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

#*****************************************************************************80
#
## circle_sample_test() compares 3 ways to sample the unit circle.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 January 2022
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np

  print ( "circle_sample_test:" )
  print ( "  Compare methods of randomly sampling the unit circle" )
  print ( "  with points x = r cos(t), y = r sin(t)" )
  print ( "" )
  print ( "  method 1: r = random, t = 2 pi * random" )
  print ( "  method 2: r = sqrt(random), t = 2 pi * random" )
  print ( "  method 3: x = random, y = random, reject if 1 < x^2+y^2" )
#
#  Get points on the circumference.
#
  nc = 100
  theta = np.linspace ( 0, 2.0 * np.pi, nc )
  xc = np.cos ( theta )
  yc = np.sin ( theta )

  ns = 1000
  for sample_function, sample_name in [ 
    [ circle_sample1, 'circle_sample1' ], 
    [ circle_sample2, 'circle_sample2' ],
    [ circle_sample3, 'circle_sample3' ] ]:
    xs, ys = sample_function ( ns )
    plt.clf ( )
    plt.plot ( xc, yc, 'b-', linewidth = 2 )
    plt.plot ( xs, ys, 'g.', markersize = 5 )
    plt.title ( sample_name )
    plt.axis ( 'equal' )
    plt.grid ( True )
    filename = sample_name + '.jpg'
    plt.savefig ( filename )
    print ( "  Graphics saved as '" + filename + "'" )
    plt.show ( )
    plt.close ( )

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

  return

def circle_sample1 ( n ):

#*****************************************************************************80
#
## circle_sample1 uses sampling method 1.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 January 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  r = np.random.rand ( n )
  theta = 2.0 * np.pi * np.random.rand ( n )
  x = r * np.cos ( theta )
  y = r * np.sin ( theta )

  return x, y

def circle_sample2 ( n ):

#*****************************************************************************80
#
## circle_sample2 uses sampling method 2.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 January 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  r = np.sqrt ( np.random.rand ( n ) )
  theta = 2.0 * np.pi * np.random.rand ( n )
  x = r * np.cos ( theta )
  y = r * np.sin ( theta )

  return x, y

def circle_sample3 ( n ):

#*****************************************************************************80
#
## circle_sample3 uses sampling method 3.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 January 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  x = 2.0 * np.random.rand ( n ) - 1.0
  y = 2.0 * np.random.rand ( n ) - 1.0

  for i in range ( 0, n ):
    while ( 1.0 < x[i]**2 + y[i]**2 ):
      x[i] = 2.0 * np.random.rand ( 1 ) - 1.0
      y[i] = 2.0 * np.random.rand ( 1 ) - 1.0

  return x, y

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