#! /usr/bin/env python
#
def v_polynomial ( m, n, x ):

#*****************************************************************************80
#
## V_POLYNOMIAL evaluates Chebyshev polynomials V(n,x).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 July 2105
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer M, the number of evaluation points.
#
#    Input, integer N, the highest polynomial to compute.
#
#    Input, real X(M,1), the evaluation points.
#
#    Output, real V(1:M,1:N+1), the values of the N+1 Chebyshev polynomials.
#
  import numpy as np
  from sys import exit

  if ( n < 0 ):
    print ( '' )
    print ( 'V_POLYNOMIAL - Fatal error!' )
    print ( '  N < 0' )
    exit ( 'V_POLYNOMIAL - Fatal error.' )

  v = np.zeros ( [ m, n + 1 ] )

  for i in range ( 0, m ):
    v[i,0] = 1.0

  if ( n < 1 ):
    return v

  for i in range ( 0, m ):
    v[i,1] = 2.0 * x[i] - 1.0

  for i in range ( 0, m ):
    for j in range ( 2, n + 1 ):
      v[i,j] = 2.0 * x[i] * v[i,j-1] - v[i,j-2]

  return v

def v_polynomial_test ( ):

#*****************************************************************************80
#
## V_POLYNOMIAL_TEST tests V_POLYNOMIAL.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from v_polynomial_values import v_polynomial_values

  print ( '' )
  print ( 'V_POLYNOMIAL_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  V_POLYNOMIAL evaluates the Chebyshev polynomial V(n,x).' )
  print ( '' )
  print ( '                        Tabulated                 Computed' )
  print ( '     N        X           V(n,x)                    V(n,x)                     Error' )
  print ( '' )

  n_data = 0
  x_vec = np.zeros ( 1 )

  while ( True ):

    n_data, n, x, fx1 = v_polynomial_values ( n_data )

    if ( n_data == 0 ):
      break

    if ( n < 0 ):
      continue

    x_vec[0] = x
    fx2_vec = v_polynomial ( 1, n, x_vec )
    fx2 = fx2_vec[0,n]
    e = fx1 - fx2

    print ( '  %4d  %12g  %24.16g  %24.16g  %8.2g' % ( n, x, fx1, fx2, e ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'V_POLYNOMIAL_TEST:' )
  print ( '  Normal end of execution.' )
  return

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