// <copyright file="SimpleRegression.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2018 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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namespace IStation.Numerics.LinearRegression
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{
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public static class SimpleRegression
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{
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/// <summary>
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/// Least-Squares fitting the points (x,y) to a line y : x -> a+b*x,
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/// returning its best fitting parameters as (a, b) tuple,
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/// where a is the intercept and b the slope.
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/// </summary>
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/// <param name="x">Predictor (independent)</param>
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/// <param name="y">Response (dependent)</param>
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public static Tuple<double, double> Fit(double[] x, double[] y)
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{
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if (x.Length != y.Length)
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{
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throw new ArgumentException($"All sample vectors must have the same length. However, vectors with disagreeing length {x.Length} and {y.Length} have been provided. A sample with index i is given by the value at index i of each provided vector.");
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}
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if (x.Length <= 1)
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{
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throw new ArgumentException($"A regression of the requested order requires at least {2} samples. Only {x.Length} samples have been provided.");
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}
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// First Pass: Mean (Less robust but faster than ArrayStatistics.Mean)
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double mx = 0.0;
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double my = 0.0;
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for (int i = 0; i < x.Length; i++)
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{
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mx += x[i];
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my += y[i];
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}
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mx /= x.Length;
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my /= y.Length;
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// Second Pass: Covariance/Variance
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double covariance = 0.0;
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double variance = 0.0;
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for (int i = 0; i < x.Length; i++)
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{
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double diff = x[i] - mx;
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covariance += diff*(y[i] - my);
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variance += diff*diff;
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}
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var b = covariance/variance;
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return new Tuple<double, double>(my - b*mx, b);
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}
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/// <summary>
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/// Least-Squares fitting the points (x,y) to a line y : x -> a+b*x,
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/// returning its best fitting parameters as (a, b) tuple,
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/// where a is the intercept and b the slope.
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/// </summary>
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/// <param name="samples">Predictor-Response samples as tuples</param>
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public static Tuple<double, double> Fit(IEnumerable<Tuple<double, double>> samples)
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{
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var xy = samples.UnpackSinglePass();
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return Fit(xy.Item1, xy.Item2);
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}
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/// <summary>
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/// Least-Squares fitting the points (x,y) to a line y : x -> b*x,
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/// returning its best fitting parameter b,
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/// where the intercept is zero and b the slope.
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/// </summary>
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/// <param name="x">Predictor (independent)</param>
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/// <param name="y">Response (dependent)</param>
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public static double FitThroughOrigin(double[] x, double[] y)
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{
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if (x.Length != y.Length)
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{
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throw new ArgumentException($"All sample vectors must have the same length. However, vectors with disagreeing length {x.Length} and {y.Length} have been provided. A sample with index i is given by the value at index i of each provided vector.");
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}
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if (x.Length <= 1)
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{
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throw new ArgumentException($"A regression of the requested order requires at least {2} samples. Only {x.Length} samples have been provided.");
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}
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double mxy = 0.0;
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double mxx = 0.0;
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for (int i = 0; i < x.Length; i++)
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{
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mxx += x[i]*x[i];
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mxy += x[i]*y[i];
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}
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return mxy / mxx;
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}
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/// <summary>
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/// Least-Squares fitting the points (x,y) to a line y : x -> b*x,
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/// returning its best fitting parameter b,
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/// where the intercept is zero and b the slope.
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/// </summary>
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/// <param name="samples">Predictor-Response samples as tuples</param>
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public static double FitThroughOrigin(IEnumerable<Tuple<double, double>> samples)
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{
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double mxy = 0.0;
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double mxx = 0.0;
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foreach (var sample in samples)
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{
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mxx += sample.Item1 * sample.Item1;
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mxy += sample.Item1 * sample.Item2;
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}
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return mxy / mxx;
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}
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}
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}
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