#include <linalg/PermutationMatrix.hpp>

Detailed Description

Class that represents matrices that permute the rows or columns of other matrices.

Stored in an efficient manner with O(n) memory requirements.

Definition at line 11 of file PermutationMatrix.hpp.

Collaboration diagram for PermutationMatrix:

Conversion to a full matrix or a permutation
using	Permutation = storage_t
	Type that represents a permutation (in the mathematical sense, a permutation of the integers 0 through n-1). More...

SquareMatrix	to_matrix (Type type=Unspecified) const
	Convert a permutation matrix into a full matrix. More...

Permutation	to_permutation () const
	Convert a permutation matrix into a mathematical permutation. More...

Constructors and assignment
	PermutationMatrix ()=default
	Default constructor. More...

	PermutationMatrix (Type type)
	Create an empty permutation matrix with the given type. More...

	PermutationMatrix (size_t rows, Type type=Unspecified)
	Create a permutation matrix without permutations. More...

	PermutationMatrix (std::initializer_list< size_t > init, Type type=Unspecified)
	Create a permutation matrix with the given permutation. More...

PermutationMatrix &	operator= (std::initializer_list< size_t > init)
	Assign the given permutation to the matrix. More...

	PermutationMatrix (const PermutationMatrix &)=default
	Default copy constructor. More...

	PermutationMatrix (PermutationMatrix &&)
	Move constructor. More...

PermutationMatrix &	operator= (const PermutationMatrix &)=default
	Default copy assignment. More...

PermutationMatrix &	operator= (PermutationMatrix &&)
	Move assignment. More...

Matrix size
size_t	size () const
	Get the size of the permutation matrix. More...

size_t	rows () const
	Get the number of rows of the permutation matrix. More...

size_t	cols () const
	Get the number of columns of the permutation matrix. More...

size_t	num_elems () const
	Get the number of elements in the matrix: More...

void	resize (size_t size)
	Resize the permutation matrix. More...

Element access
size_t &	operator() (size_t index)
	Get the element at the given position in the swap sequence. More...

const size_t &	operator() (size_t index) const
	Get the element at the given position in the swap sequence. More...

Transposition
void	reverse ()
	Reverse the order of the permutations. More...

void	transpose_inplace ()
	Transpose or invert the permutation matrix. More...

bool	is_reversed () const
	Check if the permutation should be applied in reverse. More...

Type	get_type () const
	Get the type of permutation matrix (whether it permutes rows or columns, or unspecified). More...

void	set_type (Type type)
	Set the type of permutation matrix (whether it permutes rows or columns, or unspecified). More...

Applying the permutation to matrices
void	permute_columns (Matrix &A) const
	Apply the permutation to the columns of matrix A. More...

void	permute_rows (Matrix &A) const
	Apply the permutation to the rows of matrix A. More...

Memory management
void	clear_and_deallocate ()
	Set the size to zero, and deallocate the storage. More...

Filling matrices
void	fill_identity ()
	Fill the matrix as an identity permutation. More...

void	fill_from_permutation (Permutation permutation)
	Create a permutation matrix from the given permutation. More...

void	fill_random (std::default_random_engine::result_type seed=std::default_random_engine::default_seed)
	Fill the matrix with a random permutation. More...

Iterators
storage_t::iterator	begin ()
	Get the iterator to the first element of the swapping sequence. More...

storage_t::const_iterator	begin () const
	Get the iterator to the first element of the swapping sequence. More...

storage_t::const_iterator	cbegin () const
	Get the iterator to the first element of the swapping sequence. More...

storage_t::iterator	end ()
	Get the iterator to the element past the end of the swapping sequence. More...

storage_t::const_iterator	end () const
	Get the iterator to the element past the end of the swapping sequence. More...

storage_t::const_iterator	cend () const
	Get the iterator to the element past the end of the swapping sequence. More...

Printing
void	print (std::ostream &os, uint8_t precision=0, uint8_t width=0) const
	Print a permutation matrix. More...

Generating permutations
static Permutation	random_permutation (size_t length, std::default_random_engine::result_type seed=std::default_random_engine::default_seed)
	Return a random permutation of the integers 0 through length-1. More...

static Permutation	identity_permutation (size_t length)
	Return the identity permutation (0, 1, 2, 3, ..., length-1). More...

