summaryrefslogtreecommitdiff
path: root/packages/base/src/Numeric/LinearAlgebra/Util
diff options
context:
space:
mode:
Diffstat (limited to 'packages/base/src/Numeric/LinearAlgebra/Util')
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs115
1 files changed, 115 insertions, 0 deletions
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
new file mode 100644
index 0000000..d04c46b
--- /dev/null
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
@@ -0,0 +1,115 @@
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{-# OPTIONS_HADDOCK hide #-}
14
15module Numeric.LinearAlgebra.Util.Convolution(
16 corr, conv, corrMin,
17 corr2, conv2, separable
18) where
19
20import Numeric.LinearAlgebra
21
22
23vectSS :: Element t => Int -> Vector t -> Matrix t
24vectSS n v = fromRows [ subVector k n v | k <- [0 .. dim v - n] ]
25
26
27corr :: Product t => Vector t -- ^ kernel
28 -> Vector t -- ^ source
29 -> Vector t
30{- ^ correlation
31
32>>> corr (fromList[1,2,3]) (fromList [1..10])
33fromList [14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0]
34
35-}
36corr ker v | dim ker <= dim v = vectSS (dim ker) v <> ker
37 | otherwise = error $ "corr: dim kernel ("++show (dim ker)++") > dim vector ("++show (dim v)++")"
38
39
40conv :: (Product t, Num t) => Vector t -> Vector t -> Vector t
41{- ^ convolution ('corr' with reversed kernel and padded input, equivalent to polynomial product)
42
43>>> conv (fromList[1,1]) (fromList [-1,1])
44fromList [-1.0,0.0,1.0]
45
46-}
47conv ker v = corr ker' v'
48 where
49 ker' = (flatten.fliprl.asRow) ker
50 v' | dim ker > 1 = vjoin [z,v,z]
51 | otherwise = v
52 z = constant 0 (dim ker -1)
53
54corrMin :: (Container Vector t, RealElement t, Product t)
55 => Vector t
56 -> Vector t
57 -> Vector t
58-- ^ similar to 'corr', using 'min' instead of (*)
59corrMin ker v = minEvery ss (asRow ker) <> ones
60 where
61 minEvery a b = cond a b a a b
62 ss = vectSS (dim ker) v
63 ones = konst 1 (dim ker)
64
65
66
67matSS :: Element t => Int -> Matrix t -> [Matrix t]
68matSS dr m = map (reshape c) [ subVector (k*c) n v | k <- [0 .. r - dr] ]
69 where
70 v = flatten m
71 c = cols m
72 r = rows m
73 n = dr*c
74
75
76corr2 :: Product a => Matrix a -> Matrix a -> Matrix a
77-- ^ 2D correlation
78corr2 ker mat = dims
79 . concatMap (map (udot ker' . flatten) . matSS c . trans)
80 . matSS r $ mat
81 where
82 r = rows ker
83 c = cols ker
84 ker' = flatten (trans ker)
85 rr = rows mat - r + 1
86 rc = cols mat - c + 1
87 dims | rr > 0 && rc > 0 = (rr >< rc)
88 | otherwise = error $ "corr2: dim kernel ("++sz ker++") > dim matrix ("++sz mat++")"
89 sz m = show (rows m)++"x"++show (cols m)
90
91conv2 :: (Num a, Product a, Container Vector a) => Matrix a -> Matrix a -> Matrix a
92-- ^ 2D convolution
93conv2 k m = corr2 (fliprl . flipud $ k) pm
94 where
95 pm | r == 0 && c == 0 = m
96 | r == 0 = fromBlocks [[z3,m,z3]]
97 | c == 0 = fromBlocks [[z2],[m],[z2]]
98 | otherwise = fromBlocks [[z1,z2,z1]
99 ,[z3, m,z3]
100 ,[z1,z2,z1]]
101 r = rows k - 1
102 c = cols k - 1
103 h = rows m
104 w = cols m
105 z1 = konst 0 (r,c)
106 z2 = konst 0 (r,w)
107 z3 = konst 0 (h,c)
108
109-- TODO: could be simplified using future empty arrays
110
111
112separable :: Element t => (Vector t -> Vector t) -> Matrix t -> Matrix t
113-- ^ matrix computation implemented as separated vector operations by rows and columns.
114separable f = fromColumns . map f . toColumns . fromRows . map f . toRows
115