fcppt::math::matrix Namespace Reference

Contains fcppt::math::matrix::object matrix::object and helper functions, classes and types for it. More...

Classes
struct	has_dim
	Metafunction to check if a static matrix has the specified dimensions. More...
struct	has_dim< fcppt::math::matrix::object< T, R, C, S >, DR, DC >
struct	index
	A static matrix index. More...
struct	is_matrix
	Metafunction to test if a type is a matrix type. More...
struct	is_matrix< fcppt::math::matrix::object< T, R, C, S > >
class	object
	A class representing a static matrix. More...

Typedefs
template<typename T, fcppt::math::size_type C>
using	row_type = fcppt::math::vector::static_<T, C>
	The type of matrix row.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C>
using	static_
	Typedef helper for static matrices.
template<typename Matrix>
using	to_static
	The static type of a matrix.

Functions
template<typename T, fcppt::math::size_type N, typename S>
fcppt::math::matrix::static_< T, N, N >	adjugate (fcppt::math::matrix::object< T, N, N, S > const &_matrix)
	Calculates the adjugate matrix.
template<typename Left, typename Right, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
fcppt::math::matrix::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(Left,+, Right), R, C >	operator+ (fcppt::math::matrix::object< Left, R, C, S1 > const &_left, fcppt::math::matrix::object< Right, R, C, S2 > const &_right)
	Adds two matrices.
template<typename Left, typename Right, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
fcppt::math::matrix::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(Left, -, Right), R, C >	operator- (fcppt::math::matrix::object< Left, R, C, S1 > const &_left, fcppt::math::matrix::object< Right, R, C, S2 > const &_right)
	Subtracts one matrix from another.
template<typename L, typename R, fcppt::math::size_type N, fcppt::math::size_type M1, fcppt::math::size_type M2, typename S1, typename S2>
fcppt::math::matrix::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), M1, M2 >	operator* (fcppt::math::matrix::object< L, M1, N, S1 > const &_left, fcppt::math::matrix::object< R, N, M2, S2 > const &_right)
	Multiplies two matrices.
template<typename Left, typename Right, fcppt::math::size_type R, fcppt::math::size_type C, typename S>
fcppt::math::matrix::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(Left, *, Right), R, C >	operator* (fcppt::math::matrix::object< Left, R, C, S > const &_left, Right const &_right)
	Multiplies a matrix by a scalar.
template<typename Left, typename Right, fcppt::math::size_type R, fcppt::math::size_type C, typename S>
fcppt::math::matrix::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(Left, *, Right), R, C >	operator* (Left const &_left, fcppt::math::matrix::object< Right, R, C, S > const &_right)
	Multiplies a matrix by a scalar.
template<fcppt::math::size_type Index, typename Matrix> requires fcppt::math::matrix::is_matrix<std::remove_cv_t<Matrix>>::value
fcppt::container::to_reference_type< std::remove_reference_t< Matrix > >	at_r (Matrix &_value)
	Access a row using a compile-time constant.
template<fcppt::math::size_type R, fcppt::math::size_type C, typename Matrix> requires fcppt::math::matrix::is_matrix<std::remove_cv_t<Matrix>>::value
fcppt::container::to_reference_type< fcppt::container::to_reference_type< std::remove_reference_t< Matrix > > >	at_r_c (Matrix &_value)
	Access an element using compile-time constants for both row and column.
template<typename T1, typename T2, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2, typename Function>
fcppt::math::matrix::static_< std::invoke_result_t< Function, T1, T2 >, R, C >	binary_map (fcppt::math::matrix::object< T1, R, C, S1 > const &_left, fcppt::math::matrix::object< T2, R, C, S2 > const &_right, Function const &_function)
