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authorAlberto Ruiz <aruiz@um.es>2012-06-10 14:00:08 +0200
committerAlberto Ruiz <aruiz@um.es>2012-06-10 14:00:08 +0200
commitf10af430ec9ab1cc71f8931dec9a4247fc780933 (patch)
treef8f9981cba2debe894310fb6f2ba77a8d7cde262 /lib/Numeric/LinearAlgebra
parentd109c791aef6dbb6a15fb65efe5c42121728aed0 (diff)
convolution
Diffstat (limited to 'lib/Numeric/LinearAlgebra')
-rw-r--r--lib/Numeric/LinearAlgebra/Util/Convolution.hs118
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diff --git a/lib/Numeric/LinearAlgebra/Util/Convolution.hs b/lib/Numeric/LinearAlgebra/Util/Convolution.hs
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1{-# LANGUAGE FlexibleContexts #-}
2-----------------------------------------------------------------------------
3{- |
4Module : Numeric.LinearAlgebra.Util.Convolution
5Copyright : (c) Alberto Ruiz 2012
6License : GPL
7
8Maintainer : Alberto Ruiz (aruiz at um dot es)
9Stability : provisional
10
11-}
12-----------------------------------------------------------------------------
13
14module Numeric.LinearAlgebra.Util.Convolution(
15 -- * 1D
16 corr, conv,
17 -- * 2D
18 corr2, conv2,
19 -- * Misc
20 separable, corrMin
21) where
22
23import Numeric.LinearAlgebra
24
25
26vectSS :: Element t => Int -> Vector t -> Matrix t
27vectSS n v = fromRows [ subVector k n v | k <- [0 .. dim v - n] ]
28
29
30corr :: Product t => Vector t -- ^ kernel
31 -> Vector t -- ^ source
32 -> Vector t
33{- ^ correlation
34
35@\> (fromList[1,2,3]) (fromList [1..10])
36fromList [14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0]@
37
38-}
39corr ker v | dim ker <= dim v = vectSS (dim ker) v <> ker
40 | otherwise = error $ "corr: dim kernel ("++show (dim ker)++") > dim vector ("++show (dim v)++")"
41
42
43conv :: (Product t, Num t) => Vector t -> Vector t -> Vector t
44{- ^ convolution ('corr' with reversed kernel and padded input, equivalent to polynomial product)
45
46@\> conv (fromList[1,1]) (fromList [-1,1])
47fromList [-1.0,0.0,1.0]@
48
49-}
50conv ker v = corr ker' v'
51 where
52 ker' = (flatten.fliprl.asRow) ker
53 v' | dim ker > 1 = join [z,v,z]
54 | otherwise = v
55 z = constant 0 (dim ker -1)
56
57corrMin :: (Container Vector t, RealElement t, Product t)
58 => Vector t
59 -> Vector t
60 -> Vector t
61-- ^ similar to 'corr', using 'min' instead of (*)
62corrMin ker v = minEvery ss (asRow ker) <> ones
63 where
64 minEvery a b = cond a b a a b
65 ss = vectSS (dim ker) v
66 ones = konst' 1 (dim ker)
67
68
69
70matSS :: Element t => Int -> Matrix t -> [Matrix t]
71matSS dr m = map (reshape c) [ subVector (k*c) n v | k <- [0 .. r - dr] ]
72 where
73 v = flatten m
74 c = cols m
75 r = rows m
76 n = dr*c
77
78
79corr2 :: Product a => Matrix a -> Matrix a -> Matrix a
80-- ^ 2D correlation
81corr2 ker mat = dims
82 . concatMap (map ((<.> ker') . flatten) . matSS c . trans)
83 . matSS r $ mat
84 where
85 r = rows ker
86 c = cols ker
87 ker' = flatten (trans ker)
88 rr = rows mat - r + 1
89 rc = cols mat - c + 1
90 dims | rr > 0 && rc > 0 = (rr >< rc)
91 | otherwise = error $ "corr2: dim kernel ("++sz ker++") > dim matrix ("++sz mat++")"
92 sz m = show (rows m)++"x"++show (cols m)
93
94conv2 :: (Num a, Product a) => Matrix a -> Matrix a -> Matrix a
95-- ^ 2D convolution
96conv2 k m = corr2 (fliprl . flipud $ k) pm
97 where
98 pm | r == 0 && c == 0 = m
99 | r == 0 = fromBlocks [[z3,m,z3]]
100 | c == 0 = fromBlocks [[z2],[m],[z2]]
101 | otherwise = fromBlocks [[z1,z2,z1]
102 ,[z3, m,z3]
103 ,[z1,z2,z1]]
104 r = rows k - 1
105 c = cols k - 1
106 h = rows m
107 w = cols m
108 z1 = konst' 0 (r,c)
109 z2 = konst' 0 (r,w)
110 z3 = konst' 0 (h,c)
111
112-- TODO: could be simplified using future empty arrays
113
114
115separable :: Element t => (Vector t -> Vector t) -> Matrix t -> Matrix t
116-- ^ 2D process implemented as separated 1D processes by rows and columns.
117separable f = fromColumns . map f . toColumns . fromRows . map f . toRows
118