#! /usr/bin/env python
#
def disk01_sample ( n, seed ):

#*****************************************************************************80
#
## DISK01_SAMPLE uniformly samples the unit disk.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    03 January 2014
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of points.
#
#    Input/output, integer SEED, a seed for the random 
#    number generator.
#
#    Output, real X(2,N), the points.
#
  import numpy as np
  from r8_uniform_01 import r8_uniform_01
  from r8vec_normal_01 import r8vec_normal_01

  x = np.zeros ( [ 2, n ] )

  for j in range ( 0, n ):
#
#  Fill a vector with normally distributed values.
#
    v, seed = r8vec_normal_01 ( 2, seed )
#
#  Compute the length of the vector.
#
    norm = np.sqrt ( v[0] ** 2 + v[1] ** 2 )
#
#  Normalize the vector.
#
    v[0] = v[0] / norm
    v[1] = v[1] / norm
#
#  Now compute a value to map the point ON the disk INTO the disk.
#
    r, seed = r8_uniform_01 ( seed )

    x[0,j] = np.sqrt ( r ) * v[0]
    x[1,j] = np.sqrt ( r ) * v[1]

  return x, seed

def disk01_sample_test ( ):

#*****************************************************************************80
#
## DISK01_SAMPLE_TEST tests DISK01_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8mat_transpose_print import r8mat_transpose_print

  print ( '' )
  print ( 'DISK01_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  DISK01_SAMPLE samples the unit disk.' )

  n = 10
  seed = 123456789

  x, seed = disk01_sample ( n, seed )

  r8mat_transpose_print ( 2, n, x, '  Sample points in the unit disk.' )
#
#  Terminate.
#
  print ( '' )
  print ( 'DISK01_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  disk01_sample_test ( )
  timestamp ( )