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--
-- QuickCheck tests
--
-----------------------------------------------------------------------------
import Data.Packed.Internal.Vector
import Data.Packed.Internal.Matrix
import LAPACK
import Test.QuickCheck
import Complex
{-
-- Bravo por quickCheck!
pinvProp1 tol m = (rank m == cols m) ==> pinv m <> m ~~ ident (cols m)
where infix 2 ~~
(~~) = approxEqual tol
pinvProp2 tol m = 0 < r && r <= c ==> (r==c) `trivial` (m <> pinv m <> m ~~ m)
where r = rank m
c = cols m
infix 2 ~~
(~~) = approxEqual tol
nullspaceProp tol m = cr > 0 ==> m <> nt ~~ zeros
where nt = trans (nullspace m)
cr = corank m
r = rows m
zeros = create [r,cr] $ replicate (r*cr) 0
-}
r >< c = f where
f l | dim v == r*c = matrixFromVector RowMajor c v
| otherwise = error $ "inconsistent list size = "
++show (dim v) ++"in ("++show r++"><"++show c++")"
where v = fromList l
r >|< c = f where
f l | dim v == r*c = matrixFromVector ColumnMajor c v
| otherwise = error $ "inconsistent list size = "
++show (dim v) ++"in ("++show r++"><"++show c++")"
where v = fromList l
ac = (2><3) [1 .. 6::Double]
bc = (3><4) [7 .. 18::Double]
mz = (2 >< 3) [1,2,3,4,5,6:+(1::Double)]
af = (2>|<3) [1,4,2,5,3,6::Double]
bf = (3>|<4) [7,11,15,8,12,16,9,13,17,10,14,18::Double]
a |=| b = rows a == rows b &&
cols a == cols b &&
toList (cdat a) == toList (cdat b) &&
toList (fdat a) == toList (fdat b)
aprox fun a b = rows a == rows b &&
cols a == cols b &&
eps > aproxL fun (toList (t a)) (toList (t b))
where t = if (order a == RowMajor) `xor` isTrans a then cdat else fdat
aproxL fun v1 v2 = sum (zipWith (\a b-> fun (a-b)) v1 v2) / fromIntegral (length v1)
(|~|) = aprox abs
(|~~|) = aprox magnitude
eps = 1E-8::Double
asFortran m = (rows m >|< cols m) $ toList (fdat m)
asC m = (rows m >< cols m) $ toList (cdat m)
mulC a b = multiply RowMajor a b
mulF a b = multiply ColumnMajor a b
cc = mulC ac bf
cf = mulF af bc
r = mulC cc (trans cf)
ident n = diag (constant n 1)
rd = (2><2)
[ 43492.0, 50572.0
, 102550.0, 119242.0 :: Double]
instance (Arbitrary a, RealFloat a) => Arbitrary (Complex a) where
arbitrary = do
r <- arbitrary
i <- arbitrary
return (r:+i)
coarbitrary = undefined
instance (Field a, Arbitrary a) => Arbitrary (Matrix a) where
arbitrary = do --m <- sized $ \max -> choose (1,1+3*max)
m <- choose (1,10)
n <- choose (1,10)
l <- vector (m*n)
ctype <- arbitrary
let h = if ctype then (m><n) else (m>|<n)
trMode <- arbitrary
let tr = if trMode then trans else id
return $ tr (h l)
coarbitrary = undefined
data PairM a = PairM (Matrix a) (Matrix a) deriving Show
instance (Num a, Field a, Arbitrary a) => Arbitrary (PairM a) where
arbitrary = do
a <- choose (1,10)
b <- choose (1,10)
c <- choose (1,10)
l1 <- vector (a*b)
l2 <- vector (b*c)
return $ PairM ((a><b) (map fromIntegral (l1::[Int]))) ((b><c) (map fromIntegral (l2::[Int])))
--return $ PairM ((a><b) l1) ((b><c) l2)
coarbitrary = undefined
type BaseType = Double
svdTestR fun prod m = u <> s <> trans v |~| m
&& u <> trans u |~| ident (rows m)
&& v <> trans v |~| ident (cols m)
where (u,s,v) = fun m
(<>) = prod
svdTestC fun prod m = u <> s' <> (trans v) |~~| m
&& u <> (liftMatrix conj) (trans u) |~~| ident (rows m)
&& v <> (liftMatrix conj) (trans v) |~~| ident (cols m)
where (u,s,v) = fun m
(<>) = prod
s' = liftMatrix comp s
comp v = toComplex (v,constant (dim v) 0)
main = do
quickCheck $ \l -> null l || (toList . fromList) l == (l :: [BaseType])
quickCheck $ \m -> m |=| asC (m :: Matrix BaseType)
quickCheck $ \m -> m |=| asFortran (m :: Matrix BaseType)
quickCheck $ \m -> m |=| (asC . asFortran) (m :: Matrix BaseType)
quickCheck $ \(PairM m1 m2) -> mulC m1 m2 |=| mulF m1 (m2 :: Matrix BaseType)
quickCheck $ \(PairM m1 m2) -> mulC m1 m2 |=| trans (mulF (trans m2) (trans m1 :: Matrix BaseType))
quickCheck $ \(PairM m1 m2) -> mulC m1 m2 |=| multiplyG m1 (m2 :: Matrix BaseType)
quickCheck (svdTestR svdR mulC)
quickCheck (svdTestR svdR mulF)
quickCheck (svdTestC svdC mulC)
quickCheck (svdTestC svdC mulF)
|
