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1{-# LANGUAGE TypeFamilies #-}
2{-# LANGUAGE FlexibleContexts #-}
3{-# LANGUAGE FlexibleInstances #-}
4{-# LANGUAGE UndecidableInstances #-}
5{-# LANGUAGE MultiParamTypeClasses #-}
6-----------------------------------------------------------------------------
7-- |
8-- Module : Numeric.Vector
9-- Copyright : (c) Alberto Ruiz 2011
10-- License : GPL-style
11--
12-- Maintainer : Alberto Ruiz <aruiz@um.es>
13-- Stability : provisional
14-- Portability : portable
15--
16-- Provides instances of standard classes 'Show', 'Read', 'Eq',
17-- 'Num', 'Fractional', and 'Floating' for 'Vector'.
18--
19-----------------------------------------------------------------------------
20
21module Numeric.Vector () where
22
23import Numeric.GSL.Vector
24import Numeric.Container
25
26-------------------------------------------------------------------
27
28adaptScalar f1 f2 f3 x y
29 | dim x == 1 = f1 (x@>0) y
30 | dim y == 1 = f3 x (y@>0)
31 | otherwise = f2 x y
32
33------------------------------------------------------------------
34
35instance Num (Vector Float) where
36 (+) = adaptScalar addConstant add (flip addConstant)
37 negate = scale (-1)
38 (*) = adaptScalar scale mul (flip scale)
39 signum = vectorMapF Sign
40 abs = vectorMapF Abs
41 fromInteger = fromList . return . fromInteger
42
43instance Num (Vector Double) where
44 (+) = adaptScalar addConstant add (flip addConstant)
45 negate = scale (-1)
46 (*) = adaptScalar scale mul (flip scale)
47 signum = vectorMapR Sign
48 abs = vectorMapR Abs
49 fromInteger = fromList . return . fromInteger
50
51instance Num (Vector (Complex Double)) where
52 (+) = adaptScalar addConstant add (flip addConstant)
53 negate = scale (-1)
54 (*) = adaptScalar scale mul (flip scale)
55 signum = vectorMapC Sign
56 abs = vectorMapC Abs
57 fromInteger = fromList . return . fromInteger
58
59instance Num (Vector (Complex Float)) where
60 (+) = adaptScalar addConstant add (flip addConstant)
61 negate = scale (-1)
62 (*) = adaptScalar scale mul (flip scale)
63 signum = vectorMapQ Sign
64 abs = vectorMapQ Abs
65 fromInteger = fromList . return . fromInteger
66
67---------------------------------------------------
68
69instance (Container Vector a, Num (Vector a)) => Fractional (Vector a) where
70 fromRational n = fromList [fromRational n]
71 (/) = adaptScalar f divide g where
72 r `f` v = scaleRecip r v
73 v `g` r = scale (recip r) v
74
75-------------------------------------------------------
76
77instance Floating (Vector Float) where
78 sin = vectorMapF Sin
79 cos = vectorMapF Cos
80 tan = vectorMapF Tan
81 asin = vectorMapF ASin
82 acos = vectorMapF ACos
83 atan = vectorMapF ATan
84 sinh = vectorMapF Sinh
85 cosh = vectorMapF Cosh
86 tanh = vectorMapF Tanh
87 asinh = vectorMapF ASinh
88 acosh = vectorMapF ACosh
89 atanh = vectorMapF ATanh
90 exp = vectorMapF Exp
91 log = vectorMapF Log
92 sqrt = vectorMapF Sqrt
93 (**) = adaptScalar (vectorMapValF PowSV) (vectorZipF Pow) (flip (vectorMapValF PowVS))
94 pi = fromList [pi]
95
96-------------------------------------------------------------
97
98instance Floating (Vector Double) where
99 sin = vectorMapR Sin
100 cos = vectorMapR Cos
101 tan = vectorMapR Tan
102 asin = vectorMapR ASin
103 acos = vectorMapR ACos
104 atan = vectorMapR ATan
105 sinh = vectorMapR Sinh
106 cosh = vectorMapR Cosh
107 tanh = vectorMapR Tanh
108 asinh = vectorMapR ASinh
109 acosh = vectorMapR ACosh
110 atanh = vectorMapR ATanh
111 exp = vectorMapR Exp
112 log = vectorMapR Log
113 sqrt = vectorMapR Sqrt
114 (**) = adaptScalar (vectorMapValR PowSV) (vectorZipR Pow) (flip (vectorMapValR PowVS))
115 pi = fromList [pi]
116
117-------------------------------------------------------------
118
119instance Floating (Vector (Complex Double)) where
120 sin = vectorMapC Sin
121 cos = vectorMapC Cos
122 tan = vectorMapC Tan
123 asin = vectorMapC ASin
124 acos = vectorMapC ACos
125 atan = vectorMapC ATan
126 sinh = vectorMapC Sinh
127 cosh = vectorMapC Cosh
128 tanh = vectorMapC Tanh
129 asinh = vectorMapC ASinh
130 acosh = vectorMapC ACosh
131 atanh = vectorMapC ATanh
132 exp = vectorMapC Exp
133 log = vectorMapC Log
134 sqrt = vectorMapC Sqrt
135 (**) = adaptScalar (vectorMapValC PowSV) (vectorZipC Pow) (flip (vectorMapValC PowVS))
136 pi = fromList [pi]
137
138-----------------------------------------------------------
139
140instance Floating (Vector (Complex Float)) where
141 sin = vectorMapQ Sin
142 cos = vectorMapQ Cos
143 tan = vectorMapQ Tan
144 asin = vectorMapQ ASin
145 acos = vectorMapQ ACos
146 atan = vectorMapQ ATan
147 sinh = vectorMapQ Sinh
148 cosh = vectorMapQ Cosh
149 tanh = vectorMapQ Tanh
150 asinh = vectorMapQ ASinh
151 acosh = vectorMapQ ACosh
152 atanh = vectorMapQ ATanh
153 exp = vectorMapQ Exp
154 log = vectorMapQ Log
155 sqrt = vectorMapQ Sqrt
156 (**) = adaptScalar (vectorMapValQ PowSV) (vectorZipQ Pow) (flip (vectorMapValQ PowVS))
157 pi = fromList [pi]
158
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