#! /usr/bin/env python
#
def chi_square_noncentral_check ( a, b ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_CHECK checks the parameters of the noncentral Chi Squared PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 April 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer A, the parameter of the PDF.
#    1.0 <= A.
#
#    Input, real B, the noncentrality parameter of the PDF.
#    0.0 <= B.
#
  check = True

  if ( a < 1.0 ):
    print ( '' )
    print ( 'CHI_SQUARE_NONCENTRAL_CHECK - Fatal error!' )
    print ( '  A < 1.' )
    check = False

  if ( b < 0.0 ):
    print ( '' )
    print ( 'CHI_SQUARE_NONCENTRAL_CHECK - Fatal error!' )
    print ( '  B < 0.' )
    check = False

  return check

def chi_square_noncentral_mean ( a, b ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_MEAN returns the mean of the noncentral Chi squared PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 April 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer A, the parameter of the PDF.
#    1.0 <= A.
#
#    Input, real B, the noncentrality parameter of the PDF.
#    0.0 <= B.
#
#    Output, real MEAN, the mean value.
#
  mean = a + b

  return mean

def chi_square_noncentral_sample ( a, b, seed ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_SAMPLE samples the noncentral Chi squared PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 April 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer A, the parameter of the PDF.
#    1.0 <= A.
#
#    Input, real B, the noncentrality parameter of the PDF.
#    0.0 <= B.
#
#    Input, integer SEED, a seed for the random number generator.
#
#    Output, real X, a sample of the PDF.
#
#    Output, integer SEED, an updated seed for the random number generator.
#
  import numpy as np
  from chi_square import chi_square_sample
  from normal import normal_sample

  a1 = a - 1.0

  x1, seed = chi_square_sample ( a1, seed )

  a2 = np.sqrt ( b )
  b2 = 1.0
  x2, seed = normal_sample ( a2, b2, seed )

  x = x1 + x2 * x2

  return x, seed

def chi_square_noncentral_sample_test ( ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_SAMPLE_TEST tests CHI_SQUARE_NONCENTRAL_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 April 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 ( 'CHI_SQUARE_NONCENTRAL_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHI_SQUARE_NONCENTRAL_MEAN computes the Chi Square Noncentral mean.' )
  print ( '  CHI_SQUARE_NONCENTRAL_SAMPLE samples the Chi Square Noncentral PDF.' )
  print ( '  CHI_SQUARE_NONCENTRAL_VARIANCE computes the Chi Square Noncentral variance.' )

  a = 3.0
  b = 2.0

  check = chi_square_noncentral_check ( a, b )

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

  mean = chi_square_noncentral_mean ( a, b )
  variance = chi_square_noncentral_variance ( a, b )

  print ( '' )
  print ( '  PDF parameter A = %14g' % ( a ) )
  print ( '  PDF parameter B = %14g' % ( b ) )
  print ( '  PDF mean =        %14g' % ( mean ) )
  print ( '  PDF variance =    %14g' % ( variance ) )
  print ( '' )
  print ( '  Initial seed =    %12d' % ( seed ) )

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

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

  print ( '  Final seed =      %12d' % ( seed ) )
  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 ( 'CHI_SQUARE_NONCENTRAL_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

def chi_square_noncentral_variance ( a, b ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_VARIANCE returns the variance of the noncentral Chi squared PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 April 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, the parameter of the PDF.
#    1 <= A.
#
#    Input, real B, the noncentrality parameter of the PDF.
#    0.0 <= B.
#
#    Output, real VARIANCE, the variance value.
#
  variance = 2.0 * ( a + 2.0 * b )

  return variance

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