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template<typename T = double>
class LinAlg::Matrix< T >

Row-major dense matrix with arithmetic and linear algebra support.

Owns its data as a contiguous std::vector<T> stored in row-major order. Supports scalar types T = float, double, std::complex<float>, and std::complex<double>.

Provides:

Element access via operator[] (no bounds checking) and at()/operator() (bounds-checked).
Basic arithmetic: addition, subtraction, scalar multiply/divide, and matrix multiplication via BLAS.
Linear algebra via GSL: determinant(), inverse(), transpose().
Conversion utilities: conj(), real(), imag(), complex().
Non-owning views: row_view(), column_view(), matrix_view().
GSL interop: as_gsl_view().

Note: The scalar += and -= operators treat the scalar as a multiple of the identity: M += a adds a to all diagonal elements. Only valid for square matrices.

#include <Matrix.hpp>

Inheritance diagram for LinAlg::Matrix< T >:

Public Member Functions
	Matrix ()
	Default initialiser.

	Matrix (std::size_t rows, std::size_t cols)
	Initialise a blank matrix rows*cols, filled with 0.

	Matrix (std::size_t rows, std::size_t cols, const T &value)
	Initialise a matrix rows*cols, filled with 'value'.

	Matrix (std::size_t dimension)
	Initialise a blank square matrix dimension*dimension, filled with 0.

	Matrix (std::initializer_list< std::initializer_list< T > > ll)
	Initialise a matrix from initialiser list. {{},{},{}}. Each row must be same length.

	Matrix (std::size_t rows, std::size_t cols, std::initializer_list< T > l)
	Initialise a matrix from single initialiser list. {...}.

	Matrix (std::size_t rows, std::size_t cols, std::vector< T > &&v)
	Initialise a matrix from single initialiser list. {...}.

	Matrix (std::size_t rows, std::size_t cols, const std::vector< T > &v)
	Initialise a matrix from single initialiser list. {...}.

void	resize (std::size_t rows, std::size_t cols)
	Resizes matrix to new dimension; all values reset to default.

void	resize (std::size_t rows, std::size_t cols, const T &value)
	Resizes matrix to new dimension; all values reset to 'value'.

std::size_t	rows () const
	Return rows [major index size].

std::size_t	cols () const
	Return columns [minor index size].

std::size_t	size () const
	Return rows*columns [total array size].

bool	empty () const
	Bool - is empty? (same as size==0)

T *	data ()
	Pointer to first element; for std::complex<T> this is complex<T>, not T.

const T *	data () const
	Const pointer to first element; for std::complex<T> this is const complex<T>, not const T.

T *	operator[] (std::size_t i)
	[] index access (no range checking). [i] returns pointer to ith row, mutable

const T *	operator[] (std::size_t i) const
	[] index access (no range checking). [i] returns const pointer to ith row

T &	at (std::size_t row_i, std::size_t col_j)
	at(i,j): element access with range checking, mutable

T	at (std::size_t row_i, std::size_t col_j) const
	at(i,j): element access with range checking, const

const T &	atc (std::size_t row_i, std::size_t col_j) const
	at(i,j): element access with range checking, const ref

T &	operator() (std::size_t i, std::size_t j)
	() index access with range checking, mutable

T	operator() (std::size_t i, std::size_t j) const
	() index access with range checking, const

auto	begin ()
	iterators for underlying std::vector (entire data)

auto	cbegin () const

auto	end ()

auto	cend () const

const T *	row (std::size_t row) const
	Returns raw c pointer to start of a row.

View< T >	row_view (std::size_t row)
	Returns a mutable 'View' of a row.

View< const T >	row_view (std::size_t row) const
	Returns an immutable 'View' of a row.

View< T >	column_view (std::size_t col)
	Returns a mutable 'View' of a column.

View< const T >	column_view (std::size_t col) const
	Returns an immutable 'View' of a column.

Matrix_view< T >	matrix_view ()
	Returns a mutable view of the entire matrix (no ownership, no resize)

Matrix_view< const T >	matrix_view () const
	Returns an immutable view of the entire matrix (no ownership, no resize)

auto	as_gsl_view ()
	Returns a GSL matrix view for use with GSL functions (no copy).

auto	as_gsl_view () const
	Const GSL matrix view; see as_gsl_view()

T	determinant () const
	Returns the determinant via LU decomposition (GSL).

