#! /usr/bin/env python
#
def ball01_sample ( n, seed ):

#*****************************************************************************80
#
## BALL01_SAMPLE uniformly samples the unit ball.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    21 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Russell Cheng,
#    Random Variate Generation,
#    in Handbook of Simulation,
#    edited by Jerry Banks,
#    Wiley, 1998, pages 168.
#
#    Reuven Rubinstein,
#    Monte Carlo Optimization, Simulation, and Sensitivity 
#    of Queueing Networks,
#    Krieger, 1992,
#    ISBN: 0894647644,
#    LC: QA298.R79.
#
#  Parameters:
#
#    Input, integer N, the number of points.
#
#    Input/output, integer SEED, a seed for the random 
#    number generator.
#
#    Output, real X(3,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 ( [ 3, n ] )

  for j in range ( 0, n ):
#
#  Fill a vector with normally distributed values.
#
    v, seed = r8vec_normal_01 ( 3, seed )
#
#  Compute the length of the vector.
#
    norm = np.sqrt ( v[0] ** 2 + v[1] ** 2 + v[2] ** 2 )
#
#  Normalize the vector.
#
    for i in range ( 0, 3 ):
      v[i] = v[i] / norm
#
#  Transfer the point from the surface to the interior.
#
    r, seed = r8_uniform_01 ( seed )

    r = r ** ( 1.0 / 3.0 )
    for i in range ( 0, 3 ):
      x[i,j] = r * v[i]

  return x, seed

def ball01_sample_test ( ):

#*****************************************************************************80
#
## BALL01_SAMPLE_TEST tests BALL01_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    21 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8mat_transpose_print import r8mat_transpose_print

  print ( '' )
  print ( 'BALL01_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  BALL01_SAMPLE samples the unit ball.' )

  n = 10
  seed = 123456789

  x, seed = ball01_sample ( n, seed )

  r8mat_transpose_print ( 3, n, x, '  Sample points in the unit ball.' )
#
#  Terminate.
#
  print ( '' )
  print ( 'BALL01_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  ball01_sample_test ( )
  timestamp ( )