Numeric.Matrix

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. All matrix operations will work as expected, though finding the inverse of a matrix isa tad less numerically stable than with a Double matrix.

Documentation

data family Matrix e

Matrices are represented by a type which fits best the component type. For example a Matrix Double is represented by unboxed arrays, Matrix Integer by boxed arrays.

Data instances exist for Int, Float, Double, Integer, Ratio, and Complex. Certain types do have certain disadvantages, like for example you can not compute the inverse matrix of a Matrix Int.

Every matrix (regardless of the component type) has instances for Show, Read, Num, Fractional, Eq, Typeable, Binary, and NFData. This means that you can use arithmetic operations like +, *, and /, as well as functions like show, read, or typeOf.

Show (Matrix e)

Note that a Show instance for the component type e must exist.

Read (Matrix e)

You can read a matrix like so:

read "1 0\n0 1\n" :: Matrix Double

Num (Matrix e)

+, -, *, negate, abs, signum, and fromInteger.

signum will compute the determinant and return the signum of it.

abs applies map abs on the matrix (that is, it applies abs on every component in the matrix and returns a new matrix without negative components).

fromInteger yields a 1-x-1-matrix.

Fractional (Matrix e)

Only available if there exists an instance Fractional e (the component type needs to have a Fractional instance, too). Note that while the Num operations are safe, recip and / will fail (with an error) if the involved matrix is not invertible or not a square matrix.

NFData (Matrix e)

Matrices have instances for NFData so that you can use a matrix in parallel computations using the Control.Monad.Par monad (see the monad-par package for details).

Typeable (Matrix e)

Allows you to use matrices as Dynamic values.

Binary (Matrix e)

Serialize and unserialize matrices using the binary package. See encode and decode.

Instances

MatrixElement e => Eq (Matrix e)

Defined in Numeric.Matrix

Methods

(==) :: Matrix e -> Matrix e -> Bool

(/=) :: Matrix e -> Matrix e -> Bool

(MatrixElement e, Fractional e) => Fractional (Matrix e)

Defined in Numeric.Matrix

Methods

(/) :: Matrix e -> Matrix e -> Matrix e

recip :: Matrix e -> Matrix e

fromRational :: Rational -> Matrix e

MatrixElement e => Num (Matrix e)

Defined in Numeric.Matrix

Methods

(+) :: Matrix e -> Matrix e -> Matrix e

(-) :: Matrix e -> Matrix e -> Matrix e

(*) :: Matrix e -> Matrix e -> Matrix e

negate :: Matrix e -> Matrix e

abs :: Matrix e -> Matrix e

signum :: Matrix e -> Matrix e

fromInteger :: Integer -> Matrix e

(Read e, MatrixElement e) => Read (Matrix e)

Defined in Numeric.Matrix

Methods

readsPrec :: Int -> ReadS (Matrix e)

readList :: ReadS [Matrix e]

readPrec :: ReadPrec (Matrix e)

readListPrec :: ReadPrec [Matrix e]

(MatrixElement e, Show e) => Show (Matrix e)

Defined in Numeric.Matrix

Methods

showsPrec :: Int -> Matrix e -> ShowS

show :: Matrix e -> String

showList :: [Matrix e] -> ShowS

(MatrixElement e, Binary e) => Binary (Matrix e)

Defined in Numeric.Matrix

Methods

put :: Matrix e -> Put

get :: Get (Matrix e)

putList :: [Matrix e] -> Put

MatrixElement e => NFData (Matrix e)

Defined in Numeric.Matrix

Methods

rnf :: Matrix e -> ()

data Matrix Double

Defined in Numeric.Matrix

data Matrix Double = DoubleMatrix !Int !Int (Array Int (UArray Int Double))

data Matrix Float

Defined in Numeric.Matrix

data Matrix Float = FloatMatrix !Int !Int (Array Int (UArray Int Float))

data Matrix Int

Defined in Numeric.Matrix

data Matrix Int = IntMatrix !Int !Int (Array Int (UArray Int Int))

data Matrix Integer

Defined in Numeric.Matrix

data Matrix Integer = IntegerMatrix !Int !Int (Array Int (Array Int Integer))

data Matrix (Ratio a)

Defined in Numeric.Matrix

data Matrix (Ratio a) = RatioMatrix !Int !Int (Array Int (Array Int (Ratio a)))

data Matrix (Complex a)

Defined in Numeric.Matrix

data Matrix (Complex a) = ComplexMatrix !Int !Int (Array Int (Array Int (Complex a)))

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

Minimal complete definition

matrix, fromList, toList, det, rank

Methods

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

Creates a matrix of the given size using a generator function for the value of each component.