Matrix< T > &	invert_in_place ()
	Inverts the matrix in place via LU decomposition (GSL).

Matrix< T >	inverse () const
	Returns inverse of the matrix; original is unchanged.

Matrix< T >	transpose () const
	Returns the transpose of the matrix.

Matrix< T > &	make_identity ()
	Constructs a diagonal unit matrix (identity), in place; only for square.

Matrix< T > &	zero ()
	Sets all elements to zero, in place.

Matrix< T >	conj () const
	Returns conjugate of matrix.

auto	real () const
	Returns real part of complex matrix (changes type; returns a real matrix)

auto	imag () const
	Returns imag part of complex matrix (changes type; returns a real matrix)

auto	complex () const
	Converts a real to complex matrix (changes type; returns a complex matrix)

Matrix< T > &	conj_in_place ()
	Conjugates matrix, in place.

Matrix< T > &	mult_elements_by (const Matrix< T > &a)
	Elementwise multiply in place: M_ij *= a_ij.

Matrix< T > &	operator+= (const Matrix< T > &rhs)
	In-place elementwise addition; dimensions must match.

Matrix< T > &	operator-= (const Matrix< T > &rhs)
	In-place elementwise subtraction; dimensions must match.

Matrix< T > &	operator*= (const T x)
	In-place scalar multiply: M_ij *= x.

Matrix< T > &	operator/= (const T x)
	In-place scalar divide: M_ij /= x.

Matrix< T > &	operator+= (T aI)
	M += aI: adds a to diagonal elements (scalar treated as a*Identity)

Matrix< T > &	operator-= (T aI)
	M -= aI: subtracts a from diagonal elements (scalar treated as a*Identity)

Protected Attributes
std::size_t	m_rows

std::size_t	m_cols

std::vector< T >	m_data {}

Friends
Matrix< T >	mult_elements (Matrix< T > a, const Matrix< T > &b)
	Returns new matrix C with C_ij = A_ij * B_ij (elementwise product).

Matrix< T >	operator+ (Matrix< T > lhs, const Matrix< T > &rhs)
	Elementwise addition: returns M + N.

Matrix< T >	operator- (Matrix< T > lhs, const Matrix< T > &rhs)
	Elementwise subtraction: returns M - N.

Matrix< T >	operator* (const T x, Matrix< T > rhs)
	Scalar multiply: returns x * M.

Matrix< T >	operator* (Matrix< T > lhs, const T x)
	Scalar multiply: returns M * x.

Matrix< T >	operator/ (Matrix< T > lhs, const T x)
	Scalar divide: returns M / x.

Matrix< T >	operator+ (Matrix< T > M, T aI)
	Returns M + aI (adds a to diagonal)

Matrix< T >	operator- (Matrix< T > M, T aI)
	Returns M - aI (subtracts a from diagonal)

template<typename U >
Matrix< U >	operator* (const Matrix< U > &a, const Matrix< U > &b)
	Matrix multiplication: C_ij = sum_k A_ik*B_kj.

template<typename U >
std::ostream &	operator<< (std::ostream &os, const Matrix< U > &a)
	Prints matrix elements row by row to output stream.

Constructor & Destructor Documentation

◆ Matrix() [1/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix ( )

inline

Default initialiser.

◆ Matrix() [2/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix	(	std::size_t	rows,
		std::size_t	cols
	)

inline

Initialise a blank matrix rows*cols, filled with 0.

◆ Matrix() [3/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix	(	std::size_t	rows,
		std::size_t	cols,
		const T &	value
	)

inline

Initialise a matrix rows*cols, filled with 'value'.

◆ Matrix() [4/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix ( std::size_t dimension )

inlineexplicit

Initialise a blank square matrix dimension*dimension, filled with 0.

◆ Matrix() [5/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix ( std::initializer_list< std::initializer_list< T > > ll )

inline

Initialise a matrix from initialiser list. {{},{},{}}. Each row must be same length.

◆ Matrix() [6/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix	(	std::size_t	rows,
		std::size_t	cols,
		std::initializer_list< T >	l
	)

inline

Initialise a matrix from single initialiser list. {...}.

◆ Matrix() [7/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix	(	std::size_t	rows,
		std::size_t	cols,
		std::vector< T > &&	v
	)

inline

Initialise a matrix from single initialiser list. {...}.

