A matrix which, by multiplication, permutes the rows or columns of another matrix. More...

#include <geomc/linalg/mtxtypes/PermutationMatrix.h>

Inheritance diagram for PermutationMatrix< N >:

Public Types
typedef MtxColIterator< const PermutationMatrix< N >, const elem_t >	const_col_iterator
	Read-only iterator over the elements of a column.

typedef MtxSubsetIterator< const PermutationMatrix< N >, const elem_t >	const_iterator
	Read-only row-major iterator over matrix elements.

typedef const_iterator	const_region_iterator
	Read-only row-major iterator over the matrix elements in a rectangular region.

typedef MtxRowIterator< const PermutationMatrix< N >, const elem_t >	const_row_iterator
	Read-only iterator over the elments of a row.

typedef bool	elem_t
	Element type.

typedef PermutationMatrix< N >	recurring_t

typedef Storage< storage_token_t, _ImplStorageObjCount< PermutationMatrix< N > >::count >	storagebuffer_t

Public Member Functions
	PermutationMatrix ()

	PermutationMatrix (index_t n)

const_iterator	begin () const

const_col_iterator	col (index_t i) const

index_t	cols () const

const_iterator	end () const

storagebuffer_t	get_storage_token_buffer () const

void	get_storage_tokens (storage_token_t *buf) const

const index_t *	getColDestinations () const

const index_t *	getColSources () const

const index_t *	getRowDestinations () const

const index_t *	getRowSources () const

bool	operator() (index_t row, index_t col) const

derived_const_row_iterator	operator[] (index_t i) const

const_region_iterator	region_begin (const MatrixRegion &r) const

const_region_iterator	region_end (const MatrixRegion &r) const

const_row_iterator	row (index_t i) const

index_t	rows () const

void	set_identity ()

void	setColDestinations (const index_t *p)

void	setColSources (const index_t *p)

void	setRowDestinations (const index_t *p)

void	setRowSources (const index_t *p)

index_t	sign ()

constexpr index_t	storage_token_count () const

void	swap_cols (index_t a, index_t b)

void	swap_rows (index_t a, index_t b)

void	transpose ()

Static Public Attributes
static constexpr index_t	COLDIM
	Column dimension template parameter.

static constexpr index_t	ROWDIM
	Row dimension template parameter.

Protected Member Functions
index_t	_cols () const

index_t	_rows () const

index_t *	getDstData ()

const index_t *	getDstData () const

index_t *	getSrcData ()

const index_t *	getSrcData () const

void	swapPointers ()

Friends
template<typename Md, typename Ma, typename Mb>
class	detail::_ImplMtxMul

bool	detail::mtxequal (const PermutationMatrix< N > &a, const PermutationMatrix< N > &b)

Detailed Description

template<index_t N>
class geom::PermutationMatrix< N >

A matrix which, by multiplication, permutes the rows or columns of another matrix.

A permutation matrix P permutes rows if left-multiplied (P * M), and permutes columns if right-multiplied (M * P).

Permutation matrices are always (n x n) and have only elements that are zero or 1. Each row and column has exactly one 1 element.

An (n x n) permutation matrix uses O(n) storage, and multiplications by other matrices are optimized to perform the permutation directly in _O(n²)_ (rather than _O(n³)_) time. Multiplication of two permutation matrices is O(n).

Constructor & Destructor Documentation

◆ PermutationMatrix() [1/2]

template<index_t N>

PermutationMatrix ( )

inline

Construct a new identity permutation matrix.

◆ PermutationMatrix() [2/2]

template<index_t N>

PermutationMatrix ( index_t n )

inlineexplicit

Construct a new identity permutation matrix of size n. (Dynamic only).

Member Function Documentation

◆ begin()

const_iterator begin ( ) const

inlineinherited

Returns: A read-only random-access row major-ordered iterator over the elements of this matrix, pointing to the element at (0,0).

◆ col()

const_col_iterator col ( index_t i ) const

inlineinherited

Parameters

i	Index of column (zero-indexed)

Returns: A const iterator over the elements of column i

◆ cols()

template<index_t N>

index_t cols ( ) const

inline

Returns: Number of columns in the matrix. Always equal to the number of rows.

◆ end()

const_iterator end ( ) const

inlineinherited

Returns: A read-only random-access row major-ordered iterator over the elements of this matrix, pointing to the element just beyond the last element in the lower right corner.

◆ getColDestinations()

template<index_t N>

const index_t * getColDestinations ( ) const

inline

Array containing a mapping of source columns to destination columns in a column-permuting operation.

In other words, given the column-permuting multiplication:

M * P = D

return an array a such that column D_a[i]= M_i.

Because of the property that a permutation matrix's inverse is its transpose, this function is equivalent to getRowSources().

◆ getColSources()

template<index_t N>

const index_t * getColSources ( ) const

inline

Array containing a mapping of destination columns to source columns in a column-permuting operation.

In other words, given the column-permuting multiplicaton:

M * P = D

return an array a such that column D_i= M_a[i].

◆ getRowDestinations()

template<index_t N>

const index_t * getRowDestinations ( ) const

inline

Array containing a mapping of source rows to destination rows in a row-permuting operation.

In other words, given the row-permuting multiplication:

P * M = D

return an array a such that row D_a[i]= M_i.

