From be2ec3ca8e6fda229e3ca608dcc75e085b3a0b0f Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 2 Feb 2014 18:46:48 -0500 Subject: [PATCH] Add a Normed instance for (Vec n a). --- src/Normed.hs | 49 +++++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 47 insertions(+), 2 deletions(-) diff --git a/src/Normed.hs b/src/Normed.hs index f339ebf..6f34a8d 100644 --- a/src/Normed.hs +++ b/src/Normed.hs @@ -8,12 +8,22 @@ where import BigFloat -import NumericPrelude hiding (abs) -import Algebra.Absolute (abs) +import NumericPrelude hiding ( abs ) +import Algebra.Absolute ( abs ) import qualified Algebra.Absolute as Absolute import qualified Algebra.Algebraic as Algebraic +import Algebra.Algebraic ( root ) import qualified Algebra.RealField as RealField import qualified Algebra.ToInteger as ToInteger +import qualified Algebra.ToRational as ToRational ( C ) +import Data.Vector.Fixed ( S, Z ) +import qualified Data.Vector.Fixed as V ( + Arity, + map, + maximum ) +import Data.Vector.Fixed.Boxed ( Vec ) + +import Linear.Vector ( element_sum ) class Normed a where norm_p :: (ToInteger.C c, Algebraic.C b, Absolute.C b) => c -> a -> b @@ -43,3 +53,38 @@ instance Normed Float where instance Normed Double where norm_p _ = abs . fromRational' . toRational 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. +-- +-- Examples: +-- +-- >>> import Data.Vector.Fixed (mk3) +-- >>> import Linear.Vector (Vec3) +-- >>> let b = mk3 1 2 3 :: Vec3 Double +-- >>> norm_p 1 b :: Double +-- 6.0 +-- >>> norm b == sqrt 14 +-- True +-- >>> norm_infty b :: Double +-- 3.0 +-- +instance (V.Arity n, Absolute.C a, ToRational.C a, Ord a) + => Normed (Vec (S 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 -- 2.44.2