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

# include "runge.h"

int main ( );
void runge_antideriv_test ( );
void runge_deriv_test ( );
void runge_deriv2_test ( );
void runge_fun_test ( );
void runge_power_series_test ( );
void gnuplot_fx ( int n, double *x, double *y, char *header );
void gnuplot_fxdd ( int n, double *x, double *y1, double *y2, char *header );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

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

    runge_test() tests runge().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

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

  runge_antideriv_test ( );
  runge_deriv_test ( );
  runge_deriv2_test ( );
  runge_fun_test ( );
  runge_power_series_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "runge_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void runge_antideriv_test ( )

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

    runge_antideriv_test() tests runge_antideriv().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  char *header = "runge_antideriv";
  int i;
  int n = 51;
  double *x;
  double *y;

  printf ( "\n" );
  printf ( "runge_antideriv_test():\n" );
  printf ( "  runge_antideriv() evaluates the antiderivative\n" );
  printf ( "  of the runge function.\n" );

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_antideriv ( x[i] );
  }

  gnuplot_fx ( n, x, y, header );

  free ( x );
  free ( y );

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

void runge_deriv_test ( )

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

    runge_deriv_test() tests runge_deriv().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  char *header = "runge_deriv";
  int i;
  int n = 51;
  double *x;
  double *y;

  printf ( "\n" );
  printf ( "runge_deriv_test():\n" );
  printf ( "  runge_deriv() evaluates the derivative\n" );
  printf ( "  of the runge function.\n" );

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_deriv ( x[i] );
  }

  gnuplot_fx ( n, x, y, header );

  free ( x );
  free ( y );

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

void runge_deriv2_test ( )

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

    runge_deriv2_test() tests runge_deriv2().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  char *header = "runge_deriv2";
  int i;
  int n = 51;
  double *x;
  double *y;

  printf ( "\n" );
  printf ( "runge_deriv2_test():\n" );
  printf ( "  runge_deriv2() evaluates the second derivative\n" );
  printf ( "  of the runge function.\n" );

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_deriv2 ( x[i] );
  }

  gnuplot_fx ( n, x, y, header );

  free ( x );
  free ( y );

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

void runge_fun_test ( )

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

    runge_fun_test() tests runge_fun().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  char *header = "runge_fun";
  int i;
  int n = 51;
  double *x;
  double *y;

  printf ( "\n" );
  printf ( "runge_fun_test():\n" );
  printf ( "  runge_fun() evaluates the  runge function.\n" );

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_fun ( x[i] );
  }

  gnuplot_fx ( n, x, y, header );

  free ( x );
  free ( y );

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

void runge_power_series_test ( )

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

    runge_power_series_test() tests runge_power_series().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    25 March 2025

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  char *header = "runge_power_series";
  int i;
  int n = 51;
  int n2 = 8;
  double *x;
  double *y1;
  double *y2;

  printf ( "\n" );
  printf ( "runge_power_series_test():\n" );
  printf ( "  runge_power_series() compares a power series to\n" );
  printf ( "  the Runge function.\n" );

  a = -0.2;
  b = +0.2;
  x = r8vec_linspace_new ( n, a, b );
  y1 = ( double * ) malloc ( n * sizeof ( double ) );
  y2 = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    y1[i] = runge_fun ( x[i] );
    y2[i] = runge_power_series ( x[i], n2 );
  }

  gnuplot_fxdd ( n, x, y1, y2, header );

  free ( x );
  free ( y1 );
  free ( y2 );

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

void gnuplot_fx ( int n, double *x, double *y, char *header )

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

    gnuplot_fx() plots n values y=f(x).

  Discussion:

    Actually, we simply create two files for processing by gnuplot().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2025

  Author:

    John Burkardt
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  int i;
  char png_filename[255];
/*
  Create a graphics data file.
*/
  strcpy ( data_filename, header );
  strcat ( data_filename, "_data.txt" );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < n; i++ )
  {
    fprintf ( data_unit, "%14.6g %14.6g\n", x[i], y[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );

  strcpy ( png_filename, header );
  strcat ( png_filename, ".png" );
/*
  Create graphics command file.
*/
  strcpy ( command_filename, header );
  strcat ( command_filename, "_commands.txt" );
  command_unit = fopen ( command_filename, "wt" );
  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set output '%s'\n", png_filename );
  fprintf ( command_unit, "set xlabel '<--- X --->'\n" );
  fprintf ( command_unit, "set ylabel '<-- Y(X) -->'\n" );
  fprintf ( command_unit, "set title '%s'\n", header );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, 
    "plot '%s' using 1:2 lw 3 linecolor rgb 'blue'\n", data_filename );
  fclose ( command_unit );
  printf ( "  Created command file '%s'\n", command_filename );

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

void gnuplot_fxdd ( int n, double *x, double *y1, double *y2, char *header )

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

    gnuplot_fxdd() plots n values of y1=f(x) (curve) and y2 = x2 (data)

  Discussion:

    Actually, we simply create two files for processing by gnuplot().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    25 March 2025

  Author:

    John Burkardt
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  int i;
  char png_filename[255];
/*
  Create a graphics data file.
*/
  strcpy ( data_filename, header );
  strcat ( data_filename, "_data.txt" );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < n; i++ )
  {
    fprintf ( data_unit, "%14.6g %14.6g %14.6g\n", x[i], y1[i], y2[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );

  strcpy ( png_filename, header );
  strcat ( png_filename, ".png" );
/*
  Create graphics command file.
*/
  strcpy ( command_filename, header );
  strcat ( command_filename, "_commands.txt" );
  command_unit = fopen ( command_filename, "wt" );
  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set output '%s'\n", png_filename );
  fprintf ( command_unit, "set xlabel '<--- X --->'\n" );
  fprintf ( command_unit, "set ylabel '<-- Y(X) -->'\n" );
  fprintf ( command_unit, "set title '%s'\n", header );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, 
    "plot '%s' using 1:2 lw 3 linecolor rgb 'blue',\\\n", data_filename );
  fprintf ( command_unit, 
    "     '%s' using 1:3 with points pointtype 7 linecolor 'red'\n", data_filename );
  fclose ( command_unit );
  printf ( "  Created command file '%s'\n", command_filename );

  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
}