Because of the property that a permutation matrix's inverse is its transpose, this function is equivalent to getColSources().

◆ getRowSources()

template<index_t N>

const index_t * getRowSources ( ) const

inline

Array containing a mapping of destination rows to source rows in a row-permuting operation.

In other words, given the row-permuting multiplicaton:

P * M = D

return an array a such that row D_i= M_a[i].

◆ operator()()

template<index_t N>

bool operator()	(	index_t	row,
		index_t	col ) const

inline

Get the element at (row, col).

Parameters

row	Zero-indexed row coordinate
col	Zero-indexed column coordinate

Returns: The element at (row, col); either 0 or 1.

◆ operator[]()

derived_const_row_iterator operator[] ( index_t i ) const

inlineinherited

Parameters

i	Index of row (zero-indexed)

Returns: A const iterator over the elements of row i

◆ region_begin()

const_region_iterator region_begin ( const MatrixRegion & r ) const

inlineinherited

Parameters

r	The zero-indexed region to iterate over. The upper extreme coordinates represent the index just beyond the last element to be iterated over.

Returns: A read-only, random-access, row-major iterator over the elements in region r, pointing at the first element in the region (upper left corner).

◆ region_end()

const_region_iterator region_end ( const MatrixRegion & r ) const

inlineinherited

Parameters

r	The zero-indexed region to iterate over. The upper extreme coordinates represent the index just beyond the last element to be iterated over.

Returns: A read-only, random-access, row-major iterator over the elements in region r, pointing at the element just beyond the last element in the region.

◆ row()

const_row_iterator row ( index_t i ) const

inlineinherited

Parameters

i	Index of row (zero-indexed)

Returns: A const iterator over the elements of row i

◆ rows()

template<index_t N>

index_t rows ( ) const

inline

Returns: Number of rows in the matrix. Always equal to the number of columns.

◆ set_identity()

template<index_t N>

void set_identity ( )

inline

Reset this matrix to the identity permutation.

◆ setColDestinations()

template<index_t N>

void setColDestinations ( const index_t * p )

inline

Set the permutation described by this matrix by passing an array mapping source columns to destination columns in a column-permuting operation.

In other words, define the column-permuting multiplication:

M * P = D

with an array a such that column D_a[i]= M_i.

Because of the property that a permutation matrix's inverse is its transpose, this function is equivalent to setRowSources().

Parameters

p	Array of indecies.

◆ setColSources()

template<index_t N>

void setColSources ( const index_t * p )

inline

Set the permutation described by this matrix by passing a mapping of destination columns to source columns in a column-permuting operation.

In other words, define the column-permuting multiplicaton:

M * P = D

with an array a such that column D_i= M_a[i].

Parameters

p	Array of indecies.

◆ setRowDestinations()

template<index_t N>

void setRowDestinations ( const index_t * p )

inline

Set the permutation described by this matrix by passing an array mapping source rows to destination rows in a row-permuting operation.

In other words, define the row-permuting multiplication:

P * M = D

with an array a such that row D_a[i]= M_i.

Because of the property that a permutation matrix's inverse is its transpose, this function is equivalent to setColSources().

Parameters

p	Array of indecies.

◆ setRowSources()

template<index_t N>

void setRowSources ( const index_t * p )

inline

Set the permutation described by this matrix by passing a mapping of destination rows to source rows in a row-permuting operation.

In other words, define the row-permuting multiplicaton:

P * M = D

with an array a such that row D_i= M_a[i].

Parameters

p	Array of indecies.

◆ sign()

template<index_t N>

index_t sign ( )

inline

Compute the signature of this permutation.

Runs in O(n) time; or O(1) time if previously computed.

Returns: -1 if the number of transpositions in this permutation is odd, 1 otherwise.

◆ swap_cols()

template<index_t N>

void swap_cols	(	index_t	a,
		index_t	b )

inline

Adjust this matrix such that columns a and b are swapped in the destination matrix after applying a column permutation. This operation is cumulative on any previous swaps.

Parameters

a	A column index.
b	A column index.

◆ swap_rows()

template<index_t N>

void swap_rows	(	index_t	a,
		index_t	b )

inline

Adjust this matrix such that rows a and b are swapped in the destination matrix after applying a row permutation. This operation is cumulative on any previous swaps.

Parameters

a	A row index.
b	A row index.

◆ transpose()

template<index_t N>

void transpose ( )

inline

Transpose this matrix in-place in O(1) time. For this type of matrix, also the inverse matrix.

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

geomc/linalg/LinalgTypes.h
geomc/linalg/mtxtypes/PermutationMatrix.h

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PermutationMatrix() [1/2]

◆ PermutationMatrix() [2/2]

Member Function Documentation

◆ begin()

◆ col()

◆ cols()

◆ end()

◆ getColDestinations()

◆ getColSources()

◆ getRowDestinations()

◆ getRowSources()

◆ operator()()

◆ operator[]()

◆ region_begin()

◆ region_end()

◆ row()

◆ rows()

◆ set_identity()

◆ setColDestinations()

◆ setColSources()

◆ setRowDestinations()

◆ setRowSources()

◆ sign()

◆ swap_cols()

◆ swap_rows()

◆ transpose()