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

# include "circle_integrals.h"

int main ( );
void test01 ( );

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

int main ( )

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

    MAIN is the main program for CIRCLE_INTEGRALS_TEST.

  Discussion:

    CIRCLE_INTEGRALS_TEST tests the CIRCLE_INTEGRALS library.
    
  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    12 January 2014

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "CIRCLE_INTEGRALS_TEST\n" );
  printf ( "  C version\n" );
  printf ( "  Test the CIRCLE_INTEGRALS library.\n" );

  test01 ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "CIRCLE_INTEGRALS_TEST\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void test01 ( )

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

    TEST01 uses CIRCLE01_SAMPLE with an increasing number of points.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    12 January 2014

  Author:

    John Burkardt
*/
{
  int *e;
  double error;
  double exact;
  int i;
  int m = 2;
  int n = 4192;
  double result;
  int seed;
  int test;
  int test_num = 20;
  double *value;
  double *x;

  printf ( "\n" );
  printf ( "TEST01\n" );
  printf ( "  Use CIRCLE01_SAMPLE to compare exact and\n" );
  printf ( "  estimated integrals along the circumference\n" );
  printf ( "  of the unit circle in 2D.\n" );
/*
  Get sample points.
*/
  seed = 123456789;
  x = circle01_sample ( n, &seed );

  printf ( "\n" );
  printf ( "  Number of sample points used is %d\n", n );
/*
  Randomly choose X, Y exponents.
*/
  printf ( "\n" );
  printf ( "  If any exponent is odd, the integral is zero.\n" );
  printf ( "  We restrict this test to randomly chosen even exponents.\n" );
  printf ( "\n" );
  printf ( "  Ex  Ey     MC-Estimate           Exact      Error\n" );
  printf ( "\n" );

  for ( test = 1; test <= test_num; test++ )
  {
    e = i4vec_uniform_ab_new ( m, 0, 5, &seed );

    for ( i = 0; i < m; i++ )
    {
      e[i] = e[i] * 2;
    }

    value = monomial_value ( m, n, e, x );

    result = circle01_length ( ) * r8vec_sum ( n, value ) 
      / ( double ) ( n );
    exact = circle01_monomial_integral ( e );
    error = fabs ( result - exact );

    printf ( "  %2d  %2d  %14.6g  %14.6g  %10.2e\n",
      e[0], e[1], result, exact, error );

    free ( e );
    free ( value );
  }

  free ( x );

  return;
}