Safe Haskell	None

Data.Matrix

Contents

Matrix type
Builders
Accessing
Manipulating matrices
Working with blocks
- Splitting blocks
- Joining blocks

Description

Matrix datatype an basic operations.

Synopsis

Matrix type

data Matrix a Source

Instances

Functor Matrix
Eq a => Eq (Matrix a)
Num a => Num (Matrix a)
Show a => Show (Matrix a)
NFData a => NFData (Matrix a)

prettyMatrix :: Show a => Matrix a -> String Source

Display a matrix as a String.

nrows :: Matrix a -> Int Source

Number of rows.

ncols :: Matrix a -> Int Source

Number of columns.

Builders

zero Source

Arguments

:: Num a
=> Int	Rows
-> Int	Columns
-> Matrix a

The zero matrix of the given size.

identity :: Num a => Int -> Matrix aSource

Identity matrix of the given order.

matrix Source

Arguments

:: Int	Rows
-> Int	Columns
-> ((Int, Int) -> a)	Generator function
-> Matrix a

Generate a matrix from a generator function.

Accessing

getElem Source

Arguments

:: Int	Row
-> Int	Column
-> Matrix a	Matrix
-> a

Get an element of a matrix.

(!) :: Matrix a -> (Int, Int) -> aSource

Nice alias for getElem.

Manipulating matrices

transpose :: Matrix a -> Matrix aSource

The transpose of a matrix.

extendTo Source

Arguments

:: Num a
=> Int	Minimal number of rows.
-> Int	Minimal number of columns.
-> Matrix a
-> Matrix a

Extend a matrix to a given size adding zeroes. If the matrix already has the required size, nothing happens.

Working with blocks

Splitting blocks

submatrix Source

Arguments

:: Int	Starting row
-> Int	Ending row
-> Int	Starting column
-> Int	Ending column
-> Matrix a
-> Matrix a

Extract a submatrix.

splitBlocks Source

Arguments

:: Int	Row of the splitting element.
-> Int	Column of the splitting element.
-> Matrix a	Matrix to split.
-> (Matrix a, Matrix a, Matrix a, Matrix a)	(TL,TR,BL,BR)

Make a block-partition of a matrix using a given element as reference. The element will stay in the bottom-right corner of the top-left corner matrix.

                 (             )   (      |      )
                 (             )   ( ...  | ...  )
                 (    x        )   (    x |      )
 splitBlocks i j (             ) = (-------------) , where x = a_{i,j}
                 (             )   (      |      )
                 (             )   ( ...  | ...  )
                 (             )   (      |      )

Note that some blocks can end up empty. We use the following notation for these blocks:

 ( TL | TR )
 (---------)
 ( BL | BR )

Where T = Top, B = Bottom, L = Left, R = Right.

Implementation is done via slicing of vectors.

Joining blocks

(<|>) :: Matrix a -> Matrix a -> Matrix aSource

Horizontally join two matrices. Visually:

 ( A ) <|> ( B ) = ( A | B )

Where both matrices A and B have the same number of rows.

(<->) :: Matrix a -> Matrix a -> Matrix aSource

Vertically join two matrices. Visually:

                   ( A )
 ( A ) <-> ( B ) = ( - )
                   ( B )

Where both matrices A and B have the same number of columns.

joinBlocks :: (Matrix a, Matrix a, Matrix a, Matrix a) -> Matrix aSource

Join blocks of the form detailed in splitBlocks.