dxx.math.linalg Module Reference

Linear algebra utilities for dxx::math. More...

Concepts
concept	dxx::math::container_traits::constructible
	Checks if the library knows how to construct a vector container from a runtime size value.
concept	dxx::math::container_traits::returnable
	Checks if the library knows how to use a vector container type as a return value from procedures.
concept	dxx::math::vector
	We can treat any input range as a vector.
concept	dxx::math::mut_vector
	A vector for which the elements can be written to.
concept	dxx::math::vector_like
	Vector for which the element type is convertible to a target vector's type.
concept	dxx::math::mut_vector_like
	Similar to vector_like, but also satisfies mut_vector.

Classes
struct	dxx::math::container_traits::size::Dynamic
	Size is a runtime value during construction and can be changed. More...
struct	dxx::math::container_traits::size::RuntimeFixed
	Size can't be changed but unknown at compile time. More...
struct	dxx::math::container_traits::size::Bound
	Size is a runtime value during construction and can be changed, but limited by a compile-time constant. More...
struct	dxx::math::container_traits::size::Static
	Size is a compile-time constant and cannot be modified. More...
struct	dxx::math::Norm< Func, SqFunc >
	Defines a norm. Only norm field is required, all other fields can be assigned a nullptr. More...

Typedefs
template<typename T>
using	dxx::math::RealOf = detail::RealOf<T>::Type
	(Non-cv-qualified) Real type of the linalg type

