A generic matrix with a fixed number of rows and columns. More...

#include <mat.h>

Public Types
using	iterator = mat_iterator< mat< Type, N, K >, Type & >
	Iterator for statically allocated matrices.

using	const_iterator = mat_iterator< const mat< Type, N, K >, const Type & >
	Const iterator for statically allocated matrices.

Public Member Functions
	mat ()
	Default constructor.

template<typename Matrix >
	mat (const Matrix &m)
	Copy constructor.

template<typename T = Type>
	mat (const std::initializer_list< std::initializer_list< T > > &rows)
	Constructs a matrix from an initializer list.

	mat (Type diagonal, unsigned int n=0, unsigned int k=0)
	Constructor that initializes a diagonal matrix with equal entries on the diagonal.

template<typename Matrix >
mat< Type, N, K > &	operator= (const Matrix &other)
	Assignment operator to copy from another matrix.

void	make_zeroes ()
	Sets all elements of the matrix to zero.

template<typename Matrix >
mat< Type, N, K >	operator+ (const Matrix &other) const
	Matrix addition.

template<typename Matrix >
mat< Type, N, K >	operator- (const Matrix &other) const
	Matrix subtraction.

mat< Type, N, K >	operator* (Type scalar) const
	Scalar multiplication.

mat< Type, N, K >	operator/ (Type scalar) const
	Scalar division.

template<typename Vector >
Vector	transform (const Vector &v) const
	Transforms a vector by multiplying it with the matrix.

vec< Type, N >	transform (const vec< Type, K > &v) const
	Transforms a fixed-size vector by multiplying it with the matrix.

vec< Type, N >	operator* (const vec< Type, K > &v) const
	Overloads the `*` operator to transform a fixed-size vector by the matrix.

template<unsigned int M>
mat< Type, N, M >	mul (const mat< Type, K, M > &B) const
	Matrix multiplication for matrices with different column counts.

template<typename Matrix >
Matrix	mul (const Matrix &B) const
	Matrix multiplication for matrices with any type.

template<typename Matrix >
auto	operator* (const Matrix &B) const
	Overloads the `*` operator for matrix multiplication.

template<typename Matrix >
mat< Type, N, K > &	operator+= (const Matrix &other)
	Matrix addition.

template<typename Matrix >
mat< Type, N, K > &	operator-= (const Matrix &other)
	Matrix subtraction.

mat< Type, N, K > &	operator*= (Type scalar)
	Scalar multiplication.

mat< Type, N, K > &	operator/= (Type scalar)
	Scalar division.

template<typename Matrix >
mat< Type, N, K > &	operator*= (const Matrix &B)
	Matrix multiplication with an assignment operator.

mat< Type, N, K > &	transpose ()
	Transposes the matrix in place.

Type &	at (unsigned int i, unsigned int j)
	Accesses the element at the given row and column.

const Type &	at (unsigned int i, unsigned int j) const
	Accesses the element at the given row and column.

Type &	operator() (unsigned int i, unsigned int j)
	Overloads the `()` operator to access an element.

const Type &	operator() (unsigned int i, unsigned int j) const
	Overloads the `()` operator to access an element.

Type	get (unsigned int i, unsigned int j) const
	Gets the element at the specified row and column.

auto	begin ()
	Returns an iterator to the first element of the matrix.

auto	end ()
	Returns an iterator to one past the last element of the matrix.

auto	begin () const
	Returns a const iterator to the first element of the matrix.

auto	end () const
	Returns a const iterator to one past the last element of the matrix.

TH_CONSTEXPR unsigned int	rows () const
	Returns the number of rows in the matrix.

TH_CONSTEXPR unsigned int	cols () const
	Returns the number of columns in the matrix.

unsigned int	size () const
	Returns the total number of elements in the matrix.

template<typename Matrix >
bool	operator== (const Matrix &other) const
	Checks whether this matrix is equal to another matrix element-wise.

template<typename Matrix >
bool	operator!= (const Matrix &other) const
	Checks whether this matrix is not equal to another matrix element-wise.

mat< Type, N, K > &	invert ()
	Inverts the matrix in place.

mat< Type, N, K >	resize (unsigned int n, unsigned int k) const
	Compatibility function to allow for allocation or resizing of dynamic matrices.

std::string	to_string (std::string separator=", ", bool parenthesis=true) const
	Converts the matrix to a string representation.

	operator std::string ()
	Convert the matrix to string representation.

