#! /usr/bin/env python
#
def r8vec_sct ( n, x ):

#*****************************************************************************80
#
## R8VEC_SCT computes a forward or backward "slow" cosine transform of an R8VEC.
#
#  Discussion:
#
#    This routine is provided for illustration and testing.  It is inefficient
#    relative to optimized routines that use fast Fourier techniques.
#
#      Y(1) = Sum ( 1 <= J <= N ) X(J)
#
#      For 2 <= I <= N-1:
#
#        Y(I) = 2 * Sum ( 1 <= J <= N ) X(J)
#          * cos ( PI * ( I - 1 ) * ( J - 1 ) / ( N - 1 ) )
#
#      Y(N) = Sum ( X(1:N:2) ) - Sum ( X(2:N:2) )
#
#    Applying the routine twice in succession should yield the original data,
#    multiplied by 2 * ( N + 1 ).  This is a good check for correctness
#    and accuracy.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of data values.
#
#    Input, real X(N), the data sequence.
#
#    Output, real Y(N), the transformed data.
#
  import numpy as np

  y = np.zeros ( n )

  for i in range ( 0, n ):

    y[i] = x[0] / 2.0

    for j in range ( 1, n - 1 ):
      angle = np.pi * float ( ( i * j ) % ( 2 * ( n - 1 ) ) ) / float ( n - 1 )
      y[i] = y[i] + x[j] * np.cos ( angle )

    j = n - 1

    angle = np.pi * float ( ( i * j ) % ( 2 * ( n - 1 ) ) ) / float ( n - 1 )

    y[i] = y[i] + x[n-1] * np.cos ( angle ) / 2.0

  for i in range ( 0, n ):
    y[i] = 2.0 * y[i] * np.sqrt ( float ( n ) / float ( n - 1 ) )

  return y

def r8vec_sct_test ( ):

#*****************************************************************************80
#
## R8VEC_SCT_TEST tests R8VEC_SCT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8vec_print_part import r8vec_print_part
  from r8vec_uniform_ab import r8vec_uniform_ab

  n = 256
  alo = 0.0
  ahi = 5.0

  print ( '' )
  print ( 'R8VEC_SCT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8VEC_SCT does a forward or backward slow cosine transform.' )
  print ( '' )
  print ( '  The number of data items is N = %d' % ( n ) )
#
#  Set the data values.
#
  seed = 123456789

  c, seed = r8vec_uniform_ab ( n, alo, ahi, seed )

  r8vec_print_part ( n, c, 1, 10, '  The original data:' )
#
#  Compute the coefficients.
#
  d = r8vec_sct ( n, c )

  r8vec_print_part ( n, d, 1, 10, '  The cosine coefficients:' )
#
#  Now compute inverse transform of coefficients.  Should get back the
#  original data.

  e = r8vec_sct ( n, d )

  for i in range ( 0, n ):
    e[i] = e[i] / float ( 2 * n )

  r8vec_print_part ( n, e, 1, 10, '  The retrieved data:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8VEC_SCT_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8vec_sct_test ( )
  timestamp ( )