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

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

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

import qualified Data.Vector.Storable as SV
import Data.Packed.Numeric

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

corr
:: (Container Vector t, 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 == 0 = konst 0 (dim v)
| dim ker <= dim v = vectSS (dim ker) v <> ker
| otherwise = error \$ "corr: dim kernel ("++show (dim ker)++") > dim vector ("++show (dim v)++")"

conv :: (Container Vector t, 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
| dim ker == 0 = konst 0 (dim v)
| otherwise = corr ker' v'
where
ker' = SV.reverse ker
v' = vjoin [z,v,z]
z = konst 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
| dim ker == 0 = error "corrMin: empty kernel"
| otherwise    = 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

{- | 2D correlation (without padding)

>>> disp 5 \$ corr2 (konst 1 (3,3)) (ident 10 :: Matrix Double)
8x8
3  2  1  0  0  0  0  0
2  3  2  1  0  0  0  0
1  2  3  2  1  0  0  0
0  1  2  3  2  1  0  0
0  0  1  2  3  2  1  0
0  0  0  1  2  3  2  1
0  0  0  0  1  2  3  2
0  0  0  0  0  1  2  3

-}
corr2 :: Product a => Matrix a -> Matrix a -> Matrix a
corr2 ker mat = dims
. concatMap (map (udot 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)
-- TODO check empty kernel

{- | 2D convolution

>>> disp 5 \$ conv2 (konst 1 (3,3)) (ident 10 :: Matrix Double)
12x12
1  1  1  0  0  0  0  0  0  0  0  0
1  2  2  1  0  0  0  0  0  0  0  0
1  2  3  2  1  0  0  0  0  0  0  0
0  1  2  3  2  1  0  0  0  0  0  0
0  0  1  2  3  2  1  0  0  0  0  0
0  0  0  1  2  3  2  1  0  0  0  0
0  0  0  0  1  2  3  2  1  0  0  0
0  0  0  0  0  1  2  3  2  1  0  0
0  0  0  0  0  0  1  2  3  2  1  0
0  0  0  0  0  0  0  1  2  3  2  1
0  0  0  0  0  0  0  0  1  2  2  1
0  0  0  0  0  0  0  0  0  1  1  1

-}
conv2
:: (Num (Matrix a), Product a, Container Vector a)
=> Matrix a -- ^ kernel
-> Matrix a -> Matrix a
conv2 k m
| empty     = konst 0 (rows m + r -1, cols m + c -1)
| otherwise = corr2 (fliprl . flipud \$ k) padded
where
,[0,m,0]
,[0,0,z]]
r = rows k
c = cols k
z = konst 0 (r-1,c-1)
empty = r == 0 || c == 0

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

```