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

Copyright2011 Aleksey Khudyakov 2014 Bryan O'Sullivan
LicenseBSD3
Safe HaskellNone
LanguageHaskell98

Statistics.Matrix

Contents

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

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 # 

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.