-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | native matrix based on vector -- -- Pure Haskell matrix library, supporting creating, indexing, and -- modifying dense/sparse matrices. @package matrices @version 0.4.5 module Data.Matrix.Generic.Mutable class MVector v a => MMatrix m v a dim :: MMatrix m v a => m v s a -> (Int, Int) unsafeRead :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> s a unsafeWrite :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> a -> s () -- | Create a mutable matrix without initialization new :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> s (m v (PrimState s) a) replicate :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> a -> s (m v (PrimState s) a) -- | Derived methods write :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> a -> s () read :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> s a module Data.Matrix.Symmetric.Mutable -- | mutable matrix data SymMMatrix v s a SymMMatrix :: !Int -> !(v s a) -> SymMMatrix v s a dim :: MMatrix m v a => m v s a -> (Int, Int) -- | Derived methods write :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> a -> s () unsafeWrite :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> a -> s () read :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> s a unsafeRead :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> s a -- | Create a mutable matrix without initialization new :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> s (m v (PrimState s) a) replicate :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> a -> s (m v (PrimState s) a) instance Data.Vector.Generic.Mutable.Base.MVector v a => Data.Matrix.Generic.Mutable.MMatrix Data.Matrix.Symmetric.Mutable.SymMMatrix v a module Data.Matrix.Generic class (MMatrix (Mutable m) (Mutable v) a, Vector v a) => Matrix m v a where flatten mat = generate (r * c) $ \ i -> unsafeIndex mat (i `div` c, i `mod` c) where (r, c) = dim mat unsafeTakeRow mat i = generate c $ \ j -> unsafeIndex mat (i, j) where (_, c) = dim mat unsafeTakeColumn mat j = generate r $ \ i -> unsafeIndex mat (i, j) where (r, _) = dim mat takeDiag mat = generate n $ \ i -> unsafeIndex mat (i, i) where n = uncurry min . dim $ mat dim :: Matrix m v a => m v a -> (Int, Int) unsafeIndex :: Matrix m v a => m v a -> (Int, Int) -> a unsafeFromVector :: Matrix m v a => (Int, Int) -> v a -> m v a -- | Default algorithm is O((m*n) * O(unsafeIndex)). flatten :: Matrix m v a => m v a -> v a -- | Extract a row. Default algorithm is O(n * O(unsafeIndex)). unsafeTakeRow :: Matrix m v a => m v a -> Int -> v a -- | Extract a column. Default algorithm is O(m * O(unsafeIndex)). unsafeTakeColumn :: Matrix m v a => m v a -> Int -> v a -- | Extract the diagonal. Default algorithm is O(min(m,n) * -- O(unsafeIndex)). takeDiag :: Matrix m v a => m v a -> v a thaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) unsafeThaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) freeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) unsafeFreeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) -- | Derived methods -- -- Return the number of rows rows :: Matrix m v a => m v a -> Int -- | Return the number of columns cols :: Matrix m v a => m v a -> Int -- | Indexing (!) :: Matrix m v a => m v a -> (Int, Int) -> a fromVector :: Matrix m v a => (Int, Int) -> v a -> m v a fromList :: Matrix m v a => (Int, Int) -> [a] -> m v a empty :: Matrix m v a => m v a -- | O(m*n) Create a list by concatenating rows toList :: Matrix m v a => m v a -> [a] -- | O(m*n) Create matrix from list of lists, it doesn't check if the list -- of list is a valid matrix fromLists :: Matrix m v a => [[a]] -> m v a -- | O(m*n) Matrix construction matrix :: Matrix m v a => Int -> [a] -> m v a -- | O(m*n) Create matrix from rows fromRows :: Matrix m v a => [v a] -> m v a -- | Extract a row. takeRow :: Matrix m v a => m v a -> Int -> v a -- | O(m) Return the rows toRows :: Matrix m v a => m v a -> [v a] -- | Extract a row. takeColumn :: Matrix m v a => m v a -> Int -> v a -- | O(m*n) Return the columns toColumns :: Matrix m v a => m v a -> [v a] -- | O(m*n) List of lists toLists :: Matrix m v a => m v a -> [[a]] create :: Matrix m v a => (forall s. ST s ((Mutable m) (Mutable v) s a)) -> m v a module Data.Matrix.Symmetric -- | Symmetric square matrix data SymMatrix v a SymMatrix :: !Int -> !