module Algebra.NormedSpace.Sum where
import NumericPrelude.Base
import NumericPrelude.Numeric
import qualified Prelude as P
import qualified Number.Ratio as Ratio
import qualified Algebra.PrincipalIdealDomain as PID
import qualified Algebra.Absolute as Absolute
import qualified Algebra.Additive as Additive
import qualified Algebra.Module as Module
import qualified Data.Complex as Complex98
import qualified Data.Foldable as Fold
class (Absolute.C a, Module.C a v) => C a v where
norm :: v -> a
normFoldable ::
(C a v, Fold.Foldable f) => f v -> a
normFoldable =
Fold.foldl (\a v -> a + norm v) zero
normFoldable1 ::
(C a v, Fold.Foldable f, Functor f) => f v -> a
normFoldable1 =
Fold.foldl1 (+) . fmap norm
instance C Float Float where
norm = abs
instance C Double Double where
norm = abs
instance C Int Int where
norm = abs
instance C Integer Integer where
norm = abs
instance (Absolute.C a, PID.C a) => C (Ratio.T a) (Ratio.T a) where
norm = abs
instance (Additive.C a, C a v0, C a v1) => C a (v0, v1) where
norm (x0,x1) = norm x0 + norm x1
instance (Additive.C a, C a v0, C a v1, C a v2) => C a (v0, v1, v2) where
norm (x0,x1,x2) = norm x0 + norm x1 + norm x2
instance (Additive.C a, C a v) => C a [v] where
norm = sum . map norm
instance (C a v, P.RealFloat v) => C a (Complex98.Complex v) where
norm (x0 Complex98.:+ x1) = norm x0 + norm x1