FPNLA.Matrix

This module defines classes used to handle Matrices and Vectors in a generic way.

Vector

class Vector v e where

This class represents a vector structure For any vector data structure used in this framework it must have an instance of this class. A minimal instance of this class must provide an implementation for generate_v, elem_v and length_v. The index of the first element stored in the vector must be 0. This is a multi-param type class because usually libraries of Matrix and Vector imposes restrictions over the type of the elements (for example, to have a Storable instance).

Methods

generate_v

Arguments

:: Int

The length of the vector

-> (Int -> e)

A function that returns the value for each index

-> v e

Creates a new vector from the length of the vector and a function that returns the value for each index.

fromList_v

Arguments

:: [e]

A list that contains the elements of the vector. The first element of the list will be the first element of the vector and so on.

-> v e

Creates a new vector from a list, th vector will contain all (and only) the elements of the list, and in the same order.

concat_v

Arguments

:: [v e]

A list containing the vectors to be joined. If the list is [1, 2,3, 4,5,6] then the vector will be 1,2,3,4,5,6.

-> v e

Join multiple vectors in one single vector.

elem_v :: Int -> v e -> e

Returns the element from a given index. The index must be between 0 and the length of the vector.

length_v :: v e -> Int

Returns the length of the vector.

foldr_v :: (e -> b -> b) -> b -> v e -> b

The common foldr function but specific for this instance.

map_v :: (e -> e) -> v e -> v e

The common map function but specific for this instance.

zipWith_v :: (e -> e -> e) -> v e -> v e -> v e

The common zipWith function but specific for this instance.

Matrix

class Matrix m e where

This class represents any Matrix structure For any matrix data structure used in this framework it must have an instance of this class. A minimal instance of this class must provide an implementation for generate_m, dim_m and elem_m. The index of the first element stored in the vector must be (0,0). This is a multi-param type class because usually libraries of Matrix and Vector imposes restrictions over the type of the elements (for example, to have an Storable instance).

Methods

generate_m

Arguments

:: Int

The length of the rows

-> Int

A function that returns the value for each index

-> (Int -> Int -> e)

-> m e

Creates a new matrix from the dimension (length of rows and columns) of the matrix and a function that returns the value for each index.

fromList_m :: Int -> Int -> [e] -> m e

Creates a new matrix from the dimension (length of rows and columns) of and a list.

transpose_m :: m e -> m e

Given a matrix, creates a new matrix that will be the transpose of the original.

dim_m :: m e -> (Int, Int)

Returns the dimension of a given matrix. The first element in the pair is the number of rows and the second the number of columns.

elem_m

Arguments

:: Int

The row component of the position (i).

-> Int

The column component of the position (j).

-> m e

The matrix.

-> e

Returns the element that is in the position (i,j).

map_m :: (e -> e) -> m e -> m e

The common map function but specific for this instance.

zipWith_m :: (e -> e -> e) -> m e -> m e -> m e

The common zipWith function but specific for this instance.

subMatrix_m

Arguments

:: Int

i

-> Int

j

-> Int

r

-> Int

c

-> m e

m

-> m e

Given an initial position (i,j), a dimension (r,c) and a matrix m, creates a new matrix that is a sub matrix of m containing the elements in positions [(p1, p2) | p1 <- [i..i+r], p2 <- [j..j+c]] For example, if m is: 1 2 3 4 5 6 7 8 9 and (i,j) and (r,c) are (0,1) and (2,3) respectively, then the result will be a new matrix containing: 2 3 5 6 8 9

fromBlocks_m :: [[m e]] -> m e

Constructs a new matrix from a list of list where the elements are sub-matrices. This operations is the analogue of concat_v operation from the Vector class. The 'borders' of the sub-matrices will be joined. The dimensions of the sum-matrices must be compatibles.

toBlocks_m

Arguments

:: Int

r

-> Int

c

-> m e

m

-> [[m e]]

Split a matrix m in blocks of size (r,c) (the dimension of the blocks in the right and the bottom may be smaller).

MatrixVectror

class (Vector v e, Matrix m e) => MatrixVector m v e where

This class allows us to leave separated the two concepts of Vector and Matrix. This class establishes a link between a vector and a matrix structure. We provide a default instance for any Vector and Matrix instances so any vector could be used with any matrix whenever the type of the elements are the same.

Methods

row_vm :: Int -> m e -> v e

Extracts the i-th row of the matrix m and converts it in the vector structure.

col_vm :: Int -> m e -> v e

Extracts the j-th column of the matrix m and converts it in the vector structure.

fromCols_vm :: [v e] -> m e

Joins a list of column vectors in a matrix structure. The length of every vector in the list must be the same.

toCols_vm :: m e -> [v e]

Returns a list containing every column of the matrix converted in the vector structure.

Instances

(Vector v e, Matrix m e) => MatrixVector m v e

Miscellaneous

cantRows_m :: Matrix m e => m e -> Int

Returns the number of rows of the matrix.

cantCols_m :: Matrix m e => m e -> Int

Returns the number of columns of the matrix.

size_m :: Matrix m e => m e -> Int

Returns the size of the matrix (number of rows x number of columns).

asColumn_vm :: MatrixVector m v e => v e -> m e

Converts a vector in a matrix of one column.

diagonalBlock

Arguments

:: Matrix m e

=> (Int, Int)

(r,c)

-> Int

i

-> m e

m

-> m e

Splits a matrix m into blocks of size (r,c) and returns the block on the position (i,i).

verticalBlock

Arguments

:: Matrix m e

=> Int

s

-> Int

i

-> m e

m

-> m e

Splits a matrix m into blocks of size (s, cantCols_m m) and returns the block on the position i.