#! /usr/bin/env python
#
def agud ( g ):

#*****************************************************************************80
#
## AGUD evaluates the inverse Gudermannian function.
#
#  Discussion:
#
#    The Gudermannian function relates the hyperbolic and trigonomentric
#    functions.  For any argument X, there is a corresponding value
#    G so that
#
#      SINH(X) = TAN(G).
#
#    This value G(X) is called the Gudermannian of X.  The inverse
#    Gudermannian function is given as input a value G and computes
#    the corresponding value X.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 July 2004
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real G, the value of the Gudermannian.
#
#    Output, real VALUE, the argument of the Gudermannian.
#
  import numpy as np

  value = np.log ( np.tan ( 0.25 * np.pi + 0.5 * g ) )

  return value

def agud_test ( ):

#*****************************************************************************80
#
## AGUD_TEST tests AGUD.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform
  from gud import gud

  print ( '' )
  print ( 'AGUD_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  AGUD evaluates the inverse Gudermannian function.' )
  print ( '' )
  print ( '        X            GUD(X)     AGUD(GUD(X))' )
  print ( '' )

  for i in range ( 0, 11 ):
    x = 1.0 + i / 5.0
    g = gud ( x )
    x2 = agud ( g )
    print ( '  %12f  %12f  %12f' % ( x, g, x2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'AGUD_TEST' )
  print ( '  Normal end of execution.' )
  return

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