Maximum Space (L-Infinity)

Functions
template<typename InputIterator , typename T = value_type_i<InputIterator>>
T	aaa::maximum::norm (InputIterator first, InputIterator last, T init=T{})
template<typename Container , typename T = value_type<Container>>
T	aaa::maximum::norm (const Container &a, T init=T{})
template<typename InputIterator , typename T = value_type_i<InputIterator>>
T	aaa::maximum::squared_norm (InputIterator first, InputIterator last, T init=T{})
template<typename Container , typename T = value_type<Container>>
T	aaa::maximum::squared_norm (const Container &a, T init=T{})
template<typename InputIterator1 , typename InputIterator2 , typename T = value_type_i<InputIterator1>>
T	aaa::maximum::distance (InputIterator1 first_left, InputIterator1 last_left, InputIterator2 first_right, T init=T{})
template<typename Container1 , typename Container2 , typename T = value_type<Container1>>
T	aaa::maximum::distance (const Container1 &left, const Container2 &right, T init=T{})
template<typename InputIterator1 , typename InputIterator2 , typename T = value_type_i<InputIterator1>>
T	aaa::maximum::squared_distance (InputIterator1 first_left, InputIterator1 last_left, InputIterator2 first_right, T init=T{})
template<typename Container1 , typename Container2 , typename T = value_type<Container1>>
T	aaa::maximum::squared_distance (const Container1 &left, const Container2 &right, T init=T{})

Detailed Description

Maximum space is also known as Chebyshev space or L-infinity space. Maximum space defines the following functions:

• The maximum norm or length of a vector is defined as: \( \| a \|_\infty = \max_i |a_i| \)
• The maximum distance between the vectors a and b is defined as: \( d_\infty(a, b) = \|a-b\|_\infty = \max_i |a_i-b_i| \)

We represent mathematical vectors as either containers, or ranges of iterators. The functions in this module take one or two vectors as input and output a single scalar. This is sometimes refered to as a reduction or fold operation.

Function Documentation

template<typename InputIterator1 , typename InputIterator2 , typename T = value_type_i<InputIterator1>>

T aaa::maximum::distance	(	InputIterator1	first_left,
		InputIterator1	last_left,
		InputIterator2	first_right,
		T	init = T{}
	)

The maximum distance of two vectors. Each vector is represented by a range of iterators.

template<typename Container1 , typename Container2 , typename T = value_type<Container1>>

T aaa::maximum::distance	(	const Container1 &	left,
		const Container2 &	right,
		T	init = T{}
	)

The maximum distance of two vectors. Each vector is represented by a container. The two containers should have the same size.

template<typename InputIterator , typename T = value_type_i<InputIterator>>

T aaa::maximum::norm	(	InputIterator	first,
		InputIterator	last,
		T	init = T{}
	)

The maximum norm of a vector. The vector is represented by a range of iterators.

template<typename Container , typename T = value_type<Container>>

T aaa::maximum::norm	(	const Container &	a,
		T	init = T{}
	)

The maximum norm of a vector. The vector is represented by a container.

template<typename InputIterator1 , typename InputIterator2 , typename T = value_type_i<InputIterator1>>

T aaa::maximum::squared_distance	(	InputIterator1	first_left,
		InputIterator1	last_left,
		InputIterator2	first_right,
		T	init = T{}
	)

The squared maximum distance of two vectors. Each vector is represented by a range of iterators.

template<typename Container1 , typename Container2 , typename T = value_type<Container1>>

T aaa::maximum::squared_distance	(	const Container1 &	left,
		const Container2 &	right,
		T	init = T{}
	)

The squared maximum distance of two vectors. Each vector is represented by a container. The two containers should have the same size.

template<typename InputIterator , typename T = value_type_i<InputIterator>>

T aaa::maximum::squared_norm	(	InputIterator	first,
		InputIterator	last,
		T	init = T{}
	)

The squared maximum norm of a vector. The vector is represented by a range of iterators.

template<typename Container , typename T = value_type<Container>>

T aaa::maximum::squared_norm	(	const Container &	a,
		T	init = T{}
	)

The squared maximum norm of a vector. The vector is represented by a container.