#! /usr/bin/env python
#
def line01_monomial_integral ( e ):

#*****************************************************************************80
#
## LINE01_MONOMIAL_INTEGRAL: monomial integral over the unit line in 1D.
#
#  Discussion:
#
#    The integration region is 
#
#      0 <= X <= 1.
#
#    The monomial is F(X) = X^E.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    22 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Philip Davis, Philip Rabinowitz,
#    Methods of Numerical Integration,
#    Second Edition,
#    Academic Press, 1984, page 263.
#
#  Parameters:
#
#    Input, integer E, the exponent.
#    E must not equal -1.
#
#    Output, real INTEGRAL, the integral.
#
  from sys import exit

  if ( e == -1 ):
    print ( '' )
    print ( 'LINE01_MONOMIAL_INTEGRAL - Fatal error!' )
    print ( '  Exponent E = -1 is not allowed!' )
    exit ( 'LINE01_MONOMIAL_INTEGRAL - Fatal error!' )

  integral = 1.0 / float ( e + 1 )

  return integral

def line01_monomial_integral_test ( ):

#*****************************************************************************80
#
## LINE01_MONOMIAL_INTEGRAL_TEST tests LINE01_MONOMIAL_INTEGRAL.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 June 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from line01_length import line01_length
  from line01_sample import line01_sample
  from monomial_value_1d import monomial_value_1d

  m = 1
  n = 4192
  test_num = 11

  print ( '' )
  print ( 'LINE01_MONOMIAL_INTEGRAL_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LINE01_MONOMIAL_INTEGRAL computes integrals of monomials' )
  print ( '  along the length of the unit line in 1D.' )
  print ( '  Compare with a Monte Carlo estimate.' )
#
#  Get sample points.
#
  seed = 123456789
  x, seed = line01_sample ( n, seed )

  print ( '' )
  print ( '  Number of sample points used is %d' % ( n ) )
  print ( '' )
  print ( '   E     MC-Estimate      Exact           Error' )
  print ( '' )

  for test in range ( 0, test_num ):

    e = test

    value = monomial_value_1d ( n, e, x )

    result = line01_length ( ) * np.sum ( value ) / float ( n )
    exact = line01_monomial_integral ( e )
    error = abs ( result - exact )

    print ( '  %2d  %14.6g  %14.6g  %10.2g' % ( e, result, exact, error ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LINE01_MONOMIAL_INTEGRAL_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  line01_monomial_integral_test ( )
  timestamp ( )