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Numeric.Matrix

Contents

Matrix property and utility functions.
Matrix properties

Description

Efficient matrix operations in 100% pure Haskell.

This package uses miscellaneous implementations, depending on the type of its components. Typically unboxed arrays will perform best, while unboxed arrays give you certain features such as Rational or Complex components.

The following component types are supported by Matrix:

Int: Uses unboxed arrays internally. inv will always return Nothing.
Integer: Uses boxed arrays internally. inv will always return Nothing.
Double and Float: Uses unboxed arrays internally. All matrix operations will work as expected. Matrix Double will probably yield the best peformance.
Rational: Best choice if precision is what you aim for. Uses boxed arrays internally. All matrix operations will work as expected.
Complex: Experimental. Uses boxed arrays internally. The current implementation of inv requires an instance of Ord for the component type, therefor it is currently not possible to calculate the inverse of a complex matrix (on my to do list).

Synopsis

Documentation

data family Matrix e Source

class (Eq e, Num e) => MatrixElement e whereSource

Methods

matrix :: (Int, Int) -> ((Int, Int) -> e) -> Matrix eSource

select :: ((Int, Int) -> Bool) -> Matrix e -> [e]Source

at :: Matrix e -> (Int, Int) -> eSource

row :: Int -> Matrix e -> [e]Source

col :: Int -> Matrix e -> [e]Source

dimensions :: Matrix e -> (Int, Int)Source

numRows :: Matrix e -> Int Source

numCols :: Matrix e -> Int Source

fromList :: [[e]] -> Matrix eSource

toList :: Matrix e -> [[e]]Source

unit :: Int -> Matrix eSource

zero :: Int -> Matrix eSource

diag :: [e] -> Matrix eSource

empty :: Matrix eSource

minus :: Matrix e -> Matrix e -> Matrix eSource

plus :: Matrix e -> Matrix e -> Matrix eSource

times :: Matrix e -> Matrix e -> Matrix eSource

inv :: Matrix e -> Maybe (Matrix e)Source

det :: Matrix e -> eSource

transpose :: Matrix e -> Matrix eSource

rank :: Matrix e -> eSource

trace :: Matrix e -> [e]Source

map :: MatrixElement f => (e -> f) -> Matrix e -> Matrix fSource

all :: (e -> Bool) -> Matrix e -> Bool Source

any :: (e -> Bool) -> Matrix e -> Bool Source

mapWithIndex :: MatrixElement f => ((Int, Int) -> e -> f) -> Matrix e -> Matrix fSource

allWithIndex :: ((Int, Int) -> e -> Bool) -> Matrix e -> Bool Source

anyWithIndex :: ((Int, Int) -> e -> Bool) -> Matrix e -> Bool Source

Instances

MatrixElement Double
MatrixElement Float
MatrixElement Int
MatrixElement Integer
(Show a, Integral a) => MatrixElement (Ratio a)
(Show a, RealFloat a) => MatrixElement (Complex a)

Matrix property and utility functions.

Joins two matrices horizontally.

 1 2 3     1 0 0      1 2 3 1 0 0
 3 4 5 <|> 2 1 0  ->  3 4 5 2 1 0
 5 6 7     3 2 1      5 6 7 3 2 1

(<|>) :: MatrixElement e => Matrix e -> Matrix e -> Matrix eSource

Joins two matrices vertically.

 1 2 3     1 0 0      1 2 3
 3 4 5 <-> 2 1 0  ->  3 4 5
 5 6 7     3 2 1      5 6 7
                      1 0 0
                      2 1 0
                      3 2 1

(<->) :: MatrixElement e => Matrix e -> Matrix e -> Matrix eSource

Scales a matrix by the given factor.

 scale s == map (*s)

scale :: MatrixElement e => Matrix e -> e -> Matrix eSource

Matrix properties

Check whether the matrix is an identity matrix.

 1 0 0
 0 1 0
 0 0 1 (True)

isUnit :: MatrixElement e => Matrix e -> Bool Source

Check whether the matrix consists of all zeros.

 isZero == all (== 0)

isZero :: MatrixElement e => Matrix e -> Bool Source

Checks whether the matrix is a diagonal matrix.

 4 0 0 0
 0 7 0 0
 0 0 3 0
 0 0 0 9 (True)

isDiagonal :: MatrixElement e => Matrix e -> Bool Source

Checks whether the matrix is empty.

 isEmpty m = numCols == 0 || numRows == 0

isEmpty :: MatrixElement e => Matrix e -> Bool Source

Checks whether the matrix is a square matrix.

 isSquare == uncurry (==) . dimensions

isSquare :: MatrixElement e => Matrix e -> Bool Source