#! /usr/bin/env python
#
def chebyshev_even2 ( n, f ):

#*****************************************************************************80
#
## CHEBYSHEV_EVEN2 returns the even Chebyshev coefficients of F.
#
#  Discussion:
#
#    The coefficients are calculated using the zeros of Tn(x).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    D B Hunter, H V Smith,
#    A quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function,
#    Journal of Computational and Applied Mathematics,
#    Volume 177, 2005, pages 389-400.
#
#  Parameters:
#
#    Input, integer N, the number of points to use.
#    1 <= N.
#
#    Input, real F(x), the handle for the function to be integrated with the
#    Gegenbauer weight.
#
#    Output, real B2(1+N/2), the even Chebyshev coefficients of F.
#
  import numpy as np

  s = ( n // 2 )
  sigma = ( n % 2 )

  b2 = np.zeros ( s + 1 )

  for r in range ( 0, 2 * s + 1, 2 ):
    total = 0.0
    for j in range ( 0, n + 1 ):
      total = total \
        + f ( np.cos ( float ( 2 * j + 1 ) * np.pi / 2.0 / float ( n + 1 ) ) ) \
        * np.cos ( r * float ( 2 * j + 1 ) * np.pi / 2.0 / float ( n + 1 ) )
    rh = ( r // 2 )
    b2[rh] = ( 2.0 / ( n + 1 ) ) * total

  return b2

def chebyshev_even2_test ( ):

#*****************************************************************************80
#
## CHEBYSHEV_EVEN2_TEST tests CHEBYSHEV_EVEN2.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    14 January 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8vec_print import r8vec_print

  print ( '' )
  print ( 'CHEBYSHEV_EVEN2_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBYSHEV_EVEN2 computes the even Chebyshev coefficients' )
  print ( '  of a function F, using the zeros of Tn(x).' )

  lam = 0.75
  a = 2.0
  n = 6

  b2 = chebyshev_even2 ( n, f )

  s = ( n // 2 )
  r8vec_print ( s + 1, b2, '  Computed Coefficients:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBYSHEV_EVEN2_TEST' )
  print ( '  Normal end of execution.' )
  return

def f ( x ):

#*****************************************************************************80
#
## F defines the function whose Fourier coefficients are desired.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    14 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the argument.
#
#    Output, real VALUE, the value.
#
  import numpy as np

  a = 2.0
  value = np.cos ( a * x )

  return value

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  chebyshev_even2_test ( )
  timestamp ( )