/* Program usage:  mpirun ex1 [-help] [all PETSc options] */

static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

/*T
   Concepts: KSP^solving a system of linear equations
   Processors: 1
T*/

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

  Note:  The corresponding parallel example is ex23.c
*/
#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 */
  PC             pc;           /* preconditioner context */
  PetscReal      norm;         /* norm of solution error */
  PetscErrorCode ierr;
  PetscInt       i,n = 10,col[3],its;
  PetscMPIInt    size;
  PetscScalar    neg_one = -1.0,one = 1.0,value[3];

  PetscInitialize(&argc,&args,(char *)0,help);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
         Compute the matrix and right-hand-side vector that define
         the linear system, Ax = b.
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* 
     Create vectors.  Note that we form 1 vector from scratch and
     then duplicate as needed.
  */
  ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) x, "Solution");CHKERRQ(ierr);
  ierr = VecSetSizes(x,PETSC_DECIDE,n);CHKERRQ(ierr);
  ierr = VecSetFromOptions(x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&u);CHKERRQ(ierr);

  /* 
     Create matrix.  When using MatCreate(), the matrix format can
     be specified 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.
  */
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);

  /* 
     Assemble matrix
  */
  value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
  for (i=1; i<n-1; i++) {
    col[0] = i-1; col[1] = i; col[2] = i+1;
    ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
  }
  i = n - 1; col[0] = n - 2; col[1] = n - 1;
  ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
  i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
  ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* 
     Set exact solution; then compute right-hand-side vector.
  */
  ierr = VecSet(u,one);CHKERRQ(ierr);
  ierr = MatMult(A,u,b);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,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);

  /* 
     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 four statements are optional; all of these
       parameters could alternatively be specified at runtime via
       KSPSetFromOptions();
  */
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = PCSetType(pc,PCJACOBI);CHKERRQ(ierr);
  ierr = KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);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 the linear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /* 
     Solve linear system
  */
  ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr); 

  /* 
     View solver info; we could instead use the option -ksp_view to
     print this info to the screen at the conclusion of KSPSolve().
  */
  ierr = KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
                      Check solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /* 
     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);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",
                     norm,its);CHKERRQ(ierr);
  /* 
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
  */
  ierr = VecDestroy(x);CHKERRQ(ierr); ierr = VecDestroy(u);CHKERRQ(ierr);
  ierr = VecDestroy(b);CHKERRQ(ierr); ierr = MatDestroy(A);CHKERRQ(ierr);
  ierr = KSPDestroy(ksp);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();CHKERRQ(ierr);
  return 0;
}