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. More...

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

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

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

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

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. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

mat< Type, K, N >	transposed () const
	Returns a transposed version of the matrix. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	is_square () const
	Checks if the matrix is square. More...

bool	is_diagonal () const
	Checks if the matrix is diagonal. More...

bool	is_symmetric () const
	Checks if the matrix is symmetric. More...

real	density (real tolerance=1E-12)
	Compute the density of the matrix, counting the proportion of non-zero (bigger in module than the given tolerance) elements with respect to the total number of elements. More...

real	sparsity (real tolerance=1E-12)
	Compute the sparsity of the matrix, counting the proportion of zero (smaller in module than the given tolerance) elements with respect to the total number of elements. More...

Type	trace ()
	Computes the trace of the matrix. More...

Type	diagonal_product ()
	Computes the product of the diagonal elements. More...

Type	det () const
	Computes the determinant of the matrix. More...

mat< Type, N, K >	inverse () const
	Computes the inverse of the matrix. More...

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

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

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

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

Static Public Member Functions
static mat< Type, N, K >	zeroes ()
	Returns a null matrix with all elements set to zero. More...

static mat< Type, N, K >	identity ()
	Returns the identity matrix. More...

static mat< Type, N, K >	diagonal (Type diag)
	Returns a diagonal matrix with the specified diagonal element. More...

template<typename Vector = vec<real, N - 1>>
static mat< Type, N, K >	translation (Vector &&t)
	Returns a 4x4 matrix for translation by the vector {x, y, z}. More...

static mat< Type, N, K >	rotation_2d (real theta)
	Returns a matrix for 2D rotation by theta radians. More...

static mat< Type, N, K >	rotation_3d_xaxis (real theta)
	Returns a matrix for 3D rotation around the x-axis. More...

static mat< Type, N, K >	rotation_3d_yaxis (real theta)
	Returns a matrix for 3D rotation around the y-axis. More...

static mat< Type, N, K >	rotation_3d_zaxis (real theta)
	Returns a matrix for 3D rotation around the z-axis. More...

template<typename Vector = vec<real, 3>>
static mat< Type, N, K >	rotation_3d (real theta, Vector &&axis)
	Returns a matrix for 3D rotation around an arbitrary axis. More...

static mat< Type, N, K >	perspective (real left, real right, real bottom, real top, real near, real far)
	Returns a perspective projection matrix. More...

static mat< Type, N, K >	perspective_fov (real fov, real aspect, real near, real far)
	Returns a perspective projection matrix based on field of view. More...

static mat< Type, N, K >	ortho (real left, real right, real bottom, real top, real near, real far)
	Returns an orthographic projection matrix. More...

template<typename Vector1 , typename Vector2 , typename Vector3 >
static mat< Type, 4, 4 >	look_at (const Vector1 &camera, const Vector2 &target, const Vector3 &up)
	Return a 4x4 transformation matrix that points the field of view towards a given point from the <camera> point. More...

static mat< Type, N, K >	symplectic (unsigned int n=0, unsigned int k=0)
	A symplectic NxN matrix, where \(N = 2K\) for some natural K. More...

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). More...

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. More...

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

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.

◆ density()

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

real theoretica::mat< Type, N, K >::density ( real tolerance = 1E-12 )

inline

Compute the density of the matrix, counting the proportion of non-zero (bigger in module than the given tolerance) elements with respect to the total number of elements.

Parameters

tolerance The minimum tolerance in absolute value to consider an element non-zero.

Returns: A real number between 0 and 1 representing the proportion of non-zero elements of the matrix.

◆ det()

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

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

inline

Computes the determinant of the matrix.

Returns: The determinant.

This function is only valid for square matrices.

◆ diagonal()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::diagonal ( Type diag )

inlinestatic

Returns a diagonal matrix with the specified diagonal element.

Parameters

diag	The value for the diagonal elements.

Returns: A diagonal matrix with the given diagonal value.

◆ diagonal_product()

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

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

inline

Computes the product of the diagonal elements.

Returns: The product of diagonal elements.

◆ 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).

◆ identity()

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

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

inlinestatic

Returns the identity matrix.

Returns: An identity matrix of the current dimensions.

◆ inverse()

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

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

inline

Computes the inverse of the matrix.

Returns: The inverse matrix.

This function is only valid for square matrices.

◆ 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.

◆ is_diagonal()

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

bool theoretica::mat< Type, N, K >::is_diagonal ( ) const

inline

Checks if the matrix is diagonal.

Returns: true if the matrix is diagonal, false otherwise.

◆ is_square()

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

bool theoretica::mat< Type, N, K >::is_square ( ) const

inline

Checks if the matrix is square.

Returns: true if the matrix is square (N == K), false otherwise.

◆ is_symmetric()

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

bool theoretica::mat< Type, N, K >::is_symmetric ( ) const

inline

Checks if the matrix is symmetric.

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

◆ look_at()

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

template<typename Vector1 , typename Vector2 , typename Vector3 >

static mat<Type, 4, 4> theoretica::mat< Type, N, K >::look_at	(	const Vector1 &	camera,
		const Vector2 &	target,
		const Vector3 &	up
	)

inlinestatic

Return a 4x4 transformation matrix that points the field of view towards a given point from the <camera> point.

Template Parameters

Vector1,Vector2,Vector3 Types for the camera, target, and up vectors.

Parameters

camera	The camera position.
target	The target point to look at.
up	The up direction vector.