◆ Matrix() [8/8]

template<typename T = double>

LinAlg::Matrix< T >::Matrix	(	std::size_t	rows,
		std::size_t	cols,
		const std::vector< T > &	v
	)

inline

Initialise a matrix from single initialiser list. {...}.

Member Function Documentation

◆ resize() [1/2]

template<typename T = double>

void LinAlg::Matrix< T >::resize	(	std::size_t	rows,
		std::size_t	cols
	)

inline

Resizes matrix to new dimension; all values reset to default.

◆ resize() [2/2]

template<typename T = double>

void LinAlg::Matrix< T >::resize	(	std::size_t	rows,
		std::size_t	cols,
		const T &	value
	)

inline

Resizes matrix to new dimension; all values reset to 'value'.

◆ rows()

template<typename T = double>

std::size_t LinAlg::Matrix< T >::rows ( ) const

inline

Return rows [major index size].

◆ cols()

template<typename T = double>

std::size_t LinAlg::Matrix< T >::cols ( ) const

inline

Return columns [minor index size].

◆ size()

template<typename T = double>

std::size_t LinAlg::Matrix< T >::size ( ) const

inline

Return rows*columns [total array size].

◆ empty()

template<typename T = double>

bool LinAlg::Matrix< T >::empty ( ) const

inline

Bool - is empty? (same as size==0)

◆ data() [1/2]

template<typename T = double>

T * LinAlg::Matrix< T >::data ( )

inline

Pointer to first element; for std::complex<T> this is complex<T>*, not T*.

◆ data() [2/2]

template<typename T = double>

const T * LinAlg::Matrix< T >::data ( ) const

inline

Const pointer to first element; for std::complex<T> this is const complex<T>*, not const T*.

◆ operator[]() [1/2]

template<typename T = double>

T * LinAlg::Matrix< T >::operator[] ( std::size_t i )

inline

[] index access (no range checking). [i] returns pointer to ith row, mutable

◆ operator[]() [2/2]

template<typename T = double>

const T * LinAlg::Matrix< T >::operator[] ( std::size_t i ) const

inline

[] index access (no range checking). [i] returns const pointer to ith row

◆ at() [1/2]

template<typename T = double>

T & LinAlg::Matrix< T >::at	(	std::size_t	row_i,
		std::size_t	col_j
	)

inline

at(i,j): element access with range checking, mutable

◆ at() [2/2]

template<typename T = double>

T LinAlg::Matrix< T >::at	(	std::size_t	row_i,
		std::size_t	col_j
	)		const

inline

at(i,j): element access with range checking, const

◆ atc()

template<typename T = double>

const T & LinAlg::Matrix< T >::atc	(	std::size_t	row_i,
		std::size_t	col_j
	)		const

inline

at(i,j): element access with range checking, const ref

◆ operator()() [1/2]

template<typename T = double>

T & LinAlg::Matrix< T >::operator()	(	std::size_t	i,
		std::size_t	j
	)

inline

() index access with range checking, mutable

◆ operator()() [2/2]

template<typename T = double>

T LinAlg::Matrix< T >::operator()	(	std::size_t	i,
		std::size_t	j
	)		const

inline

() index access with range checking, const

◆ begin()

template<typename T = double>

auto LinAlg::Matrix< T >::begin ( )

inline

iterators for underlying std::vector (entire data)

◆ row()

template<typename T = double>

const T * LinAlg::Matrix< T >::row ( std::size_t row ) const

inline

Returns raw c pointer to start of a row.

◆ row_view() [1/2]

template<typename T = double>

View< T > LinAlg::Matrix< T >::row_view ( std::size_t row )

inline

Returns a mutable 'View' of a row.

◆ row_view() [2/2]

template<typename T = double>

View< const T > LinAlg::Matrix< T >::row_view ( std::size_t row ) const

inline

Returns an immutable 'View' of a row.

◆ column_view() [1/2]

template<typename T = double>

View< T > LinAlg::Matrix< T >::column_view ( std::size_t col )

inline

Returns a mutable 'View' of a column.

◆ column_view() [2/2]

template<typename T = double>

View< const T > LinAlg::Matrix< T >::column_view ( std::size_t col ) const

inline

Returns an immutable 'View' of a column.