(v a) -> SymMatrix v a dim :: Matrix m v a => m v a -> (Int, Int) -- | Derived methods -- -- Return the number of rows rows :: Matrix m v a => m v a -> Int -- | Return the number of columns cols :: Matrix m v a => m v a -> Int unsafeIndex :: Matrix m v a => m v a -> (Int, Int) -> a -- | Indexing (!) :: Matrix m v a => m v a -> (Int, Int) -> a -- | Default algorithm is O((m*n) * O(unsafeIndex)). flatten :: Matrix m v a => m v a -> v a unsafeFromVector :: Matrix m v a => (Int, Int) -> v a -> m v a fromVector :: Matrix m v a => (Int, Int) -> v a -> m v a -- | Extract a row. takeRow :: Matrix m v a => m v a -> Int -> v a thaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) unsafeThaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) freeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) unsafeFreeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) create :: Matrix m v a => (forall s. ST s ((Mutable m) (Mutable v) s a)) -> m v a map :: (Vector v a, Vector v b) => (a -> b) -> SymMatrix v a -> SymMatrix v b -- | Upper triangular imap, i.e., i <= j imap :: (Vector v a, Vector v b) => ((Int, Int) -> a -> b) -> SymMatrix v a -> SymMatrix v b zip :: (Vector v a, Vector v b, Vector v (a, b)) => SymMatrix v a -> SymMatrix v b -> SymMatrix v (a, b) zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> SymMatrix v a -> SymMatrix v b -> SymMatrix v c instance GHC.Classes.Eq (v a) => GHC.Classes.Eq (Data.Matrix.Symmetric.SymMatrix v a) instance GHC.Generics.Generic (Data.Matrix.Symmetric.SymMatrix v a) instance GHC.Read.Read (v a) => GHC.Read.Read (Data.Matrix.Symmetric.SymMatrix v a) instance GHC.Show.Show (v a) => GHC.Show.Show (Data.Matrix.Symmetric.SymMatrix v a) instance Data.Vector.Generic.Base.Vector v a => Data.Matrix.Generic.Matrix Data.Matrix.Symmetric.SymMatrix v a module Data.Matrix.Dense.Generic.Mutable -- | mutable matrix data MMatrix v s a MMatrix :: !Int -> !Int -> !Int -> !Int -> !(v s a) -> MMatrix v s a dim :: MMatrix m v a => m v s a -> (Int, Int) takeRow :: MVector v a => MMatrix v m a -> Int -> v m a -- | Derived methods write :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> a -> s () unsafeWrite :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> a -> s () read :: (PrimMonad s, MMatrix m v a) => m v (PrimState s) a -> (Int, Int) -> s a unsafeRead :: (MMatrix m v a, PrimMonad s) => m v (PrimState s) a -> (Int, Int) -> s a -- | Create a mutable matrix without initialization new :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> s (m v (PrimState s) a) replicate :: (MMatrix m v a, PrimMonad s) => (Int, Int) -> a -> s (m v (PrimState s) a) instance Control.DeepSeq.NFData (v s a) => Control.DeepSeq.NFData (Data.Matrix.Dense.Generic.Mutable.MMatrix v s a) instance Data.Vector.Generic.Mutable.Base.MVector v a => Data.Matrix.Generic.Mutable.MMatrix Data.Matrix.Dense.Generic.Mutable.MMatrix v a module Data.Matrix.Mutable type MMatrix a = MMatrix MVector a module Data.Matrix.Sparse.Generic class Eq a => Zero a zero :: Zero a => a -- | Compressed Sparse Row (CSR) matrix data CSR v a CSR :: !Int -> !Int -> !(v a) -> !(Vector Int) -> !(Vector Int) -> CSR v a type AssocList a = [((Int, Int), a)] dim :: Matrix m v a => m v a -> (Int, Int) -- | Derived methods -- -- Return the number of rows rows :: Matrix m v a => m v a -> Int -- | Return the number of columns cols :: Matrix m v a => m v a -> Int unsafeIndex :: Matrix m v a => m v a -> (Int, Int) -> a -- | Indexing (!) :: Matrix m v a => m v a -> (Int, Int) -> a -- | Extract a row. takeRow :: Matrix m v a => m v a -> Int -> v a -- | Extract a row. takeColumn :: Matrix m v a => m v a -> Int -> v a -- | Extract the diagonal. Default algorithm is O(min(m,n) * -- O(unsafeIndex)). takeDiag :: Matrix m v a => m v a -> v a -- | Construct CSR from ascending association list. Items must be sorted -- first by row index, and then by column index. fromAscAL :: Vector v a => (Int, Int) -> Int -> AssocList a -> CSR v a unsafeFromVector :: Matrix m v a => (Int, Int) -> v a -> m v a fromVector :: Matrix m v a => (Int, Int) -> v a -> m v a -- | O(m*n) Matrix construction matrix :: Matrix m v a => Int -> [a] -> m v a -- | O(m*n) Create matrix from list of lists, it doesn't check if the list -- of list is a valid matrix fromLists :: Matrix m v a => [[a]] -> m v a -- | O(m*n) Create matrix from