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
|
{-# LANGUAGE UnicodeSyntax
, MultiParamTypeClasses
, FunctionalDependencies
, FlexibleInstances
, FlexibleContexts
-- , OverlappingInstances
, UndecidableInstances #-}
import Numeric.LinearAlgebra
class Scaling a b c | a b -> c where
-- ^ 0x22C5 8901 DOT OPERATOR, scaling
infixl 7 ⋅
(⋅) :: a -> b -> c
instance (Num t) => Scaling t t t where
(⋅) = (*)
instance Container Vector t => Scaling t (Vector t) (Vector t) where
(⋅) = scale
instance Container Vector t => Scaling (Vector t) t (Vector t) where
(⋅) = flip scale
instance (Num t, Container Vector t) => Scaling t (Matrix t) (Matrix t) where
(⋅) = scale
instance (Num t, Container Vector t) => Scaling (Matrix t) t (Matrix t) where
(⋅) = flip scale
class Mul a b c | a b -> c, a c -> b, b c -> a where
-- ^ 0x00D7 215 MULTIPLICATION SIGN ×, contraction
infixl 7 ×
(×) :: a -> b -> c
-------
instance Product t => Mul (Vector t) (Vector t) t where
(×) = udot
instance (Numeric t, Product t) => Mul (Matrix t) (Vector t) (Vector t) where
(×) = (#>)
instance (Numeric t, Product t) => Mul (Vector t) (Matrix t) (Vector t) where
(×) = (<#)
instance (Numeric t, Product t) => Mul (Matrix t) (Matrix t) (Matrix t) where
(×) = (<>)
--instance Scaling a b c => Contraction a b c where
-- (×) = (⋅)
--------------------------------------------------------------------------------
class Outer a
where
infixl 7 ⊗
-- | unicode 0x2297 8855 CIRCLED TIMES ⊗
--
-- vector outer product and matrix Kronecker product
(⊗) :: Product t => a t -> a t -> Matrix t
instance Outer Vector where
(⊗) = outer
instance Outer Matrix where
(⊗) = kronecker
--------------------------------------------------------------------------------
v = 3 |> [1..] :: Vector Double
m = (3 >< 3) [1..] :: Matrix Double
s = 3 :: Double
a = s ⋅ v × m × m × v ⋅ s
--b = (v ⊗ m) ⊗ (v ⊗ m)
--c = v ⊗ m ⊗ v ⊗ m
d = s ⋅ (3 |> [10,20..] :: Vector Double)
u = fromList [3,0,5]
w = konst 1 (2,3) :: Matrix Double
main = do
print $ (scale s v <# m) `udot` v
print $ scale s v `udot` (m #> v)
print $ s * ((v <# m) `udot` v)
print $ s ⋅ v × m × v
print a
-- print (b == c)
print d
print $ asColumn u ⊗ w
print $ w ⊗ asColumn u
|
