empty hmatrix-base

1 files changed, 104 insertions, 0 deletions

diff --git a/packages/hmatrix/examples/multiply.hs b/packages/hmatrix/examples/multiply.hs
new file mode 100644
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+++ b/packages/hmatrix/examples/multiply.hs
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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
+
+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
+
+
+class Mul a b c | a b -> c, a c -> b, b c -> a where
+ -- ^ 0x00D7    215     MULTIPLICATION SIGN     ×, contraction
+ infixl 7 ×
+ (×) :: a -> b -> c
+
+
+-------
+
+
+
+instance Product t => Mul (Vector t) (Vector t) t where
+    (×) = udot
+
+instance Product t => Mul (Matrix t) (Vector t) (Vector t) where
+    (×) = mXv
+
+instance Product t => Mul (Vector t) (Matrix t) (Vector t) where
+    (×) = vXm
+
+instance Product t => Mul (Matrix t) (Matrix t) (Matrix t) where
+    (×) = mXm
+
+
+--instance Scaling a b c => Contraction a b c where
+--    (×) = (⋅)
+
+--------------------------------------------------------------------------------
+
+class Outer a
+  where
+    infixl 7 ⊗
+    -- | unicode 0x2297 8855 CIRCLED TIMES      ⊗
+    --
+    -- vector outer product and matrix Kronecker product
+    (⊗) :: Product t => a t -> a t -> Matrix t
+
+instance Outer Vector where
+    (⊗) = outer
+
+instance Outer Matrix 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)
+
+u = fromList [3,0,5]
+w = konst 1 (2,3) :: Matrix 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
+    print $ asColumn u ⊗ w
+    print $ w ⊗ asColumn u
+