# include <complex.h>
# include <math.h>
# include <stdio.h>
# include <stdlib.h>

# include "r83.h"

int main ( );
void r83_cg_test ( );
void r83_cr_fa_test ( );
void r83_cr_sl_test ( );
void r83_cr_sls_test ( );
void r83_dif2_test ( );
void r83_gs_sl_test ( );
void r83_indicator_test ( );
void r83_jac_sl_test ( );
void r83_mtv_test ( );
void r83_mv_test ( );
void r83_print_test ( );
void r83_print_some_test ( );
void r83_random_test ( );
void r83_res_test ( );
void r83_to_r8ge_test ( );
void r83_zeros_test ( );

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    MAIN is the main program for R83_TEST.

  Discussion:

    R83_TEST tests R83.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "R83_TEST\n" );
  printf ( "  C version\n" );
  printf ( "  Test R83.\n" );

  r83_cg_test ( );
  r83_cr_fa_test ( );
  r83_cr_sl_test ( );
  r83_cr_sls_test ( );
  r83_dif2_test ( );
  r83_gs_sl_test ( );
  r83_indicator_test ( );
  r83_jac_sl_test ( );
  r83_mtv_test ( );
  r83_mv_test ( );
  r83_print_test ( );
  r83_print_some_test ( );
  r83_random_test ( );
  r83_res_test ( );
  r83_to_r8ge_test ( );
  r83_zeros_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "R83_TEST\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return 0;
}
/******************************************************************************/

void r83_cg_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_CG_TEST tests R83_CG.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 June 2014

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  double e_norm;
  int i;
  int n;
  double *r;
  double r_norm;
  int seed;
  double *x1;
  double *x2;

  printf ( "\n" );
  printf ( "R83_CG_TEST\n" );
  printf ( "  R83_CG applies CG to an R83 matrix.\n" );

  n = 10;
/*
  Let A be the -1 2 -1 matrix.
*/
  a = r83_dif2 ( n, n );
/*
  Choose a random solution.
*/
  seed = 123456789;
  x1 = r8vec_uniform_01_new ( n, &seed );
/*
  Compute the corresponding right hand side.
*/
  b = r83_mv ( n, n, a, x1 );
/*
  Call the CG routine.
*/
  x2 = ( double * ) malloc ( n * sizeof ( double ) );
  for ( i = 0; i < n; i++ )
  {
    x2[i] = 1.0;
  }
  r83_cg ( n, a, b, x2 );
/*
  Compute the residual.
*/
  r = r83_res ( n, n, a, x2, b );
  r_norm = r8vec_norm ( n, r );
/*
  Compute the error.
*/
  e_norm = r8vec_norm_affine ( n, x1, x2 );
/*
  Report.
*/
  printf ( "\n" );
  printf ( "  Number of variables N = %d\n", n );
  printf ( "  Norm of residual ||Ax-b|| = %g\n", r_norm );
  printf ( "  Norm of error ||x1-x2|| = %g\n", e_norm );
/*
  Free memory.
*/
  free ( a );
  free ( b );
  free ( r );
  free ( x1 );
  free ( x2 );

  return;
}
/******************************************************************************/

void r83_cr_fa_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_CR_FA_TEST tests R83_CR_FA.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    06 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *a_cr;
  double *b;
  int i;
  int j;
  int n = 10;
  double value;
  double *x;

  printf ( "\n" );
  printf ( "R83_CR_FA_TEST:\n" );
  printf ( "  R83_CR_FA factors an R83 matrix using cyclic reduction;\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  The matrix is NOT symmetric.\n" );
/*
  Set the matrix values.
*/
  a = ( double * ) malloc ( 3 * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < 3; i++ )
    {
      a[i+j*3] = 0.0;
    }
  }
 
