GCC Code Coverage Report

Directory:	./
File:	src/mfn/impls/krylov/mfnkrylov.c
Date:	2025-12-10 04:20:18

	Exec	Total	Coverage
Lines:	70	70	100.0%
Functions:	3	3	100.0%
Branches:	178	262	67.9%

  
      Line
      Branch
      Exec
      Source
    
      /*
    
         - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
         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 matrix function solver: "krylov"
    
         Method: Arnoldi with Eiermann-Ernst restart
    
         Algorithm:
    
             Build Arnoldi approximations using f(H) for the Hessenberg matrix H,
    
             restart by discarding the Krylov basis but keeping H.
    
         References:
    
             [1] M. Eiermann and O. Ernst, "A restarted Krylov subspace method
    
                 for the evaluation of matrix functions", SIAM J. Numer. Anal.
    
                 44(6):2481-2504, 2006.
    
      */
    
      #include <slepc/private/mfnimpl.h>
    
      #include <slepcblaslapack.h>
    
      160
      static PetscErrorCode MFNSetUp_Krylov(MFN mfn)
    
      {
    
      160
        PetscInt       N;
    
        1/2✓ Branch 0 taken 2 times.
✗ Branch 1 not taken.

      160
        PetscFunctionBegin;
    
        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.

      160
        PetscCall(MatGetSize(mfn->A,&N,NULL));
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      160
        if (mfn->ncv==PETSC_DETERMINE) mfn->ncv = PetscMin(30,N);
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      160
        if (mfn->max_it==PETSC_DETERMINE) mfn->max_it = 100;
    
        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.

      160
        PetscCall(MFNAllocateSolution(mfn,1));
    
        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.

      29
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      964
      static PetscErrorCode MFNSolve_Krylov(MFN mfn,Vec b,Vec x)
    
      {
    
      964
        PetscInt          n=0,m,ld,ldh,j;
    
      964
        PetscBLASInt      m_,inc=1;
    
      964
        Mat               M,G=NULL,H=NULL;
    
      964
        Vec               F=NULL;
    
      964
        PetscScalar       *marray,*farray,*harray;
    
      964
        const PetscScalar *garray;
    
      964
        PetscReal         beta,betaold=0.0,nrm=1.0;
    
      964
        PetscBool         breakdown;
    
        1/2✓ Branch 0 taken 2 times.
✗ Branch 1 not taken.

      964
        PetscFunctionBegin;
    
      964
        m  = mfn->ncv;
    
      964
        ld = m+1;
    
        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.

      964
        PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,ld,m,NULL,&M));
    
        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.

      964
        PetscCall(MatDenseGetArray(M,&marray));
    
        /* set initial vector to b/||b|| */
    
        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.

      964
        PetscCall(BVInsertVec(mfn->V,0,b));
    
        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.

      964
        PetscCall(BVScaleColumn(mfn->V,0,1.0/mfn->bnorm));
    
        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.

      964
        PetscCall(VecSet(x,0.0));
    
        /* Restart loop */
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      3262
        while (mfn->reason == MFN_CONVERGED_ITERATING) {
    
      2298
          mfn->its++;
    
          /* compute Arnoldi factorization */
    
        7/8✓ Branch 0 taken 6 times.
✓ Branch 1 taken 8 times.
✓ Branch 2 taken 2 times.
✓ Branch 3 taken 8 times.
✓ Branch 4 taken 2 times.
✓ Branch 5 taken 2 times.
✗ Branch 6 not taken.
✓ Branch 7 taken 2 times.

      2298
          PetscCall(BVMatArnoldi(mfn->V,mfn->transpose_solve?mfn->AT:mfn->A,M,0,&m,&beta,&breakdown));
    
          /* save previous Hessenberg matrix in G; allocate new storage for H and f(H) */
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->its>1) { G = H; H = NULL; }
    
      2298
          ldh = n+m;
    
        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.

      2298
          PetscCall(MFN_CreateVec(ldh,&F));
    
        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.

      2298
          PetscCall(MFN_CreateDenseMat(ldh,&H));
    
          /* glue together the previous H and the new H obtained with Arnoldi */
    
        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.

      2298
          PetscCall(MatDenseGetArray(H,&harray));
    
        7/8✓ Branch 0 taken 2 times.
✓ Branch 1 taken 8 times.
✓ Branch 2 taken 10 times.
✓ Branch 3 taken 8 times.
✗ Branch 4 not taken.
✓ Branch 5 taken 2 times.
✓ Branch 6 taken 2 times.
✓ Branch 7 taken 2 times.