◆ matrix_view() [1/2]

template<typename T = double>

Matrix_view< T > LinAlg::Matrix< T >::matrix_view ( )

inline

Returns a mutable view of the entire matrix (no ownership, no resize)

◆ matrix_view() [2/2]

template<typename T = double>

Matrix_view< const T > LinAlg::Matrix< T >::matrix_view ( ) const

inline

Returns an immutable view of the entire matrix (no ownership, no resize)

◆ as_gsl_view() [1/2]

template<typename T >

auto LinAlg::Matrix< T >::as_gsl_view ( )

Returns a GSL matrix view for use with GSL functions (no copy).

Returns a gsl_matrix_view (or _float_view, _complex_view, _complex_float_view) wrapping the matrix data in place. Access the underlying GSL matrix via .matrix on the returned object. Allows use of all GSL/BLAS built-in functions without any data copy.

Supported types: double, float, std::complex<double>, std::complex<float>.

Note: Both the Matrix and the returned view must remain in scope during use; the view is non-owning.

Warning: Fails at runtime (assert) for unsupported scalar types.

◆ as_gsl_view() [2/2]

template<typename T >

auto LinAlg::Matrix< T >::as_gsl_view ( ) const

Const GSL matrix view; see as_gsl_view()

◆ determinant()

template<typename T >

T LinAlg::Matrix< T >::determinant ( ) const

Returns the determinant via LU decomposition (GSL).

Makes an internal copy of the matrix, performs LU decomposition, and returns the determinant. The original matrix is not modified.

Returns: Determinant of the matrix.

Note: Only available for T = double or T = std::complex<double>.

Warning: Only defined for square matrices; asserts otherwise.

◆ invert_in_place()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::invert_in_place ( )

Inverts the matrix in place via LU decomposition (GSL).

Performs LU decomposition on a copy, then overwrites *this with its inverse using gsl_linalg_LU_invert (or the complex equivalent).

Returns: Reference to *this (the inverted matrix).

Note: Only available for T = double or T = std::complex<double>.

Warning: Only defined for square matrices; asserts otherwise.

◆ inverse()

template<typename T = double>

Matrix< T > LinAlg::Matrix< T >::inverse ( ) const

inline

Returns inverse of the matrix; original is unchanged.

Copies *this and calls invert_in_place() on the copy.

Note: Only available for T = double or T = std::complex<double>.

◆ transpose()

template<typename T >

Matrix< T > LinAlg::Matrix< T >::transpose ( ) const

Returns the transpose of the matrix.

Allocates and returns a new Matrix<T> of size cols() x rows() with elements transposed. Uses GSL gsl_matrix_transpose_memcpy for double, float, and their complex variants; falls back to a naive loop for other types.

Returns: New matrix of dimensions cols() x rows().

◆ make_identity()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::make_identity ( )

Constructs a diagonal unit matrix (identity), in place; only for square.

◆ zero()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::zero ( )

Sets all elements to zero, in place.

◆ conj()

template<typename T >

Matrix< T > LinAlg::Matrix< T >::conj ( ) const

Returns conjugate of matrix.

◆ real()

template<typename T >

auto LinAlg::Matrix< T >::real ( ) const

Returns real part of complex matrix (changes type; returns a real matrix)

◆ imag()

template<typename T >

auto LinAlg::Matrix< T >::imag ( ) const

Returns imag part of complex matrix (changes type; returns a real matrix)

◆ complex()

template<typename T >

auto LinAlg::Matrix< T >::complex ( ) const

Converts a real to complex matrix (changes type; returns a complex matrix)

◆ conj_in_place()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::conj_in_place ( )

Conjugates matrix, in place.

◆ mult_elements_by()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::mult_elements_by ( const Matrix< T > & a )

Elementwise multiply in place: M_ij *= a_ij.

Each element of *this is multiplied by the corresponding element of a. Matrices must have the same dimensions.

Parameters

a	Matrix whose elements multiply `*this`.

Returns: Reference to *this.

Warning: Dimensions must match; asserts otherwise.

◆ operator+=() [1/2]

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator+= ( const Matrix< T > & rhs )

In-place elementwise addition; dimensions must match.

◆ operator-=() [1/2]

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator-= ( const Matrix< T > & rhs )

In-place elementwise subtraction; dimensions must match.

◆ operator*=()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator*= ( const T x )

In-place scalar multiply: M_ij *= x.

