static char help[] = "Solves a linear system in parallel with KSP.\n\
Input parameters include:\n\
  -random_exact_sol : use a random exact solution vector\n\
  -view_exact_sol   : write exact solution vector to stdout\n\
  -m <mesh_x>       : number of mesh points in x-direction\n\
  -n <mesh_y>       : number of mesh points in y-direction\n\n";

/*
  Include "petscksp.h" so that we can use KSP solvers.  Note that this file
  automatically includes:
     petscsys.h       - base PETSc routines   petscvec.h - vectors
     petscmat.h - matrices
     petscis.h     - index sets            petscksp.h - Krylov subspace methods
     petscviewer.h - viewers               petscpc.h  - preconditioners
*/
#include <petscksp.h>

int main(int argc, char **args)
{
  Vec         x, b, u; /* approx solution, RHS, exact solution */
  Mat         A;       /* linear system matrix */
  KSP         ksp;     /* linear solver context */
  PetscRandom rctx;    /* random number generator context */
  PetscReal   norm;    /* norm of solution error */
  PetscInt    i, j, Ii, J, m = 8, n = 7, its;
  PetscBool   flg = PETSC_FALSE;
  PetscScalar v;
  PetscMPIInt rank;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
         Compute the matrix and right-hand-side vector that define
         the linear system, Ax = b.
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /*
     Create parallel matrix, specifying only its global dimensions.
     When using MatCreate(), the matrix format can be specified at
     runtime. Also, the parallel partitioning of the matrix is
     determined by PETSc at runtime.

     Performance tuning note:  For problems of substantial size,
     preallocation of matrix memory is crucial for attaining good
     performance. See the matrix chapter of the users manual for details.
  */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
  PetscCall(MatSetType(A, MATELEMENTAL));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));
  if (rank == 0) {
    PetscInt M, N;
    PetscCall(MatGetSize(A, &M, &N));
    for (Ii = 0; Ii < M; Ii++) {
      v = -1.0;
      i = Ii / n;
      j = Ii - i * n;
      if (i > 0) {
        J = Ii - n;
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
      }
      if (i < m - 1) {
        J = Ii + n;
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
      }
      if (j > 0) {
        J = Ii - 1;
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
      }
      if (j < n - 1) {
        J = Ii + 1;
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
      }
      v = 4.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

  /* PetscCall(MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE)); */

  /*
     Create parallel vectors.
      - We form 1 vector from scratch and then duplicate as needed.
      - When using VecCreate(), VecSetSizes and VecSetFromOptions()
        in this example, we specify only the
        vector's global dimension; the parallel partitioning is determined
        at runtime.
      - When solving a linear system, the vectors and matrices MUST
        be partitioned accordingly.  PETSc automatically generates
        appropriately partitioned matrices and vectors when MatCreate()
        and VecCreate() are used with the same communicator.
      - The user can alternatively specify the local vector and matrix
        dimensions when more sophisticated partitioning is needed
        (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
        below).
  */
  PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
  PetscCall(VecSetSizes(u, PETSC_DECIDE, m * n));
  PetscCall(VecSetFromOptions(u));
  PetscCall(VecDuplicate(u, &b));
  PetscCall(VecDuplicate(b, &x));

  /*
     Set exact solution; then compute right-hand-side vector.
     By default we use an exact solution of a vector with all
     elements of 1.0;  Alternatively, using the runtime option
     -random_sol forms a solution vector with random components.
  */
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-random_exact_sol", &flg, NULL));
  if (flg) {
    PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rctx));
    PetscCall(PetscRandomSetFromOptions(rctx));
    PetscCall(VecSetRandom(u, rctx));
    PetscCall(PetscRandomDestroy(&rctx));
  } else {
    PetscCall(VecSet(u, 1.0));
  }
  PetscCall(MatMult(A, u, b));

  /*
     View the exact solution vector if desired
  */
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_exact_sol", &flg, NULL));
  if (flg) PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the linear solver and set various options
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Create linear solver context
  */
  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));

  /*
     Set operators. Here the matrix that defines the linear system
     also serves as the preconditioning matrix.
  */
  PetscCall(KSPSetOperators(ksp, A, A));

  /*
     Set linear solver defaults for this problem (optional).
     - By extracting the KSP and PC contexts from the KSP context,
       we can then directly call any KSP and PC routines to set
       various options.
     - The following two statements are optional; all of these
       parameters could alternatively be specified at runtime via
       KSPSetFromOptions().  All of these defaults can be
       overridden at runtime, as indicated below.
  */
  PetscCall(KSPSetTolerances(ksp, 1.e-2 / ((m + 1) * (n + 1)), PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));

  /*
    Set runtime options, e.g.,
        -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    These options will override those specified above as long as
    KSPSetFromOptions() is called _after_ any other customization
    routines.
  */
  PetscCall(KSPSetFromOptions(ksp));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the linear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  PetscCall(KSPSolve(ksp, b, x));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Check solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Check the error
  */
  PetscCall(VecAXPY(x, -1.0, u));
  PetscCall(VecNorm(x, NORM_2, &norm));
  PetscCall(KSPGetIterationNumber(ksp, &its));

  /*
     Print convergence information.  PetscPrintf() produces a single
     print statement from all processes that share a communicator.
     An alternative is PetscFPrintf(), which prints to a file.
  */
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g iterations %" PetscInt_FMT "\n", (double)norm, its));

  /*
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
  */
  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&u));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&b));
  PetscCall(MatDestroy(&A));

  /*
     Always call PetscFinalize() before exiting a program.  This routine
       - finalizes the PETSc libraries as well as MPI
       - provides summary and diagnostic information if certain runtime
         options are chosen (e.g., -log_view).
  */
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      nsize: 6
      args: -pc_type none
      requires: elemental

   test:
      suffix: 2
      nsize: 6
      args: -pc_type lu -pc_factor_mat_solver_type elemental
      requires: elemental

TEST*/
