#! /usr/bin/env python
#
def hermite_integral ( n ):

#*****************************************************************************80
#
## HERMITE_INTEGRAL evaluates a monomial Hermite integral.
#
#  Discussion:
#
#    The integral:
#
#      Integral ( -oo < x < +oo ) x^n exp(-x^2) dx
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order of the integral.
#    0 <= N.
#
#    Output, real VALUE, the value of the integral.
#
  import numpy as np
  from r8_factorial2 import r8_factorial2
  from r8_huge import r8_huge

  if ( n < 0 ):

    value = - r8_huge ( )

  elif ( ( n % 2 ) == 1 ):

    value = 0.0

  else:

    value = r8_factorial2 ( n - 1 ) * np.sqrt ( np.pi ) / 2.0 ** ( n // 2 )

  return value

def hermite_integral_test ( ):

#*****************************************************************************80
#
## HERMITE_INTEGRAL_TEST tests HERMITE_INTEGRAL.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    12 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'HERMITE_INTEGRAL_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  HERMITE_INTEGRAL evaluates' )
  print ( '  Integral ( -oo < x < +oo ) exp(-x^2) x^m dx' )
  print ( '' )
  print ( '         N         Value' )
  print ( '' )

  for n in range ( 0, 11 ):

    value = hermite_integral ( n )

    print ( '  %8d  %24.16g' % ( n, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'HERMITE_INTEGRAL_TEST' )
  print ( '  Normal end of execution.' )
  return

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