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

Builds a list from a matrix for the indices for which the given predicate matches.

trace == select (uncurry (==))

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

Returns the component at the given position in the matrix. Note that indices start at one, not at zero.

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

Returns the row at the given index in the matrix. Note that indices start at one, not at zero.

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

Returns the row at the given index in the matrix. Note that indices start at one, not at zero.

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

The dimensions of a given matrix.

numRows :: Matrix e -> Int

The number of rows in the given matrix.

numCols :: Matrix e -> Int

The number of columns in the given matrix.

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

Builds a matrix from a list of lists.

The innermost lists represent the rows. This function will create a m-n-matrix, where m is the number of rows, which is the minimum length of the row lists and n is the number of columns, i.e. the length of the outer list.

fromList [[1,2,3],[2,1,3],[3,2,1]] :: Matrix Rational

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

Turns a matrix into a list of lists.

(toList . fromList) xs == xs

(fromList . toList) mat == mat

unit :: Int -> Matrix e

An identity square matrix of the given size.

>>> unit 4
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

zero :: Int -> Matrix e

A square matrix of the given size consisting of all zeros.

>>> zero 2
0 0
0 0

diag :: [e] -> Matrix e

A square matrix which trace is the given list, all other components set to zero.

>>> diag [1,4,7,9]
1 0 0 0
0 4 0 0
0 0 7 0
0 0 0 9

empty :: Matrix e

Check whether the matrix is the empty matrix.

dimensions empty == (0, 0)

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

Subtract a matrix from another.

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

Add two matrices.

You may also use the Num instance for matrices, i.e. matrix1 + matrix2 will work, too.

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

Multiply two matrices O(n^3).

You may also use the Num instance for matrices, i.e. matrix1 * matrix2 will work, too.

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

Compute the inverse of a matrix. Returns Nothing if the matrix is not invertible.

det :: Matrix e -> e

Applies Bareiss multistep integer-preserving algorithm for finding the determinant of a matrix. Returns 0 if the matrix is not a square matrix.

transpose :: Matrix e -> Matrix e

Flip rows and columns.

1 8 9                1 2 3
2 1 8  --transpose-> 8 1 2
3 2 1                9 8 1 

rank :: Matrix e -> e

Compute the rank of a matrix.

trace :: Matrix e -> [e]

Select the diagonal elements of a matrix as a list.

1 8 3
3 6 5 --trace-> [1, 6, 2]
7 4 2

minor :: MatrixElement e => (Int, Int) -> Matrix e -> e

Select the minor of a matrix, that is the determinant of the minorMatrix.

minor = det . minorMatrix

minorMatrix :: MatrixElement e => (Int, Int) -> Matrix e -> Matrix e

Select the minor matrix of a matrix, a matrix that is obtained by deleting the i-th row and j-th column.

10  9 95 45
 8  7  3 27                        8  3 27
13 17 19 23 --minorMatrix (1,2)-> 13 19 23
 1  2  5  8                        1  5  8

cofactors :: MatrixElement e => Matrix e -> Matrix e

adjugate :: MatrixElement e => Matrix e -> Matrix e

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

Apply a function on every component in the matrix.

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

Apply a predicate on every component in the matrix and returns True iff all components satisfy it.

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

Apply a predicate on every component in the matrix and return True if one or more components satisfy it.

sum :: Matrix e -> e

Compute the sum of the components of the matrix.

foldMap :: Monoid m => (e -> m) -> Matrix e -> m

Map each component of the matrix to a monoid, and combine the results.

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

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

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

foldMapWithIndex :: Monoid m => ((Int, Int) -> e -> m) -> Matrix e -> m

Instances

MatrixElement Double

Defined in Numeric.Matrix

Methods

matrix :: (Int, Int) -> ((Int, Int) -> Double) -> Matrix Double

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

at :: Matrix Double -> (Int, Int) -> Double

row :: Int -> Matrix Double -> [Double]

col :: Int -> Matrix Double -> [Double]

dimensions :: Matrix Double -> (Int, Int)

numRows :: Matrix Double -> Int

numCols :: Matrix Double -> Int

fromList :: [[Double]] -> Matrix Double

toList :: Matrix Double -> [[Double]]

unit :: Int -> Matrix Double

zero :: Int -> Matrix Double

diag :: [Double] -> Matrix Double

empty :: Matrix Double

minus :: Matrix Double -> Matrix Double -> Matrix Double

plus :: Matrix Double -> Matrix Double -> Matrix Double

times :: Matrix Double -> Matrix Double -> Matrix Double

inv :: Matrix Double -> Maybe (Matrix Double)