  for ( j = 0; j < n; j++ )
  {
    for ( i = i4_max ( 0, j - 1 ); i <= i4_min ( n - 1, j + 1 ); i++ )
    {
      if ( j == i - 1 )
      {
        value = ( double ) ( j + 1 );
      }
      else if ( j == i )
      {
        value = ( double ) ( 4 * ( j + 1 ) );
      }
      else if ( j == i + 1 )
      {
        value = ( double ) ( j + 1 );
      }
      a[i-j+1+j*3] = value;
    }
  }

  r83_print ( n, n, a, "  The matrix:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83_mv ( n, n, a, x );
/*
  Factor the matrix.
*/
  a_cr = r83_cr_fa ( n, a );
/*
  Solve the linear system.
*/
  x = r83_cr_sl ( n, a_cr, b );

  r8vec_print ( n, x, "  Solution:" );

  free ( a );
  free ( a_cr );
  free ( b );
  free ( x );

  return;
}
/******************************************************************************/

void r83_cr_sl_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_CR_SL_TEST tests R83_CR_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    06 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *a_cr;
  double *b;
  int i;
  int j;
  int n = 10;
  double value;
  double *x;

  printf ( "\n" );
  printf ( "R83_CR_SL_TEST:\n" );
  printf ( "  R83_CR_SL solves a linear system A*x=b with R83 matrix\n" );
  printf ( "  using cyclic reduction, after factorization by R83_CR_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  The matrix is NOT symmetric.\n" );
/*
  Set the matrix values.
*/
  a = ( double * ) malloc ( 3 * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < 3; i++ )
    {
      a[i+j*3] = 0.0;
    }
  }
 
  for ( j = 0; j < n; j++ )
  {
    for ( i = i4_max ( 0, j - 1 ); i <= i4_min ( n - 1, j + 1 ); i++ )
    {
      if ( j == i - 1 )
      {
        value = ( double ) ( j + 1 );
      }
      else if ( j == i )
      {
        value = ( double ) ( 4 * ( j + 1 ) );
      }
      else if ( j == i + 1 )
      {
        value = ( double ) ( j + 1 );
      }
      a[i-j+1+j*3] = value;
    }
  }

  r83_print ( n, n, a, "  The matrix:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83_mv ( n, n, a, x );
/*
  Factor the matrix.
*/
  a_cr = r83_cr_fa ( n, a );
/*
  Solve the linear system.
*/
  x = r83_cr_sl ( n, a_cr, b );

  r8vec_print ( n, x, "  Solution:" );

  free ( a );
  free ( a_cr );
  free ( b );
  free ( x );

  return;
}
/******************************************************************************/

void r83_cr_sls_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_CR_SLS_TEST tests R83_CR_SLS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *a_cr;
  double *b;
  int i;
  int j;
  int n = 5;
  int nb = 2;
  double *x;

  printf ( "\n" );
  printf ( "R83_CR_SLS_TEST\n" );
  printf ( "  R83_CR_SLS solves multiple linear systems A*x=b1:bn with R83 matrix\n" );
  printf ( "  using cyclic reduction, after factorization by R83_CR_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Number of linear systems = %d\n", nb );
  printf ( "  Demonstrate multiple system solution method.\n" );
/*
  Set the matrix values.
*/
  a = r83_dif2 ( n, n );

  r83_print ( n, n, a, "  System matrix:" );
/*
  Factor the matrix once.
*/
  a_cr = r83_cr_fa ( n, a );
/*
  Set up the linear systems.
*/
  b = ( double * ) malloc ( n * nb * sizeof ( double ) );

  for ( j = 0; j < nb; j++ )
  {
    for ( i = 0; i < n; i++ )
    {
      b[i+j*n] = 0.0;
    }
  }

  j = 0;
  b[n-1+j*n] = ( double ) ( n + 1 );

  j = 1;
  b[0  +j*n] = 1.0;
  b[n-1+j*n] = 1.0;

  r8ge_print ( n, nb, b, "  RHS:" );
/*
  Solve the linear systems.
*/
  x = r83_cr_sls ( n, a_cr, nb, b );

