mapMatrixWithIndex, Mul, multiply.hs

1 files changed, 100 insertions, 0 deletions

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+{-# 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
+
+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
+    (×) = dot
+
+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 <.> v 
+    print $ scale s v <.> (m <> v)
+    print $ s * (v <> m <.> v)
+    print $ s ⋅ v × m × v
+    print a
+    print (b == c)
+    print d
+