#! /usr/bin/env python
#
def circular_normal_01_mean ( ):

#*****************************************************************************80
#
## CIRCULAR_NORMAL_01_MEAN returns the mean of the Circular Normal 01 PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Output, real MEAN(2), the mean of the PDF.
#
  import numpy as np

  mean = np.zeros ( 2 )

  return mean

def circular_normal_01_pdf ( x, pdf ):

#*****************************************************************************80
#
## CIRCULAR_NORMAL_01_PDF evaluates the Circular Normal 01 PDF.
#
#  Discussion:
#
#    PDF(X) = EXP ( - 0.5 * ( X(1)^2 + X(2)^2 ) ) / ( 2 * PI )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X(2), the argument of the PDF.
#
#    Output, real PDF, the value of the PDF.
#
  import numpy as np

  pdf = np.exp ( - 0.5 * ( x[0] ** 2 + x[1] ** 2 ) ) / ( 2.0 * np.pi )

  return pdf

def circular_normal_01_sample ( seed ):

#*****************************************************************************80
#
## CIRCULAR_NORMAL_01_SAMPLE samples the Circular Normal 01 PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer SEED, a seed for the random number generator.
#
#    Output, real X(2), a sample of the PDF.
#
#    Output, integer SEED, an updated seed for the random number generator.
#
  import numpy as np
  from r8_uniform_01 import r8_uniform_01

  v1, seed = r8_uniform_01 ( seed )
  v2, seed = r8_uniform_01 ( seed )

  x = np.zeros ( 2 )
  x[0] = np.sqrt ( - 2.0 * np.log ( v1 ) ) * np.cos ( 2.0 * np.pi * v2 )
  x[1] = np.sqrt ( - 2.0 * np.log ( v1 ) ) * np.sin ( 2.0 * np.pi * v2 )

  return x, seed

def circular_normal_01_sample_test ( ):

#*****************************************************************************80
#
## CIRCULAR_NORMAL_01_SAMPLE_TEST tests CIRCULAR_NORMAL_01_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 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 ( 'CIRCULAR_NORMAL_01_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CIRCULAR_NORMAL_01_MEAN computes the Circular Normal 01 mean' )
  print ( '  CIRCULAR_NORMAL_01_SAMPLE samples the Circular Normal 01 distribution' )
  print ( '  CIRCULAR_NORMAL_01_VARIANCE computes the Circular Normal 01 variance.' )

  mean = circular_normal_01_mean ( )
  variance = circular_normal_01_variance ( )

  print ( '' )
  print ( '  PDF means =               %14g  %14g' % ( mean[0], mean[1] ) )
  print ( '  PDF variances =           %14g  %14g' % ( variance[0], variance[1] ) )
  
  x_table = np.zeros ( nsample )
  y_table = np.zeros ( nsample )

  for i in range ( 0, nsample ):
    x, seed = circular_normal_01_sample ( seed )
    x_table[i] = x[0]
    y_table[i] = x[1]

  xmean = r8vec_mean ( nsample, x_table )
  xvariance = r8vec_variance ( nsample, x_table )
  xmax = r8vec_max ( nsample, x_table )
  xmin = r8vec_min ( nsample, x_table )

  ymean = r8vec_mean ( nsample, y_table )
  yvariance = r8vec_variance ( nsample, y_table )
  ymax = r8vec_max ( nsample, y_table )
  ymin = r8vec_min ( nsample, y_table )

  print ( '' )
  print ( '  Sample size =     %6d' % ( nsample ) )
  print ( '  Sample mean =     %14g  %14g' % ( xmean, ymean ) )
  print ( '  Sample variance = %14g  %14g' % ( xvariance, yvariance ) )
  print ( '  Sample maximum =  %14g  %14g' % ( xmax, ymax ) )
  print ( '  Sample minimum =  %14g  %14g' % ( xmin, ymin ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CIRCULAR_NORMAL_01_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

def circular_normal_01_variance ( ):

#*****************************************************************************80
#
## CIRCULAR_NORMAL_01_VARIANCE returns the variance of the Circular Normal 01 PDF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Output, real VARIANCE(2), the variance of the PDF.
#
  import numpy as np

  variance = np.ones ( 2 )

  return variance

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  circular_normal_01_sample_test ( )
  timestamp ( )