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

# include "r83s.h"

int main ( );

void r83s_cg_test ( );
void r83s_dif2_test ( );
void r83s_gs_sl_test ( );
void r83s_indicator_test ( );
void r83s_jac_sl_test ( );
void r83s_mtv_test ( );
void r83s_mv_test ( );
void r83s_print_test ( );
void r83s_print_some_test ( );
void r83s_random_test ( );
void r83s_res_test ( );
void r83s_to_r8ge_test ( );
void r83s_zeros_test ( );
void timestamp ( );

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

int main ( )

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

    r83s_test() tests r83s().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 August 2022

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "r83s_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test r83s().\n" );

  r83s_cg_test ( );
  r83s_dif2_test ( );
  r83s_gs_sl_test ( );
  r83s_indicator_test ( );
  r83s_jac_sl_test ( );
  r83s_mtv_test ( );
  r83s_mv_test ( );
  r83s_print_test ( );
  r83s_print_some_test ( );
  r83s_random_test ( );
  r83s_res_test ( );
  r83s_to_r8ge_test ( );
  r83s_zeros_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "r83s_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void r83s_cg_test ( )

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

    R83S_CG_TEST tests R83S_CG.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    09 July 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 ( "R83S_CG_TEST\n" );
  printf ( "  R83S_CG applies CG to an R83S matrix.\n" );

  n = 10;
/*
  Let A be the -1 2 -1 matrix.
*/
  a = r83s_dif2 ( n, n );
/*
  Choose a random solution.
*/
  seed = 123456789;
  x1 = r8vec_uniform_01_new ( n, &seed );
/*
  Compute the corresponding right hand side.
*/
  b = r83s_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;
  }
  r83s_cg ( n, a, b, x2 );
/*
  Compute the residual.
*/
  r = r83s_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 r83s_dif2_test ( )

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

    R83S_DIF2_TEST tests R83S_DIF2.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_DIF2_TEST\n" );
  printf ( "  R83S_DIF2 sets up the second difference matrix in R83S format.\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 = r83s_dif2 ( m, n );

    r83s_print ( m, n, a, "  The R83S matrix:" );

    free ( a );
  }

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

void r83s_gs_sl_test ( )

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

    R83S_GS_SL_TEST tests R83S_GS_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_GS_SL_TEST\n" );
  printf ( "  R83S_GS_SL uses Gauss-Seidel iteration on an R83S matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
/*
  Set the matrix values.
*/
  a = r83s_dif2 ( n, n );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83s_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++ )
  {
    r83s_gs_sl ( n, a, b, x, maxit );

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

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

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

void r83s_indicator_test ( )

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

    R83S_INDICATOR_TEST tests R83S_INDICATOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_INDICATOR_TEST\n" );
  printf ( "  R83S_INDICATOR sets up an R83S indicator matrix.\n" );

  a = r83s_indicator ( m, n );

  r83s_print ( m, n, a, "  The R83S indicator matrix:" );

  free ( a );

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

void r83s_jac_sl_test ( )

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

    R83S_JAC_SL_TEST tests R83S_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 ( "R83S_JAC_SL_TEST\n" );
  printf ( "  R83S_JAC_SL solves a linear system using Jacobi iteration,\n" );
  printf ( "  for an R83S matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
/*
  Set the matrix values.
*/
  a = r83s_dif2 ( n, n );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83s_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++ )
  {
    r83s_jac_sl ( n, a, b, x, maxit );

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

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

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

void r83s_mtv_test ( )

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

    R83S_MTV_TEST tests R83S_MTV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83s;
  double *a_ge;
  double *ax_83s;
  double *ax_ge;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83S_MTV_TEST\n" );
  printf ( "  R83S_MTV computes b=A'*x, where A is an R83S 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_83s = r83s_random ( m, n, &seed );
    x = r8vec_indicator1_new ( m );
    ax_83s = r83s_mtv ( m, n, a_83s, x );
    a_ge = r83s_to_r8ge ( m, n, a_83s );
    ax_ge = r8ge_mtv ( m, n, a_ge, x );
    r8vec2_print ( n, ax_83s, ax_ge, "  Product comparison:" );

    free ( a_83s );
    free ( a_ge );
    free ( ax_83s );
    free ( ax_ge );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83s_mv_test ( )

