Description

A class representing static n times m-dimensional matrices.

Motivation

Matrices are ubiquitous in mathematics and computer science. Often, matrices represent linear operations and are applied to accordingly-sized vectors.

Constructor

A matrix can be constructed using a variadic constructor which takes the matrix components in row-major order. This way, you can arrange the matrix's components nicely in the source code, as seen in the following example:

using int_matrix_2x3 = fcppt::math::matrix::static_<int, 2, 3>;
 
void ctor()
{
  int_matrix_2x3 const m(fcppt::math::matrix::row(1, 2, 3), fcppt::math::matrix::row(4, 5, 6));
 
  // Will print: ((1,2,3),(4,5,6))
  std::cout << m << '\n';
}

Operators

Matrix defines addition, subtraction, multiplication, scalar multiplication and multiplication by a vector.

Multiplication of two matrices is special: An M1 by N matrix multiplied by an N by M2 matrix results in an M1 by M2 matrix.

void multiply()
{
  fcppt::math::matrix::static_<int, 2, 3> const result(
      fcppt::math::matrix::static_<int, 2, 4>(
          fcppt::math::matrix::row(1, 2, 3, 4), fcppt::math::matrix::row(2, 3, 4, 5)) *
      fcppt::math::matrix::static_<int, 4, 3>(
          fcppt::math::matrix::row(1, 2, 3),
          fcppt::math::matrix::row(4, 5, 6),
          fcppt::math::matrix::row(7, 8, 9),
          fcppt::math::matrix::row(10, 11, 12)));
 
  std::cout << result << '\n';
}

Matrices can also be multiplied by a vector: An R by C matrix multiplied by a C vector yields an R vector. This operation is defined in fcppt/math/matrix/vector.hpp.

void vector_multiply()
{
  fcppt::math::vector::static_<int, 2> const result(
      fcppt::math::matrix::static_<int, 2, 3>(
          fcppt::math::matrix::row(1, 2, 3), fcppt::math::matrix::row(4, 5, 6)) *
      fcppt::math::vector::static_<int, 3>(7, 8, 9));
 
  std::cout << result << '\n';
}

Representation

The matrix's internal representation is row-major, which means that a row is represented as a contiguous chunk of memory. Consequently, operator[] takes the row number and returns a row, which is represented as an fcppt::math::vector::object using a view as storage type. Here is an example:

void row_iterate()
{
  auto const m(fcppt::math::matrix::identity<int_matrix_3x3>());
 
  // Will output: (1,0,0),(0,1,0),(0,0,1),
  fcppt::algorithm::loop(
      fcppt::math::int_range_count<int_matrix_3x3::rows()>{},
      [&m]<fcppt::math::size_type Row>(fcppt::tag<fcppt::math::size_constant<Row>>)
      { std::cout << fcppt::math::matrix::at_r<Row>(m) << ','; });
}

Identity

To get the identity matrix, use the fcppt::math::matrix::identity function:

using int_matrix_3x3 = fcppt::math::matrix::static_<int, 3, 3>;
 
void identity()
{
  auto const m(fcppt::math::matrix::identity<int_matrix_3x3>());
 
  std::cout << m << '\n';
}

Header files

Header file	Description
`object_fwd.hpp`	Contains fcppt::math::matrix::object's declaration.
`object_decl.hpp`	Contains fcppt::math::matrix::object's definition.
`object_impl.hpp`	Contains the definition of fcppt::math::matrix::object's member functions.
`object.hpp`	Includes `object_fwd.hpp`, `object_decl.hpp` and `object_impl.hpp`.
`arithmetic.hpp`	Contains symmetric and scalar arithmetic operators.
`comparison.hpp`	Contains all comparison operators.
`output.hpp`	Contains `operator<<`.
`vector.hpp`	Contains `operator*` for fcppt::math::vector::object.

Classes
struct	fcppt::math::matrix::has_dim< Matrix, R, C >
	Metafunction to check if a static matrix has the specified dimensions. More...

struct	fcppt::math::matrix::index< Row, Column >
	A static matrix index. More...

struct	fcppt::math::matrix::is_matrix< T >
	Metafunction to test if a type is a matrix type. More...

class	fcppt::math::matrix::object< T, R, C, S >
	A class representing a static matrix. More...

Typedefs
template<typename T , fcppt::math::size_type C>
using	fcppt::math::matrix::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	fcppt::math::matrix::static_ = fcppt::math::matrix::object< T, R, C, fcppt::math::matrix::detail::static_storage< T, R, C > >
	Typedef helper for static matrices.

template<typename Matrix >
using	fcppt::math::matrix::to_static = fcppt::math::matrix::static_< fcppt::type_traits::value_type< Matrix >, Matrix::static_rows::value, Matrix::static_columns::value >
	The static type of a matrix.

