#! /usr/bin/env python
#
def uniform_01_order_sample ( n, seed ):

#*****************************************************************************80
#
## UNIFORM_01_ORDER_SAMPLE samples the Uniform 01 Order PDF.
#
#  Discussion:
#
#    In effect, this routine simply generates N samples of the
#    Uniform 01 PDF but it generates them in order.  (Actually,
#    it generates them in descending order, but stores them in
#    the array in ascending order).  This saves the work of
#    sorting the results.  Moreover, if the order statistics
#    for another PDF are desired, and the inverse CDF is available,
#    then the desired values may be generated, presorted, by
#    calling this routine and using the results as input to the
#    inverse CDF routine.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Jerry Banks, editor,
#    Handbook of Simulation,
#    Engineering and Management Press Books, 1998, page 168.
#
#  Parameters:
#
#    Input, integer N, the number of elements in the sample.
#
#    Input, integer SEED, a seed for the random number generator.
#
#    Output, real X(N), N samples of the Uniform 01 PDF, in
#    ascending order.
#
#    Output, integer SEED, an updated seed for the random number generator.
#
  import numpy as np
  from r8_uniform_01 import r8_uniform_01

  x = np.zeros ( n )
  v = 1.0

  for i in range ( n - 1, -1, -1 ):
    u, seed = r8_uniform_01 ( seed )
    v = v * u ** ( 1.0 / float ( i + 1  ) )
    x[i] = v

  return x, seed

def uniform_01_order_sample_test ( ):

#*****************************************************************************80
#
## UNIFORM_01_ORDER_SAMPLE_TEST tests UNIFORM_01_ORDER_SAMPLE
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8vec_print import r8vec_print

  n = 10
  seed = 123456789

  print ( '' )
  print ( 'UNIFORM_01_ORDER_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  UNIFORM_ORDER_SAMPLE samples the Uniform 01 Order distribution.' )

  x, seed = uniform_01_order_sample ( n, seed )

  r8vec_print ( n, x, '  Ordered sample:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'UNIFORM_01_ORDER_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  uniform_01_order_sample_test ( )
  timestamp ( )