#! /usr/bin/env python
#
def bradford_cdf_inv ( cdf, a, b, c ):

#*****************************************************************************80
#
## BRADFORD_CDF_INV inverts the Bradford CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real CDF, the value of the CDF.
#    0.0 <= CDF <= 1.0.
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, real X, the corresponding argument of the CDF.
#
  from sys import exit

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

  if ( cdf <= 0.0 ):
    x = a
  elif ( cdf < 1.0 ):
    x = a + ( b - a ) * ( ( c + 1.0 ) ** cdf - 1.0 ) / c
  elif ( 1.0 <= cdf ):
    x = b

  return x

def bradford_cdf ( x, a, b, c ):

#*****************************************************************************80
#
## BRADFORD_CDF evaluates the Bradford CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the argument of the CDF.
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, real CDF, the value of the CDF.
#
  import numpy as np

  if ( x <= a ):
    cdf = 0.0
  elif ( x <= b ):
    cdf = np.log ( 1.0 + c * ( x - a ) / ( b - a ) ) / np.log ( c + 1.0 )
  elif ( b < x ):
    cdf = 1.0

  return cdf

def bradford_cdf_test ( ):

#*****************************************************************************80
#
## BRADFORD_CDF_TEST tests BRADFORD_CDF, BRADFORD_CDF_INV, BRADFORD_PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'BRADFORD_CDF_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  BRADFORD_CDF evaluates the Bradford CDF' )
  print ( '  BRADFORD_CDF_INV inverts the Bradford CDF.' )
  print ( '  BRADFORD_PDF evaluates the Bradford PDF' )

  a = 1.0
  b = 2.0
  c = 3.0

  check = bradford_check ( a, b, c )

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

  print ( '' )
  print ( '  PDF parameter A = %14g' % ( a ) )
  print ( '  PDF parameter B = %14g' % ( b ) )
  print ( '  PDF parameter C = %14g' % ( c ) )

  seed = 123456789

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

  for i in range ( 0, 10 ):

    x, seed = bradford_sample ( a, b, c, seed )

    pdf = bradford_pdf ( x, a, b, c )

    cdf = bradford_cdf ( x, a, b, c )

    x2 = bradford_cdf_inv ( cdf, a, b, c )

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

def bradford_check ( a, b, c ):

#*****************************************************************************80
#
## BRADFORD_CHECK checks the parameters of the Bradford PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, logical CHECK, is TRUE if the parameters are legal.
#
  check = True

  if ( b <= a ):
    print ( '' )
    print ( 'BRADFORD_CHECK - Fatal error!' )
    print ( '  B <= A.' )
    check = False
  elif ( c <= 0.0 ):
    print ( '' )
    print ( 'BRADFORD_CHECK - Fatal error!' )
    print ( '  C <= 0.' )
    check = False

  return check

def bradford_mean ( a, b, c ):

#*****************************************************************************80
#
## BRADFORD_MEAN returns the mean of the Bradford PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, real MEAN, the mean of the PDF.
#
  import numpy as np

  mean = ( c * ( b - a ) + np.log ( c + 1.0 ) * ( a * ( c + 1.0 ) - b ) ) \
    / ( c * np.log ( c + 1.0 ) )

  return mean

def bradford_pdf ( x, a, b, c ):

#*****************************************************************************80
#
## BRADFORD_PDF evaluates the Bradford PDF.
#
#  Discussion:
#
#    PDF(X)(A,B,C) =
#      C / ( ( C * ( X - A ) + B - A ) * log ( C + 1 ) )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the argument of the PDF.
#    A <= X
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, real PDF, the value of the PDF.
#
  import numpy as np

  if ( x <= a ):
    pdf = 0.0
  elif ( x <= b ):
    pdf = c / ( ( c * ( x - a ) + b - a ) * np.log ( c + 1.0 ) )
  elif ( b < x ):
    pdf = 0.0

  return pdf

def bradford_sample ( a, b, c, seed ):

#*****************************************************************************80
#
## BRADFORD_SAMPLE samples the Bradford PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    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 r8_uniform_01 import r8_uniform_01

  cdf, seed = r8_uniform_01 ( seed )

  x = a + ( b - a ) * ( ( c + 1.0 ) ** cdf - 1.0 ) / c

  return x, seed

def bradford_sample_test ( ):

#*****************************************************************************80
#
## BRADFORD_SAMPLE_TEST tests BRADFORD_MEAN, BRADFORD_SAMPLE, BRADFORD_VARIANCE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 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

  nsample = 1000
  seed = 123456789

  print ( '' )
  print ( 'BRADFORD_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  BRADFORD_MEAN computes the Bradford mean' )
  print ( '  BRADFORD_SAMPLE samples the Bradford distribution' )
  print ( '  BRADFORD_VARIANCE computes the Bradford variance.' )

  a = 1.0
  b = 2.0
  c = 3.0

  check = bradford_check ( a, b, c )

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

  mean = bradford_mean ( a, b, c )
  variance = bradford_variance ( a, b, c )

  print ( '' )
  print ( '  PDF parameter A = %14g' % ( a ) )
  print ( '  PDF parameter B = %14g' % ( b ) )
  print ( '  PDF parameter C = %14g' % ( c ) )
  print ( '  PDF mean =        %14g' % ( mean ) )
  print ( '  PDF variance =    %14g' % ( variance ) )
  
  x = np.zeros ( nsample )

  for i in range ( 0, nsample ):
    x[i], seed = bradford_sample ( a, b, c, 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 ( 'BRADFORD_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

def bradford_variance ( a, b, c ):
 
#*****************************************************************************80
#
## BRADFORD_VARIANCE returns the variance of the Bradford PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, C, the parameters of the PDF.
#    A < B,
#    0.0 < C.
#
#    Output, real VARIANCE, the variance of the PDF.
#
  import numpy as np

  variance = ( b - a ) ** 2 * \
    ( c * ( np.log ( c + 1.0 ) - 2.0 ) + 2.0 * np.log ( c + 1.0 ) ) \
    / ( 2.0 * c * ( np.log ( c + 1.0 ) ) ** 2 )

  return variance

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  bradford_cdf_test ( )
  bradford_sample_test ( )
  timestamp ( )