualNorm (line 51)	called 3756 times	83.0%
SVDSetUp_Randomized (line 29)	called 109 times	58.0%
SVDSolve_Randomized (line 92)	called 109 times	84.0%