#! /usr/bin/env python
#
def t_polynomial_ab_value ( a, b, n, xab ):

#*****************************************************************************80
#
## T_POLYNOMIAL_AB: Chebyshev polynomial TAB(N,X) in [A,B].
#
#  Discussion:
#
#    TAB(n,x) = T(n,(2*x-a-b)/(b-a))
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, the domain of definition.
#
#    Input, integer N, the degree of the polynomial.
#
#    Input, real XAB, the evaluation points.
#    A <= XAB <= B.
#
#    Output, real V, the value.
#
  from t_polynomial_value import t_polynomial_value

  x = ( 2.0 * xab - a - b ) / ( b - a )

  v = t_polynomial_value ( n, x );
 
  return v

def t_polynomial_ab_value_test ( ):

#*****************************************************************************80
#
## T_POLYNOMIAL_AB_VALUE_TEST tests T_POLYNOMIAL_AB_VALUE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    20 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from t_polynomial_01_values import t_polynomial_01_values

  print ( '' )
  print ( 'T_POLYNOMIAL_AB_VALUE_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  T_POLYNOMIAL_AB_VALUE evaluates a Chebyshev polynomial TAB(n,x)' )
  print ( '  shifted from [-1,+1] to the domain [A,B].' )
  print ( '' )
  print ( '  Here, we will use the new domain [0,1].' )
  print ( '' )
  print ( '                    Tabulated     Computed' )
  print ( '     N      X        T01(n,x)      T01(n,x)' )
  print ( '' )

  a = 0.0
  b = 1.0

  n_data = 0

  while ( True ):

    n_data, n, x01, fx = t_polynomial_01_values ( n_data )

    if ( n_data == 0 ):
      break

    fx2 = t_polynomial_ab_value ( a, b, n, x01 )

    print ( '  %8d  %8.4f  %14.6g  %14.6g' % ( n, x01, fx, fx2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'T_POLYNOMIAL_AB_VALUE_TEST:' )
  print ( '  Normal end of execution.' )
  return

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