#! /usr/bin/env python
#
def log_normal_truncated_ab_cdf ( x, mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_CDF evaluates the truncated AB Log Normal CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the argument of the PDF.
#    0.0 < X.
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, real CDF, the value of the CDF.
#
  from log_normal import log_normal_cdf
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_CDF - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_CDF - Fatal error!' )

  if ( x <= a ):

    cdf = 0.0

  elif ( b <= x ):

    cdf = 1.0

  else:

    lncdf_a = log_normal_cdf ( a, mu, sigma )
    lncdf_b = log_normal_cdf ( b, mu, sigma )
    lncdf_x = log_normal_cdf ( x, mu, sigma )

    cdf = ( lncdf_x - lncdf_a ) / ( lncdf_b - lncdf_a )

  return cdf

def log_normal_truncated_ab_cdf_inv ( cdf, mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_CDF_INV inverts the truncated AB Log Normal CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real CDF, the value of the CDF.
#    0 < CDF < 1.
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, real X, the argument of the PDF with the given CDF.
#
  from log_normal import log_normal_cdf
  from log_normal import log_normal_cdf_inv
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_CDF_INV - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_CDF_INV - Fatal error!' )

  if ( cdf <= 0.0 ):

    x = a

  elif ( 1.0 <= cdf ):

    x = b

  else:

    lncdf_a = log_normal_cdf ( a, mu, sigma )
    lncdf_b = log_normal_cdf ( b, mu, sigma )

    lncdf_x = lncdf_a + cdf * ( lncdf_b - lncdf_a )
    x = log_normal_cdf_inv ( lncdf_x, mu, sigma )

  return x

def log_normal_truncated_ab_cdf_test ( ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_CDF_TEST tests LOG_NORMAL_TRUNCATED_AB_CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from sys import exit

  print ( '' )
  print ( 'LOG_NORMAL_TRUNCATED_AB_CDF_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LOG_NORMAL_TRUNCATED_AB_CDF evaluates the Log Normal Truncated AB CDF' )
  print ( '  LOG_NORMAL_TRUNCATED_AB_CDF_INV inverts the Log Normal Truncated AB CDF.' )
  print ( '  LOG_NORMAL_TRUNCATED_AB_PDF evaluates the Log Normal Truncated AB PDF' )

  mu = 0.5
  sigma = 3.0
  a = np.exp ( mu )
  b = np.exp ( mu + 2.0 * sigma )

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_CDF_TEST - Fatal error!' )
    print ( '  The parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_CDF_TEST - Fatal error!' )

  print ( '' )
  print ( '  PDF parameter MU =            %14g' % ( mu ) )
  print ( '  PDF parameter SIGMA =         %14g' % ( sigma ) )
  print ( '  PDF parameter A =             %14g' % ( a ) )
  print ( '  PDF parameter B =             %14g' % ( b ) )

  seed = 123456789

  print ( '' )
  print ( '              X             PDF             CDF         CDF_INV' )
  print ( '' )

  for i in range ( 0, 10 ):

    x, seed = log_normal_truncated_ab_sample ( mu, sigma, a, b, seed )

    pdf = log_normal_truncated_ab_pdf ( x, mu, sigma, a, b )

    cdf = log_normal_truncated_ab_cdf ( x, mu, sigma, a, b )

    x2 = log_normal_truncated_ab_cdf_inv ( cdf, mu, sigma, a, b )

    print ( ' %14.6g  %14g  %14g  %14g' % ( x, pdf, cdf, x2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LOG_NORMAL_TRUNCATED_AB_CDF_TEST' )
  print ( '  Normal end of execution.' )
  return

def log_normal_truncated_ab_check ( mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_CHECK checks the truncated normal AB Log Normal PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, logical CHECK, is true if the parameters are legal.
#
  check = True

  if ( sigma <= 0.0 ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_CHECK - Fatal error!' )
    print ( '  SIGMA <= 0.' )
    check = False

  if ( b <= a ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_CHECK - Fatal error!' )
    print ( '  B <= A.' )
    check = False

  return check

def log_normal_truncated_ab_mean ( mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_MEAN returns the mean of the Log Normal Truncated AB PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, real MEAN, the mean of the PDF.
#
  import numpy as np
  from normal_01 import normal_01_cdf
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_MEAN - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_MEAN - Fatal error!' )

  a0 = ( np.log ( a ) - mu ) / sigma
  b0 = ( np.log ( b ) - mu ) / sigma

  c1 = normal_01_cdf ( sigma - a0 )
  c2 = normal_01_cdf ( sigma - b0 )
  c3 = normal_01_cdf ( + a0 )
  c4 = normal_01_cdf ( + b0 )

  ln_mean = np.exp ( mu + 0.5 * sigma ** 2 )

  mean = ln_mean * ( c1 - c2 ) / ( c4 - c3 )

  return mean

def log_normal_truncated_ab_pdf ( x, mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_PDF evaluates the truncated AB Log Normal PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the argument of the PDF.
#    0.0 < X.
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, real PDF, the value of the PDF.
#
  from log_normal import log_normal_cdf
  from log_normal import log_normal_pdf
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_PDF - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_PDF - Fatal error!' )

  if ( x <= a ):

    pdf = 0.0

  elif ( b <= x ):