Public Attributes
Type	data [K][N]

Friends
mat< Type, N, K >	operator* (Type a, const mat< Type, N, K > &B)
	Friend operator for scalar multiplication (T * mat).

template<typename VecType , unsigned int M>
vec< VecType, K >	operator* (const vec< VecType, M > &a, const mat< Type, N, K > &B)
	Friend operator for vector-matrix multiplication.

std::ostream &	operator<< (std::ostream &out, const mat< Type, N, K > &obj)
	Outputs the matrix to an output stream in string format.

Detailed Description

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>
class theoretica::mat< Type, N, K >

A generic matrix with a fixed number of rows and columns.

Parameters

Type	The type of the elements
N	The number of rows
K	The number of columns

Constructor & Destructor Documentation

◆ mat() [1/4]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

theoretica::mat< Type, N, K >::mat ( )

inline

Default constructor.

Initializes the matrix with all elements set to zero.

◆ mat() [2/4]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

theoretica::mat< Type, N, K >::mat ( const Matrix & m )

inline

Copy constructor.

Template Parameters

Matrix The type of the matrix to copy from.

Parameters

m	The matrix to copy.

Copies all elements from the given matrix m into this matrix.

◆ mat() [3/4]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename T = Type>

theoretica::mat< Type, N, K >::mat ( const std::initializer_list< std::initializer_list< T > > & rows )

inline

Constructs a matrix from an initializer list.

Template Parameters

T	The type of elements in the initializer list (default is `Type`).

Parameters

rows	An initializer list representing the rows of the matrix.

Initializes the matrix with values from the initializer list. Ensures that the initializer list matches the size of the matrix (i.e., N rows and K columns).

◆ mat() [4/4]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

theoretica::mat< Type, N, K >::mat	(	Type	diagonal,
		unsigned int	n = `0`,
		unsigned int	k = `0`
	)

inline

Constructor that initializes a diagonal matrix with equal entries on the diagonal.

The size parameters are required for compatibility with mat<T, 0> and may be used for additional error prevention.

Parameters

diagonal	The value for the diagonal entries.
n	Number of rows.
k	Number of columns.

Member Function Documentation

◆ at() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

Type & theoretica::mat< Type, N, K >::at	(	unsigned int	i,
		unsigned int	j
	)

inline

Accesses the element at the given row and column.

Parameters

i	The row index.
j	The column index.

Returns: A reference to the element at position (i, j).

◆ at() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

const Type & theoretica::mat< Type, N, K >::at	(	unsigned int	i,
		unsigned int	j
	)		const

inline

Accesses the element at the given row and column.

Parameters

i	The row index.
j	The column index.

Returns: A constant reference to the element at position (i, j).

◆ begin() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

auto theoretica::mat< Type, N, K >::begin ( )

inline

Returns an iterator to the first element of the matrix.

Returns: An iterator to the beginning of the matrix.

◆ begin() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

auto theoretica::mat< Type, N, K >::begin ( ) const

inline

Returns a const iterator to the first element of the matrix.

Returns: A const iterator to the beginning of the matrix.

◆ cols()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

TH_CONSTEXPR unsigned int theoretica::mat< Type, N, K >::cols ( ) const

inline

Returns the number of columns in the matrix.

Returns: The number of columns.

◆ end() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

auto theoretica::mat< Type, N, K >::end ( )

inline

Returns an iterator to one past the last element of the matrix.

Returns: An iterator to the end of the matrix.

◆ end() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

auto theoretica::mat< Type, N, K >::end ( ) const

inline

Returns a const iterator to one past the last element of the matrix.

Returns: A const iterator to the end of the matrix.

◆ get()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

Type theoretica::mat< Type, N, K >::get	(	unsigned int	i,
		unsigned int	j
	)		const

inline

Gets the element at the specified row and column.

Parameters

i	The row index.
j	The column index.

Returns: A copy of the element at position (i, j).

◆ invert()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > & theoretica::mat< Type, N, K >::invert ( )

inline

Inverts the matrix in place.

Returns: Reference to the inverted matrix.

This function is only valid for square matrices.

◆ mul() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<unsigned int M>

mat< Type, N, M > theoretica::mat< Type, N, K >::mul ( const mat< Type, K, M > & B ) const

inline

Matrix multiplication for matrices with different column counts.