◆ operator/=()

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator/= ( const T x )

In-place scalar divide: M_ij /= x.

◆ operator+=() [2/2]

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator+= ( T aI )

M += aI: adds a to diagonal elements (scalar treated as a*Identity)

◆ operator-=() [2/2]

template<typename T >

Matrix< T > & LinAlg::Matrix< T >::operator-= ( T aI )

M -= aI: subtracts a from diagonal elements (scalar treated as a*Identity)

Friends And Related Symbol Documentation

◆ mult_elements

template<typename T = double>

Matrix< T > mult_elements	(	Matrix< T >	a,
		const Matrix< T > &	b
	)

friend

Returns new matrix C with C_ij = A_ij * B_ij (elementwise product).

Calls a.mult_elements_by(b) on a copy of a.

◆ operator+ [1/2]

template<typename T = double>

Matrix< T > operator+	(	Matrix< T >	lhs,
		const Matrix< T > &	rhs
	)

friend

Elementwise addition: returns M + N.

◆ operator- [1/2]

template<typename T = double>

Matrix< T > operator-	(	Matrix< T >	lhs,
		const Matrix< T > &	rhs
	)

friend

Elementwise subtraction: returns M - N.

◆ operator* [1/3]

template<typename T = double>

Matrix< T > operator*	(	const T	x,
		Matrix< T >	rhs
	)

friend

Scalar multiply: returns x * M.

◆ operator* [2/3]

template<typename T = double>

Matrix< T > operator*	(	Matrix< T >	lhs,
		const T	x
	)

friend

Scalar multiply: returns M * x.

◆ operator/

template<typename T = double>

Matrix< T > operator/	(	Matrix< T >	lhs,
		const T	x
	)

friend

Scalar divide: returns M / x.

◆ operator+ [2/2]

template<typename T = double>

Matrix< T > operator+	(	Matrix< T >	M,
		T	aI
	)

friend

Returns M + aI (adds a to diagonal)

◆ operator- [2/2]

template<typename T = double>

Matrix< T > operator-	(	Matrix< T >	M,
		T	aI
	)

friend

Returns M - aI (subtracts a from diagonal)

◆ operator* [3/3]

template<typename T = double>

template<typename U >

Matrix< U > operator*	(	const Matrix< U > &	a,
		const Matrix< U > &	b
	)

friend

Matrix multiplication: C_ij = sum_k A_ik*B_kj.

◆ operator<<

template<typename T = double>

template<typename U >

std::ostream & operator<<	(	std::ostream &	os,
		const Matrix< U > &	a
	)

friend

Prints matrix elements row by row to output stream.

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

LinAlg/Matrix.hpp
LinAlg/Matrix.ipp

ok

Public Member Functions

Protected Attributes

Friends

Constructor & Destructor Documentation

◆ Matrix() [1/8]

◆ Matrix() [2/8]

◆ Matrix() [3/8]

◆ Matrix() [4/8]

◆ Matrix() [5/8]

◆ Matrix() [6/8]

◆ Matrix() [7/8]

◆ Matrix() [8/8]

Member Function Documentation

◆ resize() [1/2]

◆ resize() [2/2]

◆ rows()

◆ cols()

◆ size()

◆ empty()

◆ data() [1/2]

◆ data() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ at() [1/2]

◆ at() [2/2]

◆ atc()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ begin()

◆ row()

◆ row_view() [1/2]

◆ row_view() [2/2]

◆ column_view() [1/2]

◆ column_view() [2/2]

◆ matrix_view() [1/2]

◆ matrix_view() [2/2]

◆ as_gsl_view() [1/2]

◆ as_gsl_view() [2/2]

◆ determinant()

◆ invert_in_place()

◆ inverse()

◆ transpose()

◆ make_identity()

◆ zero()

◆ conj()

◆ real()

◆ imag()

◆ complex()

◆ conj_in_place()

◆ mult_elements_by()

◆ operator+=() [1/2]

◆ operator-=() [1/2]

◆ operator*=()

◆ operator/=()

◆ operator+=() [2/2]

◆ operator-=() [2/2]

Friends And Related Symbol Documentation

◆ mult_elements

◆ operator+ [1/2]

◆ operator- [1/2]

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator/

◆ operator+ [2/2]

◆ operator- [2/2]

◆ operator* [3/3]

◆ operator<<