	Maps over two matrixs.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
bool	operator== (fcppt::math::matrix::object< T, R, C, S1 > const &_m1, fcppt::math::matrix::object< T, R, C, S2 > const &_m2)
	Compares two matrices component-wise.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
bool	operator!= (fcppt::math::matrix::object< T, R, C, S1 > const &_m1, fcppt::math::matrix::object< T, R, C, S2 > const &_m2)
	Compares two matrices component-wise.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
bool	componentwise_equal (fcppt::math::matrix::object< T, R, C, S1 > const &_m1, fcppt::math::matrix::object< T, R, C, S2 > const &_m2, T const _epsilon)
	Compares two floating point matrices componentwise using an epsilon.
template<fcppt::math::size_type DR, fcppt::math::size_type DC, typename T, typename S, fcppt::math::size_type R, fcppt::math::size_type C>
fcppt::math::matrix::static_< T, R - 1U, C - 1U >	delete_row_and_column (fcppt::math::matrix::object< T, R, C, S > const &_matrix)
	Deletes a specific row and rolumn (a cross) from the matrix.
template<typename T, fcppt::math::size_type N, typename S>
T	determinant (fcppt::math::matrix::object< T, N, N, S > const &_matrix)
	Calculates the determinant of a matrix.
template<typename T, fcppt::math::size_type DN, typename S> requires std::is_floating_point_v<T>
fcppt::math::matrix::static_< T, DN, DN >	exponential_pade (fcppt::math::matrix::object< T, DN, DN, S > const &_matrix)
	Calculates the matrix exponential e^A using a Pade approximation.
template<typename Matrix> requires fcppt::math::matrix::is_matrix<Matrix>::value
fcppt::math::matrix::to_static< Matrix >	identity ()
	Returns the identity matrix;.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S>
T	infinity_norm (fcppt::math::matrix::object< T, R, C, S > const &_matrix)
	Calculates the infinity norm.
template<typename Matrix, typename Function> requires fcppt::math::matrix::is_matrix<Matrix>::value
Matrix	init (Function const &_function)
	Initializes a matrix.
template<typename T, fcppt::math::size_type N, typename S>
fcppt::math::matrix::static_< T, N, N >	inverse (fcppt::math::matrix::object< T, N, N, S > const &_matrix)
	Calculates the inverse matrix, uses fcppt::math::matrix::adjugate and fcppt::math::matrix::determinant.
template<typename T, fcppt::math::size_type N, typename S> requires std::is_floating_point_v<T>
fcppt::math::matrix::static_< T, N, N >	logarithm (fcppt::math::matrix::object< T, N, N, S > A, T const e1, T const e2, T const e3)
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S, typename Function>
fcppt::math::matrix::static_< std::invoke_result_t< Function, T >, R, C >	map (fcppt::math::matrix::object< T, R, C, S > const &_value, Function const &_function)
	Maps over the elements of a matrix.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S, typename Ch, typename Traits>
std::basic_ostream< Ch, Traits > &	operator<< (std::basic_ostream< Ch, Traits > &_stream, fcppt::math::matrix::object< T, R, C, S > const &_matrix)
	Outputs the matrix to a basic_ostream.
template<typename T>
fcppt::math::matrix::static_< T, 2, 2 >	rotation_2d (T const _angle)
	Calculates a two dimensional rotation matrix.
template<typename T, typename S>
fcppt::math::matrix::static_< T, 4, 4 >	rotation_axis (T const _angle, fcppt::math::vector::object< T, 3, S > const &_vector)
	Calculates a 4x4 rotation matrix around an arbitrary axis given as a unit vector.
template<typename T>
fcppt::math::matrix::static_< T, 4, 4 >	rotation_x (T const _angle)
	Calculates a 4x4 rotation matrix around the x axis.
template<typename T>
fcppt::math::matrix::static_< T, 4, 4 >	rotation_y (T const _angle)
	Calculates a 4x4 rotation matrix around the y axis.
template<typename T>