Functions
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	dxx::math::add (U &&u, V &&v, Out &out)
	Element-wise vector addition. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	dxx::math::add (U &&u, V &&v)
	Element-wise vector addition. Result in return value of a user-provided type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::add (U &&u, V &&v)
	Element-wise vector addition. Result in return value of automatically selected type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator+ (U &&u, V &&v)
	Operator for a corrsponding add overload.
template<mut_vector U, vector_like< U > V>
constexpr U &	dxx::math::vector_operators::operator+= (U &u, const V &v)
	Inplace element-wise vector addition.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	dxx::math::add (U &&u, const Scalar &scalar, Out &out)
	Element-wise addition of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	dxx::math::add (U &&u, const Scalar &scalar)
	Element-wise addition of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::add (U &&u, const Scalar &scalar)
	Element-wise addition of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator+ (U &&u, const Scalar &scalar)
	Operator for a corrsponding add overload.
template<mut_vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr U &	dxx::math::vector_operators::operator+= (U &u, const Scalar &scalar)
	Inplace element-wise addition of vector with scalar.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	dxx::math::add (const Scalar &scalar, U &&u, Out &out)
	Element-wise addition of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	dxx::math::add (const Scalar &scalar, U &&u)
	Element-wise addition of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::add (const Scalar &scalar, U &&u)
	Element-wise addition of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator+ (const Scalar &scalar, U &&u)
	Operator for a corrsponding add overload.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	dxx::math::sub (U &&u, V &&v, Out &out)
	Element-wise vector subtraction. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	dxx::math::sub (U &&u, V &&v)
	Element-wise vector subtraction. Result in return value of a user-provided type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::sub (U &&u, V &&v)
	Element-wise vector subtraction. Result in return value of automatically selected type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator- (U &&u, V &&v)
	Operator for a corrsponding sub overload.
template<mut_vector U, vector_like< U > V>
constexpr U &	dxx::math::vector_operators::operator-= (U &u, const V &v)
	Inplace element-wise vector subtraction.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	dxx::math::sub (U &&u, const Scalar &scalar, Out &out)
	Element-wise subtraction of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	dxx::math::sub (U &&u, const Scalar &scalar)
	Element-wise subtraction of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::sub (U &&u, const Scalar &scalar)
	Element-wise subtraction of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator- (U &&u, const Scalar &scalar)
	Operator for a corrsponding sub overload.
template<mut_vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr U &	dxx::math::vector_operators::operator-= (U &u, const Scalar &scalar)
	Inplace element-wise subtraction of vector with scalar.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	dxx::math::sub (const Scalar &scalar, U &&u, Out &out)
	Element-wise subtraction of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	dxx::math::sub (const Scalar &scalar, U &&u)
	Element-wise subtraction of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::sub (const Scalar &scalar, U &&u)
	Element-wise subtraction of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator- (const Scalar &scalar, U &&u)
	Operator for a corrsponding sub overload.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	dxx::math::mul (U &&u, V &&v, Out &out)
	Element-wise vector multiplication. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	dxx::math::mul (U &&u, V &&v)
	Element-wise vector multiplication. Result in return value of a user-provided type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::mul (U &&u, V &&v)
	Element-wise vector multiplication. Result in return value of automatically selected type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator* (U &&u, V &&v)
	Operator for a corrsponding mul overload.
template<mut_vector U, vector_like< U > V>
constexpr U &	dxx::math::vector_operators::operator*= (U &u, const V &v)
	Inplace element-wise vector multiplication.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	dxx::math::mul (U &&u, const Scalar &scalar, Out &out)
	Element-wise multiplication of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	dxx::math::mul (U &&u, const Scalar &scalar)
	Element-wise multiplication of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::mul (U &&u, const Scalar &scalar)
	Element-wise multiplication of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator* (U &&u, const Scalar &scalar)
	Operator for a corrsponding mul overload.
template<mut_vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr U &	dxx::math::vector_operators::operator*= (U &u, const Scalar &scalar)
	Inplace element-wise multiplication of vector with scalar.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	dxx::math::mul (const Scalar &scalar, U &&u, Out &out)
	Element-wise multiplication of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	dxx::math::mul (const Scalar &scalar, U &&u)
	Element-wise multiplication of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::mul (const Scalar &scalar, U &&u)
	Element-wise multiplication of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator* (const Scalar &scalar, U &&u)
	Operator for a corrsponding mul overload.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	dxx::math::div (U &&u, V &&v, Out &out)
	Element-wise vector division. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	dxx::math::div (U &&u, V &&v)
	Element-wise vector division. Result in return value of a user-provided type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::div (U &&u, V &&v)
	Element-wise vector division. Result in return value of automatically selected type.
template<vector U, vector_like< U > V> requires container_traits::returnable<std::remove_cvref_t<U>>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator/ (U &&u, V &&v)
	Operator for a corrsponding div overload.
template<mut_vector U, vector_like< U > V>
constexpr U &	dxx::math::vector_operators::operator/= (U &u, const V &v)
	Inplace element-wise vector division.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	dxx::math::div (U &&u, const Scalar &scalar, Out &out)
	Element-wise division of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	dxx::math::div (U &&u, const Scalar &scalar)
	Element-wise division of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::div (U &&u, const Scalar &scalar)
	Element-wise division of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator/ (U &&u, const Scalar &scalar)
	Operator for a corrsponding div overload.
template<mut_vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr U &	dxx::math::vector_operators::operator/= (U &u, const Scalar &scalar)
	Inplace element-wise division of vector with scalar.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	dxx::math::div (const Scalar &scalar, U &&u, Out &out)
	Element-wise division of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	dxx::math::div (const Scalar &scalar, U &&u)
	Element-wise division of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::div (const Scalar &scalar, U &&u)
	Element-wise division of vector elements with a scalar. Result in return value of automatically selected type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator/ (const Scalar &scalar, U &&u)
	Operator for a corrsponding div overload.
template<vector U>
constexpr std::remove_cvref_t< U >	dxx::math::vector_operators::operator- (U &&u)
	Unary negation for vectors.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
void	dxx::math::cross (const U &u, const V &v, Out &out)
	Cross product of two 3D vectors (via out parameter).
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	dxx::math::cross (const U &u, const V &v)
	Cross product of two 3D vectors (via return value).
template<container_traits::returnable U, vector_like< U > V>
constexpr U	dxx::math::cross (const U &u, const V &v)
	Cross product of two 3D vectors (via return value of default type).
template<vector U, vector_like< U > V>
constexpr RealOf< U >	dxx::math::dot (const U &u, const V &v)
	Vector dot product.
template<Norm t_norm = norms::euclidean, vector V>
constexpr RealOf< V >	dxx::math::norm (const V &v)
	Calculates norm t_norm for vector v.
template<Norm t_norm = norms::euclidean, vector V>
constexpr RealOf< V >	dxx::math::sq_norm (const V &v)
	Calculates the square of the norm t_norm for vector v.
template<Norm t_norm = norms::euclidean, vector V, vector_like< V > U>
constexpr RealOf< V >	dxx::math::dist (const V &v, const U &u)
	Calculates the distance between vector v and u according to norm t_norm.
template<Norm t_norm = norms::euclidean, vector V, vector_like< V > U>
constexpr RealOf< V >	dxx::math::sq_dist (const V &v, const U &u)
	Calculates the square of the distance between vector v and u according to norm t_norm.

Variables
constexpr Norm	dxx::math::norms::euclidean
	Euclidean norm (2-norm).
constexpr Norm	dxx::math::norms::p_one
	1-norm (sum of absolute values of elements)
constexpr Norm	dxx::math::norms::infinity
	Infinity norm (max absolute value across elements).

Detailed Description

Linear algebra utilities for dxx::math.

Files
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/linalg.xx
	Linear algebra utilities for dxx::math.
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/basic_ops.xx
	Basic vector aritmetic. No documentation for functions since they are generated with macros (I know, I know, it was just too much to just write out...).
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/container_traits.xx
	Traits that help the library where std::ranges API isn't enought. READ THE DESCRIPTION OF math::container_traits CAREFULLY.
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/cross.xx
	Cross product of 3D vectors.
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/dot.xx
	Dot product.
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/norm.xx
	Vector norms.
file	//dot-xx-math/404a2e38e835a56e622ae6ce8e4a230638af3dbd/src/linalg/traits.xx
	Type traits and concepts for linear algebra utilities.