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{-# LANGUAGE FlexibleContexts #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Util.Convolution
Copyright : (c) Alberto Ruiz 2012
License : BSD3
Maintainer : Alberto Ruiz
Stability : provisional
-}
-----------------------------------------------------------------------------
{-# OPTIONS_HADDOCK hide #-}
module Numeric.LinearAlgebra.Util.Convolution(
corr, conv, corrMin,
corr2, conv2, separable
) where
import Numeric.Container
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 == 0 = constant 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 :: (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 = constant 0 (dim v)
| otherwise = corr ker' v'
where
ker' = (flatten.fliprl.asRow) ker
v' = vjoin [z,v,z]
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
| 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
padded = fromBlocks [[z,0,0]
,[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
|
