Safe Haskell	None
Language	Haskell2010

Goal.Core.Vector.Generic

Contents

Vector
Construction
Deconstruction
Matrix

Description

Vectors and Matrices with statically typed dimensions.

Synopsis

type VectorClass = Vector
doubleton :: Vector v x => x -> x -> Vector v 2 x
range :: forall v n x. (Vector v x, KnownNat n, Fractional x) => x -> x -> Vector v n x
breakEvery :: forall v n k a. (Vector v a, Vector v (Vector v k a), KnownNat n, KnownNat k) => Vector v (n * k) a -> Vector v n (Vector v k a)
concat :: (KnownNat n, Vector v x, Vector v (Vector v n x)) => Vector v m (Vector v n x) -> Vector v (m * n) x
newtype Matrix v (m :: Nat) (n :: Nat) a = Matrix {
- toVector :: Vector v (m * n) a
}
nRows :: forall v m n a. KnownNat m => Matrix v m n a -> Int
nColumns :: forall v m n a. KnownNat n => Matrix v m n a -> Int
fromRows :: (Vector v x, Vector v (Vector v n x), KnownNat n) => Vector v m (Vector v n x) -> Matrix v m n x
fromColumns :: (Vector v x, Vector v Int, Vector v (Vector v n x), Vector v (Vector v m x), KnownNat n, KnownNat m) => Vector v n (Vector v m x) -> Matrix v m n x
toPair :: Vector v a => Vector v 2 a -> (a, a)
toRows :: (Vector v a, Vector v (Vector v n a), KnownNat n, KnownNat m) => Matrix v m n a -> Vector v m (Vector v n a)
toColumns :: (Vector v a, Vector v (Vector v m a), KnownNat m, KnownNat n, Vector v Int) => Matrix v m n a -> Vector v n (Vector v m a)
columnVector :: Vector v n a -> Matrix v n 1 a
rowVector :: Vector v n a -> Matrix v 1 n a
transpose :: forall v m n a. (KnownNat m, KnownNat n, Vector v Int, Vector v a, Vector v (Vector v m a)) => Matrix v m n a -> Matrix v n m a
dotProduct :: (Vector v x, Num x) => Vector v n x -> Vector v n x -> x
weakDotProduct :: (Vector v x, Num x) => v x -> v x -> x
outerProduct :: (KnownNat m, KnownNat n, Num x, Vector v Int, Vector v x, Vector v (Vector v n x), Vector v (Vector v m x), Vector v (Vector v 1 x)) => Vector v n x -> Vector v m x -> Matrix v n m x
matrixVectorMultiply :: (KnownNat m, KnownNat n, Vector v x, Vector v (Vector v n x), Num x) => Matrix v m n x -> Vector v n x -> Vector v m x
matrixMatrixMultiply :: (KnownNat m, KnownNat n, KnownNat o, Num x, Vector v Int, Vector v x, Vector v (Vector v m x), Vector v (Vector v n x), Vector v (Vector v o x)) => Matrix v m n x -> Matrix v n o x -> Matrix v m o x

Vector

type VectorClass = Vector Source #

Construction

doubleton :: Vector v x => x -> x -> Vector v 2 x Source #

Collect two values into a length 2 Vector.

range :: forall v n x. (Vector v x, KnownNat n, Fractional x) => x -> x -> Vector v n x Source #

Uniform partition of an interval into a Vector.

breakEvery :: forall v n k a. (Vector v a, Vector v (Vector v k a), KnownNat n, KnownNat k) => Vector v (n * k) a -> Vector v n (Vector v k a) Source #

Breaks a Vector into a Vector of Vectors.

Deconstruction

concat :: (KnownNat n, Vector v x, Vector v (Vector v n x)) => Vector v m (Vector v n x) -> Vector v (m * n) x Source #

Create a Matrix from a Vector of Vectors which represent the rows.

Matrix

newtype Matrix v (m :: Nat) (n :: Nat) a Source #

Matrices with static dimensions.

