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

#*****************************************************************************80
#
## U_POLYNOMIAL_ZEROS returns zeroes of the Chebyshev polynomial T(n,x).
#
#  Discussion:
#
#    The I-th zero of U(n,x) is cos((I-1)*PI/(N-1)), I = 1 to N
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order of the polynomial.
#
#    Output, real Z(N), the zeroes.
#
  import numpy as np

  z = np.zeros ( n )

  for i in range ( 0, n ):
    angle = float ( i + 1 ) * np.pi / float ( n + 1 )
    z[i] = np.cos ( angle )

  return z

def u_polynomial_zeros_test ( ):

#*****************************************************************************80
#
## U_POLYNOMIAL_ZEROS_TEST tests U_POLYNOMIAL_ZEROS.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from u_polynomial import u_polynomial

  print ( '' )
  print ( 'U_POLYNOMIAL_ZEROS_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  U_POLYNOMIAL_ZEROS computes the zeros of U(n,x)' )
  print ( '' )
  print ( '     N      X         U(n,x)' )

  for n in range ( 0, 6 ):

    x = u_polynomial_zeros ( n )
    fx = u_polynomial ( n, n + 1, x )

    print ( '' )
    for i in range ( 0, n ):
      print ( '  %4d  %8.4g  %14.6g' % ( i, x[i], fx[i,n] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'U_POLYNOMIAL_ZEROS_TEST:' )
  print ( '  Normal end of execution.' )
  return

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