fcppt::math::matrix::static_< T, 4, 4 >	rotation_z (T const _angle)
	Calculates a 4x4 rotation matrix around the z axis.
template<typename Type, typename... Args> requires ( std::conjunction_v<std::is_same<std::remove_cvref_t<Args>, std::remove_cvref_t<Type>>...>)
fcppt::math::matrix::row_type< std::remove_cvref_t< Type >, fcppt::cast::size< fcppt::math::size_type >(sizeof...(Args)+1U)>	row (Type &&_value, Args &&..._args)
	Creates a matrix row for initialization.
template<typename T>
fcppt::math::matrix::static_< T, 4, 4 >	scaling (T const _x, T const _y, T const _z)
	Calculates a 4x4 scaling matrix.
template<typename T, typename S>
fcppt::math::matrix::static_< T, 4, 4 >	scaling (fcppt::math::vector::object< T, 3, S > const &_vec)
	Calculates a scaling matrix from a three dimensional vector.
template<typename T, fcppt::math::size_type N, typename S> requires std::is_floating_point_v<T>
fcppt::math::matrix::static_< T, N, N >	sqrt (fcppt::math::matrix::object< T, N, N, S > const &_matrix, T const _epsilon)
template<typename Dest, typename Conv, typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S> requires fcppt::math::matrix::is_matrix<Dest>::value
Dest	structure_cast (fcppt::math::matrix::object< T, R, C, S > const &src)
	Converts a matrix into a different matrix of the same dimension using Conv.
template<typename T, typename S1, typename S2>
fcppt::math::vector::static_< T, 3 >	transform_direction (fcppt::math::matrix::object< T, 4, 4, S1 > const &_matrix, fcppt::math::vector::object< T, 3, S2 > const &_vector)
	Multiplies a 4x4 matrix by a 3D vector, adding 0 for w, returns a 3D vector.
template<typename T, typename S1, typename S2>
fcppt::math::vector::static_< T, 3 >	transform_point (fcppt::math::matrix::object< T, 4, 4, S1 > const &_matrix, fcppt::math::vector::object< T, 3, S2 > const &_vector)
	Multiplies a 4x4 matrix by a 3D vector, adding 1 for w, returns a 3D vector.
template<typename T>
fcppt::math::matrix::static_< T, 4, 4 >	translation (T const _x, T const _y, T const _z)
	Calculates a 4x4 translation matrix from three coordinates.
template<typename T, typename S>
fcppt::math::matrix::static_< T, 4, 4 >	translation (fcppt::math::vector::object< T, 3, S > const &_vec)
	Calculates a 4x4 translation matrix from a three-dimensional vector.
template<typename T, fcppt::math::size_type R, fcppt::math::size_type C, typename S>
fcppt::math::matrix::static_< T, C, R >	transpose (fcppt::math::matrix::object< T, R, C, S > const &_matrix)
	Calculates a transposed matrix.
template<typename Left, typename Right, fcppt::math::size_type R, fcppt::math::size_type C, typename S1, typename S2>
fcppt::math::vector::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(Left, *, Right), R >	operator* (fcppt::math::matrix::object< Left, R, C, S1 > const &_left, fcppt::math::vector::object< Right, C, S2 > const &_right)
	Multiplies a matrix by a vector.

Detailed Description

Contains fcppt::math::matrix::object matrix::object and helper functions, classes and types for it.

Function Documentation

logarithm()

template<typename T, fcppt::math::size_type N, typename S>
requires std::is_floating_point_v<T>

fcppt::math::matrix::static_< T, N, N > fcppt::math::matrix::logarithm	(	fcppt::math::matrix::object< T, N, N, S >	A,
		T const	e1,
		T const	e2,
		T const	e3 )

scaling()

template<typename T, typename S>

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::scaling ( fcppt::math::vector::object< T, 3, S > const & _vec )

inline

Calculates a scaling matrix from a three dimensional vector.

sqrt()

template<typename T, fcppt::math::size_type N, typename S>
requires std::is_floating_point_v<T>

fcppt::math::matrix::static_< T, N, N > fcppt::math::matrix::sqrt	(	fcppt::math::matrix::object< T, N, N, S > const &	_matrix,
		T const	_epsilon )