static char help[] = "Tests matrix factorization.  Note that most users should\n\
employ the KSP  interface to the linear solvers instead of using the factorization\n\
routines directly.\n\n";

#include <petscmat.h>

int main(int argc, char **args)
{
  Mat           C, LU;
  MatInfo       info;
  PetscInt      i, j, m, n, Ii, J;
  PetscScalar   v, one = 1.0;
  IS            perm, iperm;
  Vec           x, u, b;
  PetscReal     norm, fill;
  MatFactorInfo luinfo;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));

  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Mat test ex7 options", "Mat");
  m    = 3;
  n    = 3;
  fill = 2.0;
  PetscCall(PetscOptionsInt("-m", "Number of rows in grid", NULL, m, &m, NULL));
  PetscCall(PetscOptionsInt("-n", "Number of columns in grid", NULL, n, &n, NULL));
  PetscCall(PetscOptionsReal("-fill", "Expected fill ratio for factorization", NULL, fill, &fill, NULL));

  PetscOptionsEnd();

  /* Create the matrix for the five point stencil, YET AGAIN */
  PetscCall(MatCreate(PETSC_COMM_SELF, &C));
  PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
  PetscCall(MatSetFromOptions(C));
  PetscCall(MatSetUp(C));
  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++) {
      v  = -1.0;
      Ii = j + n * i;
      if (i > 0) {
        J = Ii - n;
        PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = Ii + n;
        PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = Ii - 1;
        PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = Ii + 1;
        PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 4.0;
      PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatGetOrdering(C, MATORDERINGRCM, &perm, &iperm));
  PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(ISView(perm, PETSC_VIEWER_STDOUT_SELF));

  PetscCall(MatFactorInfoInitialize(&luinfo));

  luinfo.fill          = fill;
  luinfo.dtcol         = 0.0;
  luinfo.zeropivot     = 1.e-14;
  luinfo.pivotinblocks = 1.0;

  PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_LU, &LU));
  PetscCall(MatLUFactorSymbolic(LU, C, perm, iperm, &luinfo));
  PetscCall(MatLUFactorNumeric(LU, C, &luinfo));

  PetscCall(VecCreateSeq(PETSC_COMM_SELF, m * n, &u));
  PetscCall(VecSet(u, one));
  PetscCall(VecDuplicate(u, &x));
  PetscCall(VecDuplicate(u, &b));

  PetscCall(MatMult(C, u, b));
  PetscCall(MatSolve(LU, b, x));

  PetscCall(VecView(b, PETSC_VIEWER_STDOUT_SELF));
  PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));

  PetscCall(VecAXPY(x, -1.0, u));
  PetscCall(VecNorm(x, NORM_2, &norm));
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "Norm of error %g\n", (double)norm));

  PetscCall(MatGetInfo(C, MAT_LOCAL, &info));
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "original matrix nonzeros = %" PetscInt_FMT "\n", (PetscInt)info.nz_used));
  PetscCall(MatGetInfo(LU, MAT_LOCAL, &info));
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "factored matrix nonzeros = %" PetscInt_FMT "\n", (PetscInt)info.nz_used));

  PetscCall(VecDestroy(&u));
  PetscCall(VecDestroy(&b));
  PetscCall(VecDestroy(&x));
  PetscCall(ISDestroy(&perm));
  PetscCall(ISDestroy(&iperm));
  PetscCall(MatDestroy(&C));
  PetscCall(MatDestroy(&LU));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 1
      filter: grep -v " MPI process"

   test:
      suffix: 2
      args: -m 1 -n 1 -fill 0.49
      filter: grep -v " MPI process"

TEST*/