GCC Code Coverage Report

Directory:	./
File:	src/svd/impls/randomized/rsvd.c
Date:	2026-02-22 03:58:10

	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*/
    
      88
      static PetscErrorCode SVDSetUp_Randomized(SVD svd)
    
      {
    
      88
        PetscInt       N;
    
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      88
        PetscFunctionBegin;
    
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      88
        SVDCheckStandard(svd);
    
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      88
        SVDCheckDefinite(svd);
    
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      88
        SVDCheckUnsupported(svd,SVD_FEATURE_THRESHOLD);
    
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      88
        PetscCheck(svd->which==SVD_LARGEST,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"This solver supports only largest singular values");
    
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      88
        PetscCall(MatGetSize(svd->A,NULL,&N));
    
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      88
        PetscCall(SVDSetDimensions_Default(svd));
    
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      88
        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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      88
        if (svd->max_it==PETSC_DETERMINE) svd->max_it = PetscMax(N/svd->ncv,100);
    
      88
        svd->leftbasis = PETSC_TRUE;
    
      88
        svd->mpd = svd->ncv;
    
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      88
        PetscCall(SVDAllocateSolution(svd,0));
    
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      88
        PetscCall(DSSetType(svd->ds,DSSVD));
    
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      88
        PetscCall(DSAllocate(svd->ds,svd->ncv));
    
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      88
        PetscCall(SVDSetWorkVecs(svd,1,1));
    
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      21
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      2983
      static PetscErrorCode SVDRandomizedResidualNorm(SVD svd,PetscInt i,PetscScalar sigma,PetscReal *res)
    
      {
    
      2983
        PetscReal      norm1,norm2;
    
      2983
        Vec            u,v,wu,wv;
    
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      2983
        PetscFunctionBegin;
    
      2983
        *res = 1.0;
    
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      2983
        if (svd->conv!=SVD_CONV_MAXIT) {
    
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      2968
          wu = svd->swapped? svd->workr[0]: svd->workl[0];
    
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      2968
          wv = svd->swapped? svd->workl[0]: svd->workr[0];
    
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      2968
          PetscCall(BVGetColumn(svd->V,i,&v));
    
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      2968
          PetscCall(BVGetColumn(svd->U,i,&u));
    
          /* norm1 = ||A*v-sigma*u||_2 */
    
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      2968
          PetscCall(MatMult(svd->A,v,wu));
    
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      2968
          PetscCall(VecAXPY(wu,-sigma,u));
    
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      2968
          PetscCall(VecNorm(wu,NORM_2,&norm1));
    
          /* norm2 = ||A^T*u-sigma*v||_2 */
    
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      2968
          PetscCall(MatMult(svd->AT,u,wv));
    
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      2968
          PetscCall(VecAXPY(wv,-sigma,v));
    
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      2968
          PetscCall(VecNorm(wv,NORM_2,&norm2));
    
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      2968
          PetscCall(BVRestoreColumn(svd->V,i,&v));
    
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      2968
          PetscCall(BVRestoreColumn(svd->U,i,&u));
    
      2968
          *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 */
    
      5336
      static PetscErrorCode BlockMatMult(BV V,Mat A,BV Y,Mat AT)
    
      {
    
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      5336
        PetscFunctionBegin;
    
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      5336
        if (!PetscDefined(USE_COMPLEX)) PetscCall(BVMatMult(V,A,Y));
    
        else {
    
      2406
          PetscBool flg=PETSC_FALSE;
    
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      2406
          PetscCall(PetscObjectTypeCompare((PetscObject)A,MATHERMITIANTRANSPOSEVIRTUAL,&flg));
    
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      2406
          if (flg) PetscCall(BVMatMultHermitianTranspose(V,AT,Y));
    
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      2322
          else PetscCall(BVMatMult(V,A,Y));
    
        }
    
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      3094
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      88
      static PetscErrorCode SVDSolve_Randomized(SVD svd)
    
      {
    
      88
        PetscScalar    *w;
    
      88
        PetscReal      res=1.0;
    
      88
        PetscInt       i,k=0;
    
      88
        Mat            A,U,V;
    
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      88
        PetscFunctionBegin;
    
        /* Form random matrix, G. Complete the initial basis with random vectors */
    
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      88
        PetscCall(BVSetActiveColumns(svd->V,svd->nini,svd->ncv));
    
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      88
        PetscCall(BVSetRandomNormal(svd->V));
    
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      88
        PetscCall(PetscCalloc1(svd->ncv,&w));
    
        /* Subspace Iteration */
    
      2668
        do {
    
      2668
          svd->its++;
    
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      2668
          PetscCall(BVSetActiveColumns(svd->V,svd->nconv,svd->ncv));
    
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      2668
          PetscCall(BVSetActiveColumns(svd->U,svd->nconv,svd->ncv));
    
          /* Form AG */
    
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      2668
          PetscCall(BlockMatMult(svd->V,svd->A,svd->U,svd->AT));
    
