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

Functions
template<typename Vector >
real	theoretica::algebra::lp_norm (const Vector &v, unsigned int p)
	Norms.
template<typename Vector >
real	theoretica::algebra::l1_norm (const Vector &v)
	Compute the l1 norm of a vector: \(\mathcal{l}^1(\vec v) = \Sigma_i \ |v_i|\).
template<typename Vector >
real	theoretica::algebra::l2_norm (const Vector &v)
	Compute the l2 norm of a vector: \(\mathcal{l}^2(\vec v) = \sqrt{\Sigma_i \ v_i^2}\).
template<typename Vector >
real	theoretica::algebra::linf_norm (const Vector &v)
	Compute the linf norm of a vector: \(\mathcal{l}^{\infty}(\vec v) = max(|v_i|)\).
template<typename Vector >
real	theoretica::algebra::euclidean_distance (const Vector &v1, const Vector &v2)
	Distances.
template<typename Vector >
real	theoretica::algebra::distance (const Vector &v1, const Vector &v2)
	Compute the Euclidean distance between two vectors: \(d(\vec v_1, \vec v_2) = \mathcal{l}^2(\vec v_1 - \vec v_2)\).
real	theoretica::algebra::euclidean_distance (real a, real b)
	Compute the Euclidian distance between two real values: \(d(a, b) = |a - b|\).
template<typename T >
real	theoretica::algebra::euclidean_distance (complex< T > z1, complex< T > z2)
	Compute the Euclidean distance between two complex numbers: \(d(z_1, z_2) = |z_1 - z_2|\).
real	theoretica::algebra::distance (real a, real b)
	Compute the Euclidian distance between two values: \(d(a, b) = |a - b|\).
template<typename T >
real	theoretica::algebra::distance (complex< T > z1, complex< T > z2)
	Compute the Euclidean distance between two complex numbers: \(d(z_1, z_2) = |z_1 - z_2|\).
template<typename Vector >
real	theoretica::algebra::minkowski_distance (const Vector &v1, const Vector &v2, unsigned int p)
	Compute the Minkowski distance between two vectors: \(d(\vec v_1, \vec v_2) = \mathcal{l}^p(\vec v_1 - \vec v_2)\).
real	theoretica::algebra::minkowski_distance (real a, real b, unsigned int p)
	Compute the Minkowski distance between two real values: \(d(a, b) = \mathcal{l}^p(a - b)\).
template<typename T >
real	theoretica::algebra::minkowski_distance (complex< T > z1, complex< T > z2, unsigned int p)
	Compute the Minkowski distance between two complex values: \(d(z_1, z_2) = \mathcal{l}^p(z_1 - z_2)\).
template<typename Vector >
real	theoretica::algebra::manhattan_distance (const Vector &v1, const Vector &v2)
	Compute the Manhattan distance between two vectors: \(d(\vec v_1, \vec v_2) = \mathcal{l}^1(\vec v_1 - \vec v_2)\).
template<typename Vector >
real	theoretica::algebra::chebyshev_distance (const Vector &v1, const Vector &v2)
	Compute the Chebyshev distance between two vectors: \(d(\vec v_1, \vec v_2) = \mathcal{l}^{\infty}(\vec v_1 - \vec v_2)\).
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.
template<typename Vector >
real	theoretica::algebra::canberra_distance (const Vector &v1, const Vector &v2)
	Compute the Canberra distance between two vectors.
template<typename Vector >
real	theoretica::algebra::cosine_distance (const Vector &v1, const Vector &v2)
	Compute the cosine distance between two vectors.
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.

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.