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
|
-- Alternative interface and utilities for creation of real arrays, useful to work in interactive mode.
module Real(
module Numeric.LinearAlgebra,
(<>), (*>), (<*), (<\>), (\>),
vector,
eye,
zeros, ones,
diagl,
row,
col,
(#),(&), (//), blocks,
rand
) where
import Numeric.LinearAlgebra hiding ((<>), (<|>), (<->), (<\>), (.*), (*/))
import System.Random(randomIO)
infixl 7 <>
-- | Matrix product ('multiply')
(<>) :: Field t => Matrix t -> Matrix t -> Matrix t
(<>) = multiply
infixl 7 *>
-- | matrix x vector
(*>) :: Field t => Matrix t -> Vector t -> Vector t
m *> v = flatten $ m <> (asColumn v)
infixl 7 <*
-- | vector x matrix
(<*) :: Field t => Vector t -> Matrix t -> Vector t
v <* m = flatten $ (asRow v) <> m
-- | Least squares solution of a linear system for several right-hand sides, similar to the \\ operator of Matlab\/Octave. (\<\\\>) = 'linearSolveSVD'.
(<\>) :: (Field a) => Matrix a -> Matrix a -> Matrix a
infixl 7 <\>
(<\>) = linearSolveSVD
-- | Least squares solution of a linear system for a single right-hand side. See '(\<\\\>)'.
(\>) :: (Field a) => Matrix a -> Vector a -> Vector a
infixl 7 \>
m \> v = flatten (m <\> reshape 1 v)
-- | Pseudorandom matrix with uniform elements between 0 and 1.
rand :: Int -- ^ rows
-> Int -- ^ columns
-> IO (Matrix Double)
rand r c = do
seed <- randomIO
return (reshape c $ randomVector seed Uniform (r*c))
-- | Real identity matrix.
eye :: Int -> Matrix Double
eye = ident
-- | Create a real vector from a list.
vector :: [Double] -> Vector Double
vector = fromList
-- | Create a real diagonal matrix from a list.
diagl :: [Double] -> Matrix Double
diagl = diag . vector
-- | Create a matrix or zeros.
zeros :: Int -- ^ rows
-> Int -- ^ columns
-> Matrix Double
zeros r c = reshape c (constant 0 (r*c))
-- | Create a matrix or ones.
ones :: Int -- ^ rows
-> Int -- ^ columns
-> Matrix Double
ones r c = reshape c (constant 1 (r*c))
-- | Concatenation of real vectors.
infixl 9 #
(#) :: Vector Double -> Vector Double -> Vector Double
a # b = join [a,b]
-- | Horizontal concatenation of real matrices.
infixl 8 &
(&) :: Matrix Double -> Matrix Double -> Matrix Double
a & b = fromBlocks [[a,b]]
-- | Vertical concatenation of real matrices.
infixl 7 //
(//) :: Matrix Double -> Matrix Double -> Matrix Double
a // b = fromBlocks [[a],[b]]
-- | Real block matrix from a rectangular list of lists.
blocks :: [[Matrix Double]] -> Matrix Double
blocks = fromBlocks
-- | A real matrix with a single row, create from a list of elements.
row :: [Double] -> Matrix Double
row = asRow . vector
-- | A real matrix with a single column, created from a list of elements.
col :: [Double] -> Matrix Double
col = asColumn . vector
|
