#! /usr/bin/env python
#
def jacobi_poly_values ( n_data ):

#*****************************************************************************80
#
## JACOBI_POLY_VALUES returns some values of the Jacobi polynomial.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      JacobiP[ n, a, b, x ]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer N, the degree of the polynomial.
#
#    Output, real A, B, parameters of the function.
#
#    Output, real X, the argument of the function.
#
#    Output, real F, the value of the function.
#
  import numpy as np

  n_max = 26

  a_vec = np.array ( (\
     0.0, 0.0, 0.0, 0.0, \
     0.0, 0.0, 1.0, 2.0, \
     3.0, 4.0, 5.0, 0.0, \
     0.0, 0.0, 0.0, 0.0, \
     0.0, 0.0, 0.0, 0.0, \
     0.0, 0.0, 0.0, 0.0, \
     0.0, 0.0 ))

  b_vec = np.array ( (\
    1.0, 1.0, 1.0, 1.0, \
    1.0, 1.0, 1.0, 1.0, \
    1.0, 1.0, 1.0, 2.0, \
    3.0, 4.0, 5.0, 1.0, \
    1.0, 1.0, 1.0, 1.0, \
    1.0, 1.0, 1.0, 1.0, \
    1.0, 1.0 ))

  f_vec = np.array ( (\
      1.000000000000000, \
      0.2500000000000000, \
     -0.3750000000000000, \
     -0.4843750000000000, \
     -0.1328125000000000, \
      0.2753906250000000, \
     -0.1640625000000000, \
     -1.174804687500000, \
     -2.361328125000000, \
     -2.616210937500000, \
      0.1171875000000000, \
      0.4218750000000000, \
      0.5048828125000000, \
      0.5097656250000000, \
      0.4306640625000000, \
     -6.000000000000000, \
      0.03862000000000000, \
      0.8118400000000000, \
      0.03666000000000000, \
     -0.4851200000000000, \
     -0.3125000000000000, \
      0.1891200000000000, \
      0.4023400000000000, \
      0.01216000000000000, \
     -0.4396200000000000, \
      1.000000000000000 ))

  n_vec = np.array ( (\
     0, 1, 2, 3, \
     4, 5, 5, 5, \
     5, 5, 5, 5, \
     5, 5, 5, 5, \
     5, 5, 5, 5, \
     5, 5, 5, 5, \
     5, 5 ))

  x_vec = np.array ( (\
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
      0.5, \
     -1.0, \
     -0.8, \
     -0.6, \
     -0.4, \
     -0.2, \
      0.0, \
      0.2, \
      0.4, \
      0.6, \
      0.8, \
      1.0 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    a = 0.0
    b = 0.0
    x = 0.0
    f = 0.0
  else:
    n = n_vec[n_data]
    a = a_vec[n_data]
    b = b_vec[n_data]
    x = x_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, a, b, x, f

def jacobi_poly_values_test ( ):

#*****************************************************************************80
#
## JACOBI_POLY_VALUES_TEST demonstrates the use of JACOBI_POLY_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'JACOBI_POLY_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  JACOBI_POLY_VALUES stores values of the Jacobi polynomials.' )
  print ( '' )
  print ( '       N        A             B             X              F' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, a, b, x, f = jacobi_poly_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %12f  %12f  %12f  %24.16g' % ( n, a, b, x, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'JACOBI_POLY_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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