statistics-0.13.3.0: A library of statistical types, data, and functions

Copyright	2011 Aleksey Khudyakov, 2014 Bryan O'Sullivan
License	BSD3
Safe Haskell	None
Language	Haskell98

Statistics.Matrix

Contents

Data types
Conversion fromto listsvectors
Other

Description

Basic matrix operations.

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

Synopsis

Data types

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
Show Matrix

type Vector = Vector Double

Conversion fromto listsvectors

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.

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

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

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.

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.