/*
2-clause BSD license

Copyright (c) 1991-2014, UChicago Argonne, LLC and the PETSc Development Team
All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:

 * Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice, this
  list of conditions and the following disclaimer in the documentation and/or
  other materials provided with the distribution.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
  ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
  ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
  ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

static char help[] = "Solves a sequence of linear systems with different right-hand-side vectors.\n\
Input parameters include:\n\
  -ntimes <ntimes>  : number of linear systems to solve\n\
  -view_exact_sol   : write exact solution vector to stdout\n\
  -m <mesh_x>       : number of mesh points in x-direction\n\
  -n <mesh_n>       : number of mesh points in y-direction\n\n";

/*T
   Concepts: KSP^repeatedly solving linear systems;
   Concepts: KSP^Laplacian, 2d
   Concepts: Laplacian, 2d
   Processors: n
T*/

/*
  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>

#undef __FUNCT__
#define __FUNCT__ "main"

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 */
    PetscReal norm; /* norm of solution error */
    PetscErrorCode ierr;
    PetscInt ntimes, i, j, k, Ii, J, Istart, Iend;
    PetscInt m = 8, n = 7, its;
    PetscBool flg = PETSC_FALSE;
    PetscScalar v, one = 1.0, neg_one = -1.0, rhs;

    PetscInitialize(&argc, &args, (char*) 0, help);
    ierr = PetscOptionsGetInt(NULL, "-m", &m, NULL);
    CHKERRQ(ierr);
    ierr = PetscOptionsGetInt(NULL, "-n", &n, NULL);
    CHKERRQ(ierr);

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
           Compute the matrix for use in solving a series of
           linear systems of the form, A x_i = b_i, for i=1,2,...
       - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    /*
       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.
     */
    ierr = MatCreate(PETSC_COMM_WORLD, &A);
    CHKERRQ(ierr);
    ierr = MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m*n, m * n);
    CHKERRQ(ierr);
    ierr = MatSetFromOptions(A);
    CHKERRQ(ierr);
    ierr = MatSetUp(A);
    CHKERRQ(ierr);

    /*
       Currently, all PETSc parallel matrix formats are partitioned by
       contiguous chunks of rows across the processors.  Determine which
       rows of the matrix are locally owned.
     */
    ierr = MatGetOwnershipRange(A, &Istart, &Iend);
    CHKERRQ(ierr);

    /*
       Set matrix elements for the 2-D, five-point stencil in parallel.
        - Each processor needs to insert only elements that it owns
          locally (but any non-local elements will be sent to the
          appropriate processor during matrix assembly).
        - Always specify global rows and columns of matrix entries.
     */
    for (Ii = Istart; Ii < Iend; Ii++) {
        v = -1.0;
        i = Ii / n;
        j = Ii - i*n;
        if (i > 0) {
            J = Ii - n;
            ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
            CHKERRQ(ierr);
        }
        if (i < m - 1) {
            J = Ii + n;
            ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
            CHKERRQ(ierr);
        }
        if (j > 0) {
            J = Ii - 1;
            ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
            CHKERRQ(ierr);
        }
        if (j < n - 1) {
            J = Ii + 1;
            ierr = MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
            CHKERRQ(ierr);
        }
        v = 4.0;
        ierr = MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES);
        CHKERRQ(ierr);
    }

    /*
       Assemble matrix, using the 2-step process:
         MatAssemblyBegin(), MatAssemblyEnd()
       Computations can be done while messages are in transition
       by placing code between these two statements.
     */
    ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
    CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
    CHKERRQ(ierr);

    /*
       Create parallel vectors.
        - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
          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.
        - Note: We form 1 vector from scratch and then duplicate as needed.
     */
    ierr = VecCreate(PETSC_COMM_WORLD, &u);
    CHKERRQ(ierr);
    ierr = VecSetSizes(u, PETSC_DECIDE, m * n);
    CHKERRQ(ierr);
    ierr = VecSetFromOptions(u);
    CHKERRQ(ierr);
    ierr = VecDuplicate(u, &b);
    CHKERRQ(ierr);
    ierr = VecDuplicate(b, &x);
    CHKERRQ(ierr);

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

    /*
       Create linear solver context
     */
    ierr = KSPCreate(PETSC_COMM_WORLD, &ksp);
    CHKERRQ(ierr);

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

    /*
      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.
     */
    ierr = KSPSetFromOptions(ksp);
    CHKERRQ(ierr);

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
         Solve several linear systems of the form  A x_i = b_i
         I.e., we retain the same matrix (A) for all systems, but
         change the right-hand-side vector (b_i) at each step.

         In this case, we simply call KSPSolve() multiple times.  The
         preconditioner setup operations (e.g., factorization for ILU)
         be done during the first call to KSPSolve() only; such operations
         will NOT be repeated for successive solves.
       - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    ntimes = 2;
    ierr = PetscOptionsGetInt(NULL, "-ntimes", &ntimes, NULL);
    CHKERRQ(ierr);
    for (k = 1; k < ntimes + 1; k++) {

        /*
           Set exact solution; then compute right-hand-side vector.  We use
           an exact solution of a vector with all elements equal to 1.0*k.
         */
        rhs = one * (PetscReal) k;
        ierr = VecSet(u, rhs);
        CHKERRQ(ierr);
        ierr = MatMult(A, u, b);
        CHKERRQ(ierr);

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

        ierr = KSPSolve(ksp, b, x);
        CHKERRQ(ierr);

        /*
           Check the error
         */
        ierr = VecAXPY(x, neg_one, u);
        CHKERRQ(ierr);
        ierr = VecNorm(x, NORM_2, &norm);
        CHKERRQ(ierr);
        ierr = KSPGetIterationNumber(ksp, &its);
        CHKERRQ(ierr);
        /*
           Print convergence information.  PetscPrintf() produces a single
           print statement from all processes that share a communicator.
         */
        ierr = PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g System %D: iterations %D\n", (double) norm, k, its);
        CHKERRQ(ierr);
    }

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

    /*
       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_summary).
     */
    ierr = PetscFinalize();
    return 0;
}