Functions
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::matrix::static_< T, N, N >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >
fcppt::container::to_reference_type< std::remove_reference_t< Matrix > >	fcppt::math::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 >
fcppt::container::to_reference_type< fcppt::container::to_reference_type< std::remove_reference_t< Matrix > > >	fcppt::math::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 >	fcppt::math::matrix::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	fcppt::math::matrix::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	fcppt::math::matrix::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	fcppt::math::matrix::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 >	fcppt::math::matrix::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	fcppt::math::matrix::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 >
fcppt::math::matrix::static_< T, DN, DN >	fcppt::math::matrix::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 >
fcppt::math::matrix::to_static< Matrix >	fcppt::math::matrix::identity ()
	Returns the identity matrix;.

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S >
T	fcppt::math::matrix::infinity_norm (fcppt::math::matrix::object< T, R, C, S > const &_matrix)
	Calculates the infinity norm.

template<typename Matrix , typename Function >
Matrix	fcppt::math::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 >	fcppt::math::matrix::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 R, fcppt::math::size_type C, typename S , typename Function >
fcppt::math::matrix::static_< std::invoke_result_t< Function, T >, R, C >	fcppt::math::matrix::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 > &	fcppt::math::matrix::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 >	fcppt::math::matrix::rotation_2d (T const _angle)
	Calculates a two dimensional rotation matrix.

template<typename T , typename S >
fcppt::math::matrix::static_< T, 4, 4 >	fcppt::math::matrix::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 >	fcppt::math::matrix::rotation_x (T const _angle)
	Calculates a 4x4 rotation matrix around the x axis.

template<typename T >
fcppt::math::matrix::static_< T, 4, 4 >	fcppt::math::matrix::rotation_y (T const _angle)
	Calculates a 4x4 rotation matrix around the y axis.

template<typename T >
fcppt::math::matrix::static_< T, 4, 4 >	fcppt::math::matrix::rotation_z (T const _angle)
	Calculates a 4x4 rotation matrix around the z axis.

template<typename Type , typename... Args, typename = std::enable_if_t< 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)>	fcppt::math::matrix::row (Type &&_value, Args &&..._args)
	Creates a matrix row for initialization.

template<typename T >
fcppt::math::matrix::static_< T, 4, 4 >	fcppt::math::matrix::scaling (T const _x, T const _y, T const _z)
	Calculates a 4x4 scaling matrix.

template<typename Dest , typename Conv , typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S >
Dest	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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 >	fcppt::math::matrix::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.

Typedef Documentation

◆ row_type

template<typename T , fcppt::math::size_type C>

using fcppt::math::matrix::row_type = typedef fcppt::math::vector::static_<T, C>

The type of matrix row.

◆ static_

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C>

using fcppt::math::matrix::static_ = typedef fcppt::math::matrix::object<T, R, C, fcppt::math::matrix::detail::static_storage<T, R, C> >

Typedef helper for static matrices.

Template Parameters

T	The matrix's `value_type`

◆ to_static

template<typename Matrix >

using fcppt::math::matrix::to_static = typedef fcppt::math::matrix::static_< fcppt::type_traits::value_type<Matrix>, Matrix::static_rows::value, Matrix::static_columns::value>

The static type of a matrix.

Function Documentation

◆ adjugate()

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

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

Calculates the adjugate matrix.

Template Parameters

T	The matrix's `value_type`
N	The matrix's row (and column!) dimension type
S	The matrix's storage type

Parameters

_matrix Must be a statically sized matrix

Warning: You should consider this a slow operation.

◆ at_r()

template<fcppt::math::size_type Index, typename Matrix >

fcppt::container::to_reference_type< std::remove_reference_t< Matrix > > fcppt::math::matrix::at_r ( Matrix & _value )

inline

Access a row using a compile-time constant.

Template Parameters

Matrix Must be an fcppt::math::matrix::object.

◆ at_r_c()

template<fcppt::math::size_type R, fcppt::math::size_type C, typename Matrix >

fcppt::container::to_reference_type< fcppt::container::to_reference_type< std::remove_reference_t< Matrix > > > fcppt::math::matrix::at_r_c ( Matrix & _value )

inline

Access an element using compile-time constants for both row and column.

Template Parameters

Matrix	Must be an fcppt::math::matrix::object.
R	The index of the row
C	The index of the column

◆ binary_map()

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 > fcppt::math::matrix::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
	)

inline

Maps over two matrixs.

◆ componentwise_equal()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S1 , typename S2 >

bool fcppt::math::matrix::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
	)

inline

Compares two floating point matrices componentwise using an epsilon.

Parameters

_m1	The first matrix
_m2	The second matrix
_epsilon	The epsilon to compare with

◆ delete_row_and_column()

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 > fcppt::math::matrix::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.

