diff --git a/Math/ExpPairs/Ivic.hs b/Math/ExpPairs/Ivic.hs --- a/Math/ExpPairs/Ivic.hs +++ b/Math/ExpPairs/Ivic.hs @@ -61,7 +61,7 @@ -- and that alpha2 <= 1 for S >= 2/3 or S >= 5/8 and -- (4S-2)k + (8S-6)l + 2S-1 >=0 --- | Compute m(σ) such that ∫_1^T |ζ(σ+it)|^m(σ) dt ≪ T^(1+ε) +-- | Compute m(σ) such that ∫_1^T |ζ(σ+it)|^m(σ) dt ≪ T^(1+ε). -- See equation (8.97) in Ivić2003. mOnS :: Rational -> OptimizeResult mOnS s diff --git a/Math/ExpPairs/Matrix3.hs b/Math/ExpPairs/Matrix3.hs --- a/Math/ExpPairs/Matrix3.hs +++ b/Math/ExpPairs/Matrix3.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE BangPatterns, RecordWildCards, DeriveFunctor, DeriveFoldable, DeriveGeneric #-} {-| Module : Math.ExpPairs.Matrix3 Description : Implements matrices of order 3 @@ -10,39 +11,62 @@ Provides types and functions for matrices and vectors of order 3. Can be used instead of "Data.Matrix" to reduce overhead and simplify code. -} -module Math.ExpPairs.Matrix3 (Matrix3 (..), Vector3 (..), fromList, toList, det, multCol, normalize, prettyMatrix) where +module Math.ExpPairs.Matrix3 + ( Matrix3 (..) + , Vector3 (..) + , fromList + , toList + , det + , multCol + , normalize + , prettyMatrix + ) where -import qualified Data.List as List -import Data.Monoid +import Prelude hiding (foldl1) +import Data.Foldable (Foldable (..), toList) +import GHC.Generics (Generic (..)) -- |Three-component vector. data Vector3 t = Vector3 { - a1 :: t, - a2 :: t, - a3 :: t + a1 :: !t, + a2 :: !t, + a3 :: !t } - deriving (Eq, Show) + deriving (Eq, Show, Functor, Foldable, Generic) --- |Matrix of order 3. Instances of 'Num', 'Fractional' and 'Monoid' --- are defined in terms of the multiplicative group of matrices, +-- |Matrix of order 3. Instances of 'Num' and 'Fractional' +-- are given in terms of the multiplicative group of matrices, -- not the additive one. E. g., -- -- > toList 1 == [1,0,0,0,1,0,0,0,1] -- > toList 1 /= [1,1,1,1,1,1,1,1,1] -- data Matrix3 t = Matrix3 { - a11 :: t, - a12 :: t, - a13 :: t, - a21 :: t, - a22 :: t, - a23 :: t, - a31 :: t, - a32 :: t, - a33 :: t + a11 :: !t, + a12 :: !t, + a13 :: !t, + a21 :: !t, + a22 :: !t, + a23 :: !t, + a31 :: !t, + a32 :: !t, + a33 :: !t } - deriving (Eq, Show) + deriving (Eq, Show, Functor, Foldable, Generic) +diag :: Num t => t -> Matrix3 t +diag n = Matrix3 { + a11 = n, + a12 = 0, + a13 = 0, + a21 = 0, + a22 = n, + a23 = 0, + a31 = 0, + a32 = 0, + a33 = n + } + instance Num t => Num (Matrix3 t) where a + b = Matrix3 { a11 = a11 a + a11 b, @@ -69,128 +93,77 @@ a33 = a31 a * a13 b + a32 a * a23 b + a33 a * a33 b } - negate a = Matrix3 { - a11 = - a11 a, - a12 = - a12 a, - a13 = - a13 a, - a21 = - a21 a, - a22 = - a22 a, - a23 = - a23 a, - a31 = - a31 a, - a32 = - a32 a, - a33 = - a33 a - } + negate = fmap negate abs = undefined - signum = undefined + signum = diag . signum . det - -- Multiplicative, not additive behaviour - fromInteger n = Matrix3 { - a11 = fromInteger n, - a12 = 0, - a13 = 0, - a21 = 0, - a22 = fromInteger n, - a23 = 0, - a31 = 0, - a32 = 0, - a33 = fromInteger n - } + fromInteger = diag . fromInteger -- |Computes the determinant of a matrix. -det :: (Num t) => Matrix3 t -> t -det a = - a11 a * (a22 a * a33 a - a32 a * a23 a) - - a12 a * (a21 a * a33 a - a23 a * a31 a) - + a13 a * (a21 a * a32 a - a22 a * a31 a) +det :: Num t => Matrix3 t -> t +det Matrix3 {..