      51270
          for (j=0;j<m;j++) PetscCall(PetscArraycpy(harray+n+(j+n)*ldh,marray+j*ld,m));
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->its>1) {
    
        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.

      1334
            PetscCall(MatDenseGetArrayRead(G,&garray));
    
        7/8✓ Branch 0 taken 2 times.
✓ Branch 1 taken 8 times.
✓ Branch 2 taken 10 times.
✓ Branch 3 taken 8 times.
✗ Branch 4 not taken.
✓ Branch 5 taken 2 times.
✓ Branch 6 taken 2 times.
✓ Branch 7 taken 2 times.

      44270
            for (j=0;j<n;j++) PetscCall(PetscArraycpy(harray+j*ldh,garray+j*n,n));
    
        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.

      1334
            PetscCall(MatDenseRestoreArrayRead(G,&garray));
    
        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.

      1334
            PetscCall(MatDestroy(&G));
    
      1334
            harray[n+(n-1)*ldh] = betaold;
    
          }
    
        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.

      2298
          PetscCall(MatDenseRestoreArray(H,&harray));
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->its==1) {
    
            /* set symmetry flag of H from A */
    
        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.

      964
            PetscCall(MatPropagateSymmetryOptions(mfn->A,H));
    
          }
    
          /* evaluate f(H) */
    
        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.

      2298
          PetscCall(FNEvaluateFunctionMatVec(mfn->fn,H,F));
    
          /* x += ||b||*V*f(H)*e_1 */
    
        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.

      2298
          PetscCall(VecGetArray(F,&farray));
    
        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.

      2298
          PetscCall(PetscBLASIntCast(m,&m_));
    
      2298
          nrm = BLASnrm2_(&m_,farray+n,&inc);   /* relative norm of the update ||u||/||b|| */
    
        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.

      2298
          PetscCall(MFNMonitor(mfn,mfn->its,nrm));
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      51270
          for (j=0;j<m;j++) farray[j+n] *= mfn->bnorm;
    
        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.

      2298
          PetscCall(BVSetActiveColumns(mfn->V,0,m));
    
        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.

      2298
          PetscCall(BVMultVec(mfn->V,1.0,1.0,x,farray+n));
    
        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.

      2298
          PetscCall(VecRestoreArray(F,&farray));
    
          /* check convergence */
    
        1/2✗ Branch 0 not taken.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->its >= mfn->max_it) mfn->reason = MFN_DIVERGED_ITS;
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->its>1) {
    
        5/8✓ Branch 0 taken 10 times.
✗ Branch 1 not taken.
✓ Branch 2 taken 10 times.
✗ Branch 3 not taken.
✓ Branch 4 taken 10 times.
✗ Branch 5 not taken.
✓ Branch 6 taken 10 times.
✓ Branch 7 taken 10 times.

      1334
            if (m<mfn->ncv || breakdown || beta==0.0 || nrm<mfn->tol) mfn->reason = MFN_CONVERGED_TOL;
    
          }
    
          /* restart with vector v_{m+1} */
    
        2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 10 times.

      2298
          if (mfn->reason == MFN_CONVERGED_ITERATING) {
    
        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.

      1334
            PetscCall(BVCopyColumn(mfn->V,m,0));
    
      1334
            n += m;
    
      1334
            betaold = beta;
    
          }
    
        }
    
        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.

      964
        PetscCall(MatDestroy(&H));
    
        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.

      964
        PetscCall(MatDestroy(&G));
    
        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.

      964
        PetscCall(VecDestroy(&F));
    
        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.

      964
        PetscCall(MatDenseRestoreArray(M,&marray));
    
        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.

      964
        PetscCall(MatDestroy(&M));
    
        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.

      189
        PetscFunctionReturn(PETSC_SUCCESS);
    
      }
    
      /*MC
    
         MFNKRYLOV - MFNKRYLOV = "krylov" - A restarted Krylov method for the application
    
         of a matrix function to a vector.
    
         Note:
    
         This solver builds Arnoldi approximations using $f(H)$ for the Hessenberg matrix
    
         $H$, and restarts by discarding the Krylov basis but keeping $H$, as proposed by
    
         {cite:t}`Eie06`.
    