Returns: The result type will be (N - 1, M - 1)

Template Parameters

DR	The index of the row to delete
DC	The index of the column to delete

◆ determinant()

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

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

inline

Calculates the determinant of a matrix.

Parameters

_matrix The matrix

This function uses the Laplace extension. Consider it slow (very slow!).

See also: fcppt::math::matrix::delete_row_and_column.

◆ exponential_pade()

template<typename T , fcppt::math::size_type DN, typename S >

fcppt::math::matrix::static_< T, DN, DN > fcppt::math::matrix::exponential_pade ( fcppt::math::matrix::object< T, DN, DN, S > const & _matrix )

Calculates the matrix exponential e^A using a Pade approximation.

◆ identity()

template<typename Matrix >

fcppt::math::matrix::to_static< Matrix > fcppt::math::matrix::identity ( )

Returns the identity matrix;.

◆ infinity_norm()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S >

T fcppt::math::matrix::infinity_norm ( fcppt::math::matrix::object< T, R, C, S > const & _matrix )

Calculates the infinity norm.

◆ init()

template<typename Matrix , typename Function >

Matrix fcppt::math::matrix::init ( Function const & _function )

inline

Initializes a matrix.

Calls _function for every index of the matrix.

Template Parameters

Matrix	Must be a matrix
Function	Must be a polymorphic function of type `Matrix::value_type (fcppt::math::matrix::index<R,C>)`

◆ inverse()

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

fcppt::math::matrix::static_< T, N, N > fcppt::math::matrix::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.

Warning: Consider this a slow operation

◆ map()

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 > fcppt::math::matrix::map	(	fcppt::math::matrix::object< T, R, C, S > const &	_value,
		Function const &	_function
	)

inline

Maps over the elements of a matrix.

◆ operator!=()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S1 , typename S2 >

bool fcppt::math::matrix::operator!=	(	fcppt::math::matrix::object< T, R, C, S1 > const &	_m1,
		fcppt::math::matrix::object< T, R, C, S2 > const &	_m2
	)

inline

Compares two matrices component-wise.

Warning: This uses T's inequality comparison operator, so be careful if you want to compare floating point matrices.

◆ operator*() [1/4]

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 > fcppt::math::matrix::operator	(	fcppt::math::matrix::object< L, M1, N, S1 > const &	_left,
		fcppt::math::matrix::object< R, N, M2, S2 > const &	_right
	)

inline

Multiplies two matrices.

◆ operator*() [2/4]

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 > fcppt::math::matrix::operator	(	fcppt::math::matrix::object< Left, R, C, S > const &	_left,
		Right const &	_right
	)

inline

Multiplies a matrix by a scalar.

◆ operator*() [3/4]

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 > fcppt::math::matrix::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.

◆ operator*() [4/4]

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 > fcppt::math::matrix::operator	(	Left const &	_left,
		fcppt::math::matrix::object< Right, R, C, S > const &	_right
	)

inline

Multiplies a matrix by a scalar.

◆ operator+()

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 > fcppt::math::matrix::operator+	(	fcppt::math::matrix::object< Left, R, C, S1 > const &	_left,
		fcppt::math::matrix::object< Right, R, C, S2 > const &	_right
	)

inline

Adds two matrices.

◆ operator-()

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 > fcppt::math::matrix::operator-	(	fcppt::math::matrix::object< Left, R, C, S1 > const &	_left,
		fcppt::math::matrix::object< Right, R, C, S2 > const &	_right
	)

inline

Subtracts one matrix from another.

◆ operator<<()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S , typename Ch , typename Traits >

std::basic_ostream< Ch, Traits > & fcppt::math::matrix::operator<<	(	std::basic_ostream< Ch, Traits > &	_stream,
		fcppt::math::matrix::object< T, R, C, S > const &	_matrix
	)

inline

Outputs the matrix to a basic_ostream

Template Parameters

Ch	The stream's character type
Traits	The stream's character traits type

The format will contain no new-lines and will be of the form:

((a,b,c,...),(d,e,f,...),...,...)

So it'll be the same as if you output the column vectors using the according operator<<.

◆ operator==()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S1 , typename S2 >

bool fcppt::math::matrix::operator==	(	fcppt::math::matrix::object< T, R, C, S1 > const &	_m1,
		fcppt::math::matrix::object< T, R, C, S2 > const &	_m2
	)

inline

Compares two matrices component-wise.

Warning: This uses T's equality comparison operator, so be careful if you want to compare floating point matrices.

◆ rotation_2d()

template<typename T >

fcppt::math::matrix::static_< T, 2, 2 > fcppt::math::matrix::rotation_2d ( T const _angle )

Calculates a two dimensional rotation matrix.

Template Parameters

T	The matrix's `value_type`

Parameters

_angle The angle to rotate about

The resulting matrix will be a static one.