Returns: A 4x4 look-at transformation matrix.

◆ 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.

◆ ortho()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::ortho	(	real	left,
		real	right,
		real	bottom,
		real	top,
		real	near,
		real	far
	)

inlinestatic

Returns an orthographic projection matrix.

Parameters

left	The left boundary.
right	The right boundary.
bottom	The bottom boundary.
top	The top boundary.
near	The near boundary.
far	The far boundary.

Returns: A 4x4 orthographic projection matrix.

◆ perspective()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::perspective	(	real	left,
		real	right,
		real	bottom,
		real	top,
		real	near,
		real	far
	)

inlinestatic

Returns a perspective projection matrix.

Parameters

left	The left boundary.
right	The right boundary.
bottom	The bottom boundary.
top	The top boundary.
near	The near boundary.
far	The far boundary.

Returns: A 4x4 perspective projection matrix.

◆ perspective_fov()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::perspective_fov	(	real	fov,
		real	aspect,
		real	near,
		real	far
	)

inlinestatic

Returns a perspective projection matrix based on field of view.

Parameters

fov	The field of view angle in radians.
aspect	The aspect ratio.
near	The near boundary.
far	The far boundary.

Returns: A 4x4 perspective projection matrix.

◆ 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.

◆ rotation_2d()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::rotation_2d ( real theta )

inlinestatic

Returns a matrix for 2D rotation by theta radians.

Parameters

theta The angle of rotation in radians.

Returns: A 2x2 rotation matrix.

◆ rotation_3d()

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

template<typename Vector = vec<real, 3>>

static mat<Type, N, K> theoretica::mat< Type, N, K >::rotation_3d	(	real	theta,
		Vector &&	axis
	)

inlinestatic

Returns a matrix for 3D rotation around an arbitrary axis.

Template Parameters

Vector The type of the rotation axis vector.

Parameters

theta	The angle of rotation in radians.
axis	The axis vector to rotate around.

Returns: A 3x3 rotation matrix for the given axis.

◆ rotation_3d_xaxis()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::rotation_3d_xaxis ( real theta )

inlinestatic

Returns a matrix for 3D rotation around the x-axis.

Parameters

theta The angle of rotation in radians.

Returns: A 3x3 rotation matrix for the x-axis.

◆ rotation_3d_yaxis()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::rotation_3d_yaxis ( real theta )

inlinestatic

Returns a matrix for 3D rotation around the y-axis.

Parameters

theta The angle of rotation in radians.

Returns: A 3x3 rotation matrix for the y-axis.

◆ rotation_3d_zaxis()

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

static mat<Type, N, K> theoretica::mat< Type, N, K >::rotation_3d_zaxis ( real theta )

inlinestatic

Returns a matrix for 3D rotation around the z-axis.

Parameters

theta The angle of rotation in radians.

Returns: A 3x3 rotation matrix for the z-axis.

◆ 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).

◆ sparsity()

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

real theoretica::mat< Type, N, K >::sparsity ( real tolerance = 1E-12 )

inline

Compute the sparsity of the matrix, counting the proportion of zero (smaller in module than the given tolerance) elements with respect to the total number of elements.

Parameters

tolerance The minimum tolerance in absolute value to consider an element non-zero.

Returns: A real number between 0 and 1 representing the proportion of zero elements of the matrix.

◆ symplectic()

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

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

inlinestatic

A symplectic NxN matrix, where \(N = 2K\) for some natural K.

Parameters

n	Optional parameter for number of rows.
k	Optional parameter for number of columns.

Returns: A symplectic matrix with given dimensions.

◆ 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.

◆ trace()

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

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

inline

Computes the trace of the matrix.

Returns: The trace (sum of diagonal elements).

◆ 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.

◆ translation()

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

template<typename Vector = vec<real, N - 1>>

static mat<Type, N, K> theoretica::mat< Type, N, K >::translation ( Vector && t )

inlinestatic

Returns a 4x4 matrix for translation by the vector {x, y, z}.

Template Parameters

Vector The type of the translation vector.

Parameters

t	The translation vector.

Returns: A 4x4 translation 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.

◆ transposed()

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

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

inline

Returns a transposed version of the matrix.

Returns: A new matrix that is the transposed version of this matrix.

◆ zeroes()

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

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

inlinestatic

Returns a null matrix with all elements set to zero.

Returns: A new matrix with zero values.

Friends And Related Function 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

Static Public Member Functions

Public Attributes

Friends

Detailed Description

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

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()

◆ density()

◆ det()

◆ diagonal()

◆ diagonal_product()

◆ end() [1/2]

◆ end() [2/2]

◆ get()

◆ identity()

◆ inverse()

◆ invert()

◆ is_diagonal()

◆ is_square()

◆ is_symmetric()

◆ look_at()

◆ 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==()

◆ ortho()

◆ perspective()

◆ perspective_fov()

◆ resize()

◆ rotation_2d()

◆ rotation_3d()

◆ rotation_3d_xaxis()

◆ rotation_3d_yaxis()

◆ rotation_3d_zaxis()

◆ rows()

◆ size()

◆ sparsity()

◆ symplectic()

◆ to_string()

◆ trace()

◆ transform() [1/2]

◆ transform() [2/2]

◆ translation()

◆ transpose()

◆ transposed()

◆ zeroes()

Friends And Related Function Documentation

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator<<

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