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)
	Construct from a list of the rows.

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

void	make_zeroes ()
	Set all elements 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
	Transform a vector v by the matrix.

vec< Type, N >	transform (const vec< Type, K > &v) const
	Transform a vector by the matrix.

vec< Type, N >	operator* (const vec< Type, K > &v) const
	Transform a vector by the matrix.

template<unsigned int M>
mat< Type, N, M >	mul (const mat< Type, K, M > &B) const
	Matrix multiplication.

template<typename Matrix >
Matrix	mul (const Matrix &B) const
	Matrix multiplication by any matrix type.

template<typename Matrix >
auto	operator* (const Matrix &B) const
	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.

mat< Type, N, K > &	transpose ()
	Transpose the matrix itself.

mat< Type, K, N >	transposed () const
	Return the transposed matrix, without modifying the matrix itself.

Type &	at (unsigned int i, unsigned int j)
	Access the element at the i-th row and j-th column.

const Type &	at (unsigned int i, unsigned int j) const
	Access the element at the i-th row and j-th column.

Type &	operator() (unsigned int i, unsigned int j)
	Access the element at the i-th row and j-th column.

const Type &	operator() (unsigned int i, unsigned int j) const
	Get the element at the i-th row and j-th column.

Type	get (unsigned int i, unsigned int j) const
	Get the element at the i-th row and j-th column.

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

auto	end ()
	Get an iterator to one plus the last element of the matrix.

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

auto	end () const
	Get a const iterator to one plus the last element of the matrix.

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

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

unsigned int	size () const
	Get the total number of elements of the matrix (rows * columns)

template<typename Matrix >
bool	operator== (const Matrix &other) const
	Check whether two matrices are equal element by element.

template<typename Matrix >
bool	operator!= (const Matrix &other) const
	Check whether two matrices are unequal element by element.

bool	is_square () const
	Return whether the matrix is square.

bool	is_diagonal () const
	Return whether the matrix is diagonal.

bool	is_symmetric () const
	Return whether the matrix is symmetric.

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 ()
	Compute the trace (sum of elements on the diagonal) of a square matrix.

Type	diagonal_product ()
	Compute the product of the diagonal elements of a square matrix.

Type	det () const
	Compute the determinant of the matrix.

mat< Type, N, K >	inverse () const
	Compute the inverse of a generic square matrix.

mat< Type, N, K > &	invert ()
	Invert a generic square matrix.

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
	Convert the matrix to string representation.

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

Static Public Member Functions
static mat< Type, N, K >	zeroes ()
	Get the null matrix.

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

static mat< Type, N, K >	diagonal (Type diag)
	Get a diagonal matrix.

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

static mat< Type, N, K >	rotation_2d (real theta)
	Get a matrix which rotates the 2D plane of <theta> radians.

static mat< Type, N, K >	rotation_3d_xaxis (real theta)
	Get a matrix which rotates <theta> radians around the x axis.

static mat< Type, N, K >	rotation_3d_yaxis (real theta)
	Get a matrix which rotates <theta> radians around the y axis.

static mat< Type, N, K >	rotation_3d_zaxis (real theta)
	Get a matrix which rotates <theta> radians around the z axis.

template<typename Vector = vec<real, 3>>
static mat< Type, N, K >	rotation_3d (real theta, Vector &&axis)
	Get a matrix which rotates <theta> radians around the <axis> axis.

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

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

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

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.

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.

Public Attributes
Type	data [K][N]

Friends
mat< Type, N, K >	operator* (Type a, const mat< Type, N, K > &B)
	Friend operator to enable equations of the form (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 to enable equations of the form (vec) * (mat)

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

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

Member Function Documentation

◆ 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.

◆ 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.

◆ 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.

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

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 >

Member Function Documentation

◆ density()

◆ resize()

◆ sparsity()

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