An algebraic matrix type. More...

#include <matrix.hpp>

Public Types
using	scalar_type = T
	The type of the matrix elements.

using	mat_type = Matrix<scalar_type, mat_rows, mat_cols>
	The type of the matrix itself.

template<unsigned rows, unsigned cols>
using	generic_mat_type = Matrix<scalar_type, rows, cols>
	The type of the matrix, but without pre-defined dimensions.

Public Member Functions
constexpr	Matrix () noexcept=default
	Initializes an empty matrix.

constexpr	Matrix (T val) noexcept
	Initializes a matrix where all elements take the value provided by val .

constexpr	Matrix (array_type &&array) noexcept
	Initializes a matrix with an array of values.

constexpr	Matrix (std::initializer_list< scalar_type > elements) noexcept
	Initializes the matrix with a set of values.

template<unsigned rows, unsigned cols>
constexpr	Matrix (const Matrix< scalar_type, rows, cols > &_other)
	Initializes a copy from another matrix, that might have different dimensions.

constexpr	Matrix (Matrix &&_other) noexcept=default
	Initializes a matrix by taking over another matrix.

constexpr	Matrix (const Matrix &_other)=default
	Initializes a matrix with the values provided by another matrix.

constexpr Matrix &	operator= (Matrix &&_other) noexcept=default
	Moves the elements of the other matrix to the current matrix.

constexpr Matrix &	operator= (const Matrix &_other)=default
	Copies the elements of another matrix into the current matrix.

constexpr	~Matrix () noexcept=default
	Destroys the matrix instance.

constexpr const scalar_type *	elements () const noexcept
	Returns a pointer to the raw data of the matrix.

constexpr scalar_type *	elements () noexcept
	Returns a pointer to the raw data of the matrix.

consteval size_t	size () const noexcept
	Returns the number of elements of the matrix.

constexpr auto	begin () noexcept
	Returns an iterator for that addresses the begin of the matrix elements.

constexpr auto	end () noexcept
	Returns an iterator for that addresses the end of the matrix elements.

constexpr auto	cbegin () const noexcept
	Returns a constant iterator for that addresses the begin of the matrix elements.

constexpr auto	cend () const noexcept
	Returns a constant iterator for that addresses the end of the matrix elements.

constexpr scalar_type	at (size_t row, size_t col) const noexcept
	Returns the element at a specified position.

constexpr scalar_type &	at (size_t row, size_t col) noexcept
	Returns the element at a specified position.

constexpr std::span< const scalar_type >	row (size_t row) const noexcept
	Returns a view over a row of the matrix.

constexpr std::span< scalar_type >	row (size_t row) noexcept
	Returns a view over a row of the matrix.

constexpr std::array< scalar_type, mat_cols >	column (size_t col) const noexcept
	Returns a copy of a column over the matrix.

constexpr scalar_type	operator[] (std::pair< size_t, size_t > position) const noexcept
	Returns an element of the matrix.

constexpr scalar_type &	operator[] (std::pair< size_t, size_t > position) noexcept
	Returns an element of the matrix.

constexpr	operator std::array< T, mat_rows *mat_cols > () const noexcept
	Converts the matrix to an instance of `std::array`.

constexpr	operator std::vector< T > () const noexcept
	Converts the matrix into an instance of type `std::vector`.

constexpr	operator std::span< const scalar_type > () const noexcept
	Converts the matrix into a linear view over the elements.

constexpr	operator std::span< scalar_type > () noexcept
	Converts the matrix into a linear view over the elements.

constexpr generic_mat_type< mat_cols, mat_rows >	transpose () const noexcept
	Returns a copy of the matrix where the elements are transposed.

consteval bool	symmetric () const noexcept
	Returns whether or not the matrix is symmetric, that is the number of rows and columns are equal.

Static Public Member Functions
static constexpr mat_type	identity () noexcept
	Returns an identity matrix.

Static Public Attributes
static constexpr size_t	mat_rows = ROWS
	Stores the number of rows of the matrix.

static constexpr size_t	mat_cols = COLS
	Stores the number of columns of the matrix.

