#! /usr/bin/env python
#
def truncated_normal_a_sample ( mu, sigma, a, seed ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_SAMPLE samples the lower Truncated Normal distribution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 March 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the mean and standard deviation of the
#    parent Normal distribution.
#
#    Input, real A, the lower truncation limit.
#
#    Input, integer SEED, a seed for the random number generator.
#
#    Output, real X, a sample of the PDF.
#
#    Output, integer SEED, a seed for the random number generator.
#
  from normal_01_cdf import normal_01_cdf
  from normal_01_cdf_inv import normal_01_cdf_inv
  from r8_uniform_01 import r8_uniform_01

  alpha = ( a - mu ) / sigma

  alpha_cdf = normal_01_cdf ( alpha )
  beta_cdf = 1.0

  u, seed = r8_uniform_01 ( seed )
  xi_cdf = alpha_cdf + u * ( beta_cdf - alpha_cdf )
  xi = normal_01_cdf_inv ( xi_cdf )

  x = mu + sigma * xi

  return x, seed

def truncated_normal_a_sample_test ( ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_SAMPLE_TEST tests TRUNCATED_NORMAL_A_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 March 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  sample_num = 10
  seed = 123456789
  a = 50.0
  mu = 100.0
  sigma = 25.0

  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TRUNCATED_NORMAL_A_SAMPLE samples' )
  print ( '  the lower Truncated Normal distribution.' )

  print ( '' )
  print ( '  The "parent" normal distribution has' )
  print ( '    mean =               %g' % ( mu ) )
  print ( '    standard deviation = %g' % ( sigma ) )
  print ( '  The parent distribution is truncated to' )
  print ( '  the interval [%g,+oo)' % ( a ) )
  print ( '' )

  print ( '' )
  for i in range ( 0, sample_num ):
    x, seed = truncated_normal_a_sample ( mu, sigma, a, seed )
    print ( '  %4d  %14.6g' % ( i, x ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

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