  r8ge_print ( n, nb, x, "  Solutions:" );

  free ( a );
  free ( a_cr );
  free ( b );
  free ( x );

  return;
}
/******************************************************************************/

void r83_dif2_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_DIF2_TEST tests R83_DIF2.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    06 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83_DIF2_TEST\n" );
  printf ( "  R83_DIF2 sets up the second difference matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    a = r83_dif2 ( m, n );

    r83_print ( m, n, a, "  The R83 matrix:" );

    free ( a );
  }

  return;
}
/******************************************************************************/

void r83_gs_sl_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_GS_SL_TEST tests R83_GS_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int i;
  int maxit = 25;
  int n = 10;
  double *x;

  printf ( "\n" );
  printf ( "R83_GS_SL_TEST\n" );
  printf ( "  R83_GS_SL solves a linear system using Gauss-Seidel iteration.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
  printf ( "\n" );
/*
  Set the matrix values.
*/
  a = r83_dif2 ( n, n );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83_mv ( n, n, a, x );
/*
  Set the starting solution.
*/
  for ( i = 0; i < n; i++ )
  {
    x[i] = 0.0;
  }
/*
  Solve the linear system.
*/
  for ( i = 1; i <= 3; i++ )
  {
    r83_gs_sl ( n, a, b, x, maxit );

    r8vec_print ( n, x, "  Current estimated solution:" );
  }

  free ( a );
  free ( b );
  free ( x );

  return;
}
/******************************************************************************/

void r83_indicator_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_INDICATOR_TEST tests R83_INDICATOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    06 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83_INDICATOR_TEST\n" );
  printf ( "  R83_INDICATOR sets up an R83 indicator matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    a = r83_indicator ( m, n );

    r83_print ( m, n, a, "  The R83 indicator matrix:" );

    free ( a );
  }

  return;
}
/******************************************************************************/

void r83_jac_sl_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_JAC_SL_TEST tests R83_JAC_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    05 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int i;
  int maxit = 25;
  int n = 10;
  double *x;

  printf ( "\n" );
  printf ( "R83_JAC_SL_TEST\n" );
  printf ( "  R83_JAC_SL solves a linear system using Jacobi iteration,\n" );
  printf ( "  for an R83 matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
  printf ( "\n" );
/*
  Set the matrix values.
*/
  a = r83_dif2 ( n, n );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83_mv ( n, n, a, x );

  r8vec_print  ( n, b, "  The right hand side:" );
/*
  Set the starting solution.
*/
  for ( i = 0; i < n; i++ )
  {
    x[i] = 0.0;
  }
/*
  Solve the linear system.
*/
  for ( i = 1; i <= 3; i++ )
  {
    r83_jac_sl ( n, a, b, x, maxit );

    r8vec_print ( n, x, "  Current estimated solution:" );
  }

  free ( a );
  free ( b );
  free ( x );

  return;
}
/******************************************************************************/

void r83_mtv_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_MTV_TEST tests R83_MTV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83;
  double *a_ge;
  double *ax_83;
  double *ax_ge;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83_MTV_TEST\n" );
  printf ( "  R83_MTV computes b=A'*x, where A is an R83 matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    seed = 123456789;
    a_83 = r83_random ( m, n, &seed );
    x = r8vec_indicator1_new ( m );
    ax_83 = r83_mtv ( m, n, a_83, x );
    a_ge = r83_to_r8ge ( m, n, a_83 );
    ax_ge = r8ge_mtv ( m, n, a_ge, x );
    r8vec2_print ( n, ax_83, ax_ge, "  Product comparison:" );

