distance.h File Reference

Distances and norms of generic vectors, with real or complex elements. More...

#include "./vec.h"
#include "./algebra.h"
#include "../core/constants.h"
#include "../core/core_traits.h"
#include "../core/real_analysis.h"
#include "../complex/complex_analysis.h"

Go to the source code of this file.

Namespaces
	theoretica
	Main namespace of the library which contains all functions and objects.
	theoretica::algebra
	Linear algebra routines.

Functions
template<typename Vector >
real	theoretica::algebra::lp_norm (const Vector &v, unsigned int p)
	Norms. More...
template<typename Vector >
real	theoretica::algebra::l1_norm (const Vector &v)
	Compute the L1 norm of a vector: \(L_1(\vec v) = \Sigma_i \ |v_i|\). More...
template<typename Vector >
real	theoretica::algebra::l2_norm (const Vector &v)
	Compute the L2 norm of a vector: \(L_2(\vec v) = \sqrt{\Sigma_i \ v_i^2}\). More...
template<typename Vector >
real	theoretica::algebra::linf_norm (const Vector &v)
	Compute the Linf norm of a vector: \(L_{\infty}(\vec v) = max(|v_i|)\). More...
template<typename Vector >
real	theoretica::algebra::euclidean_distance (const Vector &v1, const Vector &v2)
	Distances. More...
template<unsigned int N>
real	theoretica::algebra::distance (const vec< real, N > &v1, const vec< real, N > &v2)
	Compute the Euclidean distance between two vectors: \(d(\vec v_1, \vec v_2) = L_2(\vec v_1 - \vec v_2)\). More...
real	theoretica::algebra::euclidean_distance (real a, real b)
	Compute the Euclidian distance between two real values: \(d(a, b) = |a - b|\). More...
real	theoretica::algebra::distance (real a, real b)
	Compute the Euclidian distance between two values: \(d(a, b) = |a - b|\). More...
template<typename T >
complex< T >	theoretica::algebra::distance (complex< T > z1, complex< T > z2)
	Compute the distance between two complex numbers: \(d(z_1, z_2) = |z_1 - z_2|\). More...
template<typename Vector >
real	theoretica::algebra::minkowski_distance (const Vector &v1, const Vector &v2, unsigned int p)
	Compute the Minkowski distance between two vectors: \(d(\vec v_1, \vec v_2) = L_p(\vec v_1 - \vec v_2)\). More...
real	theoretica::algebra::minkowski_distance (real a, real b, unsigned int p)
	Compute the Minkowski distance between two values: \(d(a, b) = L_p(a - b)\). More...
template<typename Vector , typename T = real>
auto	theoretica::algebra::hermitian_distance (const Vector &v1, const Vector &v2)
	Compute the Hermitian distance between two vectors: \(d(\vec v_1, \vec v_2) = (\vec v_1 - \vec v_2) \cdot (\vec v_1 - \vec v_2)^*\). More...
template<unsigned int N, typename T >
complex< T >	theoretica::algebra::distance (const vec< complex< T >, N > &v1, const vec< complex< T >, N > &v2)
	Compute the Hermitian distance between two vectors: \(d(\vec v_1, \vec v_2) = (\vec v_1 - \vec v_2) \cdot (\vec v_1 - \vec v_2)^*\). More...
template<typename Vector >
real	theoretica::algebra::manhattan_distance (const Vector &v1, const Vector &v2)
	Compute the Manhattan distance between two vectors: \(d(\vec v_1, \vec v_2) = L_1(\vec v_1 - \vec v_2)\). More...
template<typename Vector >
real	theoretica::algebra::chebyshev_distance (const Vector &v1, const Vector &v2)
	Compute the Chebyshev distance between two vectors: \(d(\vec v_1, \vec v_2) = L_{\infty}(\vec v_1 - \vec v_2)\). More...
template<typename Vector >
real	theoretica::algebra::discrete_distance (const Vector &v1, const Vector &v2, real tolerance=MACH_EPSILON)
	Compute the discrete distance between two vectors. More...
template<typename Vector >
real	theoretica::algebra::canberra_distance (const Vector &v1, const Vector &v2)
	Compute the Canberra distance between two vectors. More...
template<typename Vector >
real	theoretica::algebra::cosine_distance (const Vector &v1, const Vector &v2)
	Compute the cosine distance between two vectors. More...
template<typename Vector >
real	theoretica::algebra::hamming_distance (const Vector &v1, const Vector &v2, real tolerance=MACH_EPSILON)
	Compute the Hamming distance between two vectors. More...

Detailed Description

Distances and norms of generic vectors, with real or complex elements.

The element type of the vectors needs to have a function abs() which returns a real number.