#! /usr/bin/env python3
#
def zipf_probability ( n, p ):

#****************************************************************************80
#
#  Purpose:
#
#    ZIPF_PROBABILITY sets up a Zipf probability vector.
#
#  Modified:
#
#    19 February 2016
#
#  Author:
#
#    Original C version by Warren Smith.
#    Python version by John Burkardt.
#
#  Reference:
#
#    George Zipf,
#    The Psychobiology of Language,
#    1935.
#
#  Parameters:
#
#    Input, unsigned int N, indicates the size of X.
#
#    Input, double P, the Zipf parameter.
#    1.0 < P.
#
#    Output, double X[N+2], contains in X[1] through X[N] the
#    probabilities of outcomes 1 through N.
#
  import numpy as np
  from normalize import normalize

  x = np.zeros ( n + 2 )

  for i in range ( 1, n + 1 ):
    x[i] = i ** ( - p )

  x = normalize ( n, x )

  return x

def zipf_probability_test ( ):

#*****************************************************************************80
#
## ZIPF_PROBABILITY_TEST tests ZIPF_PROBABILITY.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 February 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8vec_print import r8vec_print

  print ( '' )
  print ( 'ZIPF_PROBABILITY_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ZIPF_PROBABILITY sets up a probablity vector X of N+2 elements' )
  print ( '  containing in X[1:N] the probabilities of outcomes 1 through N' )
  print ( '  in a Zipf distribution with parameter P.' )

  n = 5
  p = 1.0
  x = zipf_probability ( n, p )
  r8vec_print ( n + 2, x, '  X for N = 5, P = 1.0' )

  n = 5
  p = 2.0
  x = zipf_probability ( n, p )
  r8vec_print ( n + 2, x, '  X for N = 5, P = 2.0' )

  n = 10
  p = 2.0
  x = zipf_probability ( n, p )
  r8vec_print ( n + 2, x, '  X for N = 10, P = 2.0' )
#
#  Terminate.
#
  print ( '' )
  print ( 'ZIPF_PROBABILITY_TEST' )
  print ( '  Normal end of execution.' )
  return

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