Protected Types
using	array_type = std::array<scalar_type, mat_rows * mat_cols>

Protected Attributes
array_type	m_elements = { }

Detailed Description

template<typename T, unsigned ROWS, unsigned COLS>
requires (ROWS >= 2 && COLS >= 2) && std::is_standard_layout_v<T> && std::is_trivially_copyable_v<T>
struct LiteFX::Math::Matrix< T, ROWS, COLS >

An algebraic matrix type.

Note that matrices in the engine are row-major by convention.

Matrices act as optimized storage containers only. All algebraic operations are not part of the library itself, but rather covered by supported linear algebra libraries.

Template Parameters

T	The type of the matrix scalar elements. Must be in standard layout (i.e., `std::is_standard_layout_v<T>` must evaluate to `true`).
ROWS	The number of rows of the matrix. Must be greater than 1.
COLS	The number of columns of the matrix. Must be greater than 1.

Member Typedef Documentation

◆ array_type

template<typename T , unsigned ROWS, unsigned COLS>

using LiteFX::Math::Matrix< T, ROWS, COLS >::array_type = std::array<scalar_type, mat_rows * mat_cols>

protected

◆ generic_mat_type

template<typename T , unsigned ROWS, unsigned COLS>

template<unsigned rows, unsigned cols>

using LiteFX::Math::Matrix< T, ROWS, COLS >::generic_mat_type = Matrix<scalar_type, rows, cols>

The type of the matrix, but without pre-defined dimensions.

Template Parameters

rows	The number of rows of the matrix.
cols	The number of columns of the matrix.

◆ mat_type

template<typename T , unsigned ROWS, unsigned COLS>

using LiteFX::Math::Matrix< T, ROWS, COLS >::mat_type = Matrix<scalar_type, mat_rows, mat_cols>

The type of the matrix itself.

◆ scalar_type

template<typename T , unsigned ROWS, unsigned COLS>

using LiteFX::Math::Matrix< T, ROWS, COLS >::scalar_type = T

The type of the matrix elements.

Constructor & Destructor Documentation

◆ Matrix() [1/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( )

constexprdefaultnoexcept

Initializes an empty matrix.

◆ Matrix() [2/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( T val )

inlineconstexprnoexcept

Initializes a matrix where all elements take the value provided by val .

Parameters

val	The value to initialize all elements of the matrix with.

◆ Matrix() [3/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( array_type && array )

inlineconstexprnoexcept

Initializes a matrix with an array of values.

Parameters

array The array of values to take over by the matrix.

◆ Matrix() [4/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( std::initializer_list< scalar_type > elements )

inlineconstexprnoexcept

Initializes the matrix with a set of values.

Parameters

elements The values to initialize the matrix with.

◆ Matrix() [5/7]

template<typename T , unsigned ROWS, unsigned COLS>

template<unsigned rows, unsigned cols>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( const Matrix< scalar_type, rows, cols > & _other )

inlineconstexpr

Initializes a copy from another matrix, that might have different dimensions.

Template Parameters

rows	The rows of the other matrix.
cols	The columns of the other matrix.

Parameters

_other The other matrix.

◆ Matrix() [6/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( Matrix< T, ROWS, COLS > && _other )

constexprdefaultnoexcept

Initializes a matrix by taking over another matrix.

Parameters

_other The matrix to take over.

◆ Matrix() [7/7]

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::Matrix ( const Matrix< T, ROWS, COLS > & _other )

constexprdefault

Initializes a matrix with the values provided by another matrix.

Parameters

_other The other matrix to copy the values from.

◆ ~Matrix()

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::~Matrix ( )

constexprdefaultnoexcept

Destroys the matrix instance.

Member Function Documentation

◆ at() [1/2]

template<typename T , unsigned ROWS, unsigned COLS>

scalar_type LiteFX::Math::Matrix< T, ROWS, COLS >::at	(	size_t	row,
		size_t	col ) const

inlineconstexprnoexcept

Returns the element at a specified position.

Parameters

row	The row of the element.
col	The column of the element.

Returns: The scalar value at the provided row and column.

◆ at() [2/2]

template<typename T , unsigned ROWS, unsigned COLS>

scalar_type & LiteFX::Math::Matrix< T, ROWS, COLS >::at	(	size_t	row,
		size_t	col )

inlineconstexprnoexcept

Returns the element at a specified position.

Parameters

row	The row of the element.
col	The column of the element.

Returns: A reference of the scalar value at the provided row and column.

