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{-# LANGUAGE CPP, FlexibleContexts, UndecidableInstances, FlexibleInstances, ScopedTypeVariables #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Tests.Instances
Copyright : (c) Alberto Ruiz 2008
License : BSD3
Maintainer : Alberto Ruiz
Stability : provisional
Arbitrary instances for vectors, matrices.
-}
module Numeric.LinearAlgebra.Tests.Instances(
Sq(..), rSq,cSq,
Sq2WC(..), rSq2WC,cSq2WC,
Rot(..), rRot,cRot,
rHer,cHer,
WC(..), rWC,cWC,
SqWC(..), rSqWC, cSqWC, rSymWC, cSymWC,
PosDef(..), rPosDef, cPosDef,
Consistent(..), rConsist, cConsist,
RM,CM, rM,cM,
FM,ZM, fM,zM
) where
import System.Random
import Numeric.LinearAlgebra.HMatrix hiding (vector)
import Control.Monad(replicateM)
import Test.QuickCheck(Arbitrary,arbitrary,choose,vector,sized,shrink)
import GHC.TypeLits
import Data.Proxy (Proxy(..))
import qualified Numeric.LinearAlgebra.Static as Static
#if MIN_VERSION_base(4,11,0)
import Prelude hiding ((<>))
#endif
shrinkListElementwise :: (Arbitrary a) => [a] -> [[a]]
shrinkListElementwise [] = []
shrinkListElementwise (x:xs) = [ y:xs | y <- shrink x ]
++ [ x:ys | ys <- shrinkListElementwise xs ]
shrinkPair :: (Arbitrary a, Arbitrary b) => (a,b) -> [(a,b)]
shrinkPair (a,b) = [ (a,x) | x <- shrink b ] ++ [ (x,b) | x <- shrink a ]
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
-- shrink any one of the components
shrink = map fromList . shrinkListElementwise . toList
instance KnownNat n => Arbitrary (Static.R n) where
arbitrary = do
l <- vector n
return (Static.fromList l)
where
n :: Int
n = fromIntegral (natVal (Proxy :: Proxy n))
shrink _v = []
instance (Element a, Arbitrary a) => Arbitrary (Matrix a) where
arbitrary = do
m <- chooseDim
n <- chooseDim
l <- vector (m*n)
return $ (m><n) l
-- shrink any one of the components
shrink a = map (rows a >< cols a)
. shrinkListElementwise
. concat . toLists
$ a
instance (KnownNat n, KnownNat m) => Arbitrary (Static.L m n) where
arbitrary = do
l <- vector (m * n)
return (Static.fromList l)
where
m :: Int
m = fromIntegral (natVal (Proxy :: Proxy m))
n :: Int
n = fromIntegral (natVal (Proxy :: Proxy n))
shrink _mat = []
-- 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
shrink (Sq a) = [ Sq b | b <- shrink a ]
-- a pair of square matrices
newtype (Sq2WC a) = Sq2WC (Matrix a, Matrix a) deriving Show
instance (ArbitraryField a, Numeric a) => Arbitrary (Sq2WC a) where
arbitrary = do
n <- chooseDim
l <- vector (n*n)
r <- vector (n*n)
l' <- makeWC $ (n><n) l
r' <- makeWC $ (n><n) r
return $ Sq2WC (l', r')
where
makeWC m = do
let (u,_,v) = svd m
n = rows m
sv' <- replicateM n (choose (1,100))
let s = diag (fromList sv')
return $ u <> real s <> tr v
-- 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)
-- a complex hermitian or real symmetric matrix
instance (Field a, Arbitrary a, Num (Vector a)) => Arbitrary (Herm a) where
arbitrary = do
Sq m <- arbitrary
let m' = m/2
return $ sym m'
class (Field a, Arbitrary a, Element (RealOf a), Random (RealOf a)) => ArbitraryField a
instance ArbitraryField Double
instance ArbitraryField (Complex Double)
-- a well-conditioned general matrix (the singular values are between 1 and 100)
newtype (WC a) = WC (Matrix a) deriving Show
instance (Numeric a, ArbitraryField 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 0 (fromList sv') r c
return $ WC (u <> real s <> tr v)
-- a well-conditioned square matrix (the singular values are between 1 and 100)
newtype (SqWC a) = SqWC (Matrix a) deriving Show
instance (ArbitraryField a, Numeric a) => Arbitrary (SqWC a) where
arbitrary = do
Sq m <- arbitrary
let (u,_,v) = svd m
n = rows m
sv' <- replicateM n (choose (1,100))
let s = diag (fromList sv')
return $ SqWC (u <> real s <> tr v)
-- a positive definite square matrix (the eigenvalues are between 0 and 100)
newtype (PosDef a) = PosDef (Matrix a) deriving Show
instance (Numeric a, ArbitraryField a, Num (Vector a))
=> Arbitrary (PosDef a) where
arbitrary = do
m <- arbitrary
let (_,v) = eigSH m
n = rows (unSym m)
l <- replicateM n (choose (0,100))
let s = diag (fromList l)
p = v <> real s <> tr v
return $ PosDef (0.5 * p + 0.5 * tr p)
-- a pair of matrices that can be multiplied
newtype (Consistent a) = Consistent (Matrix a, Matrix a) deriving Show
instance (Field a, Arbitrary a) => Arbitrary (Consistent a) where
arbitrary = do
n <- chooseDim
k <- chooseDim
m <- chooseDim
la <- vector (n*k)
lb <- vector (k*m)
return $ Consistent ((n><k) la, (k><m) lb)
shrink (Consistent (x,y)) = [ Consistent (u,v) | (u,v) <- shrinkPair (x,y) ]
type RM = Matrix Double
type CM = Matrix (Complex Double)
type FM = Matrix Float
type ZM = Matrix (Complex Float)
rM m = m :: RM
cM m = m :: CM
fM m = m :: FM
zM m = m :: ZM
rHer m = unSym m :: RM
cHer m = unSym m :: CM
rRot (Rot m) = m :: RM
cRot (Rot m) = m :: CM
rSq (Sq m) = m :: RM
cSq (Sq m) = m :: CM
rSq2WC (Sq2WC (a, b)) = (a, b) :: (RM, RM)
cSq2WC (Sq2WC (a, b)) = (a, b) :: (CM, CM)
rWC (WC m) = m :: RM
cWC (WC m) = m :: CM
rSqWC (SqWC m) = m :: RM
cSqWC (SqWC m) = m :: CM
rSymWC (SqWC m) = sym m :: Herm R
cSymWC (SqWC m) = sym m :: Herm C
rPosDef (PosDef m) = m :: RM
cPosDef (PosDef m) = m :: CM
rConsist (Consistent (a,b)) = (a,b::RM)
cConsist (Consistent (a,b)) = (a,b::CM)
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