Template Parameters

M	The number of columns in matrix `B`.

Parameters

B	The matrix to multiply with.

Returns: A new matrix resulting from the multiplication.

◆ mul() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

Matrix theoretica::mat< Type, N, K >::mul ( const Matrix & B ) const

inline

Matrix multiplication for matrices with any type.

Template Parameters

Matrix The type of the matrix to multiply with.

Parameters

B	The matrix to multiply with.

Returns: The resulting matrix.

This function multiplies this matrix with another matrix B. It checks if the number of rows in B matches the number of columns in this matrix.

◆ operator!=()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

bool theoretica::mat< Type, N, K >::operator!= ( const Matrix & other ) const

inline

Checks whether this matrix is not equal to another matrix element-wise.

Template Parameters

Matrix The type of the other matrix.

Parameters

other The matrix to compare with.

Returns: true if any elements are unequal, false otherwise.

◆ operator()() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

Type & theoretica::mat< Type, N, K >::operator()	(	unsigned int	i,
		unsigned int	j
	)

inline

Overloads the () operator to access an element.

Parameters

i	The row index.
j	The column index.

Returns: A reference to the element at position (i, j).

◆ operator()() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

const Type & theoretica::mat< Type, N, K >::operator()	(	unsigned int	i,
		unsigned int	j
	)		const

inline

Overloads the () operator to access an element.

Parameters

i	The row index.
j	The column index.

Returns: A constant reference to the element at position (i, j).

◆ operator*() [1/3]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

auto theoretica::mat< Type, N, K >::operator* ( const Matrix & B ) const

inline

Overloads the * operator for matrix multiplication.

Template Parameters

Matrix The type of the matrix to multiply with.

Parameters

B	The matrix to multiply with.

Returns: The resulting matrix.

◆ operator*() [2/3]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

vec< Type, N > theoretica::mat< Type, N, K >::operator* ( const vec< Type, K > & v ) const

inline

Overloads the * operator to transform a fixed-size vector by the matrix.

Parameters

v	The vector to transform.

Returns: The transformed vector.

◆ operator*() [3/3]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > theoretica::mat< Type, N, K >::operator* ( Type scalar ) const

inline

Scalar multiplication.

Parameters

scalar The scalar value to multiply.

Returns: A new matrix that is the result of multiplying this matrix by scalar.

◆ operator*=() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator*= ( const Matrix & B )

inline

Matrix multiplication with an assignment operator.

Template Parameters

Matrix The type of the matrix to multiply with.

Parameters

B	The matrix to multiply with.

Returns: Reference to this matrix after multiplication.

◆ operator*=() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator*= ( Type scalar )

inline

Scalar multiplication.

Parameters

scalar The scalar value to multiply with.

Returns: Reference to this matrix after multiplication.

◆ operator+()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > theoretica::mat< Type, N, K >::operator+ ( const Matrix & other ) const

inline

Matrix addition.

Template Parameters

Matrix The type of the matrix to add.

Parameters

other The matrix to add.

Returns: A new matrix that is the result of adding other to this matrix.

◆ operator+=()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator+= ( const Matrix & other )

inline

Matrix addition.

Template Parameters

Matrix The type of the matrix to add.

Parameters

other The matrix to add to this matrix.

Returns: Reference to this matrix after addition.

◆ operator-()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > theoretica::mat< Type, N, K >::operator- ( const Matrix & other ) const

inline

Matrix subtraction.

Template Parameters

Matrix The type of the matrix to subtract.

Parameters

other The matrix to subtract.

Returns: A new matrix that is the result of subtracting other from this matrix.

◆ operator-=()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator-= ( const Matrix & other )

inline

Matrix subtraction.

Template Parameters

Matrix The type of the matrix to subtract.

Parameters

other The matrix to subtract from this matrix.

Returns: Reference to this matrix after subtraction.

◆ operator/()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > theoretica::mat< Type, N, K >::operator/ ( Type scalar ) const

inline

Scalar division.

Parameters

scalar The scalar divisor.

Returns: A new matrix that is the result of dividing this matrix by scalar.

If scalar is close to zero, an error is raised.

◆ operator/=()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator/= ( Type scalar )

inline

Scalar division.

Parameters

scalar The scalar value to divide by.

Returns: Reference to this matrix after division.

If the scalar value is close to zero, this function raises a division by zero error.

