#! /usr/bin/env python
#
def chebyshev_even1 ( n, f ):

#*****************************************************************************80
#
## CHEBYSHEV_EVEN1 returns the even Chebyshev coefficients of F.
#
#  Discussion:
#
#    The coefficients are calculated using the extreme points of Tn(x).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    14 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 A2(1+N/2), the even Chebyshev coefficients of F.
#
  import numpy as np
  from r8_mop import r8_mop

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

  a2 = np.zeros ( s + 1 )

  for r in range ( 0, 2 * s + 1, 2 ):
    total = 0.5 * f ( 1.0 )
    for j in range ( 1, n ):
      total = total + f ( np.cos ( float ( j ) * np.pi / float ( n ) ) ) \
      * np.cos ( float ( r * j ) * np.pi / float ( n ) )
    total = total + 0.5 * r8_mop ( r ) * f ( -1.0 )
    rh = ( r // 2 )
    a2[rh] = ( 2.0 / float ( n ) ) * total

  return a2

def chebyshev_even1_test ( ):

#*****************************************************************************80
#
## CHEBYSHEV_EVEN1_TEST tests CHEBYSHEV_EVEN1.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    14 January 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec2_print import r8vec2_print

  print ( '' )
  print ( 'CHEBYSHEV_EVEN1_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBYSHEV_EVEN1 computes the even Chebyshev coefficients' )
  print ( '  of a function F, using the extreme points of Tn(x).' )

  a2_exact = np.array ( [ \
    0.4477815660, \
   -0.7056685603, \
    0.0680357987, \
   -0.0048097159 ] )

  lam = 0.75
  a = 2.0
  n = 6

  a2 = chebyshev_even1 ( n, f )

  s = ( n // 2 )
  r8vec2_print ( s + 1, a2, a2_exact, '  Computed and Exact Coefficients:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBYSHEV_EVEN1_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_even1_test ( )
  timestamp ( )