#! /usr/bin/env python
#
def hypersphere01_sample ( m, n, seed ):

#*****************************************************************************80
#
## HYPERSPHERE01_SAMPLE uniformly samples the surface of the unit hypersphere.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    22 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer M, the spatial dimension.
#
#    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 r8vec_norm import r8vec_norm
  from r8vec_normal_01 import r8vec_normal_01

  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 = r8vec_norm ( m, v )
#
#  Normalize the vector.
#
    for i in range ( 0, m ):
      x[i,j] = v[i] / norm

  return x, seed

def hypersphere01_sample_test ( ):

#*****************************************************************************80
#
## HYPERSPHERE01_SAMPLE_TEST tests HYPERSPHERE01_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 ( 'HYPERSPHERE01_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  HYPERSPHERE01_SAMPLE samples the unit hypersphere' )
  print ( '  in M dimensions.' )

  m = 3
  n = 10
  seed = 123456789

  x, seed = hypersphere01_sample ( m, n, seed )

  r8mat_transpose_print ( m, n, x, '  Sample points on the unit hypersphere.' )
#
#  Terminate.
#
  print ( '' )
  print ( 'HYPERSPHERE01_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  hypersphere01_sample_test ( )
  timestamp ( )