GCC Code Coverage Report

Directory:	./
File:	src/lme/tutorials/ex32.c
Date:	2025-11-19 04:19:03

	Exec	Total	Coverage
Lines:	87	88	98.9%
Functions:	1	1	100.0%
Branches:	279	418	66.7%

  
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      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).
    
         - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
      */
    
      static char help[] = "Solves a Lypunov equation with the shifted 2-D Laplacian.\n\n"
    
        "The command line options are:\n"
    
        "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
    
        "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
    
      #include <slepclme.h>
    
      20
      int main(int argc,char **argv)
    
      {
    
      20
        Mat                A;           /* problem matrix */
    
      20
        Mat                C,C1;        /* right-hand side */
    
      20
        Mat                X,X1;        /* solution */
    
      20
        LME                lme;
    
      20
        PetscReal          tol,errest,error;
    
      20
        PetscScalar        *u,sigma=0.0;
    
      20
        PetscInt           N,n=10,m,Istart,Iend,II,maxit,its,ncv,i,j,rank=0;
    
      20
        PetscBool          flag;
    
      20
        LMEConvergedReason reason;
    
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      20
        PetscFunctionBeginUser;
    
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      20
        PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
    
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      20
        PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
    
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      20
        PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
    
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      20
        if (!flag) m=n;
    
      20
        N = n*m;
    
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      20
        PetscCall(PetscOptionsGetScalar(NULL,NULL,"-sigma",&sigma,NULL));
    
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      20
        PetscCall(PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL));
    
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      20
        PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));
    
        /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
                             Create the 2-D Laplacian, A
    
           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    
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      20
        PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
    
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      20
        PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
    
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      20
        PetscCall(MatSetFromOptions(A));
    
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      20
        PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
    
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      2020
        for (II=Istart;II<Iend;II++) {
    
      2000
          i = II/n; j = II-i*n;
    
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      2000
          if (i>0) PetscCall(MatSetValue(A,II,II-n,1.0,INSERT_VALUES));
    
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          if (i<m-1) PetscCall(MatSetValue(A,II,II+n,1.0,INSERT_VALUES));
    
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          if (j>0) PetscCall(MatSetValue(A,II,II-1,1.0,INSERT_VALUES));
    
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          if (j<n-1) PetscCall(MatSetValue(A,II,II+1,1.0,INSERT_VALUES));
    
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      2000
          PetscCall(MatSetValue(A,II,II,-4.0-sigma,INSERT_VALUES));
    
        }
    
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      20
        PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    
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      20
        PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    
        /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
             Create a low-rank Mat to store the right-hand side C = C1*C1'
    
           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    
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      20
        PetscCall(MatCreate(PETSC_COMM_WORLD,&C1));
    
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      20
        PetscCall(MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2));
    
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        PetscCall(MatSetType(C1,MATDENSE));
    
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      20
        PetscCall(MatGetOwnershipRange(C1,&Istart,&Iend));
    
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      20
        PetscCall(MatDenseGetArray(C1,&u));
    
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        for (i=Istart;i<Iend;i++) {
    
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      2000
          if (i<N/2) u[i-Istart] = 1.0;
    
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          if (i==0) u[i+Iend-2*Istart] = -2.0;
    
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          if (i==1) u[i+Iend-2*Istart] = -1.0;
    
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          if (i==2) u[i+Iend-2*Istart] = -1.0;
    
        }
    
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        PetscCall(MatDenseRestoreArray(C1,&u));
    
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      20
        PetscCall(MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY));
    
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        PetscCall(MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY));
    
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      20
        PetscCall(MatCreateLRC(NULL,C1,NULL,NULL,&C));
    
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      20
        PetscCall(MatDestroy(&C1));
    
        /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
                      Create the solver and set various options
    
           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    
        /*
    
           Create the matrix equation solver context
    
        */
    
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      20
        PetscCall(LMECreate(PETSC_COMM_WORLD,&lme));
    
        /*
    
           Set the type of equation
    
        */
    
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      20
        PetscCall(LMESetProblemType(lme,LME_LYAPUNOV));
    
        /*
    
           Set the matrix coefficients, the right-hand side, and the solution.
    
           In this case, it is a Lyapunov equation A*X+X*A'=-C where both
    
           C and X are symmetric and low-rank, C=C1*C1', X=X1*X1'
    
        */
    
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      20
        PetscCall(LMESetCoefficients(lme,A,NULL,NULL,NULL));
    
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      20
        PetscCall(LMESetRHS(lme,C));
    
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      20
        if (rank) {  /* Create X only if the user has specified a nonzero value of rank */
    
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      10
          PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%" PetscInt_FMT "\n",rank));
    
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          PetscCall(MatCreate(PETSC_COMM_WORLD,&X1));
    
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          PetscCall(MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank));
    
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          PetscCall(MatSetType(X1,MATDENSE));
    
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          PetscCall(MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY));
    
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          PetscCall(MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY));
    
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          PetscCall(MatCreateLRC(NULL,X1,NULL,NULL,&X));
    
