Added FFT based convolution in Haskell (#396)

Author: jiegillet

contents/convolutions/code/haskell/convolution.hs

@@ -1,5 +1,21 @@
+import Data.Array.CArray
+import Data.Complex
 import Data.List (tails)
+import Math.FFT (dft, idft)
 
 convolution :: (Num a) => [a] -> [a] -> [a]
 convolution x = map (sum . zipWith (*) (reverse x)) . spread
-  where spread = init . tails . (replicate (length x - 1) 0 ++)
+  where
+    spread = init . tails . (replicate (length x - 1) 0 ++)
+
+convolutionFFT :: [Complex Double] -> [Complex Double] -> [Complex Double]
+convolutionFFT x y = elems $ idft $ liftArray2 (*) (fft x) (fft y)
+  where
+    fft a = dft $ listArray (1, length a) a
+
+main :: IO ()
+main = do
+  let x = [1, 2, 1, 2, 1]
+      y = [2, 1, 2, 1, 2]
+  print $ convolution x y
+  print $ convolutionFFT x y

contents/convolutions/convolutions.md

@@ -39,7 +39,7 @@ In code, this looks something like:
 {% sample lang="jl" %}
 [import:1-17, lang:"julia"](code/julia/conv.jl)
 {% sample lang="hs" %}
-[import:1-5, lang:"haskell"](code/haskell/convolution.hs)
+[import:6-9, lang:"haskell"](code/haskell/convolution.hs)
 {% sample lang="c"%}
 [import:5-18, lang:"c_cpp"](code/c/convolutions.c)
 {% sample lang="cpp"%}
@@ -88,8 +88,7 @@ That said, Julia has an in-built fft routine, so the code for this method could
 [import:19-22, lang:"julia"](code/julia/conv.jl)
 Where the `.*` operator is an element-wise multiplication.
 {% sample lang="hs" %}
-The FFT-based convolution in Haskell is complicated, so here is some simple julia code:
-[import:19-22, lang:"julia"](code/julia/conv.jl)
+[import:11-14, lang:"haskell"](code/haskell/convolution.hs)
 Where the `.*` operator is an element-wise multiplication.
 {% sample lang="c"%}
 [import:20-30, lang:"c_cpp"](code/c/convolutions.c)