    free ( a_83 );
    free ( a_ge );
    free ( ax_83 );
    free ( ax_ge );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83_mv_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_MV_TEST tests R83_MV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83;
  double *a_ge;
  double *ax_83;
  double *ax_ge;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83_MV_TEST\n" );
  printf ( "  R83_MV computes b=A*x, where A is an R83 matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    seed = 123456789;
    a_83 = r83_random ( m, n, &seed );
    x = r8vec_indicator1_new ( n );
    ax_83 = r83_mv ( m, n, a_83, x );
    a_ge = r83_to_r8ge ( m, n, a_83 );
    ax_ge = r8ge_mv ( m, n, a_ge, x );
    r8vec2_print ( m, ax_83, ax_ge, "  Product comparison:" );

    free ( a_83 );
    free ( a_ge );
    free ( ax_83 );
    free ( ax_ge );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83_print_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_PRINT_TEST tests R83_PRINT.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int m = 5;
  int n = 4;

  printf ( "\n" );
  printf ( "R83_PRINT_TEST\n" );
  printf ( "  R83_PRINT prints an R83 matrix.\n" );

  a = r83_indicator ( m, n );

  r83_print ( m, n, a, "  The R83  matrix:" );

  free ( a );

  return;
}
/******************************************************************************/

void r83_print_some_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_PRINT_SOME_TEST tests R83_PRINT_SOME.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int m = 5;
  int n = 5;

  printf ( "\n" );
  printf ( "R83_PRINT_SOME_TEST\n" );
  printf ( "  R83_PRINT_SOME prints some of an R83 matrix.\n" );

  a = r83_indicator ( m, n );

  r83_print_some ( m, n, a, 1, 1, 4, 3, "  Rows 1-4, Cols 1-3:" );

  free ( a );

  return;
}
/******************************************************************************/

void r83_random_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_RANDOM_TEST tests R83_RANDOM.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int m = 5;
  int n = 4;
  int seed;

  printf ( "\n" );
  printf ( "R83_RANDOM_TEST\n" );
  printf ( "  R83_RANDOM randomizes an R83 matrix.\n" );

  seed = 123456789;
  a = r83_random ( m, n, &seed );

  r83_print ( m, n, a, "  The R83  matrix:" );

  free ( a );

  return;
}
/******************************************************************************/

void r83_res_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_RES_TEST tests R83_RES.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    02 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int i;
  int m;
  int n;
  double *r;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83_RES_TEST\n" );
  printf ( "  R83_RES computes b-A*x, where A is an R83 matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    seed = 123456789;
    a = r83_random ( m, n, &seed );
    x = r8vec_indicator1_new ( n );
    b = r83_mv ( m, n, a, x );
    r = r83_res ( m, n, a, x, b );
    r8vec_print ( m, r, "  Residual A*x-b:" );

    free ( a );
    free ( b );
    free ( r );
    free ( x );
  }

  return;
}
/******************************************************************************/

void r83_to_r8ge_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_TO_R8GE_TEST tests R83_TO_R8GE.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83;
  double *a_ge;
  int i;
  int m;
  int n;
  int seed;

  printf ( "\n" );
  printf ( "R83_TO_R8GE_TEST\n" );
  printf ( "  R83_TO_R8GE converts an R83 matrix to R8GE format.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 0; i < 3; i++ )
  {
    if ( i == 0 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 1 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 3;
    }

    seed = 123456789;
    a_83 = r83_random ( m, n, &seed );
    r83_print ( m, n, a_83, "  The R83 matrix:" );
    a_ge = r83_to_r8ge ( m, n, a_83 );
    r8ge_print ( m, n, a_ge, "  The R8GE matrix:" );

    free ( a_83 );
    free ( a_ge );
  }
  return;
}
/******************************************************************************/

void r83_zeros_test ( )

/******************************************************************************/
/*
  Purpose:

    R83_ZEROS_TEST tests R83_ZEROS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 September 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int m = 5;
  int n = 4;

  printf ( "\n" );
  printf ( "R83_ZEROS_TEST\n" );
  printf ( "  R83_ZEROS zeros an R83 matrix.\n" );

  a = r83_zeros ( m, n );

  r83_print ( m, n, a, "  The R83  matrix:" );

  free ( a );

  return;
}