#! /usr/bin/env python
#
def truncated_normal_a_cdf_inv ( cdf, mu, sigma, a ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_CDF_INV inverts the lower truncated Normal CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 March 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real CDF, the value of the CDF.
#    0.0 <= CDF <= 1.0.
#
#    Input, real MU, SIGMA, the mean and standard deviation of the
#    parent Normal distribution.
#
#    Input, real A, the lower truncation limit.
#
#    Output, real X, the corresponding argument.
#
  from normal_01_cdf import normal_01_cdf
  from normal_01_cdf_inv import normal_01_cdf_inv
  from sys import exit

  if ( cdf < 0.0 or 1.0 < cdf ):
    print ( '' )
    print ( 'TRUNCATED_NORMAL_A_CDF_INV - Fatal error!' )
    print ( '  CDF < 0 or 1 < CDF.' )
    exit ( 'TRUNCATED_NORMAL_A_CDF_INV - Fatal error!' )

  alpha = ( a - mu ) / sigma

  alpha_cdf = normal_01_cdf ( alpha )
  beta_cdf = 1.0

  xi_cdf = ( beta_cdf - alpha_cdf ) * cdf + alpha_cdf
  xi = normal_01_cdf_inv ( xi_cdf )

  x = mu + sigma * xi

  return x

def truncated_normal_a_cdf_inv_test ( ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_CDF_INV_TEST tests TRUNCATED_NORMAL_A_CDF_INV.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 March 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from truncated_normal_a_cdf import truncated_normal_a_cdf
  from truncated_normal_a_sample import truncated_normal_a_sample

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

  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_CDF_INV_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TRUNCATED_NORMAL_A_CDF_INV inverts the CDF of' )
  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 ( '             X            CDF            CDF_INV' )
  print ( '' )

  for i in range ( 0, sample_num ):
    x, seed = truncated_normal_a_sample ( mu, sigma, a, seed )
    cdf = truncated_normal_a_cdf ( x, mu, sigma, a )
    x2 = truncated_normal_a_cdf_inv ( cdf, mu, sigma, a )
    print ( '  %14.6g  %14.6g  %14.6g' % ( x, cdf, x2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_CDF_INV_TEST' )
  print ( '  Normal end of execution.' )
  return

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