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          PetscCall(MatDestroy(&X1));
    
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          PetscCall(LMESetSolution(lme,X));
    
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          PetscCall(MatDestroy(&X));
    
        }
    
        /*
    
           (Optional) Set other solver options
    
        */
    
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      20
        PetscCall(LMESetTolerances(lme,1e-07,PETSC_CURRENT));
    
        /*
    
           Set solver parameters at runtime
    
        */
    
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      20
        PetscCall(LMESetFromOptions(lme));
    
        /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
                         Solve the matrix equation, A*X+X*A'=-C
    
           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    
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        PetscCall(LMESolve(lme));
    
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        PetscCall(LMEGetConvergedReason(lme,&reason));
    
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        PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
    
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      20
        if (!rank) {  /* X1 was created by the solver, so extract it and see how many columns it has */
    
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          PetscCall(LMEGetSolution(lme,&X));
    
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          PetscCall(MatLRCGetMats(X,NULL,&X1,NULL,NULL));
    
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          PetscCall(MatGetSize(X1,NULL,&rank));
    
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          PetscCall(PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%" PetscInt_FMT "\n",rank));
    
        }
    
        /*
    
           Optional: Get some information from the solver and display it
    
        */
    
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        PetscCall(LMEGetIterationNumber(lme,&its));
    
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        PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
    
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        PetscCall(LMEGetDimensions(lme,&ncv));
    
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        PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
    
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        PetscCall(LMEGetTolerances(lme,&tol,&maxit));
    
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      20
        PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
    
        /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    
                              Compute residual error
    
           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    
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        PetscCall(LMEGetErrorEstimate(lme,&errest));
    
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        PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest));
    
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        if (n<=150) {
    
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          PetscCall(LMEComputeError(lme,&error));
    
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          PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error));
    
      ✗
        } else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Matrix too large to compute residual norm\n\n"));
    
        /*
    
           Free work space
    
        */
    
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        PetscCall(LMEDestroy(&lme));
    
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        PetscCall(MatDestroy(&A));
    
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        PetscCall(MatDestroy(&C));
    
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      20
        PetscCall(SlepcFinalize());
    
        return 0;
    
      }
    
      /*TEST
    
         test:
    
            suffix: 1
    
            requires: !single
    
         test:
    
