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

# include "kdv_exact.h"

int main ( );
void kdv_exact_rational_test ( );
void kdv_exact_sech_test ( );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

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

    kdv_exact_test() tests kdv_exact().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 May 2024

  Author:

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

  kdv_exact_rational_test ( );
  kdv_exact_sech_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "kdv_exact_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void kdv_exact_rational_test ( )

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

    kdv_exact_rational_test() tests kdv_exact_rational().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 May 2024

  Author:

    John Burkardt
*/
{

  int nt = 6;
  int nx = 6;

  int i;
  int j;
  double r;
  double *t;
  double t0;
  double tstop;
  double u;
  double ut;
  double ux;
  double uxx;
  double uxxx;
  double *x;

  printf ( "\n" );
  printf ( "kdv_exact_rational_test():\n" );
  printf ( "  Test kdv_exact_rational().\n" );

  kdv_parameters ( NULL, NULL, NULL, NULL, NULL, NULL, &t0, &tstop );

  printf ( "\n" );
  printf ( "  Parameters:\n" );
  printf ( "    t0    = %g\n", t0 );
  printf ( "    tstop = %g\n", tstop );

  printf ( "\n" );
  printf ( "  Evaluate solution and residual at selected points (X,T)\n" );
  
  x = r8vec_linspace_new ( nx, 0.0, 1.0 );
  t = r8vec_linspace_new ( nt, t0, tstop );

  printf ( "\n" );
  printf ( "      T       X       U(X,T)      Resid(X,T)\n" );
  printf ( "\n" );

  for ( i = 0; i < nt; i++ )
  {
    for ( j = 0; j < nx; j++ )
    {
      kdv_exact_rational ( x[j], t[i], &u, &ut, &ux, &uxx, &uxxx );
      r = kdv_residual ( u, ut, ux, uxxx );

      if ( t[i] == 0.0 && x[j] == 0.0 )
      {
        printf ( "%14.6g%14.6g     Undefined     Undefined\n", t[i], x[j] );
      }
      else
      {
        printf ( "%14.6g%14.6g%14.6g%14.6g\n", t[i], x[j], u, r );
      }
    }
    printf ( "\n" );
  }

  free ( t );
  free ( x );

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

void kdv_exact_sech_test ( )

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

    kdv_exact_sech_test() tests kdv_exact_sech().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 May 2024

  Author:

    John Burkardt
*/
{
  int nt = 6;
  int nx = 6;

  double a;
  int i;
  int j;
  double r;
  double *t;
  double t0;
  double tstop;
  double u;
  double ut;
  double ux;
  double uxx;
  double uxxx;
  double v;
  double *x;

  printf ( "\n" );
  printf ( "kdv_exact_sech_test():\n" );
  printf ( "  Test kdv_exact_sech().\n" );

  kdv_parameters ( NULL, NULL, NULL, NULL, &a, &v, &t0, &tstop );

  printf ( "\n" );
  printf ( "  Parameters:\n" );
  printf ( "    a     = %g\n", a );
  printf ( "    v     = %g\n", v );
  printf ( "    t0    = %g\n", t0 );
  printf ( "    tstop = %g\n", tstop );

  printf ( "\n" );
  printf ( "  Evaluate solution and residual at selected points (X,T)\n" );
  
  x = r8vec_linspace_new ( nx, 0.0, 1.0 );
  t = r8vec_linspace_new ( nt, t0, tstop );

  printf ( "\n" );
  printf ( "      T       X       U(X,T)      Resid(X,T)\n" );
  printf ( "\n" );

  for ( i = 0; i < nt; i++ )
  {
    for ( j = 0; j < nx; j++ )
    {
      kdv_exact_sech ( x[j], t[i], &u, &ut, &ux, &uxx, &uxxx );
      r = kdv_residual ( u, ut, ux, uxxx );

      if ( t[i] == 0.0 && x[j] == 0.0 )
      {
        printf ( "%14.6g%14.6g     Undefined     Undefined\n", t[i], x[j] );
      }
      else
      {
        printf ( "%14.6g%14.6g%14.6g%14.6g\n", t[i], x[j], u, r );
      }
    }
    printf ( "\n" );
  }

  free ( t );
  free ( x );

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

double *r8vec_linspace_new ( int n, double a, double b )

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

    r8vec_linspace_new() creates a vector of linearly spaced values.

  Discussion:

    An R8VEC is a vector of R8's.

    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
 
    In other words, the interval is divided into N-1 even subintervals,
    and the endpoints of intervals are used as the points.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    29 March 2011

  Author:

    John Burkardt

  Input:

    int N, the number of entries in the vector.

    double A, B, the first and last entries.

  Output:

    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
*/
{
  int i;
  double *x;

  x = ( double * ) malloc ( n * sizeof ( double ) );

  if ( n == 1 )
  {
    x[0] = ( a + b ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      x[i] = ( ( double ) ( n - 1 - i ) * a 
             + ( double ) (         i ) * b ) 
             / ( double ) ( n - 1     );
    }
  }
  return x;
}
/******************************************************************************/

void timestamp ( )

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

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

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  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
}