} = + a11 * (a22 * a33 - a32 * a23) + - a12 * (a21 * a33 - a23 * a31) + + a13 * (a21 * a32 - a22 * a31) instance Fractional t => Fractional (Matrix3 t) where - -- Multiplicative, not additive behaviour - fromRational n = Matrix3 { - a11 = fromRational n, - a12 = 0, - a13 = 0, - a21 = 0, - a22 = fromRational n, - a23 = 0, - a31 = 0, - a32 = 0, - a33 = fromRational n - } + fromRational = diag . fromRational - recip a = Matrix3 { - a11 = (a22 a * a33 a - a32 a * a23 a) / d, - a12 = -(a21 a * a33 a - a23 a * a31 a) / d, - a13 = (a21 a * a32 a - a22 a * a31 a) / d, - a21 = -(a12 a * a33 a - a13 a * a32 a) / d, - a22 = (a11 a * a33 a - a13 a * a31 a) / d, - a23 = -(a11 a * a32 a - a12 a * a31 a) / d, - a31 = (a12 a * a23 a - a13 a * a22 a) / d, - a32 = -(a11 a * a23 a - a13 a * a21 a) / d, - a33 = (a11 a * a22 a - a12 a * a21 a) / d + recip a@(Matrix3 {..}) = Matrix3 { + a11 = (a22 * a33 - a32 * a23) / d, + a12 = -(a21 * a33 - a23 * a31) / d, + a13 = (a21 * a32 - a22 * a31) / d, + a21 = -(a12 * a33 - a13 * a32) / d, + a22 = (a11 * a33 - a13 * a31) / d, + a23 = -(a11 * a32 - a12 * a31) / d, + a31 = (a12 * a23 - a13 * a22) / d, + a32 = -(a11 * a23 - a13 * a21) / d, + a33 = (a11 * a22 - a12 * a21) / d } where d = det a - -instance Num t => Monoid (Matrix3 t) where - mempty = 1 - mappend = (*) - --- |Convert 'Matrix3' into a list of 9 elements. -toList :: Matrix3 t -> [t] -toList a = [a11 a, a12 a, a13 a, a21 a, a22 a, a23 a, a31 a, a32 a, a33 a] - --- |Convert a list of 9 elements into 'Matrix3'. +-- |Convert a list of 9 elements into 'Matrix3'. Reverse conversion can be done using 'Foldable' instance. fromList :: [t] -> Matrix3 t -fromList as = Matrix3 { - a11 = as!!0, - a12 = as!!1, - a13 = as!!2, - a21 = as!!3, - a22 = as!!4, - a23 = as!!5, - a31 = as!!6, - a32 = as!!7, - a33 = as!!8 - } - -instance Functor Matrix3 where - fmap f = fromList . List.map f . toList +fromList [a11, a12, a13, a21, a22, a23, a31, a32, a33] = Matrix3 { + a11 = a11, + a12 = a12, + a13 = a13, + a21 = a21, + a22 = a22, + a23 = a23, + a31 = a31, + a32 = a32, + a33 = a33 + } +fromList _ = error "The list must contain exactly 9 elements" -- |Divide all elements of the matrix by their greatest common -- divisor. This is useful for matrices of projective -- transformations to reduce the magnitude of computations. normalize :: Integral t => Matrix3 t -> Matrix3 t -normalize m = m' where - l = toList m - d = foldl1 gcd l - m' = if d==0 then m else fromList $ List.map (`div`d) l - --- |Return the maximal element of a matrix. -maximum :: Ord t => Matrix3 t -> t -maximum = List.maximum . toList +normalize a = case foldl1 gcd a of + 0 -> a + d -> fmap (`div` d) a -- |Print a matrix, separating rows with new lines and elements -- with spaces. -prettyMatrix :: (Show t) => Matrix3 t -> String -prettyMatrix m = - show (a11 m) ++ " " ++ - show (a12 m) ++ " " ++ - show (a13 m) ++ "\n" ++ - show (a21 m) ++ " " ++ - show (a22 m) ++ " " ++ - show (a23 m) ++ "\n" ++ - show (a31 m) ++ " " ++ - show (a32 m) ++ " " ++ - show (a33 m) +prettyMatrix :: Show t => Matrix3 t -> String +prettyMatrix Matrix3 {..