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{-# OPTIONS #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Tests.Properties
Copyright : (c) Alberto Ruiz 2008
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : portable
Arbitrary instances for vectors, matrices.
-}
module Numeric.LinearAlgebra.Tests.Properties
where
import Numeric.LinearAlgebra
import Numeric.LinearAlgebra.Tests.Instances(Sq(..),Her(..),Rot(..))
-- relative error
dist :: (Normed t, Num t) => t -> t -> Double
dist a b = r
where norm = pnorm Infinity
na = norm a
nb = norm b
nab = norm (a-b)
mx = max na nb
mn = min na nb
r = if mn < eps
then mx
else nab/mx
infixl 4 |~|
a |~| b = a :~10~: b
--a |~| b = dist a b < 10^^(-10)
data Aprox a = (:~) a Int
(~:) :: (Normed a, Num a) => Aprox a -> a -> Bool
a :~n~: b = dist a b < 10^^(-n)
------------------------------------------------------
square m = rows m == cols m
unitary m = square m && m <> ctrans m |~| ident (rows m)
hermitian m = square m && m |~| ctrans m
degenerate m = rank m < min (rows m) (cols m)
wellCond m = rcond m > 1/100
-----------------------------------------------------
luTest m = m |~| p <> l <> u && det p == s
where (l,u,p,s) = lu m
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