1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
|
{-# OPTIONS_GHC -fglasgow-exts #-}
{-# LANGUAGE UndecidableInstances #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Interface
Copyright : (c) Alberto Ruiz 2007
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : portable
Some useful operators, and Show, Read, Eq, Num, Fractional, and Floating instances for Vector and Matrix.
In the context of the standard numeric operators, one-component vectors and matrices automatically expand to match the dimensions of the other operand.
-}
-----------------------------------------------------------------------------
module Numeric.LinearAlgebra.Interface(
(<>),(<.>),
(<\>),
(.*),(*/),
(<|>),(<->),
) where
import Numeric.Vector
import Numeric.Matrix
import Numeric.LinearAlgebra.Algorithms
import Numeric.LinearAlgebra.Linear
class Mul a b c | a b -> c where
infixl 7 <>
-- | Matrix-matrix, matrix-vector, and vector-matrix products.
(<>) :: Product t => a t -> b t -> c t
instance Mul Matrix Matrix Matrix where
(<>) = mXm
instance Mul Matrix Vector Vector where
(<>) m v = flatten $ m <> (asColumn v)
instance Mul Vector Matrix Vector where
(<>) v m = flatten $ (asRow v) <> m
---------------------------------------------------
-- | Dot product: @u \<.\> v = dot u v@
--(<.>) :: (Field t) => Vector t -> Vector t -> t
(<.>) :: Vectors Vector t => Vector t -> Vector t -> t
infixl 7 <.>
(<.>) = dot
----------------------------------------------------
{-# DEPRECATED (.*) "use scale a x or scalar a * x" #-}
-- -- | @x .* a = scale x a@
-- (.*) :: (Linear c a) => a -> c a -> c a
infixl 7 .*
a .* x = scale a x
----------------------------------------------------
{-# DEPRECATED (*/) "use scale (recip a) x or x / scalar a" #-}
-- -- | @a *\/ x = scale (recip x) a@
-- (*/) :: (Linear c a) => c a -> a -> c a
infixl 7 */
v */ x = scale (recip x) v
-- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD).
(<\>) :: (Field a) => Matrix a -> Vector a -> Vector a
infixl 7 <\>
m <\> v = flatten (linearSolveSVD m (reshape 1 v))
------------------------------------------------
{-# DEPRECATED (<|>) "define operator a & b = fromBlocks[[a,b]] and use asRow/asColumn to join vectors" #-}
{-# DEPRECATED (<->) "define operator a // b = fromBlocks[[a],[b]] and use asRow/asColumn to join vectors" #-}
class Joinable a b where
joinH :: Element t => a t -> b t -> Matrix t
joinV :: Element t => a t -> b t -> Matrix t
instance Joinable Matrix Matrix where
joinH m1 m2 = fromBlocks [[m1,m2]]
joinV m1 m2 = fromBlocks [[m1],[m2]]
instance Joinable Matrix Vector where
joinH m v = joinH m (asColumn v)
joinV m v = joinV m (asRow v)
instance Joinable Vector Matrix where
joinH v m = joinH (asColumn v) m
joinV v m = joinV (asRow v) m
infixl 4 <|>
infixl 3 <->
{-- - | Horizontal concatenation of matrices and vectors:
@> (ident 3 \<-\> 3 * ident 3) \<|\> fromList [1..6.0]
(6><4)
[ 1.0, 0.0, 0.0, 1.0
, 0.0, 1.0, 0.0, 2.0
, 0.0, 0.0, 1.0, 3.0
, 3.0, 0.0, 0.0, 4.0
, 0.0, 3.0, 0.0, 5.0
, 0.0, 0.0, 3.0, 6.0 ]@
-}
-- (<|>) :: (Element t, Joinable a b) => a t -> b t -> Matrix t
a <|> b = joinH a b
-- -- | Vertical concatenation of matrices and vectors.
-- (<->) :: (Element t, Joinable a b) => a t -> b t -> Matrix t
a <-> b = joinV a b
|
