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

#*****************************************************************************80
#
## distance_histogram() shows the distribution of distances for the circle.
#
#  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 ( "distance_histogram():" )
  print ( "  Given two random points p1 and p2 in the unit circle:" )
  print ( "  * Let d be the distance between two random points;" )
  print ( "  * create a histogram of the likelihood of each value of d;" )
  print ( "  * compare to an exact formula;" )
#
#  Do sn simulations
#
  sn = 10000
  print ( "" )
  print ( "  Number of simulations was ", sn )
#
#  Get coordinates of pairs of random points in the circle.
#
  x1, y1 = circle_sample2 ( sn )
  x2, y2 = circle_sample2 ( sn )
  xv = x1 - x2
  yv = y1 - y2
#
#  Compute d, the distance between each pair.
#
  d = np.zeros ( sn )
  for si in range ( 0, sn ):
    v = np.array ( [ xv[si], yv[si] ] )
    d[si] = np.linalg.norm ( v )
#
#  Create a histogram.
#
  d1 = np.linspace ( 0.0, 2.0, 101 )
  p1 = d1 * ( 4.0 * np.arccos ( d1 / 2.0 ) - d1 * np.sqrt ( 4.0 - d1**2 ) ) / np.pi

  plt.clf ( )
  plt.hist ( d, bins = 25, density = True )
  plt.plot ( d1, p1, 'r-', linewidth = 3 )
  filename = 'distance_histogram.jpg'
  plt.grid ( True )
  plt.xlabel ( '<-- distance -->' )
  plt.ylabel ( '<-- probability density -->' )
  plt.title ( 'PDF for pairwise distances' )
  plt.savefig ( filename )
  print ( "  Graphics saved as '" + filename + "'" )
  plt.show ( )

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

  return

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