◆ begin()

template<typename T , unsigned ROWS, unsigned COLS>

auto LiteFX::Math::Matrix< T, ROWS, COLS >::begin ( )

inlineconstexprnoexcept

Returns an iterator for that addresses the begin of the matrix elements.

Returns: An iterator for that addresses the begin of the matrix elements.

◆ cbegin()

template<typename T , unsigned ROWS, unsigned COLS>

auto LiteFX::Math::Matrix< T, ROWS, COLS >::cbegin ( ) const

inlineconstexprnoexcept

Returns a constant iterator for that addresses the begin of the matrix elements.

Returns: A constant iterator for that addresses the begin of the matrix elements.

◆ cend()

template<typename T , unsigned ROWS, unsigned COLS>

auto LiteFX::Math::Matrix< T, ROWS, COLS >::cend ( ) const

inlineconstexprnoexcept

Returns a constant iterator for that addresses the end of the matrix elements.

Returns: A constant iterator for that addresses the end of the matrix elements.

◆ column()

template<typename T , unsigned ROWS, unsigned COLS>

std::array< scalar_type, mat_cols > LiteFX::Math::Matrix< T, ROWS, COLS >::column ( size_t col ) const

inlineconstexprnoexcept

Returns a copy of a column over the matrix.

Note that this call involves a copy, which may be inefficient if done frequently. Prefer converting the matrix into an std::mdspan instead, if supported.

Parameters

col	The index of the column of the matrix.

Returns: An array containing a copy of the specified column.

◆ elements() [1/2]

template<typename T , unsigned ROWS, unsigned COLS>

const scalar_type * LiteFX::Math::Matrix< T, ROWS, COLS >::elements ( ) const

inlineconstexprnoexcept

Returns a pointer to the raw data of the matrix.

Returns: A pointer to the raw data of the matrix.

◆ elements() [2/2]

template<typename T , unsigned ROWS, unsigned COLS>

scalar_type * LiteFX::Math::Matrix< T, ROWS, COLS >::elements ( )

inlineconstexprnoexcept

Returns a pointer to the raw data of the matrix.

Returns: A pointer to the raw data of the matrix.

◆ end()

template<typename T , unsigned ROWS, unsigned COLS>

auto LiteFX::Math::Matrix< T, ROWS, COLS >::end ( )

inlineconstexprnoexcept

Returns an iterator for that addresses the end of the matrix elements.

Returns: An iterator for that addresses the end of the matrix elements.

◆ identity()

template<typename T , unsigned ROWS, unsigned COLS>

static constexpr mat_type LiteFX::Math::Matrix< T, ROWS, COLS >::identity ( )

inlinestaticconstexprnoexcept

Returns an identity matrix.

Returns: An identity matrix instance.

◆ operator std::array< T, mat_rows *mat_cols >()

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::operator std::array< T, mat_rows *mat_cols > ( ) const

inlineconstexprnoexcept

Converts the matrix to an instance of std::array.

◆ operator std::span< const scalar_type >()

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::operator std::span< const scalar_type > ( ) const

inlineconstexprnoexcept

Converts the matrix into a linear view over the elements.

◆ operator std::span< scalar_type >()

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::operator std::span< scalar_type > ( )

inlineconstexprnoexcept

Converts the matrix into a linear view over the elements.

◆ operator std::vector< T >()

template<typename T , unsigned ROWS, unsigned COLS>

LiteFX::Math::Matrix< T, ROWS, COLS >::operator std::vector< T > ( ) const

inlineconstexprnoexcept

Converts the matrix into an instance of type std::vector.

◆ operator=() [1/2]

template<typename T , unsigned ROWS, unsigned COLS>

Matrix & LiteFX::Math::Matrix< T, ROWS, COLS >::operator= ( const Matrix< T, ROWS, COLS > & _other )

constexprdefault

Copies the elements of another matrix into the current matrix.

Parameters

_other The matrix to copy the elements from.

Returns: A reference to the current matrix instance.

◆ operator=() [2/2]

template<typename T , unsigned ROWS, unsigned COLS>

Matrix & LiteFX::Math::Matrix< T, ROWS, COLS >::operator= ( Matrix< T, ROWS, COLS > && _other )

constexprdefaultnoexcept

Moves the elements of the other matrix to the current matrix.

Parameters

_other The matrix to take over.

