Algebra.Matrix

A small simple matrix library.

Documentation

newtype Vector r

Row vectors

Constructors

Vec [r]

Instances

Functor Vector

Eq r => Eq (Vector r)

Show r => Show (Vector r)

Arbitrary r => Arbitrary (Vector r)

unVec :: Vector r -> [r]

lengthVec :: Vector r -> Int

newtype Matrix r

Matrices

Constructors

M [Vector r]

Instances

Functor Matrix

Eq r => Eq (Matrix r)

Show r => Show (Matrix r)

Arbitrary r => Arbitrary (Matrix r)

matrix :: [[r]] -> Matrix r

Construct a mxn matrix.

matrixToVector :: Matrix r -> Vector r

vectorToMatrix :: Vector r -> Matrix r

unMVec :: Matrix r -> [[r]]

unM :: Matrix r -> [Vector r]

(!!!) :: Matrix a -> (Int, Int) -> a

identity :: IntegralDomain r => Int -> Matrix r

Construct a nxn identity matrix.

propLeftIdentity :: (IntegralDomain r, Eq r) => Matrix r -> Bool

propRightIdentity :: (IntegralDomain r, Eq r) => Matrix r -> Bool

mulM :: Ring r => Matrix r -> Matrix r -> Matrix r

Matrix multiplication.

addM :: Ring r => Matrix r -> Matrix r -> Matrix r

Matrix addition.

transpose :: Matrix r -> Matrix r

Transpose a matrix.

isSquareMatrix :: Matrix r -> Bool

dimension :: Matrix r -> (Int, Int)

Compute the dimension of a matrix.

scale :: CommutativeRing a => Matrix a -> Int -> a -> Matrix a

Scale a row in a matrix.

swap :: Matrix a -> Int -> Int -> Matrix a

Swap two rows of a matrix.

pivot :: CommutativeRing a => Matrix a -> a -> Int -> Int -> Matrix a

addRow :: CommutativeRing a => Matrix a -> Vector a -> Int -> Matrix a

subRow :: CommutativeRing a => Matrix a -> Vector a -> Int -> Matrix a

addCol :: CommutativeRing a => Matrix a -> Vector a -> Int -> Matrix a

subCol :: CommutativeRing a => Matrix a -> Vector a -> Int -> Matrix a

findPivot :: (CommutativeRing a, Eq a) => Matrix a -> (Int, Int) -> Maybe (a, Int)

forwardElim :: (Field a, Eq a) => (Matrix a, Vector a) -> (Matrix a, Vector a)

Compute row echelon form of a system Ax=b.

gaussElim :: (Field a, Eq a, Show a) => (Matrix a, Vector a) -> (Matrix a, Vector a)

Gauss-Jordan elimination: Given A and B solve Ax=B.

gaussElimCorrect :: (Field a, Eq a, Arbitrary a, Show a) => (Matrix a, Vector a) -> Property