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

    R83S_MV_TEST tests R83S_MV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83s;
  double *a_ge;
  double *ax_83s;
  double *ax_ge;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83S_MV_TEST\n" );
  printf ( "  R83S_MV computes b=A*x, where A is an R83S 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_83s = r83s_random ( m, n, &seed );
    x = r8vec_indicator1_new ( n );
    ax_83s = r83s_mv ( m, n, a_83s, x );
    a_ge = r83s_to_r8ge ( m, n, a_83s );
    ax_ge = r8ge_mv ( m, n, a_ge, x );
    r8vec2_print ( m, ax_83s, ax_ge, "  Product comparison:" );

    free ( a_83s );
    free ( a_ge );
    free ( ax_83s );
    free ( ax_ge );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83s_print_test ( )

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

    R83S_PRINT_TEST tests R83S_PRINT.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_PRINT_TEST\n" );
  printf ( "  R83S_PRINT prints an R83S matrix.\n" );

  a = r83s_indicator ( m, n );

  r83s_print ( m, n, a, "  The R83S  matrix:" );

  free ( a );

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

void r83s_print_some_test ( )

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

    R83S_PRINT_SOME_TEST tests R83S_PRINT_SOME.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_PRINT_SOME_TEST\n" );
  printf ( "  R83S_PRINT_SOME prints some of an R83S matrix.\n" );

  a = r83s_indicator ( m, n );

  r83s_print_some ( m, n, a, 1, 1, 4, 3, "  Rows 1-4, Cols 1-3:" );

  free ( a );

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

void r83s_random_test ( )

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

    R83S_RANDOM_TEST tests R83S_RANDOM.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_RANDOM_TEST\n" );
  printf ( "  R83S_RANDOM randomizes an R83S matrix.\n" );

  seed = 123456789;
  a = r83s_random ( m, n, &seed );

  r83s_print ( m, n, a, "  The R83  matrix:" );

  free ( a );

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

void r83s_res_test ( )

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

    R83S_RES_TEST tests R83S_RES.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_RES_TEST\n" );
  printf ( "  R83S_RES computes b-A*x, where A is an R83S 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 = r83s_random ( m, n, &seed );
    x = r8vec_indicator1_new ( n );
    b = r83s_mv ( m, n, a, x );
    r = r83s_res ( m, n, a, x, b );
    r8vec_print ( m, r, "  Residual A*x-b:" );

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

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

void r83s_to_r8ge_test ( )

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

    R83S_TO_R8GE_TEST tests R83S_TO_R8GE.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 September 2015

  Author:

    John Burkardt
*/
{
  double *a_83s;
  double *a_ge;
  int i;
  int m;
  int n;
  int seed;

  printf ( "\n" );
  printf ( "R83S_TO_R8GE_TEST\n" );
  printf ( "  R83S_TO_R8GE converts an R83S matrix to R8GE format.\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_83s = r83s_random ( m, n, &seed );
    r83s_print ( m, n, a_83s, "  The R83S matrix:" );
    a_ge = r83s_to_r8ge ( m, n, a_83s );
    r8ge_print ( m, n, a_ge, "  The R8GE matrix:" );

    free ( a_83s );
    free ( a_ge );
  }
  return;
}
/******************************************************************************/

void r83s_zeros_test ( )

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

    R83S_ZEROS_TEST tests R83S_ZEROS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 September 2015

  Author:

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

  printf ( "\n" );
  printf ( "R83S_ZEROS_TEST\n" );
  printf ( "  R83S_ZEROS zeros an R83S matrix.\n" );

  a = r83s_zeros ( m, n );

  r83s_print ( m, n, a, "  The R83S matrix:" );

  free ( a );

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

void timestamp ( )

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

    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    31 May 2001 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    24 September 2003

  Author:

    John Burkardt
*/
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}