hmatrix-0.5.1.1: Linear algebra and numerical computations

Portability portable provisional Alberto Ruiz

Data.Packed.Matrix

Description

A Matrix representation suitable for numerical computations using LAPACK and GSL.

Synopsis

# Documentation

class (Storable a, Floating a) => Element a Source

Auxiliary class.

Instances

 Element Double Element (Complex Double)

data Matrix t Source

Matrix representation suitable for GSL and LAPACK computations.

Instances

 Container Matrix Double (Linear Vector a, Container Matrix a) => Linear Matrix a Joinable Vector Matrix Joinable Matrix Vector Joinable Matrix Matrix Mul Vector Matrix Vector Mul Matrix Vector Vector Mul Matrix Matrix Matrix Container Matrix (Complex Double) (Eq a, Element a) => Eq (Matrix a) (Linear Vector a, Floating (Vector a), Fractional (Matrix a)) => Floating (Matrix a) (Linear Vector a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a) (Linear Matrix a, Num (Vector a)) => Num (Matrix a) (Element a, Read a) => Read (Matrix a) (Show a, Element a) => Show (Matrix a) (Element a, Arbitrary a) => Arbitrary (Matrix a) Normed (Matrix Double) Normed (Matrix (Complex Double))

(><) :: Element a => Int -> Int -> [a] -> Matrix aSource

An easy way to create a matrix:

```> (2><3)[1..6]
(2><3)
[ 1.0, 2.0, 3.0
, 4.0, 5.0, 6.0 ]```

This is the format produced by the instances of Show (Matrix a), which can also be used for input.

trans :: Matrix t -> Matrix tSource

Matrix transpose.

reshape :: Element t => Int -> Vector t -> Matrix tSource

Unsafe matrix access without range checking

Creates a matrix from a vector by grouping the elements in rows with the desired number of columns. (GNU-Octave groups by columns. To do it you can define `reshapeF r = trans . reshape r` where r is the desired number of rows.)

```> reshape 4 (`fromList` [1..12])
(3><4)
[ 1.0,  2.0,  3.0,  4.0
, 5.0,  6.0,  7.0,  8.0
, 9.0, 10.0, 11.0, 12.0 ]```

flatten :: Element t => Matrix t -> Vector tSource

Creates a vector by concatenation of rows

```> flatten (`ident` 3)
9 |> [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]```

fromLists :: Element t => [[t]] -> Matrix tSource

Creates a `Matrix` from a list of lists (considered as rows).

```> fromLists [[1,2],[3,4],[5,6]]
(3><2)
[ 1.0, 2.0
, 3.0, 4.0
, 5.0, 6.0 ]```

toLists :: Element t => Matrix t -> [[t]]Source

the inverse of `Data.Packed.Matrix.fromLists`

(@@>) :: Storable t => Matrix t -> (Int, Int) -> tSource

asRow :: Element a => Vector a -> Matrix aSource

creates a 1-row matrix from a vector

asColumn :: Element a => Vector a -> Matrix aSource

creates a 1-column matrix from a vector

fromRows :: Element t => [Vector t] -> Matrix tSource

creates a Matrix from a list of vectors

toRows :: Element t => Matrix t -> [Vector t]Source

extracts the rows of a matrix as a list of vectors

fromColumns :: Element t => [Vector t] -> Matrix tSource

Creates a matrix from a list of vectors, as columns

toColumns :: Element t => Matrix t -> [Vector t]Source

Creates a list of vectors from the columns of a matrix

fromBlocks :: Element t => [[Matrix t]] -> Matrix tSource

Creates a matrix from blocks given as a list of lists of matrices:

```> let a = `diag` \$ `fromList` [5,7,2]
> let b = `reshape` 4 \$ `constant` (-1) 12
> fromBlocks [[a,b],[b,a]]
(6><7)
[  5.0,  0.0,  0.0, -1.0, -1.0, -1.0, -1.0
,  0.0,  7.0,  0.0, -1.0, -1.0, -1.0, -1.0
,  0.0,  0.0,  2.0, -1.0, -1.0, -1.0, -1.0
, -1.0, -1.0, -1.0, -1.0,  5.0,  0.0,  0.0
, -1.0, -1.0, -1.0, -1.0,  0.0,  7.0,  0.0
, -1.0, -1.0, -1.0, -1.0,  0.0,  0.0,  2.0 ]```

repmat :: Element t => Matrix t -> Int -> Int -> Matrix tSource

creates matrix by repetition of a matrix a given number of rows and columns

```> repmat (ident 2) 2 3 :: Matrix Double
(4><6)
[ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0
, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0 ]```

flipud :: Element t => Matrix t -> Matrix tSource

Reverse rows

fliprl :: Element t => Matrix t -> Matrix tSource

Reverse columns

Arguments

 :: Element a => (Int, Int) (r0,c0) starting position -> (Int, Int) (rt,ct) dimensions of submatrix -> Matrix a input matrix -> Matrix a result

Extracts a submatrix from a matrix.

takeRows :: Element t => Int -> Matrix t -> Matrix tSource

Creates a matrix with the first n rows of another matrix

dropRows :: Element t => Int -> Matrix t -> Matrix tSource

Creates a copy of a matrix without the first n rows

takeColumns :: Element t => Int -> Matrix t -> Matrix tSource

Creates a matrix with the first n columns of another matrix

dropColumns :: Element t => Int -> Matrix t -> Matrix tSource

Creates a copy of a matrix without the first n columns

extractRows :: Element t => [Int] -> Matrix t -> Matrix tSource

rearranges the rows of a matrix according to the order given in a list of integers.

ident :: Element a => Int -> Matrix aSource

creates the identity matrix of given dimension

diag :: Element a => Vector a -> Matrix aSource

Creates a square matrix with a given diagonal.

diagRect :: (Element t, Num t) => Vector t -> Int -> Int -> Matrix tSource

creates a rectangular diagonal matrix

```> diagRect (constant 5 3) 3 4 :: Matrix Double
(3><4)
[ 5.0, 0.0, 0.0, 0.0
, 0.0, 5.0, 0.0, 0.0
, 0.0, 0.0, 5.0, 0.0 ]```

takeDiag :: Element t => Matrix t -> Vector tSource

extracts the diagonal from a rectangular matrix

liftMatrix :: (Element a, Element b) => (Vector a -> Vector b) -> Matrix a -> Matrix bSource

application of a vector function on the flattened matrix elements

liftMatrix2 :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix tSource

application of a vector function on the flattened matrices elements

format :: Element t => String -> (t -> String) -> Matrix t -> StringSource

Creates a string from a matrix given a separator and a function to show each entry. Using this function the user can easily define any desired display function:

`import Text.Printf(printf)`
`disp = putStrLn . format "  " (printf "%.2f")`

creates a matrix from a table of numbers.

fromFile :: FilePath -> (Int, Int) -> IO (Matrix Double)Source

loads a matrix efficiently from formatted ASCII text file (the number of rows and columns must be known in advance).