         Level: beginner
    
      .seealso: [](ch:mfn), `MFN`, `MFNType`, `MFNSetType()`
    
      M*/
    
      174
      SLEPC_EXTERN PetscErrorCode MFNCreate_Krylov(MFN mfn)
    
      {
    
        1/2✓ Branch 0 taken 2 times.
✗ Branch 1 not taken.

      174
        PetscFunctionBegin;
    
      174
        mfn->ops->solve          = MFNSolve_Krylov;
    
      174
        mfn->ops->setup          = MFNSetUp_Krylov;
    
        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.

      174
        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 matrix function solver: "krylov"
12
13			Method: Arnoldi with Eiermann-Ernst restart
14
15			Algorithm:
16
17			Build Arnoldi approximations using f(H) for the Hessenberg matrix H,
18			restart by discarding the Krylov basis but keeping H.
19
20			References:
21
22			[1] M. Eiermann and O. Ernst, "A restarted Krylov subspace method
23			for the evaluation of matrix functions", SIAM J. Numer. Anal.
24			44(6):2481-2504, 2006.
25			*/
26
27			#include <slepc/private/mfnimpl.h>
28			#include <slepcblaslapack.h>
29
30		160	static PetscErrorCode MFNSetUp_Krylov(MFN mfn)
31			{
32		160	PetscInt N;
33
34	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	160	PetscFunctionBegin;
35	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.	160	PetscCall(MatGetSize(mfn->A,&N,NULL));
36	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	160	if (mfn->ncv==PETSC_DETERMINE) mfn->ncv = PetscMin(30,N);
37	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	160	if (mfn->max_it==PETSC_DETERMINE) mfn->max_it = 100;
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.	160	PetscCall(MFNAllocateSolution(mfn,1));
39	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.	29	PetscFunctionReturn(PETSC_SUCCESS);
40			}
41
42		964	static PetscErrorCode MFNSolve_Krylov(MFN mfn,Vec b,Vec x)
43			{
44		964	PetscInt n=0,m,ld,ldh,j;
45		964	PetscBLASInt m_,inc=1;
46		964	Mat M,G=NULL,H=NULL;
47		964	Vec F=NULL;
48		964	PetscScalar marray,farray,*harray;
49		964	const PetscScalar *garray;
50		964	PetscReal beta,betaold=0.0,nrm=1.0;
51		964	PetscBool breakdown;
52
53	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	964	PetscFunctionBegin;
54		964	m = mfn->ncv;
55		964	ld = m+1;
56	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.	964	PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,ld,m,NULL,&M));
57	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.	964	PetscCall(MatDenseGetArray(M,&marray));
58
59			/* set initial vector to b/\|\|b\|\| */
60	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.	964	PetscCall(BVInsertVec(mfn->V,0,b));
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.	964	PetscCall(BVScaleColumn(mfn->V,0,1.0/mfn->bnorm));
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.	964	PetscCall(VecSet(x,0.0));
63
64			/* Restart loop */
65	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	3262	while (mfn->reason == MFN_CONVERGED_ITERATING) {
66		2298	mfn->its++;
67
68			/* compute Arnoldi factorization */
69	7/8 ✓ Branch 0 taken 6 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 2 times. ✓ Branch 3 taken 8 times. ✓ Branch 4 taken 2 times. ✓ Branch 5 taken 2 times. ✗ Branch 6 not taken. ✓ Branch 7 taken 2 times.	2298	PetscCall(BVMatArnoldi(mfn->V,mfn->transpose_solve?mfn->AT:mfn->A,M,0,&m,&beta,&breakdown));
70
71			/* save previous Hessenberg matrix in G; allocate new storage for H and f(H) */
72	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2298	if (mfn->its>1) { G = H; H = NULL; }
73		2298	ldh = n+m;
74	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.	2298	PetscCall(MFN_CreateVec(ldh,&F));
75	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.	2298	PetscCall(MFN_CreateDenseMat(ldh,&H));
76
77			/* glue together the previous H and the new H obtained with Arnoldi */
78	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.	2298	PetscCall(MatDenseGetArray(H,&harray));
79	7/8 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 10 times. ✓ Branch 3 taken 8 times. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times. ✓ Branch 6 taken 2 times. ✓ Branch 7 taken 2 times.	51270	for (j=0;j<m;j++) PetscCall(PetscArraycpy(harray+n+(j+n)ldh,marray+jld,m));
80	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2298	if (mfn->its>1) {
81	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.	1334	PetscCall(MatDenseGetArrayRead(G,&garray));
