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{-# LANGUAGE UnicodeSyntax
, MultiParamTypeClasses
, FunctionalDependencies
, FlexibleInstances
, FlexibleContexts
-- , OverlappingInstances
, UndecidableInstances #-}
import Numeric.LinearAlgebra hiding (Contraction(..))
class Scaling a b c | a b -> c where
-- ^ 0x22C5 8901 DOT OPERATOR, scaling
infixl 7 ⋅
(⋅) :: a -> b -> c
class Contraction a b c | a b -> c where
-- ^ 0x00D7 215 MULTIPLICATION SIGN ×, contraction
infixl 7 ×
(×) :: a -> b -> c
class Outer a b c | a b -> c where
-- ^ 0x2297 8855 CIRCLED TIMES ⊗, outer product (not associative)
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 Container Vector t => Scaling t (Matrix t) (Matrix t) where
(⋅) = scale
instance Container Vector t => Scaling (Matrix t) t (Matrix t) where
(⋅) = flip scale
instance Product t => Contraction (Vector t) (Vector t) t where
(×) = udot
instance Product t => Contraction (Matrix t) (Vector t) (Vector t) where
(×) = mXv
instance Product t => Contraction (Vector t) (Matrix t) (Vector t) where
(×) = vXm
instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
(×) = mXm
--instance Scaling a b c => Contraction a b c where
-- (×) = (⋅)
-----
instance Product t => Outer (Vector t) (Vector t) (Matrix t) where
(⊗) = outer
instance Product t => Outer (Vector t) (Matrix t) (Matrix t) where
v ⊗ m = kronecker (asColumn v) m
instance Product t => Outer (Matrix t) (Vector t) (Matrix t) where
m ⊗ v = kronecker m (asRow v)
instance Product t => Outer (Matrix t) (Matrix t) (Matrix t) 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)
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
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