#! /usr/bin/env python
#
def gamma_values ( n_data ):

#*****************************************************************************80
#
## GAMMA_VALUES returns some values of the Gamma function.
#
#  Discussion:
#
#    The Gamma function is defined as:
#
#      Gamma(Z) = Integral ( 0 <= T < Infinity) T^(Z-1) exp(-T) dT
#
#    It satisfies the recursion:
#
#      Gamma(X+1) = X * Gamma(X)
#
#    Gamma is undefined for nonpositive integral X.
#    Gamma(0.5) = sqrt(PI)
#    For N a positive integer, Gamma(N+1) = N!, the standard factorial.
#
#    In Mathematica, the function can be evaluated by:
#
#      Gamma[x]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    25 July 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, real X, the argument of the function.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 25

  fx_vec = np.array ( ( \
     -0.3544907701811032E+01, \
     -0.1005871979644108E+03, \
      0.9943258511915060E+02, \
      0.9513507698668732E+01, \
      0.4590843711998803E+01, \
      0.2218159543757688E+01, \
      0.1772453850905516E+01, \
      0.1489192248812817E+01, \
      0.1164229713725303E+01, \
      0.1000000000000000E+01, \
      0.9513507698668732E+00, \
      0.9181687423997606E+00, \
      0.8974706963062772E+00, \
      0.8872638175030753E+00, \
      0.8862269254527580E+00, \
      0.8935153492876903E+00, \
      0.9086387328532904E+00, \
      0.9313837709802427E+00, \
      0.9617658319073874E+00, \
      0.1000000000000000E+01, \
      0.2000000000000000E+01, \
      0.6000000000000000E+01, \
      0.3628800000000000E+06, \
      0.1216451004088320E+18, \
      0.8841761993739702E+31 ) )

  x_vec = np.array ( ( \
     -0.50E+00, \
     -0.01E+00, \
      0.01E+00, \
      0.10E+00, \
      0.20E+00, \
      0.40E+00, \
      0.50E+00, \
      0.60E+00, \
      0.80E+00, \
      1.00E+00, \
      1.10E+00, \
      1.20E+00, \
      1.30E+00, \
      1.40E+00, \
      1.50E+00, \
      1.60E+00, \
      1.70E+00, \
      1.80E+00, \
      1.90E+00, \
      2.00E+00, \
      3.00E+00, \
      4.00E+00, \
     10.00E+00, \
     20.00E+00, \
     30.00E+00 ) )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    x = 0.0
    fx = 0.0
  else:
    x = x_vec[n_data]
    fx = fx_vec[n_data]
    n_data = n_data + 1

  return n_data, x, fx

def gamma_values_test ( ):

#*****************************************************************************80
#
## GAMMA_VALUE_TEST demonstrates the use of GAMMA_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 February 2009
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'GAMMA_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  GAMMA_VALUES stores values of the Gamma function.' )
  print ( '' )
  print ( '      X            GAMMA(X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, fx = gamma_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %24.16f' % ( x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'GAMMA_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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