◆ rotation_axis()

template<typename T , typename S >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::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 Parameters

T	The matrix's `value_type`

Parameters

_angle	The angle to rotate about
_vector	The axis to rotate around

The resulting matrix will be static.

See also: fcppt::math::matrix::rotation_x; fcppt::math::matrix::rotation_y; fcppt::math::matrix::rotation_z; fcppt::math::matrix::rotation_axis

◆ rotation_x()

template<typename T >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::rotation_x ( T const _angle )

Calculates a 4x4 rotation matrix around the x axis.

Template Parameters

T	The matrix's `value_type`

Parameters

_angle The angle to rotate about

The resulting matrix will be static.

See also: fcppt::math::matrix::rotation_x; fcppt::math::matrix::rotation_y; fcppt::math::matrix::rotation_z; fcppt::math::matrix::rotation_axis

◆ rotation_y()

template<typename T >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::rotation_y ( T const _angle )

Calculates a 4x4 rotation matrix around the y axis.

Template Parameters

T	The matrix's `value_type`

Parameters

_angle The angle to rotate about

The resulting matrix will be static.

See also: fcppt::math::matrix::rotation_x; fcppt::math::matrix::rotation_y; fcppt::math::matrix::rotation_z; fcppt::math::matrix::rotation_axis

◆ rotation_z()

template<typename T >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::rotation_z ( T const _angle )

Calculates a 4x4 rotation matrix around the z axis.

Template Parameters

T	The matrix's `value_type`

Parameters

_angle The angle to rotate about

The resulting matrix will be static.

See also: fcppt::math::matrix::rotation_x; fcppt::math::matrix::rotation_y; fcppt::math::matrix::rotation_z; fcppt::math::matrix::rotation_axis

◆ row()

template<typename Type , typename... Args, typename = std::enable_if_t< 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)> fcppt::math::matrix::row	(	Type &&	_value,
		Args &&...	_args
	)

inline

Creates a matrix row for initialization.

◆ scaling()

template<typename T >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::scaling	(	T const	_x,
		T const	_y,
		T const	_z
	)

Calculates a 4x4 scaling matrix.

Parameters

_x	Scaling in x direction
_y	Scaling in y direction
_z	Scaling in z direction

◆ structure_cast()

template<typename Dest , typename Conv , typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S >

Dest fcppt::math::matrix::structure_cast ( fcppt::math::matrix::object< T, R, C, S > const & src )

inline

Converts a matrix into a different matrix of the same dimension using Conv.

Template Parameters

Dest	The destination matrix's `value_type`

◆ transform_direction()

template<typename T , typename S1 , typename S2 >

fcppt::math::vector::static_< T, 3 > fcppt::math::matrix::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.

Parameters

_matrix	A 4x4 matrix
_vector	A 3D vector

See also: fcppt::math::matrix::transform_point

◆ transform_point()

template<typename T , typename S1 , typename S2 >

fcppt::math::vector::static_< T, 3 > fcppt::math::matrix::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.

Parameters

_matrix	A 4x4 matrix
_vector	A 3D vector

See also: fcppt::math::matrix::transform_direction

◆ translation() [1/2]

template<typename T , typename S >

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

inline

Calculates a 4x4 translation matrix from a three-dimensional vector.

Parameters

_vec	A three-dimensional vector

◆ translation() [2/2]

template<typename T >

fcppt::math::matrix::static_< T, 4, 4 > fcppt::math::matrix::translation	(	T const	_x,
		T const	_y,
		T const	_z
	)

Calculates a 4x4 translation matrix from three coordinates.

Parameters

_x	The x translation
_y	The y translation
_z	The z translation

◆ transpose()

template<typename T , fcppt::math::size_type R, fcppt::math::size_type C, typename S >

fcppt::math::matrix::static_< T, C, R > fcppt::math::matrix::transpose ( fcppt::math::matrix::object< T, R, C, S > const & _matrix )

Calculates a transposed matrix.

	4.4.0
Freundlich's C++ toolkit

Description

Motivation

Constructor

Operators

Representation

Identity

Header files

Classes

Typedefs

Functions

Typedef Documentation

◆ row_type

◆ static_

◆ to_static

Function Documentation

◆ adjugate()

◆ at_r()

◆ at_r_c()

◆ binary_map()

◆ componentwise_equal()

◆ delete_row_and_column()

◆ determinant()

◆ exponential_pade()

◆ identity()

◆ infinity_norm()

◆ init()

◆ inverse()

◆ map()

◆ operator!=()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator+()

◆ operator-()

◆ operator<<()

◆ operator==()

◆ rotation_2d()

◆ rotation_axis()

◆ rotation_x()

◆ rotation_y()

◆ rotation_z()

◆ row()

◆ scaling()

◆ structure_cast()

◆ transform_direction()

◆ transform_point()

◆ translation() [1/2]

◆ translation() [2/2]

◆ transpose()