```{-# LANGUAGE FlexibleContexts #-}
-----------------------------------------------------------------------------
{- |
Module      :  Numeric.LinearAlgebra.Util.Convolution
Copyright   :  (c) Alberto Ruiz 2012

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

-}
-----------------------------------------------------------------------------

module Numeric.LinearAlgebra.Util.Convolution(
corr, conv, corrMin,
corr2, conv2, separable
) where

import Numeric.LinearAlgebra

vectSS :: Element t => Int -> Vector t -> Matrix t
vectSS n v = fromRows [ subVector k n v | k <- [0 .. dim v - n] ]

corr :: Product t => Vector t -- ^ kernel
-> Vector t -- ^ source
-> Vector t
{- ^ correlation

>>> corr (fromList[1,2,3]) (fromList [1..10])
fromList [14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0]

-}
corr ker v | dim ker <= dim v = vectSS (dim ker) v <> ker
| otherwise = error \$ "corr: dim kernel ("++show (dim ker)++") > dim vector ("++show (dim v)++")"

conv :: (Product t, Num t) => Vector t -> Vector t -> Vector t
{- ^ convolution ('corr' with reversed kernel and padded input, equivalent to polynomial product)

>>> conv (fromList[1,1]) (fromList [-1,1])
fromList [-1.0,0.0,1.0]

-}
conv ker v = corr ker' v'
where
ker' = (flatten.fliprl.asRow) ker
v' | dim ker > 1 = join [z,v,z]
| otherwise   = v
z = constant 0 (dim ker -1)

corrMin :: (Container Vector t, RealElement t, Product t)
=> Vector t
-> Vector t
-> Vector t
-- ^ similar to 'corr', using 'min' instead of (*)
corrMin ker v = minEvery ss (asRow ker) <> ones
where
minEvery a b = cond a b a a b
ss = vectSS (dim ker) v
ones = konst' 1 (dim ker)

matSS :: Element t => Int -> Matrix t -> [Matrix t]
matSS dr m = map (reshape c) [ subVector (k*c) n v | k <- [0 .. r - dr] ]
where
v = flatten m
c = cols m
r = rows m
n = dr*c

corr2 :: Product a => Matrix a -> Matrix a -> Matrix a
-- ^ 2D correlation
corr2 ker mat = dims
. concatMap (map ((<.> ker') . flatten) . matSS c . trans)
. matSS r \$ mat
where
r = rows ker
c = cols ker
ker' = flatten (trans ker)
rr = rows mat - r + 1
rc = cols mat - c + 1
dims | rr > 0 && rc > 0 = (rr >< rc)
| otherwise = error \$ "corr2: dim kernel ("++sz ker++") > dim matrix ("++sz mat++")"
sz m = show (rows m)++"x"++show (cols m)

conv2 :: (Num a, Product a) => Matrix a -> Matrix a -> Matrix a
-- ^ 2D convolution
conv2 k m = corr2 (fliprl . flipud \$ k) pm
where
pm | r == 0 && c == 0 = m
| r == 0           = fromBlocks [[z3,m,z3]]
|           c == 0 = fromBlocks [[z2],[m],[z2]]
| otherwise        = fromBlocks [[z1,z2,z1]
,[z3, m,z3]
,[z1,z2,z1]]
r = rows k - 1
c = cols k - 1
h = rows m
w = cols m
z1 = konst' 0 (r,c)
z2 = konst' 0 (r,w)
z3 = konst' 0 (h,c)

-- TODO: could be simplified using future empty arrays

separable :: Element t => (Vector t -> Vector t) -> Matrix t -> Matrix t
-- ^ matrix computation implemented as separated vector operations by rows and columns.
separable f = fromColumns . map f . toColumns . fromRows . map f . toRows

```