Portability | portable |
---|---|

Stability | provisional |

Maintainer | Alberto Ruiz <aruiz@um.es> |

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

This module provides basic functions for manipulation of structure.

- data Matrix t
- class Storable a => Element a
- rows :: Matrix t -> Int
- cols :: Matrix t -> Int
- (><) :: Storable a => Int -> Int -> [a] -> Matrix a
- trans :: Matrix t -> Matrix t
- reshape :: Storable t => Int -> Vector t -> Matrix t
- flatten :: Element t => Matrix t -> Vector t
- fromLists :: Element t => [[t]] -> Matrix t
- toLists :: Element t => Matrix t -> [[t]]
- buildMatrix :: Element a => Int -> Int -> ((Int, Int) -> a) -> Matrix a
- (@@>) :: Storable t => Matrix t -> (Int, Int) -> t
- asRow :: Storable a => Vector a -> Matrix a
- asColumn :: Storable a => Vector a -> Matrix a
- fromRows :: Element t => [Vector t] -> Matrix t
- toRows :: Element t => Matrix t -> [Vector t]
- fromColumns :: Element t => [Vector t] -> Matrix t
- toColumns :: Element t => Matrix t -> [Vector t]
- fromBlocks :: Element t => [[Matrix t]] -> Matrix t
- toBlocks :: Element t => [Int] -> [Int] -> Matrix t -> [[Matrix t]]
- toBlocksEvery :: Element t => Int -> Int -> Matrix t -> [[Matrix t]]
- repmat :: Element t => Matrix t -> Int -> Int -> Matrix t
- flipud :: Element t => Matrix t -> Matrix t
- fliprl :: Element t => Matrix t -> Matrix t
- subMatrix :: Element a => (Int, Int) -> (Int, Int) -> Matrix a -> Matrix a
- takeRows :: Element t => Int -> Matrix t -> Matrix t
- dropRows :: Element t => Int -> Matrix t -> Matrix t
- takeColumns :: Element t => Int -> Matrix t -> Matrix t
- dropColumns :: Element t => Int -> Matrix t -> Matrix t
- extractRows :: Element t => [Int] -> Matrix t -> Matrix t
- diagRect :: Storable t => t -> Vector t -> Int -> Int -> Matrix t
- takeDiag :: Element t => Matrix t -> Vector t
- liftMatrix :: (Storable a, Storable b) => (Vector a -> Vector b) -> Matrix a -> Matrix b
- liftMatrix2 :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
- liftMatrix2Auto :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
- fromArray2D :: Storable e => Array (Int, Int) e -> Matrix e

# Documentation

Matrix representation suitable for GSL and LAPACK computations.

The elements are stored in a continuous memory array.

Complexable Matrix | |

Joinable Vector Matrix | |

Joinable Matrix Vector | |

Joinable Matrix Matrix | |

Container Vector a => Container Matrix a | |

Normed Matrix Double | |

Normed Matrix Float | |

Mul Vector Matrix Vector | |

Mul Matrix Vector Vector | |

Mul Matrix Matrix Matrix | |

Normed Matrix (Complex Double) | |

Normed Matrix (Complex Float) | |

Container Matrix a => Eq (Matrix a) | |

(Floating a, Container Vector a, Floating (Vector a), Fractional (Matrix a)) => Floating (Matrix a) | |

(Container Vector a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a) | |

(Container 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) | |

(Binary a, Element a, Storable a) => Binary (Matrix a) |

class Storable a => Element a Source

Supported matrix elements.

This class provides optimized internal
operations for selected element types.
It provides unoptimised defaults for any `Storable`

type,
so you can create instances simply as:
`instance Element Foo`

.

(><) :: Storable 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.

The input list is explicitly truncated, so that it can safely be used with lists that are too long (like infinite lists).

Example:

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

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

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 ]

buildMatrix :: Element a => Int -> Int -> ((Int, Int) -> a) -> Matrix aSource

creates a Matrix of the specified size using the supplied function to to map the row/column position to the value at that row/column position.

> buildMatrix 3 4 ( (r,c) -> fromIntegral r * fromIntegral c) (3><4) [ 0.0, 0.0, 0.0, 0.0, 0.0 , 0.0, 1.0, 2.0, 3.0, 4.0 , 0.0, 2.0, 4.0, 6.0, 8.0]

Hilbert matrix of order N:

hilb n = buildMatrix n n ((i,j)->1/(fromIntegral i + fromIntegral j +1))

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

Create a matrix from a list of vectors. All vectors must have the same dimension, or dimension 1, which is are automatically expanded.

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.

Single row/column components are automatically expanded to match the corresponding common row and column:

> let disp = putStr . dispf 2 > let vector xs = fromList xs :: Vector Double > let diagl = diag . vector > let rowm = asRow . vector > disp $ fromBlocks [[ident 5, 7, rowm[10,20]], [3, diagl[1,2,3], 0]] 8x10 1 0 0 0 0 7 7 7 10 20 0 1 0 0 0 7 7 7 10 20 0 0 1 0 0 7 7 7 10 20 0 0 0 1 0 7 7 7 10 20 0 0 0 0 1 7 7 7 10 20 3 3 3 3 3 1 0 0 0 0 3 3 3 3 3 0 2 0 0 0 3 3 3 3 3 0 0 3 0 0

toBlocks :: Element t => [Int] -> [Int] -> Matrix t -> [[Matrix t]]Source

Partition a matrix into blocks with the given numbers of rows and columns. The remaining rows and columns are discarded.

toBlocksEvery :: Element t => Int -> Int -> Matrix t -> [[Matrix t]]Source

Fully partition a matrix into blocks of the same size. If the dimensions are not a multiple of the given size the last blocks will be smaller.

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 ]

:: 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.

diagRect :: Storable t => t -> Vector t -> Int -> Int -> Matrix tSource

creates a rectangular diagonal matrix:

> diagRect 7 (fromList [10,20,30]) 4 5 :: Matrix Double (4><5) [ 10.0, 7.0, 7.0, 7.0, 7.0 , 7.0, 20.0, 7.0, 7.0, 7.0 , 7.0, 7.0, 30.0, 7.0, 7.0 , 7.0, 7.0, 7.0, 7.0, 7.0 ]

liftMatrix :: (Storable a, Storable 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