#! /usr/bin/env python
#
def normal_ms_variance ( mu, sigma ):

#*****************************************************************************80
#
## NORMAL_MS_VARIANCE returns the variance of the Normal MS distribution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 March 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real MU, SIGMA, the parameters of the PDF.
#    0.0 < SIGMA.
#
#    Output, real VALUE, the variance of the PDF.
# 
  value = sigma * sigma

  return value

def normal_ms_variance_test ( ):

#*****************************************************************************80
#
## NORMAL_MS_VARIANCE_TEST tests NORMAL_MS_VARIANCE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 March 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from normal_ms_sample import normal_ms_sample
  from r8vec_variance import r8vec_variance

  print ( '' )
  print ( 'NORMAL_MS_VARIANCE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  NORMAL_MS_VARIANCE computes the variance' )
  print ( '  of the Normal MS distribution.' )

  mu = 100.0
  sigma = 15.0

  value = normal_ms_variance ( mu, sigma )

  print ( '' )
  print ( '  PDF parameter MU = %g' % ( mu ) )
  print ( '  PDF parameter SIGMA = %g' % ( sigma ) )
  print ( '  PDF variance = %g' % ( value ) )

  nsample = 1000
  seed = 123456789

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

  value = r8vec_variance ( nsample, x )

  print ( '' )
  print ( '  Sample size =     %6d' % ( nsample ) )
  print ( '  Sample variance = %14g' % ( value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'NORMAL_MS_VARIANCE_TEST:' )
  print ( '  Normal end of execution.' )
  return

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