Manhattan Space (L-1)

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

Detailed Description

Manhattan space is also known as taxicab geometry or L-1 space. Manhattan space defines the following functions:

• The Manhattan norm or length of a vector is defined as: \( \| a \|_1 = \sum_i |a_i| \)
• The Manhattan distance between the vectors a and b is defined as: \( d_1(a, b) = \|a-b\|_1 = \sum_i |a_i-b_i| \)

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

The manhattan distance of two vectors. Each vector is represented by a range of iterators. The two containers should have the same size.

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

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

The manhattan 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::manhattan::norm	(	InputIterator	first,
		InputIterator	last,
		T	init = T{}
	)

The manhattan norm of a vector. The vector is represented a range of iterators.

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

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

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

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

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

The squared manhattan 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::manhattan::squared_distance	(	const Container1 &	left,
		const Container2 &	right,
		T	init = T{}
	)

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

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

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

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

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

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

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