rows fromRows :: Matrix m v a => [v a] -> m v a empty :: Matrix m v a => m v a -- | Default algorithm is O((m*n) * O(unsafeIndex)). flatten :: Matrix m v a => m v a -> v a -- | O(m) Return the rows toRows :: Matrix m v a => m v a -> [v a] -- | O(m*n) Return the columns toColumns :: Matrix m v a => m v a -> [v a] -- | O(m*n) Create a list by concatenating rows toList :: Matrix m v a => m v a -> [a] -- | O(m*n) List of lists toLists :: Matrix m v a => m v a -> [[a]] instance GHC.Generics.Generic (Data.Matrix.Sparse.Generic.CSR v a) instance GHC.Classes.Eq (v a) => GHC.Classes.Eq (Data.Matrix.Sparse.Generic.CSR v a) instance GHC.Read.Read (v a) => GHC.Read.Read (Data.Matrix.Sparse.Generic.CSR v a) instance GHC.Show.Show (v a) => GHC.Show.Show (Data.Matrix.Sparse.Generic.CSR v a) instance Data.Matrix.Sparse.Generic.Zero GHC.Types.Int instance Data.Matrix.Sparse.Generic.Zero GHC.Types.Double instance GHC.Classes.Eq a => Data.Matrix.Sparse.Generic.Zero [a] instance (Data.Matrix.Sparse.Generic.Zero a, Data.Vector.Generic.Base.Vector v a) => Data.Matrix.Generic.Matrix Data.Matrix.Sparse.Generic.CSR v a module Data.Matrix.Storable.Mutable type MMatrix a = MMatrix MVector a module Data.Matrix.Unboxed.Mutable type MMatrix a = MMatrix MVector a module Data.Matrix.Dense.Generic -- | Row-major matrix supporting efficient slice data Matrix v a Matrix :: !Int -> !Int -> !Int -> !Int -> !(v a) -> Matrix v a dim :: Matrix m v a => m v a -> (Int, Int) -- | Derived methods -- -- Return the number of rows rows :: Matrix m v a => m v a -> Int -- | Return the number of columns cols :: Matrix m v a => m v a -> Int unsafeIndex :: Matrix m v a => m v a -> (Int, Int) -> a -- | Indexing (!) :: Matrix m v a => m v a -> (Int, Int) -> a -- | Extract a row. takeRow :: Matrix m v a => m v a -> Int -> v a -- | Extract a row. takeColumn :: Matrix m v a => m v a -> Int -> v a -- | Extract the diagonal. Default algorithm is O(min(m,n) * -- O(unsafeIndex)). takeDiag :: Matrix m v a => m v a -> v a unsafeFromVector :: Matrix m v a => (Int, Int) -> v a -> m v a fromVector :: Matrix m v a => (Int, Int) -> v a -> m v a -- | O(m*n) Matrix construction matrix :: Matrix m v a => Int -> [a] -> m v a -- | O(m*n) Create matrix from list of lists, it doesn't check if the list -- of list is a valid matrix fromLists :: Matrix m v a => [[a]] -> m v a -- | O(m*n) Create matrix from rows fromRows :: Matrix m v a => [v a] -> m v a -- | O(m*n) Create matrix from columns fromColumns :: Vector v a => [v a] -> Matrix v a empty :: Matrix m v a => m v a -- | Default algorithm is O((m*n) * O(unsafeIndex)). flatten :: Matrix m v a => m v a -> v a -- | O(m) Return the rows toRows :: Matrix m v a => m v a -> [v a] -- | O(m*n) Return the columns toColumns :: Matrix m v a => m v a -> [v a] -- | O(m*n) Create a list by concatenating rows toList :: Matrix m v a => m v a -> [a] -- | O(m*n) List of lists toLists :: Matrix m v a => m v a -> [[a]] -- | O(m*n) Convert different matrix type convert :: (Vector v a, Vector w a) => Matrix v a -> Matrix w a -- | O(m*n) Matrix transpose tr :: Vector v a => Matrix v a -> Matrix v a -- | O(1) Extract sub matrix subMatrix :: Vector v a => (Int, Int) -> (Int, Int) -> Matrix v a -> Matrix v a -- | O(m*n) Create an identity matrix ident :: (Num a, Vector v a) => Int -> Matrix v a -- | O(m*n) Create a square matrix with given diagonal, other entries -- default to 0 diag :: (Num a, Vector v a, Foldable t) => t a -> Matrix v a -- | O(m*n) Create a rectangular matrix with default values and given -- diagonal diagRect :: (Vector v a, Foldable t) => a -> (Int, Int) -> t a -> Matrix v a fromBlocks :: Vector v a => a -> [[Matrix v a]] -> Matrix v a isSymmetric :: (Eq a, Vector v a) => Matrix v a -> Bool force :: Vector v a => Matrix v a -> Matrix v a foldl :: Vector v b => (a -> b -> a) -> a -> Matrix v b -> a map :: (Vector v a, Vector v b) => (a -> b) -> Matrix v a -> Matrix v b imap :: (Vector v a, Vector v b) => ((Int, Int) -> a -> b) -> Matrix v a -> Matrix v b mapM :: (Vector v a, Vector v b, Monad m) => (a -> m b) -> Matrix v a -> m (Matrix v b) -- | O(m*n) Apply the monadic action to every element and its index, -- yielding a matrix of results. imapM :: (Vector v a, Vector v b, Monad m) => ((Int, Int) -> a -> m b) -> Matrix v a -> m (Matrix v b) mapM_ :: (Vector v a, Monad m) => (a -> m b) -> Matrix