Create special matrices
static PermutationMatrix	identity (size_t rows, Type type=Unspecified)
	Create an identity permutation matrix. More...

static PermutationMatrix	from_permutation (Permutation permutation, Type type=Unspecified)
	Create a permutation matrix from the given permutation. More...

static PermutationMatrix	random (size_t rows, Type type=Unspecified, std::default_random_engine::result_type seed=std::default_random_engine::default_seed)
	Create a random permutation matrix. More...

Public Types
enum	Type { Unspecified = 0 , RowPermutation = 1 , ColumnPermutation = 2 }

Protected Attributes
storage_t	storage

bool	reverse_ = false

Type	type = Unspecified

Private Types
using	storage_t = util::storage_t< size_t >
	Container to store the elements of the permutation matrix internally. More...

Related Functions
(Note that these are not member functions.)
std::ostream &	operator<< (std::ostream &os, const PermutationMatrix &M)
	Print a permutation matrix. More...

Member Typedef Documentation

◆ storage_t

using storage_t = util::storage_t<size_t>

private

Container to store the elements of the permutation matrix internally.

Definition at line 14 of file PermutationMatrix.hpp.

◆ Permutation

using Permutation = storage_t

Type that represents a permutation (in the mathematical sense, a permutation of the integers 0 through n-1).

Definition at line 118 of file PermutationMatrix.hpp.

Member Enumeration Documentation

◆ Type

enum Type

Enumerator
Unspecified	Can be used for permuting rows or columns.
RowPermutation	Can be used for permuting rows only.
ColumnPermutation	Can be used for permuting columns only.

Definition at line 17 of file PermutationMatrix.hpp.

Constructor & Destructor Documentation

◆ PermutationMatrix() [1/6]

PermutationMatrix ( )

default

Default constructor.

◆ PermutationMatrix() [2/6]

PermutationMatrix ( Type type )

inline

Create an empty permutation matrix with the given type.

Definition at line 31 of file PermutationMatrix.hpp.

◆ PermutationMatrix() [3/6]

PermutationMatrix	(	size_t	rows,
		Type	type = `Unspecified`
	)

inline

Create a permutation matrix without permutations.

Definition at line 34 of file PermutationMatrix.hpp.

◆ PermutationMatrix() [4/6]

PermutationMatrix	(	std::initializer_list< size_t >	init,
		Type	type = `Unspecified`
	)

inline

Create a permutation matrix with the given permutation.

Definition at line 383 of file PermutationMatrix.hpp.

◆ PermutationMatrix() [5/6]

PermutationMatrix ( const PermutationMatrix & )

default

Default copy constructor.

◆ PermutationMatrix() [6/6]

PermutationMatrix ( PermutationMatrix && other )

inline

Move constructor.

Definition at line 368 of file PermutationMatrix.hpp.

Member Function Documentation

◆ operator=() [1/3]

PermutationMatrix & operator= ( std::initializer_list< size_t > init )

inline

Assign the given permutation to the matrix.

Definition at line 425 of file PermutationMatrix.hpp.

◆ operator=() [2/3]

PermutationMatrix& operator= ( const PermutationMatrix & )

default

Default copy assignment.

◆ operator=() [3/3]

PermutationMatrix & operator= ( PermutationMatrix && other )

inline

Move assignment.

Definition at line 373 of file PermutationMatrix.hpp.

◆ size()

size_t size ( ) const

inline

Get the size of the permutation matrix.

Definition at line 62 of file PermutationMatrix.hpp.

◆ rows()

size_t rows ( ) const

inline

Get the number of rows of the permutation matrix.

Definition at line 64 of file PermutationMatrix.hpp.

◆ cols()

size_t cols ( ) const

inline

Get the number of columns of the permutation matrix.

Definition at line 66 of file PermutationMatrix.hpp.

◆ num_elems()

size_t num_elems ( ) const

inline

Get the number of elements in the matrix:

Definition at line 68 of file PermutationMatrix.hpp.

◆ resize()

void resize ( size_t size )

inline

Resize the permutation matrix.

Definition at line 70 of file PermutationMatrix.hpp.

◆ operator()() [1/2]

size_t& operator() ( size_t index )

inline

Get the element at the given position in the swap sequence.

