#! /usr/bin/env python3
#
def circle_distance ( ):

#*****************************************************************************80
#
## circle_distance() averages the distance between random pairs of points.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 January 2022
#
#  Author:
#
#    John Burkardt
#
  from circle_sample import circle_sample2
  from numpy import linalg as LA
  import matplotlib.pyplot as plt
  import numpy as np

  print ( "circle_distance():" )
  print ( "  Given two random points p1 and p2 in the unit circle," )
  print ( "  * compute the distance d between the points;" )
  print ( "  * estimate the average value of d over 1000 cases;" )
  print ( "  * estimate the variance s of d over 1000 cases;" )
#
#  Do sn simulations
#
  sn = 1000
#
#  Get coordinates of two random points in the circle.
#
  x1, y1 = circle_sample2 ( sn )
  x2, y2 = circle_sample2 ( sn )
  xv = x1 - x2
  yv = y1 - y2

  d = np.zeros ( sn )
  for si in range ( 0, sn ):
    v = np.array ( [ xv[si], yv[si] ] )
    d[si] = np.linalg.norm ( v )

  d_est = np.mean ( d )
  s_est = np.var ( d )

  d_exact = 128.0 / 45.0 / np.pi
  s_exact = ( 2025 * np.pi**2 - 128**2 ) / 45**2 / np.pi**2

  print ( "" )
  print ( "  Number of simulations was ", sn )
  print ( "  d:  estimate = ", d_est, "exact = ", d_exact )
  print ( "  s:  estimate = ", s_est, "exact = ", s_exact )

  print ( "" )
  print ( "circle_distance:" )
  print ( "  Normal end of execution." )

  return

if ( __name__ == '__main__' ):
  circle_distance_test ( )