Returns: A reference to the current matrix instance.

◆ operator[]() [1/2]

template<typename T , unsigned ROWS, unsigned COLS>

scalar_type LiteFX::Math::Matrix< T, ROWS, COLS >::operator[] ( std::pair< size_t, size_t > position ) const

inlineconstexprnoexcept

Returns an element of the matrix.

Parameters

position The row and column position of the matrix element.

Returns: The scalar value at the provided position.

◆ operator[]() [2/2]

template<typename T , unsigned ROWS, unsigned COLS>

scalar_type & LiteFX::Math::Matrix< T, ROWS, COLS >::operator[] ( std::pair< size_t, size_t > position )

inlineconstexprnoexcept

Returns an element of the matrix.

Parameters

position The row and column position of the matrix element.

Returns: A reference of the scalar value at the provided position.

◆ row() [1/2]

template<typename T , unsigned ROWS, unsigned COLS>

std::span< const scalar_type > LiteFX::Math::Matrix< T, ROWS, COLS >::row ( size_t row ) const

inlineconstexprnoexcept

Returns a view over a row of the matrix.

Parameters

row	The index of the row to view.

Returns: A view over the specified matrix row.

◆ row() [2/2]

template<typename T , unsigned ROWS, unsigned COLS>

std::span< scalar_type > LiteFX::Math::Matrix< T, ROWS, COLS >::row ( size_t row )

inlineconstexprnoexcept

Returns a view over a row of the matrix.

Parameters

row	The index of the row to view.

Returns: A view over the specified matrix row.

◆ size()

template<typename T , unsigned ROWS, unsigned COLS>

size_t LiteFX::Math::Matrix< T, ROWS, COLS >::size ( ) const

inlineconstevalnoexcept

Returns the number of elements of the matrix.

Returns: The number of elements of the matrix.

◆ symmetric()

template<typename T , unsigned ROWS, unsigned COLS>

bool LiteFX::Math::Matrix< T, ROWS, COLS >::symmetric ( ) const

inlineconstevalnoexcept

Returns whether or not the matrix is symmetric, that is the number of rows and columns are equal.

Returns: true, if the matrix is symmetric and false otherwise.

◆ transpose()

template<typename T , unsigned ROWS, unsigned COLS>

generic_mat_type< mat_cols, mat_rows > LiteFX::Math::Matrix< T, ROWS, COLS >::transpose ( ) const

inlineconstexprnoexcept

Returns a copy of the matrix where the elements are transposed.

You can use this operations, if you want to iterate all columns of the matrix in a more efficient way. Transposing effectively turns a row-major matrix into a column-major one.

Returns: A copy of the matrix where the elements are transposed.

Member Data Documentation

◆ m_elements

template<typename T , unsigned ROWS, unsigned COLS>

array_type LiteFX::Math::Matrix< T, ROWS, COLS >::m_elements = { }

protected

◆ mat_cols

template<typename T , unsigned ROWS, unsigned COLS>

size_t LiteFX::Math::Matrix< T, ROWS, COLS >::mat_cols = COLS

staticconstexpr

Stores the number of columns of the matrix.

◆ mat_rows

template<typename T , unsigned ROWS, unsigned COLS>

size_t LiteFX::Math::Matrix< T, ROWS, COLS >::mat_rows = ROWS

staticconstexpr

Stores the number of rows of the matrix.

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Types

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ array_type

◆ generic_mat_type

◆ mat_type

◆ scalar_type

Constructor & Destructor Documentation

◆ Matrix() [1/7]

◆ Matrix() [2/7]

◆ Matrix() [3/7]

◆ Matrix() [4/7]

◆ Matrix() [5/7]

◆ Matrix() [6/7]

◆ Matrix() [7/7]

◆ ~Matrix()

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ begin()

◆ cbegin()

◆ cend()

◆ column()

◆ elements() [1/2]

◆ elements() [2/2]

◆ end()

◆ identity()

◆ operator std::array< T, mat_rows *mat_cols >()

◆ operator std::span< const scalar_type >()

◆ operator std::span< scalar_type >()

◆ operator std::vector< T >()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ row() [1/2]

◆ row() [2/2]

◆ size()

◆ symmetric()

◆ transpose()

Member Data Documentation

◆ m_elements

◆ mat_cols

◆ mat_rows