det :: Matrix Double -> Double

transpose :: Matrix Double -> Matrix Double

rank :: Matrix Double -> Double

trace :: Matrix Double -> [Double]

minor :: (Int, Int) -> Matrix Double -> Double

minorMatrix :: (Int, Int) -> Matrix Double -> Matrix Double

cofactors :: Matrix Double -> Matrix Double

adjugate :: Matrix Double -> Matrix Double

map :: MatrixElement f => (Double -> f) -> Matrix Double -> Matrix f

all :: (Double -> Bool) -> Matrix Double -> Bool

any :: (Double -> Bool) -> Matrix Double -> Bool

sum :: Matrix Double -> Double

foldMap :: Monoid m => (Double -> m) -> Matrix Double -> m

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

allWithIndex :: ((Int, Int) -> Double -> Bool) -> Matrix Double -> Bool

anyWithIndex :: ((Int, Int) -> Double -> Bool) -> Matrix Double -> Bool

foldMapWithIndex :: Monoid m => ((Int, Int) -> Double -> m) -> Matrix Double -> m

MatrixElement Float

Defined in Numeric.Matrix

Methods

matrix :: (Int, Int) -> ((Int, Int) -> Float) -> Matrix Float

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

at :: Matrix Float -> (Int, Int) -> Float

row :: Int -> Matrix Float -> [Float]

col :: Int -> Matrix Float -> [Float]

dimensions :: Matrix Float -> (Int, Int)

numRows :: Matrix Float -> Int

numCols :: Matrix Float -> Int

fromList :: [[Float]] -> Matrix Float

toList :: Matrix Float -> [[Float]]

unit :: Int -> Matrix Float

zero :: Int -> Matrix Float

diag :: [Float] -> Matrix Float

empty :: Matrix Float

minus :: Matrix Float -> Matrix Float -> Matrix Float

plus :: Matrix Float -> Matrix Float -> Matrix Float

times :: Matrix Float -> Matrix Float -> Matrix Float

inv :: Matrix Float -> Maybe (Matrix Float)

det :: Matrix Float -> Float

transpose :: Matrix Float -> Matrix Float

rank :: Matrix Float -> Float

trace :: Matrix Float -> [Float]

minor :: (Int, Int) -> Matrix Float -> Float

minorMatrix :: (Int, Int) -> Matrix Float -> Matrix Float

cofactors :: Matrix Float -> Matrix Float

adjugate :: Matrix Float -> Matrix Float

map :: MatrixElement f => (Float -> f) -> Matrix Float -> Matrix f

all :: (Float -> Bool) -> Matrix Float -> Bool

any :: (Float -> Bool) -> Matrix Float -> Bool

sum :: Matrix Float -> Float

foldMap :: Monoid m => (Float -> m) -> Matrix Float -> m

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

allWithIndex :: ((Int, Int) -> Float -> Bool) -> Matrix Float -> Bool

anyWithIndex :: ((Int, Int) -> Float -> Bool) -> Matrix Float -> Bool

foldMapWithIndex :: Monoid m => ((Int, Int) -> Float -> m) -> Matrix Float -> m

MatrixElement Int

Defined in Numeric.Matrix

Methods

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

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

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

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

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

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

numRows :: Matrix Int -> Int

numCols :: Matrix Int -> Int

fromList :: [[Int]] -> Matrix Int

toList :: Matrix Int -> [[Int]]

unit :: Int -> Matrix Int

zero :: Int -> Matrix Int

diag :: [Int] -> Matrix Int

empty :: Matrix Int

minus :: Matrix Int -> Matrix Int -> Matrix Int

plus :: Matrix Int -> Matrix Int -> Matrix Int

times :: Matrix Int -> Matrix Int -> Matrix Int

inv :: Matrix Int -> Maybe (Matrix Int)

det :: Matrix Int -> Int

transpose :: Matrix Int -> Matrix Int

rank :: Matrix Int -> Int

trace :: Matrix Int -> [Int]