} = + show a11 ++ ' ' : + show a12 ++ ' ' : + show a13 ++ '\n' : + show a21 ++ ' ' : + show a22 ++ ' ' : + show a23 ++ '\n' : + show a31 ++ ' ' : + show a32 ++ ' ' : + show a33 -- |Multiplicate a matrix by a vector (considered as a column). -multCol :: (Num t) => Matrix3 t -> Vector3 t -> Vector3 t -multCol m v = Vector3 { - a1 = a11 m * a1 v + a12 m * a2 v + a13 m * a3 v, - a2 = a21 m * a1 v + a22 m * a2 v + a23 m * a3 v, - a3 = a31 m * a1 v + a32 m * a2 v + a33 m * a3 v +multCol :: Num t => Matrix3 t -> Vector3 t -> Vector3 t +multCol Matrix3 {..} Vector3 {..} = Vector3 { + a1 = a11 * a1 + a12 * a2 + a13 * a3, + a2 = a21 * a1 + a22 * a2 + a23 * a3, + a3 = a31 * a1 + a32 * a2 + a33 * a3 } - - - diff --git a/Math/ExpPairs/Tests.hs b/Math/ExpPairs/Tests.hs deleted file mode 100644 --- a/Math/ExpPairs/Tests.hs +++ /dev/null @@ -1,20 +0,0 @@ ---module Math.ExpPairs.Tests where - -import qualified Math.ExpPairs.Tests.RatioInf as RatioInf (testSuite) -import qualified Math.ExpPairs.Tests.Pair as Pair (testSuite) -import qualified Math.ExpPairs.Tests.Ivic as Ivic (testSuite) -import qualified Math.ExpPairs.Tests.MenzerNowak as MenzerNowak (testSuite) -import qualified Math.ExpPairs.Tests.Matrix3 as Matrix3 (testSuite) -import qualified Math.ExpPairs.Tests.Kratzel as Kratzel (testSuite) -import qualified Math.ExpPairs.Tests.LinearForm as LinearForm (testSuite) - -main :: IO () -main = do - print "done" - --RatioInf.testSuite - --Pair.testSuite - --Ivic.testSuite - --MenzerNowak.testSuite - --Matrix3.testSuite - --Kratzel.testSuite - --LinearForm.testSuite diff --git a/exp-pairs.cabal b/exp-pairs.cabal --- a/exp-pairs.cabal +++ b/exp-pairs.cabal @@ -1,5 +1,5 @@ name: exp-pairs -version: 0.1.1.0 +version: 0.1.2.0 synopsis: Linear programming over exponent pairs description: Package implements an algorithm to minimize rational objective function over the set of exponent pairs homepage: https://github.com/Bodigrim/exp-pairs @@ -9,7 +9,7 @@ maintainer: andrew.lelechenko@gmail.com category: Math build-type: Simple -cabal-version: >=1.8 +cabal-version: >=1.10 source-repository head type: git @@ -27,15 +27,24 @@ Math.ExpPairs.RatioInf build-depends: base >=4 && <5, memoize >=0.1, - matrix >=0.1 + ghc-prim + default-language: Haskell2010 + ghc-options: -Wall test-suite tests - ghc-options: -Wall - type: exitcode-stdio-1.0 - main-is: Math/ExpPairs/Tests.hs + type: exitcode-stdio-1.0 + main-is: Tests.hs build-depends: base >=4 && <5, + tasty >=0.7, + tasty-quickcheck, + tasty-smallcheck, + tasty-hunit, QuickCheck >=2.4.2, smallcheck >=0.2.1, exp-pairs, memoize >=0.1, - matrix >=0.1 + matrix >=0.1, + random + hs-source-dirs: tests + default-language: Haskell2010 + ghc-options: -Wall diff --git a/tests/Tests.hs b/tests/Tests.hs new file mode 100644 --- /dev/null +++ b/tests/Tests.hs @@ -0,0 +1,27 @@ +import qualified LinearForm (testSuite) +import qualified Matrix3 (testSuite) +import qualified RatioInf (testSuite) +import qualified Pair (testSuite) + +import qualified Ivic (testSuite) +import qualified Kratzel (testSuite) +import qualified MenzerNowak (testSuite) + +import Test.Tasty + +main :: IO () +main = defaultMain tests + +tests :: TestTree +tests = testGroup "Tests" + [ LinearForm.testSuite + , Matrix3.testSuite + , RatioInf.testSuite + , Pair.testSuite + , Ivic.testSuite + , Kratzel.testSuite + , MenzerNowak.testSuite + ] + + +