#! /usr/bin/env python
#
def angle_cdf ( x, n ):

#*****************************************************************************80
#
## ANGLE_CDF evaluates the Angle CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Reuven Rubinstein,
#    Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
#    Wiley, 1986.
#
#  Parameters:
#
#    Input, real X, the argument of the PDF.
#
#    Input, integer N, the spatial dimension.
#    N must be at least 2.
#
#    Output, real CDF, the value of the CDF.
#
  import numpy as np
  from r8_gamma import r8_gamma
  from sin_power_int import sin_power_int
  from sys import exit

  if ( n < 2 ):
    print ( '' )
    print ( 'ANGLE_CDF - Fatal error!' )
    print ( '  N must be at least 2.' )
    print ( '  The input value of N = %d' % ( n ) )
    exit ( 'ANGLE_CDF - Fatal error!' )

  if ( x <= 0.0 ):
    cdf = 0.0
  elif ( np.pi <= x ):
    cdf = 1.0
  elif ( n == 2 ):
    cdf = x / np.pi
  else:
    cdf = sin_power_int ( 0.0, x, n - 2 ) * r8_gamma ( n / 2.0 ) \
      / ( np.sqrt ( np.pi ) * r8_gamma ( ( n - 1 ) / 2.0 ) )

  return cdf

def angle_cdf_test ( ):

#*****************************************************************************80
#
## ANGLE_CDF_TEST tests ANGLE_CDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'ANGLE_CDF_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ANGLE_CDF evaluates the Angle CDF' )

  n = 5
  x = 0.50

  cdf = angle_cdf ( x, n )

  print ( '' )
  print ( '  PDF parameter N = %6d' % ( n ) )
  print ( '  PDF argument X =  %14g' % ( x ) )
  print ( '  CDF value =       %14g' % ( cdf ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'ANGLE_CDF_TEST' )
  print ( '  Normal end of execution.' )
  return

def angle_mean ( n ):

#*****************************************************************************80
#
## ANGLE_MEAN returns the mean of the Angle PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the spatial dimension.
#    N must be at least 2.
#
#    Output, real MEAN, the mean of the PDF.
#
  import numpy as np

  mean = np.pi / 2.0

  return mean

def angle_mean_test ( ):

#*****************************************************************************80
#
## ANGLE_MEAN_TEST tests ANGLE_MEAN
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'ANGLE_MEAN_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ANGLE_MEAN computes the Angle mean' )

  n = 5
  mean = angle_mean ( n )

  print ( '' )
  print ( '  PDF parameter N = %6d' % ( n ) )
  print ( '  PDF mean =        %14g' % ( mean ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'ANGLE_MEAN_TEST' )
  print ( '  Normal end of execution.' )
  return

def angle_pdf ( x, n ):

#*****************************************************************************80
#
## ANGLE_PDF evaluates the Angle PDF.
#
#  Discussion:
#
#    X is an angle between 0 and PI, corresponding to the angle
#    made in an N-dimensional space, between a fixed line passing
#    through the origin, and an arbitrary line that also passes
#    through the origin, which is specified by a choosing any point
#    on the N-dimensional sphere with uniform probability.
#
#  Formula:
#
#    PDF(X) = ( sin ( X ) )**(N-2) * Gamma ( N / 2 )
#             / ( sqrt ( PI ) * Gamma ( ( N - 1 ) / 2 ) )
#
#    PDF(X) = 1 / PI if N = 2.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Reuven Rubinstein,
#    Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
#    Wiley, 1986.
#
#  Parameters:
#
#    Input, real X, the argument of the PDF.
#
#    Input, integer N, the spatial dimension.
#    N must be at least 2.
#
#    Output, real PDF, the value of the PDF.
#
  import numpy as np
  from r8_gamma import r8_gamma
  from sys import exit

  if ( n < 2 ):
    print ( '' )
    print ( 'ANGLE_PDF - Fatal error!' )
    print ( '  N must be at least 2.' )
    print ( '  The input value of N = %d' % ( n ) )
    exit ( 'ANGLE_PDF - Fatal error!' )

  if ( x < 0.0 or np.pi < x ):
    pdf = 0.0
  elif ( n == 2 ):
    pdf = 1.0 / np.pi
  else:
    pdf = ( np.sin ( x ) ) ** ( n - 2 ) * r8_gamma ( n / 2.0 ) \
      / ( np.sqrt ( np.pi ) * r8_gamma ( ( n - 1 ) / 2.0 ) )

  return pdf

def angle_pdf_test ( ):

#*****************************************************************************80
#
## ANGLE_PDF_TEST tests ANGLE_PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'ANGLE_PDF_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ANGLE_PDF evaluates the Angle PDF' )

  n = 5
  x = 0.50

  pdf = angle_pdf ( x, n )

  print ( '' )
  print ( '  PDF parameter N = %6d' % ( n ) )
  print ( '  PDF argument X =  %14g' % ( x ) )
  print ( '  PDF value =       %14g' % ( pdf ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'ANGLE_PDF_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  angle_cdf_test ( )
  angle_mean_test ( )
  angle_pdf_test ( )
  timestamp ( )