//===========================================================================
//  CVS Information:                                                         
//                                                                           
//     $RCSfile: ilu.cpp,v $  $Revision: 1.3 $  $State: Exp $ 
//     $Author: llee $  $Date: 2001/10/18 14:08:31 $ 
//     $Locker:  $ 
//---------------------------------------------------------------------------
//                                                                           
// DESCRIPTION                                                               
//                                                                           
//---------------------------------------------------------------------------
//                                                                           
// LICENSE AGREEMENT                                                         
//     $COPYRIGHT$
//---------------------------------------------------------------------------
//                                                                           
// REVISION HISTORY:                                                         
//                                                                           
// $Log: ilu.cpp,v $
// Revision 1.3  2001/10/18 14:08:31  llee
// re-organize the directory structures
//
// Revision 1.2  2000/07/27 04:39:18  llee1
// *** empty log message ***
//
// Revision 1.1  2000/07/26 21:49:22  llee1
// change file extension from .cc to .cpp
//
// Revision 1.2  2000/07/17 15:44:04  llee1
// *** empty log message ***
//
//                                                                           
//===========================================================================

#include "mtl/matrix.h"
#include "mtl/mtl.h"
#include "mtl/utils.h"

#include <itl/interface/mtl.h>
#include "itl/krylov/qmr.h"
#include "itl/preconditioner/ilu.h"

/*
  In thsi example, we show how to use ILU algorithm, the output should be:

iteration 0: resid 2.23607
iteration 1: resid 4.37539
iteration 2: resid 0.338066
iteration 3: resid 1.60609e-12
finished! error code = 0
3 iterations
1.60609e-12 is actual final residual.
7.18266e-13 is actual relative tolerance achieved.
Relative tol: 1e-06  Absolute tol: 0
     1      2      0      0      3   x          0.205847  =       1
     4      5      0      6      0   x         0.0419363  =       1
     0      7      8      0      9   x         -0.178049  =       1
     0      0     10     11     12   x       -0.00551162  =       1
     0      0     13      0     14   x           0.23676  =       1
*/

using namespace mtl;
using namespace itl;

typedef  double Type;
//begin
typedef matrix< Type, rectangle<>, 
	        array< compressed<> >, 
                row_major >::type Matrix;
//end
int main (int , char* []) 
{
  using std::cout;
  using std::endl;
  int max_iter = 50;
  //begin
  Matrix A(5, 5);
  //end
  A(0, 0) = 1.0;
  A(0, 1) = 2.0;
  A(0, 4) = 3.0;
  A(1, 0) = 4.0;
  A(1, 1) = 5.0;
  A(1, 3) = 6.0;
  A(2, 1) = 7.0;
  A(2, 2) = 8.0;
  A(2, 4) = 9.0;
  A(3, 2) = 10.;
  A(3, 3) = 11.;
  A(3, 4) = 12.;
  A(4, 2) = 13.; 
  A(4, 4) = 14.;
  //begin
  dense1D<Type> x(A.nrows(), Type(0));
  dense1D<Type> b(A.ncols());
  for (dense1D<Type>::iterator i=b.begin(); i!=b.end(); i++)
    *i = 1.;
  // ilu preconditioner 
  ILU<Matrix> precond(A);
  //iteration
  noisy_iteration<double> iter(b, max_iter, 1.e-6);
  //qmr algorithm
  qmr(A, x, b, precond.left(), precond.right(), iter);
  //end

  //verify the result
  dense1D<Type> b1(A.ncols());
  itl::mult(A, x, b1);
  itl::add(b1, itl::scaled(b, -1.), b1);

  if ( itl::two_norm(b1) < 1.e-6) { //output
    for (int i=0; i<5; i++) {
      for (int j=0; j<5; j++) {
	cout.width(6);
	//!!! it is not recommended to use A(i,j) for sparse matrices
	cout << A(i, j) << " ";
      }
      cout << "  x  ";
      cout.width(16);
      cout << x[i] << "  =  ";
      cout.width(6);
      cout << b[i] << endl;
    }
  } else {
    cout << "Residual " << iter.resid() << endl;
  }

  return 0;
  }