{-# LANGUAGE ForeignFunctionInterface #-}
-----------------------------------------------------------------------------
{- |
Module      : Numeric.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 Numeric.GSL.Fourier (
    fft,
    ifft
) where

import Data.Packed.Internal
import Data.Complex
import Foreign.C.Types(CInt(..))
import System.IO.Unsafe (unsafePerformIO)

genfft code v = unsafePerformIO $ do
    r <- createVector (dim v)
    app2 (c_fft code) vec v vec r "fft"
    return r

foreign import ccall "gsl-aux.h fft" c_fft ::  CInt -> TCVCV


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

@> fft ('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