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

#*****************************************************************************80
#
## LAGUERRE_GENERAL_VALUES: values of the generalized Laguerre polynomials.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      LaguerreL[n,a,x]
#
#    The functions satisfy the following differential equation:
#
#      X * Y'' + (ALPHA+1-X) * Y' + N * Y = 0
#
#    Function values can be generated by the recursion:
#
#      L(0,ALPHA)(X) = 1
#      L(1,ALPHA)(X) = 1+ALPHA-X
#
#      L(N,ALPHA)(X) = ( (2*N-1+ALPHA-X) * L(N-1,ALPHA)(X) 
#                     - (N-1+ALPHA) * L(N-2,ALPHA)(X) ) / N
#
#    The parameter ALPHA is required to be greater than -1.
#
#    For ALPHA = 0, the generalized Laguerre function L(N,ALPHA)(X)
#    is equal to the Laguerre polynomial L(N)(X).
#
#    For ALPHA integral, the generalized Laguerre function
#    L(N,ALPHA)(X) equals the associated Laguerre polynomial L(N,ALPHA)(X).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    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 order of the function.
#
#    Output, real A, the parameter.
#
#    Output, real X, the point where the function is evaluated.
#
#    Output, real F, the value of the function.
#
  import numpy as np

  n_max = 20

  a_vec = np.array ( ( \
     0.00E+00, \
     0.25E+00, \
     0.50E+00, \
     0.75E+00, \
     1.50E+00, \
     2.50E+00, \
     5.00E+00, \
     1.20E+00, \
     1.20E+00, \
     1.20E+00, \
     1.20E+00, \
     1.20E+00, \
     1.20E+00, \
     5.20E+00, \
     5.20E+00, \
     5.20E+00, \
     5.20E+00, \
     5.20E+00, \
     5.20E+00, \
     5.20E+00 ))

  f_vec = np.array ( ( \
      0.3726399739583333E-01, \
      0.3494791666666667E+00, \
      0.8710042317708333E+00, \
      0.1672395833333333E+01, \
      0.6657625325520833E+01, \
      0.2395726725260417E+02, \
      0.2031344319661458E+03, \
      0.1284193996800000E+02, \
      0.5359924801587302E+01, \
      0.9204589064126984E+00, \
     -0.1341585114857143E+01, \
     -0.2119726307555556E+01, \
     -0.1959193658349206E+01, \
      0.1000000000000000E+01, \
      0.5450000000000000E+01, \
      0.1720125000000000E+02, \
      0.4110393750000000E+02, \
      0.8239745859375000E+02, \
      0.1460179186171875E+03, \
      0.2359204608298828E+03 ))

  n_vec = np.array ( ( \
     5, \
     5, \
     5, \
     5, \
     5, \
     5, \
     5, \
     8, \
     8, \
     8, \
     8, \
     8, \
     8, \
     0, \
     1, \
     2, \
     3, \
     4, \
     5, \
     6 ))

  x_vec = np.array ( ( \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.00E+00, \
     0.20E+00, \
     0.40E+00, \
     0.60E+00, \
     0.80E+00, \
     1.00E+00, \
     0.75E+00, \
     0.75E+00, \
     0.75E+00, \
     0.75E+00, \
     0.75E+00, \
     0.75E+00, \
     0.75E+00 ))

  if ( n_data < 0 ):
    n_data = 0

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

  return n_data, n, a, x, f

def laguerre_general_values_test ( ):

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

  print ( '' )
  print ( 'LAGUERRE_GENERAL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LAGUERRE_GENERAL_VALUES stores values of the general Laguerre function.' )
  print ( '' )
  print ( '      N             A            X            F' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, a, x, f = laguerre_general_values ( n_data )

    if ( n_data == 0 ):
      break

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

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