          /* Orthogonalization Q=qr(AG)*/
    
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      2668
          PetscCall(BVOrthogonalize(svd->U,NULL));
    
          /* Form B^*= AQ */
    
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      2668
          PetscCall(BlockMatMult(svd->U,svd->AT,svd->V,svd->A));
    
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      2668
          PetscCall(DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv));
    
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      2668
          PetscCall(DSSVDSetDimensions(svd->ds,svd->ncv));
    
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      2668
          PetscCall(DSGetMat(svd->ds,DS_MAT_A,&A));
    
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      2668
          PetscCall(MatZeroEntries(A));
    
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      2668
          PetscCall(BVOrthogonalize(svd->V,A));
    
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      2668
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_A,&A));
    
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      2668
          PetscCall(DSSetState(svd->ds,DS_STATE_RAW));
    
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      2668
          PetscCall(DSSolve(svd->ds,w,NULL));
    
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      2668
          PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
    
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      2668
          PetscCall(DSSynchronize(svd->ds,w,NULL));
    
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      2668
          PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
    
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      2668
          PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
    
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      2668
          PetscCall(BVMultInPlace(svd->U,V,svd->nconv,svd->ncv));
    
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      2668
          PetscCall(BVMultInPlace(svd->V,U,svd->nconv,svd->ncv));
    
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      2668
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
    
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      2668
          PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
    
          /* Check convergence */
    
      2668
          k = 0;
    
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      2989
          for (i=svd->nconv;i<svd->ncv;i++) {
    
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      2983
            PetscCall(SVDRandomizedResidualNorm(svd,i,w[i],&res));
    
      2983
            svd->sigma[i] = PetscRealPart(w[i]);
    
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      2983
            PetscCall((*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx));
    
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      2983
            if (svd->errest[i] < svd->tol) k++;
    
            else break;
    
          }
    
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      2668
          if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
    
      15
            k = svd->nsv;
    
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      165
            for (i=0;i<svd->ncv;i++) svd->sigma[i] = PetscRealPart(w[i]);
    
          }
    
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      2668
          PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx));
    
      2668
          svd->nconv += k;
    
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      2668
          PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv));
    
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      2668
        } while (svd->reason == SVD_CONVERGED_ITERATING);
    
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      88
        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*/
    
      72
      SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
    
      {
    
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      72
        PetscFunctionBegin;
    
      72
        svd->ops->setup          = SVDSetUp_Randomized;
    
      72
        svd->ops->solve          = SVDSolve_Randomized;
    