If the k-th element is i, that is P(k) == i, this means that the k-th step of the swapping algorithm will swap i and k.

Definition at line 81 of file PermutationMatrix.hpp.

◆ operator()() [2/2]

const size_t& operator() ( size_t index ) const

inline

Get the element at the given position in the swap sequence.

If the k-th element is i, that is P(k) == i, this means that the k-th step of the swapping algorithm will swap i and k.

Definition at line 83 of file PermutationMatrix.hpp.

◆ reverse()

void reverse ( )

inline

Reverse the order of the permutations.

Definition at line 92 of file PermutationMatrix.hpp.

◆ transpose_inplace()

void transpose_inplace ( )

inline

Transpose or invert the permutation matrix.

Definition at line 95 of file PermutationMatrix.hpp.

◆ is_reversed()

bool is_reversed ( ) const

inline

Check if the permutation should be applied in reverse.

Definition at line 98 of file PermutationMatrix.hpp.

◆ get_type()

Type get_type ( ) const

inline

Get the type of permutation matrix (whether it permutes rows or columns, or unspecified).

Definition at line 102 of file PermutationMatrix.hpp.

◆ set_type()

void set_type ( Type type )

inline

Set the type of permutation matrix (whether it permutes rows or columns, or unspecified).

Definition at line 105 of file PermutationMatrix.hpp.

◆ to_matrix()

SquareMatrix to_matrix ( Type type = Unspecified ) const

inline

Convert a permutation matrix into a full matrix.

Definition at line 389 of file PermutationMatrix.hpp.

◆ to_permutation()

PermutationMatrix::Permutation to_permutation ( ) const

inline

Convert a permutation matrix into a mathematical permutation.

Definition at line 407 of file PermutationMatrix.hpp.

◆ permute_columns()

void permute_columns ( Matrix & A ) const

inline

Apply the permutation to the columns of matrix A.

Definition at line 433 of file PermutationMatrix.hpp.

◆ permute_rows()

void permute_rows ( Matrix & A ) const

inline

Apply the permutation to the rows of matrix A.

Definition at line 450 of file PermutationMatrix.hpp.

◆ clear_and_deallocate()

void clear_and_deallocate ( )

inline

Set the size to zero, and deallocate the storage.

Definition at line 141 of file PermutationMatrix.hpp.

◆ random_permutation()

PermutationMatrix::Permutation random_permutation	(	size_t	length,
		std::default_random_engine::result_type	seed = `std::default_random_engine::default_seed`
	)

static

Return a random permutation of the integers 0 through length-1.

Definition at line 6 of file PermutationMatrix.cpp.

◆ identity_permutation()

PermutationMatrix::Permutation identity_permutation ( size_t length )

static

Return the identity permutation (0, 1, 2, 3, ..., length-1).

Definition at line 22 of file PermutationMatrix.cpp.

◆ fill_identity()

void fill_identity ( )

inline

Fill the matrix as an identity permutation.

Definition at line 168 of file PermutationMatrix.hpp.

◆ fill_from_permutation()

void fill_from_permutation ( Permutation permutation )

Create a permutation matrix from the given permutation.

Note: This isn't a very fast method, it's mainly used for tests. Internally, the permutation matrix is represented by a sequence of swap operations. Converting from this representation to a mathematical permutation is fast, but the other way around requires O(n²) operations (with the naive implementation used here, anyway).

Definition at line 28 of file PermutationMatrix.cpp.

◆ fill_random()

void fill_random ( std::default_random_engine::result_type seed = std::default_random_engine::default_seed )

inline

Fill the matrix with a random permutation.

Note: This isn't a very fast method, it's mainly used for tests.

Definition at line 181 of file PermutationMatrix.hpp.

◆ identity()

static PermutationMatrix identity	(	size_t	rows,
		Type	type = `Unspecified`
	)

inlinestatic

Create an identity permutation matrix.

Definition at line 193 of file PermutationMatrix.hpp.

◆ from_permutation()

static PermutationMatrix from_permutation	(	Permutation	permutation,
		Type	type = `Unspecified`
	)

inlinestatic

Create a permutation matrix from the given permutation.

