#! /usr/bin/env python
#
def u_polynomial_coefficients ( n ):

#*****************************************************************************80
#
## U_POLYNOMIAL_COEFFICIENTS: coefficients of the Chebyshev polynomial U(n,x).
#
#  First terms:
#
#    N/K     0     1      2      3       4     5      6    7      8    9   10
#
#     0      1
#     1      0     2
#     2     -1     0      4
#     3      0    -4      0      8
#     4      1     0    -12      0      16
#     5      0     6      0    -32       0    32
#     6     -1     0     24      0     -80     0     64
#     7      0    -8      0     80       0  -192      0   128
#
#  Recursion:
#
#    U(0)(X) = 1,
#    U(1)(X) = 2*X,
#    U(N)(X) = 2 * X * U(N-1)(X) - U(N-2)(X)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#  Parameters:
#
#    Input, integer N, the highest order polynomial to compute.
#    Note that polynomials 0 through N will be computed.
#
#    Output, real C(1:N+1,1:N+1), the coefficients of the Chebyshev T
#    polynomials.
#
  import numpy as np

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

  c[0,0] = 1.0

  if ( 0 < n ):

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

def u_polynomial_coefficients_test ( ):

#*****************************************************************************80
#
## U_POLYNOMIAL_COEFFICIENTS_TEST tests U_POLYNOMIAL_COEFFICIENTS.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8poly_print import r8poly_print

  n = 5

  print ( '' )
  print ( 'U_POLYNOMIAL_COEFFICIENTS_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  U_POLYNOMIAL_COEFFICIENTS determines the Chebyshev' )
  print ( '  polynomial coefficients.' )

  c = u_polynomial_coefficients ( n )
 
  for i in range ( 0, n + 1 ):
    c2 = np.zeros ( i + 1 )
    for j in range ( 0, i + 1 ):
      c2[j] = c[i,j]
    r8poly_print ( i, c2, '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'U_POLYNOMIAL_COEFFICIENTS_TEST:' )
  print ( '  Normal end of execution.' )
  return

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