src/Linear/Vector.hs: add a Vec0 type.

[numerical-analysis.git] / src / Linear / Vector.hs

diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs
index 9774dcd40c8132413ddd541a2a65be8976a462e1..c9307153cc65330b2e0ec8e4f5eeec85d933607b 100644 (file)
--- a/src/Linear/Vector.hs
+++ b/src/Linear/Vector.hs
@@ -1,80 +1,53 @@
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE NoMonomorphismRestriction #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies #-}
 
-module Linear.Vector
+module Linear.Vector (
+  module Data.Vector.Fixed.Boxed,
+  Vec0,
+  Vec1,
+  (!?),
+  delete,
+  element_sum )
 where
 
-import Data.List (intercalate)
+import qualified Algebra.Additive as Additive ( C )
+import qualified Algebra.Ring as Ring ( C )
 import Data.Vector.Fixed (
   Dim,
-  Fun(..),
   N1,
-  N2,
-  N3,
-  N4,
+  S,
   Vector(..),
-  construct,
-  inspect,
-  toList,
-  )
-import qualified Data.Vector.Fixed as V (
-  length,
-  )
-
-import Normed
-
-
--- * Low-dimension vector wrappers.
---
--- These wrappers are instances of 'Vector', so they inherit all of
--- the userful instances defined above. But, they use fixed
--- constructors, so you can pattern match out the individual
--- components.
-
-data D1 a = D1 a
-type instance Dim D1 = N1
-instance Vector D1 a where
-  inspect (D1 x) (Fun f) = f x
-  construct = Fun D1
-
-data D2 a = D2 a a
-type instance Dim D2 = N2
-instance Vector D2 a where
-  inspect (D2 x y) (Fun f) = f x y
-  construct = Fun D2
-
-data D3 a = D3 a a a
-type instance Dim D3 = N3
-instance Vector D3 a where
-  inspect (D3 x y z) (Fun f) = f x y z
-  construct = Fun D3
+  Z,
+  fromList,
+  toList )
+import Data.Vector.Fixed (
+  (!),
+  foldl,
+  length )
+import Data.Vector.Fixed.Boxed (
+  Vec,
+  Vec2,
+  Vec3,
+  Vec4,
+  Vec5 )
+import NumericPrelude hiding ( abs, length, foldl )
 
-data D4 a = D4 a a a a
-type instance Dim D4 = N4
-instance Vector D4 a where
-  inspect (D4 w x y z) (Fun f) = f w x y z
-  construct = Fun D4
+type Vec0 = Vec Z
+type Vec1 = Vec N1
 
 
--- | Unsafe indexing.
---
---   Examples:
---
---   >>> let v1 = Vec2D 1 2
---   >>> v1 ! 1
---   2
---
-(!) :: (Vector v a) => v a -> Int -> a
-(!) v1 idx = (toList v1) !! idx
 
 -- | Safe indexing.
 --
 --   Examples:
 --
---   >>> let v1 = Vec3D 1 2 3
+--   >>> import Data.Vector.Fixed (mk3)
+--   >>> let v1 = mk3 1 2 3 :: Vec3 Int
 --   >>> v1 !? 2
 --   Just 3
 --   >>> v1 !? 3
@@ -82,56 +55,41 @@ instance Vector D4 a where
 --
 (!?) :: (Vector v a) => v a -> Int -> Maybe a
 (!?) v1 idx
-  | idx < 0 || idx >= V.length v1 = Nothing
-  | otherwise                     = Just $ v1 ! idx
+  | idx < 0 || idx >= length v1 = Nothing
+  | otherwise                   = Just $ v1 ! idx
 
 
-
-
---instance (RealFloat a, Ord a, Vector v a) => Normed (Vn v a) where
-  -- | The infinity norm. We don't use V.maximum here because it
-  --   relies on a type constraint that the vector be non-empty and I
-  --   don't know how to pattern match it away.
-  --
-  --   Examples:
-  --
-  --   >>> let v1 = make3d (1,5,2)
-  --   >>> norm_infty v1
-  --   5
-  --
---  norm_infty (Vn v1) = realToFrac $ V.foldl max 0 v1
-
-  -- | Generic p-norms. The usual norm in R^n is (norm_p 2).
-  --
-  --   Examples:
-  --
-  --   >>> let v1 = make2d (3,4)
-  --   >>> norm_p 1 v1
-  --   7.0
-  --   >>> norm_p 2 v1
-  --   5.0
-  --
---  norm_p p (Vn v1) =
---    realToFrac $ root $ V.sum $ V.map (exponentiate . abs) v1
---    where
---      exponentiate = (** (fromIntegral p))
---      root = (** (recip (fromIntegral p)))
-
-
-
-
-
--- | Convenient constructor for 2D vectors.
+-- | Remove an element of the given vector.
+--
+--   Examples:
+--
+--   >>> import Data.Vector.Fixed (mk3)
+--   >>> let b = mk3 1 2 3 :: Vec3 Int
+--   >>> delete b 1 :: Vec2 Int
+--   fromList [1,3]
+--
+delete :: (Vector v a,
+           Vector w a,
+           Dim v ~ S (Dim w))
+       => v a
+       -> Int
+       -> w a
+delete v1 idx =
+  fromList (lhalf ++ rhalf')
+  where
+    (lhalf, rhalf) = splitAt idx (toList v1)
+    rhalf' = tail rhalf
+
+
+-- | We provide our own sum because sum relies on a Num instance
+--   from the Prelude that we don't have.
 --
 --   Examples:
 --
---   >>> import Roots.Simple
---   >>> let h = 0.5 :: Double
---   >>> let g1 (Vn (Vec2D x y)) = 1.0 + h*exp(-(x^2))/(1.0 + y^2)
---   >>> let g2 (Vn (Vec2D x y)) = 0.5 + h*atan(x^2 + y^2)
---   >>> let g u = make2d ((g1 u), (g2 u))
---   >>> let u0 = make2d (1.0, 1.0)
---   >>> let eps = 1/(10^9)
---   >>> fixed_point g eps u0
---   (1.0728549599342185,1.0820591495686167)
+--   >>> import Data.Vector.Fixed (mk3)
+--   >>> let b = mk3 1 2 3 :: Vec3 Int
+--   >>> element_sum b
+--   6
 --
+element_sum :: (Additive.C a, Ring.C a, Vector v a) => v a -> a
+element_sum = foldl (+) (fromInteger 0)