v a -> m () -- | O(m*n) Apply the monadic action to every element and its index, -- ignoring the results. imapM_ :: (Vector v a, Monad m) => ((Int, Int) -> a -> m b) -> Matrix v a -> m () forM :: (Vector v a, Vector v b, Monad m) => Matrix v a -> (a -> m b) -> m (Matrix v b) forM_ :: (Vector v a, Monad m) => Matrix v a -> (a -> m b) -> m () zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> Matrix v a -> Matrix v b -> Matrix v c zipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (a -> b -> c -> d) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d zipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (a -> b -> c -> d -> e) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e zipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (a -> b -> c -> d -> e -> f) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f zipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (a -> b -> c -> d -> e -> f -> g) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v g izipWith :: (Vector v a, Vector v b, Vector v c) => ((Int, Int) -> a -> b -> c) -> Matrix v a -> Matrix v b -> Matrix v c izipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => ((Int, Int) -> a -> b -> c -> d) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d izipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => ((Int, Int) -> a -> b -> c -> d -> e) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e izipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => ((Int, Int) -> a -> b -> c -> d -> e -> f) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f izipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => ((Int, Int) -> a -> b -> c -> d -> e -> f -> g) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v g zip :: (Vector v a, Vector v b, Vector v (a, b)) => Matrix v a -> Matrix v b -> Matrix v (a, b) zip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v (a, b, c) zip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v (a, b, c, d) zip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v (a, b, c, d, e) zip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v (a, b, c, d, e, f) zipWithM :: (Monad m, Vector v a, Vector v b, Vector v c) => (a -> b -> m c) -> Matrix v a -> Matrix v b -> m (Matrix v c) zipWithM_ :: (Monad m, Vector v a, Vector v b) => (a -> b -> m c) -> Matrix v a -> Matrix v b -> m () unzip :: (Vector v a, Vector v b, Vector v (a, b)) => Matrix v (a, b) -> (Matrix v a, Matrix v b) unzip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => Matrix v (a, b, c) -> (Matrix v a, Matrix v b, Matrix v c) unzip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => Matrix v (a, b, c, d) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d) unzip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => Matrix v (a, b, c, d, e) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d, Matrix v e) unzip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => Matrix v (a, b, c, d, e, f) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d, Matrix v e, Matrix v f) sequence :: (Vector v a, Vector v (m a), Monad m) => Matrix v (m a) -> m (Matrix v a) sequence_ :: (Vector v (m a), Monad m) => Matrix v (m a) -> m () generate :: Vector v a => (Int, Int) -> ((Int, Int) -> a) -> Matrix v a thaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) unsafeThaw :: (Matrix m v a, PrimMonad s) => m v a -> s ((Mutable m) (Mutable v) (PrimState s) a) freeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) unsafeFreeze :: (Matrix m v a, PrimMonad s) => (Mutable m) (Mutable v) (PrimState s) a -> s (m v a) create :: Matrix m v a => (forall s. ST s ((Mutable m) (Mutable v) s a)) -> m v a instance GHC.Generics.Generic (Data.Matrix.Dense.Generic.Matrix v a) instance GHC.Classes.Eq (v a) => GHC.Classes.Eq (Data.Matrix.Dense.Generic.Matrix v a) instance GHC.Read.Read (v a) => GHC.Read.Read (Data.Matrix.Dense.Generic.Matrix v a) instance GHC.Show.Show (v a) => GHC.Show.Show (Data.Matrix.Dense.Generic.Matrix v a) instance Control.DeepSeq.NFData (v a) => Control.DeepSeq.NFData (Data.Matrix.Dense.Generic.Matrix v a) instance Data.Vector.Generic.Base.Vector v a => Data.Matrix.Generic.Matrix Data.Matrix.Dense.Generic.Matrix v a module Data.Matrix.Storable type Matrix a = Matrix Vector a module Data.Matrix.Unboxed type Matrix a = Matrix Vector a module Data.Matrix type Matrix = Matrix Vector