minor :: (Int, Int) -> Matrix Int -> Int

minorMatrix :: (Int, Int) -> Matrix Int -> Matrix Int

cofactors :: Matrix Int -> Matrix Int

adjugate :: Matrix Int -> Matrix Int

map :: MatrixElement f => (Int -> f) -> Matrix Int -> Matrix f

all :: (Int -> Bool) -> Matrix Int -> Bool

any :: (Int -> Bool) -> Matrix Int -> Bool

sum :: Matrix Int -> Int

foldMap :: Monoid m => (Int -> m) -> Matrix Int -> m

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

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

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

foldMapWithIndex :: Monoid m => ((Int, Int) -> Int -> m) -> Matrix Int -> m

MatrixElement Integer

Defined in Numeric.Matrix

Methods

matrix :: (Int, Int) -> ((Int, Int) -> Integer) -> Matrix Integer

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

at :: Matrix Integer -> (Int, Int) -> Integer

row :: Int -> Matrix Integer -> [Integer]

col :: Int -> Matrix Integer -> [Integer]

dimensions :: Matrix Integer -> (Int, Int)

numRows :: Matrix Integer -> Int

numCols :: Matrix Integer -> Int

fromList :: [[Integer]] -> Matrix Integer

toList :: Matrix Integer -> [[Integer]]

unit :: Int -> Matrix Integer

zero :: Int -> Matrix Integer

diag :: [Integer] -> Matrix Integer

empty :: Matrix Integer

minus :: Matrix Integer -> Matrix Integer -> Matrix Integer

plus :: Matrix Integer -> Matrix Integer -> Matrix Integer

times :: Matrix Integer -> Matrix Integer -> Matrix Integer

inv :: Matrix Integer -> Maybe (Matrix Integer)

det :: Matrix Integer -> Integer

transpose :: Matrix Integer -> Matrix Integer

rank :: Matrix Integer -> Integer

trace :: Matrix Integer -> [Integer]

minor :: (Int, Int) -> Matrix Integer -> Integer

minorMatrix :: (Int, Int) -> Matrix Integer -> Matrix Integer

cofactors :: Matrix Integer -> Matrix Integer

adjugate :: Matrix Integer -> Matrix Integer

map :: MatrixElement f => (Integer -> f) -> Matrix Integer -> Matrix f

all :: (Integer -> Bool) -> Matrix Integer -> Bool

any :: (Integer -> Bool) -> Matrix Integer -> Bool

sum :: Matrix Integer -> Integer

foldMap :: Monoid m => (Integer -> m) -> Matrix Integer -> m

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

allWithIndex :: ((Int, Int) -> Integer -> Bool) -> Matrix Integer -> Bool

anyWithIndex :: ((Int, Int) -> Integer -> Bool) -> Matrix Integer -> Bool

foldMapWithIndex :: Monoid m => ((Int, Int) -> Integer -> m) -> Matrix Integer -> m

(Show a, Integral a) => MatrixElement (Ratio a)

Defined in Numeric.Matrix

Methods

matrix :: (Int, Int) -> ((Int, Int) -> Ratio a) -> Matrix (Ratio a)

select :: ((Int, Int) -> Bool) -> Matrix (Ratio a) -> [Ratio a]

at :: Matrix (Ratio a) -> (Int, Int) -> Ratio a

row :: Int -> Matrix (Ratio a) -> [Ratio a]

col :: Int -> Matrix (Ratio a) -> [Ratio a]

dimensions :: Matrix (Ratio a) -> (Int, Int)

numRows :: Matrix (Ratio a) -> Int

numCols :: Matrix (Ratio a) -> Int

fromList :: [[Ratio a]] -> Matrix (Ratio a)

toList :: Matrix (Ratio a) -> [[Ratio a]]

unit :: Int -> Matrix (Ratio a)

zero :: Int -> Matrix (Ratio a)

diag :: [Ratio a] -> Matrix (Ratio a)

empty :: Matrix (Ratio a)

minus :: Matrix (Ratio a) -> Matrix (Ratio a) -> Matrix (Ratio a)

plus :: Matrix (Ratio a) -> Matrix (Ratio a) -> Matrix (Ratio a)

times :: Matrix (Ratio a) -> Matrix (Ratio a) -> Matrix (Ratio a)

inv :: Matrix (Ratio a) -> Maybe (Matrix (Ratio a))

det :: Matrix (Ratio a) -> Ratio a

transpose :: Matrix (Ratio a) -> Matrix (Ratio a)

rank :: Matrix (Ratio a) -> Ratio a

trace :: Matrix (Ratio a) -> [Ratio a]

minor :: (Int, Int) -> Matrix (Ratio a) -> Ratio a

minorMatrix :: (Int, Int) -> Matrix (Ratio a) -> Matrix (Ratio a)

cofactors :: Matrix (Ratio a) -> Matrix (Ratio a)

adjugate :: Matrix (Ratio a) -> Matrix (Ratio a)

