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Euclidean.cs
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Euclidean.cs
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// Accord Math Library
// The Accord.NET Framework
// http://accord-framework.net
//
// Copyright © César Souza, 2009-2017
// cesarsouza at gmail.com
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
//
namespace Accord.Math.Distances
{
using System;
using Accord.Compat;
using System.Runtime.CompilerServices;
/// <summary>
/// Euclidean distance metric.
/// </summary>
///
/// <example>
/// <code source="Unit Tests\Accord.Tests.Math\DistanceTest.cs" region="doc_euclidean_4" />
/// </example>
///
/// <seealso cref="SquareEuclidean"/>
/// <seealso cref="WeightedSquareEuclidean"/>
/// <seealso cref="WeightedEuclidean"/>
///
[Serializable]
public struct Euclidean :
IMetric<double>, ISimilarity<double>,
IMetric<double[]>, ISimilarity<double[]>,
IMetric<Tuple<double, double>>, ISimilarity<Tuple<double, double>>,
IDistance<Sparse<double>>, ISimilarity<Sparse<double>>
{
/// <summary>
/// Computes the distance <c>d(x,y)</c> between points
/// <paramref name="x"/> and <paramref name="y"/>.
/// </summary>
///
/// <param name="x">The first point <c>x</c>.</param>
/// <param name="y">The second point <c>y</c>.</param>
///
/// <returns>
/// A double-precision value representing the distance <c>d(x,y)</c>
/// between <paramref name="x"/> and <paramref name="y"/> according
/// to the distance function implemented by this class.
/// </returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(double x, double y)
{
return Math.Abs(x - y);
}
/// <summary>
/// Computes the distance <c>d(x,y)</c> between points
/// <paramref name="x"/> and <paramref name="y"/>.
/// </summary>
///
/// <param name="x">The first point <c>x</c>.</param>
/// <param name="y">The second point <c>y</c>.</param>
///
/// <returns>
/// A double-precision value representing the distance <c>d(x,y)</c>
/// between <paramref name="x"/> and <paramref name="y"/> according
/// to the distance function implemented by this class.
/// </returns>
///
/// <example>
/// <code source="Unit Tests\Accord.Tests.Math\DistanceTest.cs" region="doc_euclidean_4" />
/// </example>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(double[] x, double[] y)
{
double sum = 0.0;
for (int i = 0; i < x.Length; i++)
{
double u = x[i] - y[i];
sum += u * u;
}
return Math.Sqrt(sum);
}
/// <summary>
/// Gets the Euclidean distance between two points. Note: this function
/// is dangerous as it is too easy to invert its arguments by mistake.
/// Please consider using the Tuple<double, double> overload instead.
/// </summary>
///
/// <param name="vector1x">The first coordinate of first point in space.</param>
/// <param name="vector1y">The second coordinate of first point in space.</param>
/// <param name="vector2x">The first coordinate of second point in space.</param>
/// <param name="vector2y">The second coordinate of second point in space.</param>
///
/// <returns>The Euclidean distance between x and y.</returns>
///
/// <example>
/// <code source="Unit Tests\Accord.Tests.Math\DistanceTest.cs" region="doc_euclidean_4" />
/// </example>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(double vector1x, double vector1y, double vector2x, double vector2y)
{
double dx = vector1x - vector2x;
double dy = vector1y - vector2y;
return Math.Sqrt(dx * dx + dy * dy);
}
/// <summary>
/// Gets the Euclidean distance between two points.
/// </summary>
///
/// <param name="x">The first point in space.</param>
/// <param name="y">The second point in space.</param>
///
/// <returns>The Euclidean distance between x and y.</returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(Tuple<double, double> x, Tuple<double, double> y)
{
double dx = x.Item1 - y.Item1;
double dy = y.Item1 - y.Item2;
return Math.Sqrt(dx * dx + dy * dy);
}
/// <summary>
/// Computes the distance <c>d(x,y)</c> between points
/// <paramref name="x"/> and <paramref name="y"/>.
/// </summary>
///
/// <param name="x">The first point <c>x</c>.</param>
/// <param name="y">The second point <c>y</c>.</param>
///
/// <returns>
/// A double-precision value representing the distance <c>d(x,y)</c>
/// between <paramref name="x"/> and <paramref name="y"/> according
/// to the distance function implemented by this class.
/// </returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(Sparse<double> x, Sparse<double> y)
{
return Math.Sqrt(SquareEuclidean.Sparse(x, y));
}
/// <summary>
/// Gets a similarity measure between two points.
/// </summary>
///
/// <param name="x">The first point to be compared.</param>
/// <param name="y">The second point to be compared.</param>
///
/// <returns>A similarity measure between x and y.</returns>
///
public double Similarity(double x, double y)
{
return 1.0 / (1.0 + Math.Abs(x - y));
}
/// <summary>
/// Gets a similarity measure between two points.
/// </summary>
///
/// <param name="x">The first point to be compared.</param>
/// <param name="y">The second point to be compared.</param>
///
/// <returns>A similarity measure between x and y.</returns>
///
public double Similarity(double[] x, double[] y)
{
double sum = 0.0;
for (int i = 0; i < x.Length; i++)
{
double u = x[i] - y[i];
sum += u * u;
}
return 1.0 / (1.0 + Math.Sqrt(sum));
}
/// <summary>
/// Gets a similarity measure between two points.
/// </summary>
///
/// <param name="x">The first point to be compared.</param>
/// <param name="y">The second point to be compared.</param>
///
/// <returns>A similarity measure between x and y.</returns>
///
public double Similarity(Tuple<double, double> x, Tuple<double, double> y)
{
double dx = x.Item1 - y.Item1;
double dy = y.Item1 - y.Item2;
return 1.0 / (1.0 + Math.Sqrt(dx * dx + dy * dy));
}
/// <summary>
/// Gets a similarity measure between two points.
/// </summary>
///
/// <param name="x">The first point to be compared.</param>
/// <param name="y">The second point to be compared.</param>
///
/// <returns>A similarity measure between x and y.</returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Similarity(Sparse<double> x, Sparse<double> y)
{
return 1.0 / (1.0 + Distance(x, y));
}
}
}