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
|
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Matrix
-- Copyright : (c) Alberto Ruiz 2007
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Numeric instances and functions for 'Data.Packed.Matrix's
--
-----------------------------------------------------------------------------
module Numeric.Matrix (
module Data.Packed.Matrix,
) where
-------------------------------------------------------------------
import Data.Packed.Vector
import Data.Packed.Matrix
import Numeric.Container
import Numeric.LinearAlgebra.Linear
--import Numeric.Vector
import Control.Monad(ap)
-------------------------------------------------------------------
instance Linear Matrix a => Eq (Matrix a) where
(==) = equal
instance (Linear Matrix a, Num (Vector a)) => Num (Matrix a) where
(+) = liftMatrix2Auto (+)
(-) = liftMatrix2Auto (-)
negate = liftMatrix negate
(*) = liftMatrix2Auto (*)
signum = liftMatrix signum
abs = liftMatrix abs
fromInteger = (1><1) . return . fromInteger
---------------------------------------------------
instance (Linear Vector a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a) where
fromRational n = (1><1) [fromRational n]
(/) = liftMatrix2Auto (/)
---------------------------------------------------------
instance (Linear Vector a, Floating (Vector a), Fractional (Matrix a)) => Floating (Matrix a) where
sin = liftMatrix sin
cos = liftMatrix cos
tan = liftMatrix tan
asin = liftMatrix asin
acos = liftMatrix acos
atan = liftMatrix atan
sinh = liftMatrix sinh
cosh = liftMatrix cosh
tanh = liftMatrix tanh
asinh = liftMatrix asinh
acosh = liftMatrix acosh
atanh = liftMatrix atanh
exp = liftMatrix exp
log = liftMatrix log
(**) = liftMatrix2Auto (**)
sqrt = liftMatrix sqrt
pi = (1><1) [pi]
---------------------------------------------------------------
instance (Linear Vector a, NumericContainer Matrix) => (Linear Matrix a) where
scale x = liftMatrix (scale x)
scaleRecip x = liftMatrix (scaleRecip x)
addConstant x = liftMatrix (addConstant x)
add = liftMatrix2 add
sub = liftMatrix2 sub
mul = liftMatrix2 mul
divide = liftMatrix2 divide
equal a b = cols a == cols b && flatten a `equal` flatten b
scalar x = (1><1) [x]
instance (Linear Vector a, NumericContainer Matrix) => (Container Matrix a) where
minIndex m = let (r,c) = (rows m,cols m)
i = 1 + (minIndex $ flatten m)
in (i `div` r,i `mod` r)
maxIndex m = let (r,c) = (rows m,cols m)
i = 1 + (maxIndex $ flatten m)
in (i `div` r,i `mod` r)
minElement = ap (@@>) minIndex
maxElement = ap (@@>) maxIndex
----------------------------------------------------
|