            suffix: 2
    
            args: -rank 40
    
            requires: !single
    
      TEST*/

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			static char help[] = "Solves a Lypunov equation with the shifted 2-D Laplacian.\n\n"
12			"The command line options are:\n"
13			" -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
14			" -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
15
16			#include <slepclme.h>
17
18		20	int main(int argc,char **argv)
19			{
20		20	Mat A; /* problem matrix */
21		20	Mat C,C1; /* right-hand side */
22		20	Mat X,X1; /* solution */
23		20	LME lme;
24		20	PetscReal tol,errest,error;
25		20	PetscScalar *u,sigma=0.0;
26		20	PetscInt N,n=10,m,Istart,Iend,II,maxit,its,ncv,i,j,rank=0;
27		20	PetscBool flag;
28		20	LMEConvergedReason reason;
29
30	1/2 ✓ Branch 0 taken 2 times. ✗ Branch 1 not taken.	20	PetscFunctionBeginUser;
31	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.	20	PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
32
33	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.	20	PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
34	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.	20	PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
35	1/2 ✓ Branch 0 taken 10 times. ✗ Branch 1 not taken.	20	if (!flag) m=n;
36		20	N = n*m;
37	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.	20	PetscCall(PetscOptionsGetScalar(NULL,NULL,"-sigma",&sigma,NULL));
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.	20	PetscCall(PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL));
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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));
40
41			/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42			Create the 2-D Laplacian, A
43			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
44
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.	20	PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
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.	20	PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
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.	20	PetscCall(MatSetFromOptions(A));
48	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.	20	PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
49	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2020	for (II=Istart;II<Iend;II++) {
50		2000	i = II/n; j = II-i*n;
51	6/8 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times. ✓ 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.	2000	if (i>0) PetscCall(MatSetValue(A,II,II-n,1.0,INSERT_VALUES));
52	6/8 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times. ✓ 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.	2000	if (i<m-1) PetscCall(MatSetValue(A,II,II+n,1.0,INSERT_VALUES));
53	6/8 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times. ✓ 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.	2000	if (j>0) PetscCall(MatSetValue(A,II,II-1,1.0,INSERT_VALUES));
54	6/8 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times. ✓ 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.	2000	if (j<n-1) PetscCall(MatSetValue(A,II,II+1,1.0,INSERT_VALUES));
55	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.	2000	PetscCall(MatSetValue(A,II,II,-4.0-sigma,INSERT_VALUES));
56			}
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.	20	PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
58	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.	20	PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
59
60			/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61			Create a low-rank Mat to store the right-hand side C = C1*C1'
62			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63
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.	20	PetscCall(MatCreate(PETSC_COMM_WORLD,&C1));
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.	20	PetscCall(MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2));
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.	20	PetscCall(MatSetType(C1,MATDENSE));
67	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.	20	PetscCall(MatGetOwnershipRange(C1,&Istart,&Iend));
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.	20	PetscCall(MatDenseGetArray(C1,&u));
69	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2020	for (i=Istart;i<Iend;i++) {
70	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2000	if (i<N/2) u[i-Istart] = 1.0;
71	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2000	if (i==0) u[i+Iend-2*Istart] = -2.0;
72	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2000	if (i==1) u[i+Iend-2*Istart] = -1.0;
73	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	2000	if (i==2) u[i+Iend-2*Istart] = -1.0;
74			}
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.	20	PetscCall(MatDenseRestoreArray(C1,&u));
76	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.	20	PetscCall(MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY));
77	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.	20	PetscCall(MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY));
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.	20	PetscCall(MatCreateLRC(NULL,C1,NULL,NULL,&C));
79	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.	20	PetscCall(MatDestroy(&C1));
80
81			/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82			Create the solver and set various options
83			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84			/*
85			Create the matrix equation solver context
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.	20	PetscCall(LMECreate(PETSC_COMM_WORLD,&lme));
88
89			/*
90			Set the type of equation
91			*/
92	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.	20	PetscCall(LMESetProblemType(lme,LME_LYAPUNOV));
93
94			/*
95			Set the matrix coefficients, the right-hand side, and the solution.
96			In this case, it is a Lyapunov equation AX+XA'=-C where both
97			C and X are symmetric and low-rank, C=C1C1', X=X1X1'
98			*/
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.	20	PetscCall(LMESetCoefficients(lme,A,NULL,NULL,NULL));
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.	20	PetscCall(LMESetRHS(lme,C));
101
102	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	20	if (rank) { /* Create X only if the user has specified a nonzero value of rank */
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.	10	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%" PetscInt_FMT "\n",rank));
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.	10	PetscCall(MatCreate(PETSC_COMM_WORLD,&X1));
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.	10	PetscCall(MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank));
106	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.	10	PetscCall(MatSetType(X1,MATDENSE));
107	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.	10	PetscCall(MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY));
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.	10	PetscCall(MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY));
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.	10	PetscCall(MatCreateLRC(NULL,X1,NULL,NULL,&X));
110	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.	10	PetscCall(MatDestroy(&X1));
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.	10	PetscCall(LMESetSolution(lme,X));
112	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.	10	PetscCall(MatDestroy(&X));
113			}
114
115			/*
116			(Optional) Set other solver options
117			*/
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.	20	PetscCall(LMESetTolerances(lme,1e-07,PETSC_CURRENT));
119
120			/*
121			Set solver parameters at runtime
122			*/
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.	20	PetscCall(LMESetFromOptions(lme));
124
125			/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126			Solve the matrix equation, AX+XA'=-C
127			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128
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.	20	PetscCall(LMESolve(lme));
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.	20	PetscCall(LMEGetConvergedReason(lme,&reason));
131	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 10 times. ✗ Branch 2 not taken. ✗ Branch 3 not taken.	20	PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
132
133	2/2 ✓ Branch 0 taken 10 times. ✓ Branch 1 taken 10 times.	20	if (!rank) { /* X1 was created by the solver, so extract it and see how many columns it has */
134	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.	10	PetscCall(LMEGetSolution(lme,&X));
135	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.	10	PetscCall(MatLRCGetMats(X,NULL,&X1,NULL,NULL));
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.	10	PetscCall(MatGetSize(X1,NULL,&rank));
137	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.	10	PetscCall(PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%" PetscInt_FMT "\n",rank));
138			}
139
140			/*
141			Optional: Get some information from the solver and display it
142			*/
143	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.	20	PetscCall(LMEGetIterationNumber(lme,&its));
144	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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
145	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.	20	PetscCall(LMEGetDimensions(lme,&ncv));
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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
147	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.	20	PetscCall(LMEGetTolerances(lme,&tol,&maxit));
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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
149
150			/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151			Compute residual error
152			- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153
154	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.	20	PetscCall(LMEGetErrorEstimate(lme,&errest));
155	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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest));
156	1/2 ✓ Branch 0 taken 10 times. ✗ Branch 1 not taken.	20	if (n<=150) {
157	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.	20	PetscCall(LMEComputeError(lme,&error));
158	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.	20	PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error));
159		✗	} else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Matrix too large to compute residual norm\n\n"));
160
161			/*
162			Free work space
163			*/
164	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.	20	PetscCall(LMEDestroy(&lme));
165	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.	20	PetscCall(MatDestroy(&A));
166	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.	20	PetscCall(MatDestroy(&C));
167	3/6 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 2 times. ✓ Branch 2 taken 2 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken. ✗ Branch 5 not taken.	20	PetscCall(SlepcFinalize());
168			return 0;
169			}
170
171			/*TEST
172
173			test:
174			suffix: 1
175			requires: !single
176
177			test:
178			suffix: 2
179			args: -rank 40
180			requires: !single
181
182			TEST*/
183