Note: This isn't a very fast method, it's mainly used for tests. Internally, the permutation matrix is represented by a sequence of swap operations. Converting from this representation to a mathematical permutation is fast, but the other way around requires O(n²) operations (with the naive implementation used here, anyway).

Definition at line 199 of file PermutationMatrix.hpp.

◆ random()

static PermutationMatrix random	(	size_t	rows,
		Type	type = `Unspecified`,
		std::default_random_engine::result_type	seed = `std::default_random_engine::default_seed`
	)

inlinestatic

Create a random permutation matrix.

Note: This isn't a very fast method, it's mainly used for tests.

Definition at line 209 of file PermutationMatrix.hpp.

◆ begin() [1/2]

storage_t::iterator begin ( )

inline

Get the iterator to the first element of the swapping sequence.

Definition at line 224 of file PermutationMatrix.hpp.

◆ begin() [2/2]

storage_t::const_iterator begin ( ) const

inline

Get the iterator to the first element of the swapping sequence.

Definition at line 226 of file PermutationMatrix.hpp.

◆ cbegin()

storage_t::const_iterator cbegin ( ) const

inline

Get the iterator to the first element of the swapping sequence.

Definition at line 228 of file PermutationMatrix.hpp.

◆ end() [1/2]

storage_t::iterator end ( )

inline

Get the iterator to the element past the end of the swapping sequence.

Definition at line 231 of file PermutationMatrix.hpp.

◆ end() [2/2]

storage_t::const_iterator end ( ) const

inline

Get the iterator to the element past the end of the swapping sequence.

Definition at line 233 of file PermutationMatrix.hpp.

◆ cend()

storage_t::const_iterator cend ( ) const

inline

Get the iterator to the element past the end of the swapping sequence.

Definition at line 235 of file PermutationMatrix.hpp.

◆ print()

void print	(	std::ostream &	os,
		uint8_t	precision = `0`,
		uint8_t	width = `0`
	)		const

Print a permutation matrix.

Parameters

os	The stream to print to.
precision	The number of significant figures to print. (0 = auto)
width	The width of each element (number of characters). (0 = auto)

Definition at line 60 of file PermutationMatrix.cpp.

Friends And Related Function Documentation

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	os,
		const PermutationMatrix &	M
	)

Definition at line 73 of file PermutationMatrix.cpp.

Member Data Documentation

◆ storage

storage_t storage

protected

Definition at line 258 of file PermutationMatrix.hpp.

◆ reverse_

bool reverse_ = false

protected

Definition at line 259 of file PermutationMatrix.hpp.

◆ type

Type type = Unspecified

protected

Definition at line 260 of file PermutationMatrix.hpp.

The documentation for this class was generated from the following files:

Detailed Description

Conversion to a full matrix or a permutation

Constructors and assignment

Matrix size

Element access

Transposition

Applying the permutation to matrices

Memory management

Filling matrices

Iterators

Printing

Generating permutations

Create special matrices

Public Types

Protected Attributes

Private Types

Related Functions

Member Typedef Documentation

◆ storage_t

◆ Permutation

Member Enumeration Documentation

◆ Type

Constructor & Destructor Documentation

◆ PermutationMatrix() [1/6]

◆ PermutationMatrix() [2/6]

◆ PermutationMatrix() [3/6]

◆ PermutationMatrix() [4/6]

◆ PermutationMatrix() [5/6]

◆ PermutationMatrix() [6/6]

Member Function Documentation

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ size()

◆ rows()

◆ cols()

◆ num_elems()

◆ resize()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ reverse()

◆ transpose_inplace()

◆ is_reversed()

◆ get_type()

◆ set_type()

◆ to_matrix()

◆ to_permutation()

◆ permute_columns()

◆ permute_rows()

◆ clear_and_deallocate()

◆ random_permutation()

◆ identity_permutation()

◆ fill_identity()

◆ fill_from_permutation()

◆ fill_random()

◆ identity()

◆ from_permutation()

◆ random()

◆ begin() [1/2]

◆ begin() [2/2]

◆ cbegin()

◆ end() [1/2]

◆ end() [2/2]

◆ cend()

◆ print()

Friends And Related Function Documentation

◆ operator<<()

Member Data Documentation

◆ storage

◆ reverse_

◆ type