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      72
        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		88	static PetscErrorCode SVDSetUp_Randomized(SVD svd)
30			{
31		88	PetscInt N;
32
33	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	88	PetscFunctionBegin;
34	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 8 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	88	SVDCheckStandard(svd);
35	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 8 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	88	SVDCheckDefinite(svd);
36	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 8 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	88	SVDCheckUnsupported(svd,SVD_FEATURE_THRESHOLD);
37	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 8 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	88	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 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(MatGetSize(svd->A,NULL,&N));
39	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(SVDSetDimensions_Default(svd));
40	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 8 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	88	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 8 times. ✓ Branch 1 taken 8 times.	88	if (svd->max_it==PETSC_DETERMINE) svd->max_it = PetscMax(N/svd->ncv,100);
42		88	svd->leftbasis = PETSC_TRUE;
43		88	svd->mpd = svd->ncv;
44	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(SVDAllocateSolution(svd,0));
45	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(DSSetType(svd->ds,DSSVD));
46	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(DSAllocate(svd->ds,svd->ncv));
47	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	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		2983	static PetscErrorCode SVDRandomizedResidualNorm(SVD svd,PetscInt i,PetscScalar sigma,PetscReal *res)
52			{
53		2983	PetscReal norm1,norm2;
54		2983	Vec u,v,wu,wv;
55
56	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	2983	PetscFunctionBegin;
57		2983	*res = 1.0;
58	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	2983	if (svd->conv!=SVD_CONV_MAXIT) {
59	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	2968	wu = svd->swapped? svd->workr[0]: svd->workl[0];
60	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	2968	wv = svd->swapped? svd->workl[0]: svd->workr[0];
61	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(BVGetColumn(svd->V,i,&v));
62	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(BVGetColumn(svd->U,i,&u));
63			/* norm1 = \|\|Av-sigmau\|\|_2 */
64	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(MatMult(svd->A,v,wu));
65	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(VecAXPY(wu,-sigma,u));
66	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(VecNorm(wu,NORM_2,&norm1));
67			/* norm2 = \|\|A^Tu-sigmav\|\|_2 */
68	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(MatMult(svd->AT,u,wv));
69	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(VecAXPY(wv,-sigma,v));
70	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(VecNorm(wv,NORM_2,&norm2));
71	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(BVRestoreColumn(svd->V,i,&v));
72	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2968	PetscCall(BVRestoreColumn(svd->U,i,&u));
73		2968	*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		5336	static PetscErrorCode BlockMatMult(BV V,Mat A,BV Y,Mat AT)
80			{
81	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	5336	PetscFunctionBegin;
82	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 3 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	5336	if (!PetscDefined(USE_COMPLEX)) PetscCall(BVMatMult(V,A,Y));
83			else {
84		2406	PetscBool flg=PETSC_FALSE;
85	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 3 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	2406	PetscCall(PetscObjectTypeCompare((PetscObject)A,MATHERMITIANTRANSPOSEVIRTUAL,&flg));
86	6/8 ✓ Branch 0 taken 4 times. ✓ Branch 1 taken 4 times. ✓ Branch 2 taken 1 times. ✓ Branch 3 taken 3 times. ✓ Branch 4 taken 1 times. ✗ Branch 5 not taken. ✗ Branch 6 not taken. ✓ Branch 7 taken 1 times.	2406	if (flg) PetscCall(BVMatMultHermitianTranspose(V,AT,Y));
87	4/6 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 3 times. ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 1 times.	2322	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.	3094	PetscFunctionReturn(PETSC_SUCCESS);
90			}
91
92		88	static PetscErrorCode SVDSolve_Randomized(SVD svd)
93			{
94		88	PetscScalar *w;
95		88	PetscReal res=1.0;
96		88	PetscInt i,k=0;
97		88	Mat A,U,V;
98
99	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	88	PetscFunctionBegin;
100			/* Form random matrix, G. Complete the initial basis with random vectors */
101	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(BVSetActiveColumns(svd->V,svd->nini,svd->ncv));
102	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(BVSetRandomNormal(svd->V));
103	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	88	PetscCall(PetscCalloc1(svd->ncv,&w));
104
105			/* Subspace Iteration */
106		2668	do {
107		2668	svd->its++;
108	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVSetActiveColumns(svd->V,svd->nconv,svd->ncv));
109	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVSetActiveColumns(svd->U,svd->nconv,svd->ncv));
110			/* Form AG */
111	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	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 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVOrthogonalize(svd->U,NULL));
114			/* Form B^= AQ /
115	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BlockMatMult(svd->U,svd->AT,svd->V,svd->A));
116
117	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSetDimensions(svd->ds,svd->ncv,svd->nconv,svd->ncv));
118	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSVDSetDimensions(svd->ds,svd->ncv));
119	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSGetMat(svd->ds,DS_MAT_A,&A));
120	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(MatZeroEntries(A));
121	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVOrthogonalize(svd->V,A));
122	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSRestoreMat(svd->ds,DS_MAT_A,&A));
123	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSetState(svd->ds,DS_STATE_RAW));
124	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSolve(svd->ds,w,NULL));
125	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
126	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSSynchronize(svd->ds,w,NULL));
127	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
128	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
129	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVMultInPlace(svd->U,V,svd->nconv,svd->ncv));
130	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(BVMultInPlace(svd->V,U,svd->nconv,svd->ncv));
131	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
132	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
133			/* Check convergence */
134		2668	k = 0;
135	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 6 times.	2989	for (i=svd->nconv;i<svd->ncv;i++) {
136	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2983	PetscCall(SVDRandomizedResidualNorm(svd,i,w[i],&res));
137		2983	svd->sigma[i] = PetscRealPart(w[i]);
138	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2983	PetscCall((*svd->converged)(svd,svd->sigma[i],res,&svd->errest[i],svd->convergedctx));
139	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	2983	if (svd->errest[i] < svd->tol) k++;
140			else break;
141			}
142	3/4 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 8 times. ✗ Branch 3 not taken.	2668	if (svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it) {
143		15	k = svd->nsv;
144	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	165	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 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx));
147		2668	svd->nconv += k;
148	4/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 6 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times.	2668	PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv));
149	2/2 ✓ Branch 0 taken 8 times. ✓ Branch 1 taken 8 times.	2668	} while (svd->reason == SVD_CONVERGED_ITERATING);
150	5/8 ✓ Branch 0 taken 8 times. ✗ Branch 1 not taken. ✓ Branch 2 taken 2 times. ✓ Branch 3 taken 6 times. ✓ Branch 4 taken 2 times. ✗ Branch 5 not taken. ✗ Branch 6 not taken. ✓ Branch 7 taken 2 times.	88	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		72	SLEPC_EXTERN PetscErrorCode SVDCreate_Randomized(SVD svd)
176			{
177	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	72	PetscFunctionBegin;
178		72	svd->ops->setup = SVDSetUp_Randomized;
179		72	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.	72	PetscFunctionReturn(PETSC_SUCCESS);
181			}
182

Function (Line)	Call count	Block coverage
BlockMatMult (line 79)	called 5336 times	77.0%
SVDCreate_Randomized (line 175)	called 72 times	100.0%
SVDRandomizedResidualNorm (line 51)	called 2983 times	83.0%
SVDSetUp_Randomized (line 29)	called 88 times	58.0%
SVDSolve_Randomized (line 92)	called 88 times	84.0%