//===========================================================================
//  CVS Information:                                                         
//                                                                           
//     $RCSfile: gmres.cpp,v $  $Revision: 1.2 $  $State: Exp $ 
//     $Author: llee $  $Date: 2001/10/18 14:08:31 $ 
//     $Locker:  $ 
//---------------------------------------------------------------------------
//                                                                           
// DESCRIPTION                                                               
//                                                                           
//---------------------------------------------------------------------------
//                                                                           
// LICENSE AGREEMENT                                                         
// Copyright 1997, University of Notre Dame.
// Authors: Andrew Lumsdaine, Lie-Quan Lee
//
// This file is part of the Iterative Template Library
//
// You should have received a copy of the License Agreement for the
// Iterative Template Library along with the software;  see the
// file LICENSE.  If not, contact Office of Research, University of Notre
// Dame, Notre Dame, IN  46556.
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// Permission to modify the code and to distribute modified code is
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// with the COPYRIGHT NOTICE in the LICENSE file, and that the LICENSE
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// By way of example, but not limitation, Licensor MAKES NO
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//---------------------------------------------------------------------------
//                                                                           
// REVISION HISTORY:                                                         
//                                                                           
// $Log: gmres.cpp,v $
// Revision 1.2  2001/10/18 14:08:31  llee
// re-organize the directory structures
//
// Revision 1.1  2000/07/26 21:49:24  llee1
// change file extension from .cc to .cpp
//
// Revision 1.3  2000/07/26 04:19:35  llee1
// *** empty log message ***
//
// Revision 1.2  2000/07/26 01:06:34  llee1
// *** empty log message ***
//
// Revision 1.1  2000/07/25 22:57:53  llee1
// *** empty log message ***
//
// Revision 1.3  2000/07/19 19:58:00  llee1
// *** empty log message ***
//
// 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/blas.h"

#include "itl/preconditioner/ssor.h"
#include "itl/krylov/gmres.h"
#include <vector>

/*
  In thsi example, we show how to use GMRES(m) algorithm, the output should be:

iteriteration 0: resid 2.23607
iteration 1: resid 0.920575
iteration 2: resid 0.666842
iteration 3: resid 0.622789
iteration 4: resid 0.541757
iteration 5: resid 2.90594e-16
iteration 5: resid 7.77156e-16
finished! error code = 0
5 iterations
7.77156e-16 is actual final residual.
3.47555e-16 is actual relative tolerance achieved.
Relative tol: 1e-06  Absolute tol: 0
   x          0.205847  =       1
   x         0.0419363  =       1
   x         -0.178049  =       1
   x       -0.00551162  =       1
   x           0.23676  =       1
*/

using namespace itl;
using namespace std;

typedef  double Type;

//begin
typedef sparse_matrix<Type> Matrix;
typedef std::vector<Type> Vector;
//end

int main (int , char* []) 
{
  int max_iter = 50;

  std::vector<double> val(14);
  std::vector<int> ind(14);
  std::vector<int> ptr(6);
  for (int i = 0; i<14;i++) val[i] = i+1;
//   Matrix A(5, 5);
//   A(0, 0) = 1.0;
  ptr[0] = 0;
  ind[0] = 0;
//   A(0, 1) = 2.0;
  ind[1] = 1;
//   A(0, 4) = 3.0;
  ind[2] = 4;
  ptr[1] = 3;
//   A(1, 0) = 4.0;
  ind[3] = 0;
//   A(1, 1) = 5.0;
  ind[4] = 1;
//   A(1, 3) = 6.0;
  ind[5] = 3;
  ptr[2] = 6;
//   A(2, 1) = 7.0;
  ind[6] = 1;
//   A(2, 2) = 8.0;
  ind[7] = 2;
//   A(2, 4) = 9.0;
  ind[8] = 4;
  ptr[3] = 9;
//   A(3, 2) = 10.;
  ind[9] = 2;
//   A(3, 3) = 11.;
  ind[10] = 3;
//   A(3, 4) = 12.;
  ind[11] = 4;
  ptr[4] = 12;
//   A(4, 2) = 13.; 
  ind[12] = 2;
//   A(4, 4) = 14.;
  ind[13] = 4;
  ptr[5] = 14;

  //begin
  Matrix A(5, 5, 14, &val[0], &ind[0], &ptr[0]);
  //end

  Vector x(A.nrows(), Type(0));
  Vector b(A.ncols());
  for (Vector::iterator i=b.begin(); i!=b.end(); i++)
    *i = 1.;
  //begin
  identity_preconditioner p;

  Vector b2(A.ncols());
  itl::solve(p, b, b2); //gmres needs teh preconditioned b to pass into iter object.
  //iteration
  noisy_iteration<double> iter(b2, max_iter, 1e-6);
  int restart = 10;

  //modified_gram_schmidt<Vector> basis(restart, size(x));
  //gmres algorithm, by default, modified gram schmidt is used.
  gmres(A, x, b, p, restart, iter); //restart constant: 10
  //end

  //verify the result
  Vector b1(A.ncols());
  itl::mult(A, x, b1);
  itl::add(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);
	//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;
  }