Math.Algebra.Determinant

Contents

• matrices
• a type class for determinants
• C implementation of determinant in a prime field (gaussian elimination, fitting into 64 bit)
• Bareiss determinant algorithm
• Gaussian elimination
• naive determinant algorithm (for testing purposes)
• random matrices
• testing

Description

Synopsis

• type Matrix a = Array (Int, Int) a
• printMatrix :: Show a => Matrix a -> IO ()
• showMatrix :: Show a => Matrix a -> String
• showMatrix' :: Show a => Matrix a -> [String]
• class (Eq a, Num a, Show a) => Determinant a where
• c_inv_modp :: Int64 -> Int64 -> Int64
• c_det_modp :: Int64 -> CInt -> Ptr Int64 -> IO Int64
• fastDetModP :: Int64 -> Matrix Int64 -> Int64
• ioFastDetModP :: Int64 -> Matrix Int64 -> IO Int64
• gaussElimDeterminantInt64 :: Matrix Zp -> Zp
• type STMatrix s a = STArray s (Int, Int) a
• bareissDeterminantFullRank :: forall a. Integral a => Matrix a -> a
• gaussElimDeterminant :: forall a. (Eq a, Show a, Fractional a) => Matrix a -> a
• naiveDeterminant :: forall a. Num a => Matrix a -> a
• mkSquareMatrix :: (Int -> Int -> a) -> Int -> Matrix a
• testMatrix :: Num a => Int -> Matrix a
• randomMatrix :: (Random a, Num a) => Int -> IO (Matrix a)
• randomMatrix' :: (Random a, Num a) => a -> Int -> IO (Matrix a)
• printST :: Show a => a -> ST s ()
• test :: IO ()

matrices

a type class for determinants

C implementation of determinant in a prime field (gaussian elimination, fitting into 64 bit)

Bareiss determinant algorithm

Gaussian elimination

naive determinant algorithm (for testing purposes)

random matrices

testing