#! /usr/bin/env python
#
def cheby_u01_poly_values ( n_data ):

#*****************************************************************************80
#
## CHEBY_U01_POLY_VALUES: values of shifted Chebyshev polynomials U01(n,x).
#
#  Discussion:
#
#    U01(n,x) = U(n,2*x-1)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 July 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 order of the function.
#
#    Output, real X, the point where the function is evaluated.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 25

  fx_vec = np.array ( ( \
     0.000000000000000, \
     1.000000000000000, \
     1.400000000000000, \
     0.9600000000000000, \
    -0.05600000000000000, \
    -1.038400000000000, \
    -1.397760000000000, \
    -0.9184640000000000, \
     0.1119104000000000, \
     1.075138560000000, \
     1.393283584000000, \
     0.8754584576000000, \
    -0.1676417433600000, \
    -1.110156898304000, \
    -8.000000000000000, \
     1.511014400000000, \
    -1.133260800000000, \
    -0.1636352000000000, \
     1.019801600000000, \
     0.000000000000000, \
    -1.019801600000000, \
     0.1636352000000000, \
     1.133260800000000, \
    -1.511014400000000, \
     8.000000000000000  ) )

  n_vec = np.array ( ( \
    -1, \
     0,  1,  2, \
     3,  4,  5, \
     6,  7,  8, \
     9, 10, 11, \
    12,  7,  7, \
     7,  7,  7, \
     7,  7,  7, \
     7,  7,  7 ))

  x_vec = np.array ( ( \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.85, \
    0.00, \
    0.10, \
    0.20, \
    0.30, \
    0.40, \
    0.50, \
    0.60, \
    0.70, \
    0.80, \
    0.90, \
    1.00  ) )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    x = 0.0
    fx = 0.0
  else:
    n = n_vec[n_data]
    x = x_vec[n_data]
    fx = fx_vec[n_data]
    n_data = n_data + 1

  return n_data, n, x, fx

def cheby_u01_poly_values_test ( ):

#*****************************************************************************80
#
## CHEBY_U01_POLY_VALUES_TEST demonstrates the use of CHEBY_U01_POLY_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHEBY_U01_POLY_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBY_U01_POLY_VALUES: values of the shifted Chebyshev U polynomials.' )
  print ( '' )
  print ( '      N            X            FX' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, x, fx = cheby_u01_poly_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %12f  %24.16g' % ( n, x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBY_U01_POLY_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  cheby_u01_poly_values_test ( )
  timestamp ( )