◆ operator=()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

mat< Type, N, K > & theoretica::mat< Type, N, K >::operator= ( const Matrix & other )

inline

Assignment operator to copy from another matrix.

Template Parameters

Matrix The type of the matrix to copy from.

Parameters

other The matrix to copy.

Returns: Reference to this matrix after assignment.

◆ operator==()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Matrix >

bool theoretica::mat< Type, N, K >::operator== ( const Matrix & other ) const

inline

Checks whether this matrix is equal to another matrix element-wise.

Template Parameters

Matrix The type of the other matrix.

Parameters

other The matrix to compare with.

Returns: true if all elements are equal, false otherwise.

◆ resize()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > theoretica::mat< Type, N, K >::resize	(	unsigned int	n,
		unsigned int	k
	)		const

inline

Compatibility function to allow for allocation or resizing of dynamic matrices.

Since statically allocated matrices cannot change size, this function only checks whether the target size is the same as the matrix's.

◆ rows()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

TH_CONSTEXPR unsigned int theoretica::mat< Type, N, K >::rows ( ) const

inline

Returns the number of rows in the matrix.

Returns: The number of rows.

◆ size()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

unsigned int theoretica::mat< Type, N, K >::size ( ) const

inline

Returns the total number of elements in the matrix.

Returns: The total number of elements (rows * columns).

◆ to_string()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

std::string theoretica::mat< Type, N, K >::to_string	(	std::string	separator = `", "`,
		bool	parenthesis = `true`
	)		const

inline

Converts the matrix to a string representation.

Parameters

separator	Separator between elements (default is ", ").
parenthesis	Whether to enclose each row in parentheses (default is true).

Returns: The matrix as a formatted string.

◆ transform() [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

vec< Type, N > theoretica::mat< Type, N, K >::transform ( const vec< Type, K > & v ) const

inline

Transforms a fixed-size vector by multiplying it with the matrix.

Parameters

v	The vector to transform.

Returns: The transformed vector as a new vec<Type, N>.

◆ transform() [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename Vector >

Vector theoretica::mat< Type, N, K >::transform ( const Vector & v ) const

inline

Transforms a vector by multiplying it with the matrix.

Template Parameters

Vector The type of the vector to transform.

Parameters

v	The vector to transform.

Returns: The transformed vector.

This function multiplies the given vector v by the matrix. It checks if the size of v matches the number of columns in the matrix.

◆ transpose()

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > & theoretica::mat< Type, N, K >::transpose ( )

inline

Transposes the matrix in place.

Returns: Reference to this matrix after transposition.

This function only works if the matrix is square. An assertion will trigger if the matrix is not square.

Friends And Related Symbol Documentation

◆ operator* [1/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

template<typename VecType , unsigned int M>

vec< VecType, K > operator*	(	const vec< VecType, M > &	a,
		const mat< Type, N, K > &	B
	)

friend

Friend operator for vector-matrix multiplication.

Template Parameters

VecType	The type of vector elements.
M	The number of elements in the vector.

Parameters

a	The vector to multiply.
B	The matrix to be multiplied by.

Returns: The resulting vector after multiplication.

◆ operator* [2/2]

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

mat< Type, N, K > operator*	(	Type	a,
		const mat< Type, N, K > &	B
	)

friend

Friend operator for scalar multiplication (T * mat).

Parameters

a	The scalar multiplier.
B	The matrix to be multiplied.

Returns: A new matrix that is the result of multiplying B by a.

◆ operator<<

template<typename Type = real, unsigned int N = 0, unsigned int K = 0>

std::ostream & operator<<	(	std::ostream &	out,
		const mat< Type, N, K > &	obj
	)

friend

Outputs the matrix to an output stream in string format.

Parameters

out	The output stream.
obj	The matrix to output.

Returns: The modified output stream.

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

/home/runner/work/theoretica/theoretica/src/algebra/mat.h

Public Types

Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ mat() [1/4]

◆ mat() [2/4]

◆ mat() [3/4]

◆ mat() [4/4]

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ cols()

◆ end() [1/2]

◆ end() [2/2]

◆ get()

◆ invert()

◆ mul() [1/2]

◆ mul() [2/2]

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ resize()

◆ rows()

◆ size()

◆ to_string()

◆ transform() [1/2]

◆ transform() [2/2]

◆ transpose()

Friends And Related Symbol Documentation

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator<<