#! /usr/bin/env python
#
def disk01_quarter_monte_carlo_test ( ):

#*****************************************************************************80
#
## DISK01_QUARTER_MONTE_CARLO_TEST tests Monte Carlo in the unit quarter disk.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 May 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from disk01_quarter_area import disk01_quarter_area
  from disk01_quarter_monomial_integral import disk01_quarter_monomial_integral
  from disk01_quarter_sample import disk01_quarter_sample
  from monomial_value import monomial_value

  print ( '' )
  print ( 'DISK01_QUARTER_MONTE_CARLO_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Use DISK01_QUARTER_SAMPLE to estimate integrals' )
  print ( '  in the unit quarter disk.' )

  e = np.zeros ( 2, dtype = np.int32 )

  for i in range ( 0, 5 ):
    e[0] = i 
    for j in range ( 0, 5 - e[0] ):
      e[1] = j
      exact = disk01_quarter_monomial_integral ( e )
      print ( '' )
      print ( '  Estimate integral of X^%d Y^%d' % ( e[0], e[1] ) )
      print ( '' )
      print ( '         N        Estimate       Error' )
      print ( '' )

      n = 1
      seed = 123456789

      while ( n <= 65536 ):

        x, seed = disk01_quarter_sample ( n, seed )
        value = monomial_value ( 2, n, e, x )

        q = disk01_quarter_area ( ) * np.sum ( value ) / n

        err = abs ( q - exact )
        print ( '  %8d  %14.6g  %10.2e' % ( n, q, err ) )
        n = 2 * n

      print ( '    Exact:  %14.6g  %10.2g' % ( exact, 0.0 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'DISK01_QUARTER_MONTE_CARLO_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  disk01_quarter_monte_carlo_test ( )
  timestamp ( )