X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FNormed.hs;h=28fbd2878a2d02641820081da67578ba1166bce3;hb=40154d27bb940fc69f97870ef7ff7fb22ce97b87;hp=6f34a8dca406c13393896179b6b08c023874e9a3;hpb=be2ec3ca8e6fda229e3ca608dcc75e085b3a0b0f;p=numerical-analysis.git

diff --git a/src/Normed.hs b/src/Normed.hs
index 6f34a8d..28fbd28 100644
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -8,28 +8,33 @@ where
 
 import BigFloat
 
-import NumericPrelude hiding ( abs )
+-- Ensure that we don't use the Lattice.C "max" function, that
+-- only works on Integer/Bool.
+import NumericPrelude hiding ( abs, max )
 import Algebra.Absolute ( abs )
-import qualified Algebra.Absolute as Absolute
-import qualified Algebra.Algebraic as Algebraic
+import qualified Algebra.Absolute as Absolute ( C )
+import qualified Algebra.Algebraic as Algebraic ( C )
 import Algebra.Algebraic ( root )
-import qualified Algebra.RealField as RealField
-import qualified Algebra.ToInteger as ToInteger
+import qualified Algebra.RealField as RealField ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
 import qualified Algebra.ToRational as ToRational ( C )
-import Data.Vector.Fixed ( S, Z )
 import qualified Data.Vector.Fixed as V (
   Arity,
-  map,
-  maximum )
+  foldl,
+  map )
 import Data.Vector.Fixed.Boxed ( Vec )
-
+import qualified Prelude as P ( max )
 import Linear.Vector ( element_sum )
 
+
+-- | Instances of the 'Normed' class know how to compute their own
+--   p-norms for p=1,2,...,infinity.
+--
 class Normed a where
   norm_p :: (ToInteger.C c, Algebraic.C b, Absolute.C b) => c -> a -> b
   norm_infty :: (RealField.C b) => a -> b
 
-  -- | The "usual" norm. Defaults to the Euclidean norm.
+  -- | The \"usual\" norm. Defaults to the 2-norm.
   norm :: (Algebraic.C b, Absolute.C b) => a -> b
   norm = norm_p (2 :: Integer)
 
@@ -55,22 +60,14 @@ instance Normed Double where
   norm_infty = abs . fromRational' . toRational
 
 
--- | 'Normed' instance for vectors of length zero. These are easy.
-instance Normed (Vec Z a) where
-  norm_p _ = const (fromInteger 0)
-  norm_infty = const (fromInteger 0)
-
-
--- | 'Normed' instance for vectors of length greater than zero. We
---   need to know that the length is non-zero in order to invoke
---   V.maximum. We will generally be working with n-by-1 /matrices/
---   instead of vectors, but sometimes it's convenient to have these
---   instances anyway.
+-- | 'Normed' instance for vectors of any length. We will generally be
+--   working with n-by-1 /matrices/ instead of vectors, but sometimes
+--   it's convenient to have these instances anyway.
 --
 --   Examples:
 --
 --   >>> import Data.Vector.Fixed (mk3)
---   >>> import Linear.Vector (Vec3)
+--   >>> import Linear.Vector (Vec0, Vec3)
 --   >>> let b = mk3 1 2 3 :: Vec3 Double
 --   >>> norm_p 1 b :: Double
 --   6.0
@@ -79,12 +76,16 @@ instance Normed (Vec Z a) where
 --   >>> norm_infty b :: Double
 --   3.0
 --
+--   >>> let b = undefined :: Vec0 Int
+--   >>> norm b
+--   0.0
+--
 instance (V.Arity n, Absolute.C a, ToRational.C a, Ord a)
-         => Normed (Vec (S n) a) where
+         => Normed (Vec n a) where
   norm_p p x =
     (root p') $ element_sum $ V.map element_function x
     where
       element_function y = fromRational' $ (toRational y)^p'
       p' = toInteger p
 
-  norm_infty x = fromRational' $ toRational $ V.maximum $ V.map abs x
+  norm_infty x = fromRational' $ toRational $ (V.foldl P.max 0) $ V.map abs x