Statistics.Matrix

Basic matrix operations.

There isn't a widely used matrix package for Haskell yet, so we implement the necessary minimum here.

Data types

data Matrix

Two-dimensional matrix, stored in row-major order.

Constructors

Matrix

Fields

• rows :: !Int

  Rows of matrix.

• cols :: !Int

  Columns of matrix.

• exponent :: !Int

  In order to avoid overflows during matrix multiplication, a large exponent is stored separately.

• _vector :: !Vector

  Matrix data.

Instances

Eq Matrix

Methods

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

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

Show Matrix

Methods

showsPrec :: Int -> Matrix -> ShowS

show :: Matrix -> String

showList :: [Matrix] -> ShowS

type Vector = Vector Double

Conversion fromto listsvectors

fromVector

Arguments

:: Int

Number of rows.

-> Int

Number of columns.

-> Vector Double

Flat list of values, in row-major order.

-> Matrix

Convert from a row-major vector.

fromList

Arguments

:: Int

Number of rows.

-> Int

Number of columns.

-> [Double]

Flat list of values, in row-major order.

-> Matrix

Convert from a row-major list.

fromRowLists :: [[Double]] -> Matrix

create a matrix from a list of lists, as rows

fromRows :: [Vector] -> Matrix

create a matrix from a list of vectors, as rows

fromColumns :: [Vector] -> Matrix

create a matrix from a list of vectors, as columns

toVector :: Matrix -> Vector Double

Convert to a row-major flat vector.

toList :: Matrix -> [Double]

Convert to a row-major flat list.

toRows :: Matrix -> [Vector]

Convert to a list of vectors, as rows

toColumns :: Matrix -> [Vector]

Convert to a list of vectors, as columns

toRowLists :: Matrix -> [[Double]]

Convert to a list of lists, as rows

Other

generate

Arguments

:: Int

Number of rows

-> Int

Number of columns

-> (Int -> Int -> Double)

Function which takes row and column as argument.

-> Matrix

Generate matrix using function

generateSym

Arguments

:: Int

Number of rows and columns

-> (Int -> Int -> Double)

Function which takes row and column as argument. It must be symmetric in arguments: f i j == f j i

-> Matrix

Generate symmetric square matrix using function

ident :: Int -> Matrix

Create the square identity matrix with given dimensions.

diag :: Vector -> Matrix

Create a square matrix with given diagonal, other entries default to 0

dimension :: Matrix -> (Int, Int)

Return the dimensions of this matrix, as a (row,column) pair.

center :: Matrix -> Double

Element in the center of matrix (not corrected for exponent).

multiply :: Matrix -> Matrix -> Matrix

Matrix-matrix multiplication. Matrices must be of compatible sizes (note: not checked).

multiplyV :: Matrix -> Vector -> Vector

Matrix-vector multiplication.

transpose :: Matrix -> Matrix

power :: Matrix -> Int -> Matrix

Raise matrix to nth power. Power must be positive (/note: not checked).

norm :: Vector -> Double

Calculate the Euclidean norm of a vector.

column :: Matrix -> Int -> Vector

Return the given column.

row :: Matrix -> Int -> Vector

Return the given row.

map :: (Double -> Double) -> Matrix -> Matrix

Apply function to every element of matrix

for :: Monad m => Int -> Int -> (Int -> m ()) -> m ()

Simple for loop. Counts from start to end-1.

unsafeIndex

Arguments

:: Matrix

-> Int

Row.

-> Int

Column.

-> Double

hasNaN :: Matrix -> Bool

Indicate whether any element of the matrix is NaN.

bounds :: (Vector -> Int -> r) -> Matrix -> Int -> Int -> r

Given row and column numbers, calculate the offset into the flat row-major vector.

unsafeBounds :: (Vector -> Int -> r) -> Matrix -> Int -> Int -> r

Given row and column numbers, calculate the offset into the flat row-major vector, without checking.