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

#*****************************************************************************80
#
## V_POLYNOMIAL_AB: Chebyshev polynomials VAB(N,X) in [A,B].
#
#  Discussion:
#
#    VAB(n,x) = V(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 M, the number of evaluation points.
#
#    Input, integer N, the highest polynomial to compute.
#
#    Input, real XAB(M,1), the evaluation points.
#    It must be the case that A <= XAB(*) <= B.
#
#    Output, real V(M,N+1), the values of the Chebyshev polynomials.
#
  from v_polynomial import v_polynomial

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

  v = v_polynomial ( m, n, x );
 
  return v

def v_polynomial_ab_test ( ):

#*****************************************************************************80
#
## V_POLYNOMIAL_AB_TEST tests V_POLYNOMIAL_AB.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    20 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_print import r8mat_print

  print ( '' )
  print ( 'V_POLYNOMIAL_AB_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  V_POLYNOMIAL_AB evaluates Chebyshev polynomials VAB(n,x)' )
  print ( '  shifted from [-1,+1] to the domain [A,B].' )
  print ( '' )
  print ( '  Here, we will use the new domain [0,1]' )
  print ( '  and the desired maximum polynomial degree will be N = 5.' )

  a = 0.0
  b = 1.0
  m = 11
  n = 5
  x = np.linspace ( a, b, m )
  
  v = v_polynomial_ab ( a, b, m, n, x )

  r8mat_print ( m, n + 1, v, '  Tables of V values:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'V_POLYNOMIAL_AB_TEST:' )
  print ( '  Normal end of execution.' )
  return

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