Replace the custom 'Vector' typeclass with 'Normed' everywhere.

diff --git a/src/FixedVector.hs b/src/FixedVector.hs
index 6dabfb60ab07d4e3574deb57ab4192b388ed2a72..531c0fd7b9155a1db0987959f6544fcbf8747cfc 100644 (file)
--- a/src/FixedVector.hs
+++ b/src/FixedVector.hs
@@ -154,7 +154,7 @@ angle v1 v2 =
   acos theta
   where
     theta = (v1 `dot` v2) / norms
-    norms = (norm_p (2 :: Integer) v1) * (norm_p (2 :: Integer) v2)
+    norms = (norm v1) * (norm v2)
 
 
 -- | Convenience function for creating 2d vectors.

diff --git a/src/Normed.hs b/src/Normed.hs
index b60c2b12fe84d51e0bf83b60ce0f958af55f7c10..7f4131aee78958b0938c907855a840ada4b47dfe 100644 (file)
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -7,10 +7,18 @@ where
 
 import Data.Number.BigFloat
 
-class Normed a where
+-- Since the norm is defined on a vector space, we should be able to
+-- add and subtract anything on which a norm is defined. Of course
+-- 'Num' is a bad choice here, but we really prefer to use the normal
+-- addition and subtraction operators.
+class (Num a) => Normed a where
   norm_p :: (Integral c, RealFrac b) => c -> a -> b
   norm_infty :: RealFrac b => a -> b
 
+  -- | The "usual" norm. Defaults to the Euclidean norm.
+  norm :: RealFrac b => a -> b
+  norm = norm_p (2 :: Integer)
+
 -- Define instances for common numeric types.
 instance Normed Integer where
   norm_p _ = fromInteger

diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index cda999ceab62a2fcc3b1f77e07560fb22403d6d3..5efdf3be99eec871931d18c6095333b8bd31ce83 100644 (file)
--- a/src/Roots/Fast.hs
+++ b/src/Roots/Fast.hs
@@ -8,7 +8,7 @@ where
 
 import Data.List (find)
 
-import Vector
+import Normed
 
 
 has_root :: (Fractional a, Ord a, Ord b, Num b)
@@ -104,7 +104,7 @@ fixed_point_iterations f x0 =
 --
 --   We also return the number of iterations required.
 --
-fixed_point_with_iterations :: (Vector a, RealFrac b)
+fixed_point_with_iterations :: (Normed a, RealFrac b)
                             => (a -> a)  -- ^ The function @f@ to iterate.
                             -> b        -- ^ The tolerance, @epsilon@.
                             -> a        -- ^ The initial value @x0@.
@@ -115,7 +115,7 @@ fixed_point_with_iterations f epsilon x0 =
     xn = fixed_point_iterations f x0
     xn_plus_one = tail xn
 
-    abs_diff v w = norm_2 (v - w)
+    abs_diff v w = norm (v - w)
 
     -- The nth entry in this list is the absolute value of x_{n} -
     -- x_{n+1}.

diff --git a/src/Roots/Simple.hs b/src/Roots/Simple.hs
index f9b36fad6578733fe8cad0308e573a77aa37640b..6e3ff5153b20a7e6ff7589c6b2c77a1914406e02 100644 (file)
--- a/src/Roots/Simple.hs
+++ b/src/Roots/Simple.hs
@@ -11,7 +11,7 @@ where
 
 import Data.List (find)
 
-import Vector
+import Normed
 
 import qualified Roots.Fast as F
 
@@ -219,7 +219,7 @@ secant_method f epsilon x0 x1
 --   at x0. We delegate to the version that returns the number of
 --   iterations and simply discard the number of iterations.
 --
-fixed_point :: (Vector a, RealFrac b)
+fixed_point :: (Normed a, RealFrac b)
             => (a -> a) -- ^ The function @f@ to iterate.
             -> b       -- ^ The tolerance, @epsilon@.
             -> a       -- ^ The initial value @x0@.
@@ -232,7 +232,7 @@ fixed_point f epsilon x0 =
 --   the function @f@ with the search starting at x0 and tolerance
 --   @epsilon@. We delegate to the version that returns the number of
 --   iterations and simply discard the fixed point.
-fixed_point_iteration_count :: (Vector a, RealFrac b)
+fixed_point_iteration_count :: (Normed a, RealFrac b)
                             => (a -> a) -- ^ The function @f@ to iterate.
                             -> b       -- ^ The tolerance, @epsilon@.
                             -> a       -- ^ The initial value @x0@.
@@ -250,7 +250,7 @@ fixed_point_iteration_count f epsilon x0 =
 --
 --   This is used to determine the rate of convergence.
 --
-fixed_point_error_ratios :: (Vector a, RealFrac b)
+fixed_point_error_ratios :: (Normed a, RealFrac b)
                    => (a -> a) -- ^ The function @f@ to iterate.
                    -> a       -- ^ The initial value @x0@.
                    -> a       -- ^ The true solution, @x_star@.
@@ -260,6 +260,6 @@ fixed_point_error_ratios f x0 x_star p =
   zipWith (/) en_plus_one en_exp
   where
     xn = F.fixed_point_iterations f x0
-    en = map (\x -> norm_2 (x_star - x)) xn
+    en = map (\x -> norm (x_star - x)) xn
     en_plus_one = tail en
     en_exp = map (^p) en

diff --git a/src/TwoTuple.hs b/src/TwoTuple.hs
index 3950fee9afeabd5bfb8d884ca6543c4689873c24..becb11eb05435f5a3b45223a5d718475f32e9878 100644 (file)
--- a/src/TwoTuple.hs
+++ b/src/TwoTuple.hs
@@ -6,7 +6,7 @@
 module TwoTuple
 where
 
-import Vector
+import Normed
 
 
 data TwoTuple a = TwoTuple a a
@@ -18,10 +18,10 @@ instance (Show a) => Show (TwoTuple a) where
 instance Functor TwoTuple where
   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
 
-instance (RealFloat a) => Vector (TwoTuple a) where
+instance (RealFloat a) => Normed (TwoTuple a) where
   -- The standard Euclidean 2-norm. We need RealFloat for the square
   -- root.
-  norm_2 (TwoTuple x y) = fromRational $ toRational (sqrt(x^2 + y^2))
+  norm (TwoTuple x y) = fromRational $ toRational (sqrt(x^2 + y^2))
 
   -- The infinity norm, i.e. the maximum entry.
   norm_infty (TwoTuple x y) =

diff --git a/src/Vector.hs b/src/Vector.hs
deleted file mode 100644 (file)
index 6953031..0000000
--- a/src/Vector.hs
+++ /dev/null
@@ -1,29 +0,0 @@
-{-# LANGUAGE FlexibleInstances #-}
-
--- | The 'Vector' class represents elements of a normed vector
---   space. We define instances for all common numeric types.
-module Vector
-where
-
-import Data.Number.BigFloat
-
-class (Num a) => Vector a where
-  norm_2 :: RealFrac b => a -> b
-  norm_infty :: RealFrac b => a -> b
-
--- Define instances for common numeric types.
-instance Vector Integer where
-  norm_2 = fromInteger
-  norm_infty = fromInteger
-
-instance Vector Rational where
-  norm_2 = fromRational
-  norm_infty = fromRational
-
-instance Epsilon e => Vector (BigFloat e) where
-  norm_2 = fromRational . toRational
-  norm_infty = fromRational . toRational
-
-instance Vector Double where
-  norm_2 = fromRational . toRational
-  norm_infty = fromRational . toRational