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|
{-# OPTIONS #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Tests.Instances
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.Instances(
Sq(..),
Rot(..),
Her(..),
WC(..)
) where
import Numeric.LinearAlgebra
import Test.QuickCheck
import Control.Monad(replicateM)
instance (Arbitrary a, RealFloat a) => Arbitrary (Complex a) where
arbitrary = do
r <- arbitrary
i <- arbitrary
return (r:+i)
coarbitrary = undefined
chooseDim = sized $ \m -> choose (1,max 1 m)
instance (Field a, Arbitrary a) => Arbitrary (Vector a) where
arbitrary = do m <- chooseDim
l <- vector m
return $ fromList l
coarbitrary = undefined
instance (Element a, Arbitrary a) => Arbitrary (Matrix a) where
arbitrary = do
m <- chooseDim
n <- chooseDim
l <- vector (m*n)
return $ (m><n) l
coarbitrary = undefined
-- a square matrix
newtype (Sq a) = Sq (Matrix a) deriving Show
instance (Element a, Arbitrary a) => Arbitrary (Sq a) where
arbitrary = do
n <- chooseDim
l <- vector (n*n)
return $ Sq $ (n><n) l
coarbitrary = undefined
-- a unitary matrix
newtype (Rot a) = Rot (Matrix a) deriving Show
instance (Field a, Arbitrary a) => Arbitrary (Rot a) where
arbitrary = do
Sq m <- arbitrary
let (q,_) = qr m
return (Rot q)
coarbitrary = undefined
-- a complex hermitian or real symmetric matrix
newtype (Her a) = Her (Matrix a) deriving Show
instance (Field a, Arbitrary a) => Arbitrary (Her a) where
arbitrary = do
Sq m <- arbitrary
let m' = m/2
return $ Her (m' + ctrans m')
coarbitrary = undefined
-- a well-conditioned matrix (the singular values are between 1 and 100)
newtype (WC a) = WC (Matrix a) deriving Show
instance (Field a, Arbitrary a) => Arbitrary (WC a) where
arbitrary = do
m <- arbitrary
let (u,_,v) = svd m
r = rows m
c = cols m
n = min r c
sv <- replicateM n (choose (1,100))
let s = diagRect (fromList sv) r c
return $ WC (u <> real s <> trans v)
coarbitrary = undefined
|
