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

#*****************************************************************************80
#
## ERF_VALUES returns some values of the ERF or "error" function.
#
#  Discussion:
#
#    The error function is defined by:
#
#      ERF(X) = ( 2 / sqrt ( PI ) * integral ( 0 <= T <= X ) exp ( - T^2 ) dT
#
#    In Mathematica, the function can be evaluated by:
#
#      Erf[x]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 September 2004
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    National Bureau of Standards, 1964,
#    ISBN: 0-486-61272-4,
#    LC: QA47.A34.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Cambridge University Press, 1999,
#    ISBN: 0-521-64314-7,
#    LC: QA76.95.W65.
#
#  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 = 21

  fx_vec = np.array ( ( \
     0.0000000000000000E+00, \
     0.1124629160182849E+00, \
     0.2227025892104785E+00, \
     0.3286267594591274E+00, \
     0.4283923550466685E+00, \
     0.5204998778130465E+00, \
     0.6038560908479259E+00, \
     0.6778011938374185E+00, \
     0.7421009647076605E+00, \
     0.7969082124228321E+00, \
     0.8427007929497149E+00, \
     0.8802050695740817E+00, \
     0.9103139782296354E+00, \
     0.9340079449406524E+00, \
     0.9522851197626488E+00, \
     0.9661051464753107E+00, \
     0.9763483833446440E+00, \
     0.9837904585907746E+00, \
     0.9890905016357307E+00, \
     0.9927904292352575E+00, \
     0.9953222650189527E+00 ) )

  x_vec = np.array ( ( \
     0.0E+00, \
     0.1E+00, \
     0.2E+00, \
     0.3E+00, \
     0.4E+00, \
     0.5E+00, \
     0.6E+00, \
     0.7E+00, \
     0.8E+00, \
     0.9E+00, \
     1.0E+00, \
     1.1E+00, \
     1.2E+00, \
     1.3E+00, \
     1.4E+00, \
     1.5E+00, \
     1.6E+00, \
     1.7E+00, \
     1.8E+00, \
     1.9E+00, \
     2.0E+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 erf_values_test ( ):

#*****************************************************************************80
#
## ERF_VALUES_TEST demonstrates the use of ERF_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'ERF_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ERF_VALUES stores values of the error function.' )
  print ( '' )
  print ( '      X         ERF(X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, fx = erf_values ( n_data )

    if ( n_data == 0 ):
      break

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

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