#! /usr/bin/env python
#
def uniform_in_sphere01_map ( m, n, seed ):

#*****************************************************************************80
#
## UNIFORM_IN_SPHERE01_MAP maps uniform points in the unit M-dimensional sphere.
#
#  Discussion:
#
#    The sphere has center 0 and radius 1.
#
#    We first generate a point ON the sphere, and then distribute it
#    IN the sphere.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 November 2016
#
#  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,
#    Wiley, 1986, page 232.
#
#  Parameters:
#
#    Input, integer M, the dimension of the space.
#
#    Input, integer N, the number of points.
#
#    Input/output, integer SEED, a seed for the random number generator.
#
#    Output, real X(M,N), the points.
#
  import numpy as np
  from r8_uniform_01 import r8_uniform_01
  from r8vec_normal_01 import r8vec_normal_01

  exponent = 1.0 / float ( m )

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

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

    x[0:m,j] = r ** exponent * v[0:m]
  
  return x, seed

def uniform_in_sphere01_map_test ( ):

#*****************************************************************************80
#
## UNIFORM_IN_SPHERE01_MAP_TEST tests UNIFORM_IN_SPHERE01_MAP.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 November 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8mat_transpose_print import r8mat_transpose_print

  print ( '' )
  print ( 'UNIFORM_IN_SPHERE01_MAP_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  UNIFORM_IN_SPHERE01_MAP computes points uniformly distributed' )
  print ( '  inside the M-dimensional unit sphere.' )

  m = 3
  n = 10
  seed = 123456789

  x, seed = uniform_in_sphere01_map ( m, n, seed )

  r8mat_transpose_print ( m, n, x, '  Random points inside unit 3-sphere' )
#
#  Terminate.
#
  print ( '' )
  print ( 'UNIFORM_IN_SPHERE01_MAP_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  uniform_in_sphere01_map_test ( )
  timestamp ( )