{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
{- |
Module      : GSL.Fourier
Copyright   :  (c) Alberto Ruiz 2006
License     :  GPL-style

Maintainer  :  Alberto Ruiz (aruiz at um dot es)
Stability   :  provisional
Portability :  uses ffi

Fourier Transform.

<http://www.gnu.org/software/gsl/manual/html_node/Fast-Fourier-Transforms.html#Fast-Fourier-Transforms>

-}
-----------------------------------------------------------------------------
module GSL.Fourier (
    fft,
    ifft
) where

import Data.Packed.Internal
import Complex
import Foreign

genfft code v = unsafePerformIO $ do
    r <- createVector (dim v)
    c_fft code // vec v // vec r // check "fft" [v]
    return r

foreign import ccall "gsl-aux.h fft" c_fft ::  Int -> Complex Double :> Complex Double :>  IO Int


{- | Fast 1D Fourier transform of a 'Vector' @(@'Complex' 'Double'@)@ using /gsl_fft_complex_forward/. It uses the same scaling conventions as GNU Octave.

@> fft ('GSL.Matrix.fromList' [1,2,3,4])
vector (4) [10.0 :+ 0.0,(-2.0) :+ 2.0,(-2.0) :+ 0.0,(-2.0) :+ (-2.0)]@

-}
fft :: Vector (Complex Double) -> Vector (Complex Double)
fft = genfft 0

-- | The inverse of 'fft', using /gsl_fft_complex_inverse/.
ifft :: Vector (Complex Double) -> Vector (Complex Double)
ifft = genfft 1