Constructors

Matrix
Fields toVector :: Vector v (m * n) a

Instances

Instances details

Eq (v a) => Eq (Matrix v m n a) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods (==) :: Matrix v m n a -> Matrix v m n a -> Bool # (/=) :: Matrix v m n a -> Matrix v m n a -> Bool #
(KnownNat m, KnownNat n, Numeric x, Floating x) => Floating (Matrix Vector m n x) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods pi :: Matrix Vector m n x # exp :: Matrix Vector m n x -> Matrix Vector m n x # log :: Matrix Vector m n x -> Matrix Vector m n x # sqrt :: Matrix Vector m n x -> Matrix Vector m n x # (**) :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # logBase :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # sin :: Matrix Vector m n x -> Matrix Vector m n x # cos :: Matrix Vector m n x -> Matrix Vector m n x # tan :: Matrix Vector m n x -> Matrix Vector m n x # asin :: Matrix Vector m n x -> Matrix Vector m n x # acos :: Matrix Vector m n x -> Matrix Vector m n x # atan :: Matrix Vector m n x -> Matrix Vector m n x # sinh :: Matrix Vector m n x -> Matrix Vector m n x # cosh :: Matrix Vector m n x -> Matrix Vector m n x # tanh :: Matrix Vector m n x -> Matrix Vector m n x # asinh :: Matrix Vector m n x -> Matrix Vector m n x # acosh :: Matrix Vector m n x -> Matrix Vector m n x # atanh :: Matrix Vector m n x -> Matrix Vector m n x # log1p :: Matrix Vector m n x -> Matrix Vector m n x # expm1 :: Matrix Vector m n x -> Matrix Vector m n x # log1pexp :: Matrix Vector m n x -> Matrix Vector m n x # log1mexp :: Matrix Vector m n x -> Matrix Vector m n x #
(KnownNat m, KnownNat n, Numeric x, Fractional x) => Fractional (Matrix Vector m n x) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods (/) :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # recip :: Matrix Vector m n x -> Matrix Vector m n x # fromRational :: Rational -> Matrix Vector m n x #
(KnownNat m, KnownNat n, Numeric x, Num x) => Num (Matrix Vector m n x) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods (+) :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # (-) :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # (*) :: Matrix Vector m n x -> Matrix Vector m n x -> Matrix Vector m n x # negate :: Matrix Vector m n x -> Matrix Vector m n x # abs :: Matrix Vector m n x -> Matrix Vector m n x # signum :: Matrix Vector m n x -> Matrix Vector m n x # fromInteger :: Integer -> Matrix Vector m n x #
Show (v a) => Show (Matrix v m n a) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods showsPrec :: Int -> Matrix v m n a -> ShowS # show :: Matrix v m n a -> String # showList :: [Matrix v m n a] -> ShowS #
(KnownNat m, KnownNat n, Storable x) => Storable (Matrix Vector m n x) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods sizeOf :: Matrix Vector m n x -> Int # alignment :: Matrix Vector m n x -> Int # peekElemOff :: Ptr (Matrix Vector m n x) -> Int -> IO (Matrix Vector m n x) # pokeElemOff :: Ptr (Matrix Vector m n x) -> Int -> Matrix Vector m n x -> IO () # peekByteOff :: Ptr b -> Int -> IO (Matrix Vector m n x) # pokeByteOff :: Ptr b -> Int -> Matrix Vector m n x -> IO () # peek :: Ptr (Matrix Vector m n x) -> IO (Matrix Vector m n x) # poke :: Ptr (Matrix Vector m n x) -> Matrix Vector m n x -> IO () #
NFData (v a) => NFData (Matrix v m n a) Source #
Instance details Defined in Goal.Core.Vector.Generic Methods rnf :: Matrix v m n a -> () #

nRows :: forall v m n a. KnownNat m => Matrix v m n a -> Int Source #

The number of rows in the Matrix.

nColumns :: forall v m n a. KnownNat n => Matrix v m n a -> Int Source #

The number of columns in the Matrix.

Construction

fromRows :: (Vector v x, Vector v (Vector v n x), KnownNat n) => Vector v m (Vector v n x) -> Matrix v m n x Source #

Create a Matrix from a Vector of Vectors which represent the rows.

fromColumns :: (Vector v x, Vector v Int, Vector v (Vector v n x), Vector v (Vector v m x), KnownNat n, KnownNat m) => Vector v n (Vector v m x) -> Matrix v m n x Source #

Create a Matrix from a Vector of Vectors which represent the columns.

Deconstruction

toPair :: Vector v a => Vector v 2 a -> (a, a) Source #

Reshapes a length 2 Vector into a pair of values.

toRows :: (Vector v a, Vector v (Vector v n a), KnownNat n, KnownNat m) => Matrix v m n a -> Vector v m (Vector v n a) Source #

Convert a Matrix into a Vector of Vectors of rows.

toColumns :: (Vector v a, Vector v (Vector v m a), KnownNat m, KnownNat n, Vector v Int) => Matrix v m n a -> Vector v n (Vector v m a) Source #

Convert a Matrix into a Vector of Vectors of columns.

Manipulation

columnVector :: Vector v n a -> Matrix v n 1 a Source #

Turn a Vector into a single column Matrix.

rowVector :: Vector v n a -> Matrix v 1 n a Source #

Turn a Vector into a single row Matrix.

BLAS

transpose :: forall v m n a. (KnownNat m, KnownNat n, Vector v Int, Vector v a, Vector v (Vector v m a)) => Matrix v m n a -> Matrix v n m a Source #

Pure implementation of Matrix transposition.

dotProduct :: (Vector v x, Num x) => Vector v n x -> Vector v n x -> x Source #

Pure implementation of the dot product.

weakDotProduct :: (Vector v x, Num x) => v x -> v x -> x Source #

Pure implementation of the dot product on standard vectors.

outerProduct :: (KnownNat m, KnownNat n, Num x, Vector v Int, Vector v x, Vector v (Vector v n x), Vector v (Vector v m x), Vector v (Vector v 1 x)) => Vector v n x -> Vector v m x -> Matrix v n m x Source #

Pure implementation of the outer product.

matrixVectorMultiply :: (KnownNat m, KnownNat n, Vector v x, Vector v (Vector v n x), Num x) => Matrix v m n x -> Vector v n x -> Vector v m x Source #

Pure Matrix x Vector multiplication.

matrixMatrixMultiply :: (KnownNat m, KnownNat n, KnownNat o, Num x, Vector v Int, Vector v x, Vector v (Vector v m x), Vector v (Vector v n x), Vector v (Vector v o x)) => Matrix v m n x -> Matrix v n o x -> Matrix v m o x Source #

Pure Matrix x Matrix multiplication.