def in_circle ( ):

#*****************************************************************************80
#
## in_circle() shows which random points are inside a circle.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    29 January 2025
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np

  n = 400

  print ( '' )
  print ( 'in_circle():' )
  print ( '  Compute ', n, ' random points in [-1,+1]x[-1,+1].' )
  print ( '  Show which ones are inside the unit circle.' )
  print ( '  Demonstrate numpy conditional indexing.' )
#
#  Pick NC points on unit circle boundary.
#
  nc = 101
  t = np.linspace ( 0.0, 2.0 * np.pi, nc )
  xc = np.zeros ( [ nc, 2 ] )
  xc[:,0] = np.cos ( t )
  xc[:,1] = np.sin ( t )
#
#  Sample N points in [-1,+1] x [-1,+1]
#
  x = 2.0 * np.random.random ( [ n ] ) - 1.0
  y = 2.0 * np.random.random ( [ n ] ) - 1.0
#
#  Measure RSQ, the squared distance of X from center.
#
  rsq = x[:]**2 + y[:]**2
#
#  Green: circle boundary.
#  Red: points with 1.0 < RSQ
#  Blue: points with RSQ <= 1.0
#
  plt.clf ( )
  plt.plot ( xc[:,0], xc[:,1], 'g', linewidth = 3 )
  plt.plot ( x[1.0<rsq],  y[1.0<rsq], 'ro' )
  plt.plot ( x[rsq<=1.0], y[rsq<=1.0], 'bo' )
  plt.xlabel ( '<--- X --->' )
  plt.ylabel ( '<--- Y --->' )
  plt.title ( 'in or out of circle?' )
  plt.grid ( 'True' )
  plt.axis ( 'equal' )
  filename = 'in_circle.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )
  plt.close ( )

  return

if ( __name__ == "__main__" ):
  in_circle ( )