82	7/8 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 8 times. ✓ Branch 2 taken 10 times. ✓ Branch 3 taken 8 times. ✗ Branch 4 not taken. ✓ Branch 5 taken 2 times. ✓ Branch 6 taken 2 times. ✓ Branch 7 taken 2 times.	44270	for (j=0;j<n;j++) PetscCall(PetscArraycpy(harray+jldh,garray+jn,n));
83	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.	1334	PetscCall(MatDenseRestoreArrayRead(G,&garray));
84	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.	1334	PetscCall(MatDestroy(&G));
85		1334	harray[n+(n-1)*ldh] = betaold;
86			}
87	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.	2298	PetscCall(MatDenseRestoreArray(H,&harray));
88
89	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2298	if (mfn->its==1) {
90			/* set symmetry flag of H from A */
91	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.	964	PetscCall(MatPropagateSymmetryOptions(mfn->A,H));
92			}
93
94			/* evaluate f(H) */
95	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.	2298	PetscCall(FNEvaluateFunctionMatVec(mfn->fn,H,F));
96
97			/* x += \|\|b\|\|Vf(H)e_1 /
98	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.	2298	PetscCall(VecGetArray(F,&farray));
99	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.	2298	PetscCall(PetscBLASIntCast(m,&m_));
100		2298	nrm = BLASnrm2_(&m_,farray+n,&inc); /* relative norm of the update \|\|u\|\|/\|\|b\|\| */
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.	2298	PetscCall(MFNMonitor(mfn,mfn->its,nrm));
102	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	51270	for (j=0;j<m;j++) farray[j+n] *= mfn->bnorm;
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.	2298	PetscCall(BVSetActiveColumns(mfn->V,0,m));
104	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.	2298	PetscCall(BVMultVec(mfn->V,1.0,1.0,x,farray+n));
105	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.	2298	PetscCall(VecRestoreArray(F,&farray));
106
107			/* check convergence */
108	1/2 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times.	2298	if (mfn->its >= mfn->max_it) mfn->reason = MFN_DIVERGED_ITS;
109	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2298	if (mfn->its>1) {
110	5/8 ✓ Branch 0 taken 10 times. ✗ Branch 1 not taken. ✓ Branch 2 taken 10 times. ✗ Branch 3 not taken. ✓ Branch 4 taken 10 times. ✗ Branch 5 not taken. ✓ Branch 6 taken 10 times. ✓ Branch 7 taken 10 times.	1334	if (m<mfn->ncv \|\| breakdown \|\| beta==0.0 \|\| nrm<mfn->tol) mfn->reason = MFN_CONVERGED_TOL;
111			}
112
113			/* restart with vector v_{m+1} */
114	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2298	if (mfn->reason == MFN_CONVERGED_ITERATING) {
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.	1334	PetscCall(BVCopyColumn(mfn->V,m,0));
116		1334	n += m;
117		1334	betaold = beta;
118			}
119			}
120
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.	964	PetscCall(MatDestroy(&H));
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.	964	PetscCall(MatDestroy(&G));
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.	964	PetscCall(VecDestroy(&F));
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.	964	PetscCall(MatDenseRestoreArray(M,&marray));
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.	964	PetscCall(MatDestroy(&M));
126	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.	189	PetscFunctionReturn(PETSC_SUCCESS);
127			}
128
129			/*MC
130			MFNKRYLOV - MFNKRYLOV = "krylov" - A restarted Krylov method for the application
131			of a matrix function to a vector.
132
133			Note:
134			This solver builds Arnoldi approximations using $f(H)$ for the Hessenberg matrix
135			$H$, and restarts by discarding the Krylov basis but keeping $H$, as proposed by
136			{cite:t}`Eie06`.
137
138			Level: beginner
139
140			.seealso: [](ch:mfn), `MFN`, `MFNType`, `MFNSetType()`
141			M*/
142		174	SLEPC_EXTERN PetscErrorCode MFNCreate_Krylov(MFN mfn)
143			{
144	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	174	PetscFunctionBegin;
145		174	mfn->ops->solve = MFNSolve_Krylov;
146		174	mfn->ops->setup = MFNSetUp_Krylov;
147	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.	174	PetscFunctionReturn(PETSC_SUCCESS);
148			}
149

Function (Line)	Call count	Block coverage
MFNCreate_Krylov (line 142)	called 174 times	100.0%
MFNSetUp_Krylov (line 30)	called 160 times	82.0%
MFNSolve_Krylov (line 42)	called 964 times	84.0%