map :: MatrixElement f => (Ratio a -> f) -> Matrix (Ratio a) -> Matrix f

all :: (Ratio a -> Bool) -> Matrix (Ratio a) -> Bool

any :: (Ratio a -> Bool) -> Matrix (Ratio a) -> Bool

sum :: Matrix (Ratio a) -> Ratio a

foldMap :: Monoid m => (Ratio a -> m) -> Matrix (Ratio a) -> m

mapWithIndex :: MatrixElement f => ((Int, Int) -> Ratio a -> f) -> Matrix (Ratio a) -> Matrix f

allWithIndex :: ((Int, Int) -> Ratio a -> Bool) -> Matrix (Ratio a) -> Bool

anyWithIndex :: ((Int, Int) -> Ratio a -> Bool) -> Matrix (Ratio a) -> Bool

foldMapWithIndex :: Monoid m => ((Int, Int) -> Ratio a -> m) -> Matrix (Ratio a) -> m

(Show a, RealFloat a) => MatrixElement (Complex a)

Defined in Numeric.Matrix

Methods

matrix :: (Int, Int) -> ((Int, Int) -> Complex a) -> Matrix (Complex a)

select :: ((Int, Int) -> Bool) -> Matrix (Complex a) -> [Complex a]

at :: Matrix (Complex a) -> (Int, Int) -> Complex a

row :: Int -> Matrix (Complex a) -> [Complex a]

col :: Int -> Matrix (Complex a) -> [Complex a]

dimensions :: Matrix (Complex a) -> (Int, Int)

numRows :: Matrix (Complex a) -> Int

numCols :: Matrix (Complex a) -> Int

fromList :: [[Complex a]] -> Matrix (Complex a)

toList :: Matrix (Complex a) -> [[Complex a]]

unit :: Int -> Matrix (Complex a)

zero :: Int -> Matrix (Complex a)

diag :: [Complex a] -> Matrix (Complex a)

empty :: Matrix (Complex a)

minus :: Matrix (Complex a) -> Matrix (Complex a) -> Matrix (Complex a)

plus :: Matrix (Complex a) -> Matrix (Complex a) -> Matrix (Complex a)

times :: Matrix (Complex a) -> Matrix (Complex a) -> Matrix (Complex a)

inv :: Matrix (Complex a) -> Maybe (Matrix (Complex a))

det :: Matrix (Complex a) -> Complex a

transpose :: Matrix (Complex a) -> Matrix (Complex a)

rank :: Matrix (Complex a) -> Complex a

trace :: Matrix (Complex a) -> [Complex a]

minor :: (Int, Int) -> Matrix (Complex a) -> Complex a

minorMatrix :: (Int, Int) -> Matrix (Complex a) -> Matrix (Complex a)

cofactors :: Matrix (Complex a) -> Matrix (Complex a)

adjugate :: Matrix (Complex a) -> Matrix (Complex a)

map :: MatrixElement f => (Complex a -> f) -> Matrix (Complex a) -> Matrix f

all :: (Complex a -> Bool) -> Matrix (Complex a) -> Bool

any :: (Complex a -> Bool) -> Matrix (Complex a) -> Bool

sum :: Matrix (Complex a) -> Complex a

foldMap :: Monoid m => (Complex a -> m) -> Matrix (Complex a) -> m

mapWithIndex :: MatrixElement f => ((Int, Int) -> Complex a -> f) -> Matrix (Complex a) -> Matrix f

allWithIndex :: ((Int, Int) -> Complex a -> Bool) -> Matrix (Complex a) -> Bool

anyWithIndex :: ((Int, Int) -> Complex a -> Bool) -> Matrix (Complex a) -> Bool

foldMapWithIndex :: Monoid m => ((Int, Int) -> Complex a -> m) -> Matrix (Complex a) -> m

Matrix property and utility functions.

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

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 e

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

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

Scales a matrix by the given factor.

scale s == map (*s)

Matrix properties

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

Check whether the matrix is an identity matrix.

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

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

Check whether the matrix consists of all zeros.

isZero == all (== 0)

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

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)

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

Checks whether the matrix is empty.

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

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

Checks whether the matrix is a square matrix.

isSquare == uncurry (==) . dimensions

Conversions

toDoubleMatrix :: (MatrixElement a, Integral a) => Matrix a -> Matrix Double

toComplexMatrix :: (MatrixElement a, RealFloat a, Show a) => Matrix a -> Matrix (Complex a)

toRationalMatrix :: (MatrixElement a, Real a) => Matrix a -> Matrix Rational