#! /usr/bin/env python
#
def disk_sample ( center, r, n, seed ):

#*****************************************************************************80
#
## DISK_SAMPLE uniformly samples the unit disk.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    05 July 2018
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real CENTER(2), the center of the disk. 
#
#    Input, real R, the radius of the disk.
#
#    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.
#
    r2, seed = r8_uniform_01 ( seed )

    x[0,j] = center[0] + r * np.sqrt ( r2 ) * v[0]
    x[1,j] = center[1] + r * np.sqrt ( r2 ) * v[1]

  return x, seed

def disk_sample_test ( center, r ):

#*****************************************************************************80
#
## DISK_SAMPLE_TEST tests DISK_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 July 2018
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real CENTER(2), the center of the disk. 
#
#    Input, real R, the radius of the disk.
#
  import platform
  import numpy as np
  from disk_area import disk_area
  from disk01_monomial_integral import disk01_monomial_integral
  from monomial_value import monomial_value

  print ( '' )
  print ( 'DISK_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Use DISK_SAMPLE to estimate integrals in the disk' )
  print ( '  with center (%g,%g) and radius %g' \
    % ( center[0], center[1], r ) )

  e_test = np.array ( [ \
    [ 0, 0 ], \
    [ 2, 0 ], \
    [ 0, 2 ], \
    [ 4, 0 ], \
    [ 2, 2 ], \
    [ 0, 4 ], \
    [ 6, 0 ] ] )

  seed = 123456789

  print ( '' )
  print ( '         N        1              X^2             Y^2             X^4             X^2Y^2           Y^4             X^6' )
  print ( '' )

  n = 1

  while ( n <= 65536 ):

    x, seed = disk_sample ( center, r, n, seed )

    print ( '  %8d' % ( n ), end = '' )

    for i in range ( 0, 7 ):

      e = e_test[i,:]

      value = monomial_value ( 2, n, e, x )

      result = disk_area ( center, r ) * np.sum ( value[:] ) / n
      print ( '  %14.6g' %  ( result ), end = '' )

    print ( '' )

    n = 2 * n

  if ( \
    center[0] == 0.0 and \
    center[1] == 0.0 and \
    r == 1.0 ):
    print ( '' )
    print ( '     Exact', end = '' )
    for i in range ( 0, 7 ):
      e = e_test[i,:]
      result = disk01_monomial_integral ( e )
      print ( '  %14.6g' % ( result ), end = '' )
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'DISK01_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  import numpy as np
  timestamp ( )
  center = np.array ( [ 1.0, 2.0 ] )
  r = 3.0
  disk_sample_test ( center, r )
  timestamp ( )