    pdf = 0.0

  else:

    lncdf_a = log_normal_cdf ( a, mu, sigma )
    lncdf_b = log_normal_cdf ( b, mu, sigma )
    lnpdf_x = log_normal_pdf ( x, mu, sigma )

    pdf = lnpdf_x / ( lncdf_b - lncdf_a )

  return pdf

def log_normal_truncated_ab_sample ( mu, sigma, a, b, seed ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_SAMPLE samples the truncated AB Log Normal CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Input/output, integer SEED, a seed for the random number generator.
#
#    Output, real X, a random sample
#
  from log_normal import log_normal_cdf
  from log_normal import log_normal_cdf_inv
  from r8_uniform_ab import r8_uniform_ab
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE - Fatal error!' )

  lncdf_a = log_normal_cdf ( a, mu, sigma )
  lncdf_b = log_normal_cdf ( b, mu, sigma )

  cdf, seed = r8_uniform_ab ( lncdf_a, lncdf_b, seed )

  x = log_normal_cdf_inv ( cdf, mu, sigma )

  return x, seed

def log_normal_truncated_ab_sample_test ( ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_SAMPLE_TEST tests LOG_NORMAL_TRUNCATED_AB_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_max import r8vec_max
  from r8vec_mean import r8vec_mean
  from r8vec_min import r8vec_min
  from r8vec_variance import r8vec_variance
  from sys import exit

  nsample = 1000
  seed = 123456789

  print ( '' )
  print ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LOG_NORMAL_TRUNCATED_AB_MEAN computes the Log Normal Truncated AB mean' )
  print ( '  LOG_NORMAL_TRUNCATED_AB_SAMPLE samples the Log Normal Truncated AB distribution' )
  print ( '  LOG_NORMAL_TRUNCATED_AB_VARIANCE computes the Log Normal Truncated AB variance.' )

  mu = 0.5
  sigma = 3.0
  a = np.exp ( mu )
  b = np.exp ( mu + 2.0 * sigma )

  print ( '' )
  print ( '  PDF parameter MU =             %14g' % ( mu ) )
  print ( '  PDF parameter SIGMA =          %14g' % ( sigma ) )
  print ( '  PDF parameter A =              %14g' % ( a ) )
  print ( '  PDF parameter B =              %14g' % ( b ) )

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE_TEST - Fatal error!' )
    print ( '  The parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE_TEST - Fatal error!' )

  mean = log_normal_truncated_ab_mean ( mu, sigma, a, b )
  variance = log_normal_truncated_ab_variance ( mu, sigma, a, b )

  print ( '' )
  print ( '  PDF mean =                    %14g' % ( mean ) )
  print ( '  PDF variance =                %14g' % ( variance ) )

  x = np.zeros ( nsample )
  for i in range ( 0, nsample ):
    x[i], seed = log_normal_truncated_ab_sample ( mu, sigma, a, b, seed )

  mean = r8vec_mean ( nsample, x )
  variance = r8vec_variance ( nsample, x )
  xmax = r8vec_max ( nsample, x )
  xmin = r8vec_min ( nsample, x )

  print ( '' )
  print ( '  Sample size =     %6d' % ( nsample ) )
  print ( '  Sample mean =     %14g' % ( mean ) )
  print ( '  Sample variance = %14g' % ( variance ) )
  print ( '  Sample maximum =  %14g' % ( xmax ) )
  print ( '  Sample minimum =  %14g' % ( xmin ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LOG_NORMAL_TRUNCATED_AB_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

def log_normal_truncated_ab_variance ( mu, sigma, a, b ):

#*****************************************************************************80
#
## LOG_NORMAL_TRUNCATED_AB_VARIANCE: variance of the Log Normal Truncated AB PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the parameters of the log normal PDF.
#    0.0 < SIGMA.
#
#    Input, real A, B, the lower and upper truncation limits.
#    A < B.
#
#    Output, real VARIANCE, the mean of the PDF.
#
  import numpy as np
  from normal_01 import normal_01_cdf
  from sys import exit

  check = log_normal_truncated_ab_check ( mu, sigma, a, b )

  if ( not check ):
    print ( '' )
    print ( 'LOG_NORMAL_TRUNCATED_AB_VARIANCE - Fatal error!' )
    print ( '  Parameters are not legal.' )
    exit ( 'LOG_NORMAL_TRUNCATED_AB_VARIANCE - Fatal error!' )

  mean = log_normal_truncated_ab_mean ( mu, sigma, a, b )

  a0 = ( np.log ( a ) - mu ) / sigma
  b0 = ( np.log ( b ) - mu ) / sigma

  c1 = normal_01_cdf ( 2.0 * sigma - a0 )
  c2 = normal_01_cdf ( 2.0 * sigma - b0 )
  c3 = normal_01_cdf ( + a0 )
  c4 = normal_01_cdf ( + b0 )

  ln_xsquared = np.exp ( 2.0 * mu + 2.0 * sigma ** 2 )

  lntab_xsquared = ln_xsquared * ( c1 - c2 ) / ( c4 - c3 )

  variance = lntab_xsquared - mean ** 2

  return variance

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  log_normal_truncated_ab_cdf_test ( )
  log_normal_truncated_ab_sample_test ( )
  timestamp ( )