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Curve Fitting: add Fit.Exponential, Fit.Logarithm, Fit.Power

spatial
Christoph Ruegg 9 years ago
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2 changed files with 191 additions and 0 deletions
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  1. 121
      src/Numerics.Tests/FitTests.cs
  2. 70
      src/Numerics/Fit.cs

121
src/Numerics.Tests/FitTests.cs
View File

@ -98,6 +98,127 @@ namespace MathNet.Numerics.UnitTests
Assert.AreEqual(-0.467791, respSeq, 1e-4);
}
[Test]
public void FitsToLineSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = -1.078 + 0.7932*x
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Line(x, y);
Assert.AreEqual(-1.078, resp.Item1, 1e-3);
Assert.AreEqual(0.7932, resp.Item2, 1e-3);
var resf = Fit.LineFunc(x, y);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(-1.078 + 0.7932*z, resf(z), 1e-2);
}
}
[Test]
public void FitsToExponentialSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = 0.0981*exp(0.6284*x)
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Exponential(x, y);
Assert.AreEqual(0.0981, resp.Item1, 1e-3);
Assert.AreEqual(0.6284, resp.Item2, 1e-3);
var resf = Fit.ExponentialFunc(x, y);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(0.0981 * Math.Exp(0.6284 * z), resf(z), 1e-2);
}
}
[Test]
public void FitsToLogarithmSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = -0.4338 + 1.9981*ln(x)
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Logarithm(x, y);
Assert.AreEqual(-0.4338, resp.Item1, 1e-3);
Assert.AreEqual(1.9981, resp.Item2, 1e-3);
var resf = Fit.LogarithmFunc(x, y);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(-0.4338 + 1.9981 * Math.Log(z), resf(z), 1e-2);
}
}
[Test]
public void FitsToPowerSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = 0.1454*x^1.7044
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Power(x, y);
Assert.AreEqual(0.1454, resp.Item1, 1e-3);
Assert.AreEqual(1.7044, resp.Item2, 1e-3);
var resf = Fit.PowerFunc(x, y);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(0.1454 * Math.Pow(z, 1.7044), resf(z), 1e-2);
}
}
[Test]
public void FitsToOrder2PolynomialSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = 0.7101 - 0.6675*x + 0.2077*x^2
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Polynomial(x, y, 2);
Assert.AreEqual(0.7101, resp[0], 1e-3);
Assert.AreEqual(-0.6675, resp[1], 1e-3);
Assert.AreEqual(0.2077, resp[2], 1e-3);
var resf = Fit.PolynomialFunc(x, y, 2);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(0.7101 - 0.6675*z + 0.2077*z*z, resf(z), 1e-2);
}
}
[Test]
public void FitsToMeanOnOrder0Polynomial()
{

70
src/Numerics/Fit.cs
View File

@ -111,6 +111,76 @@ namespace MathNet.Numerics
return WeightedRegression.Weighted(x, y, w);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to an exponential y : x -> a*exp(r*x),
/// returning its best fitting parameters as (a, r) tuple.
/// </summary>
public static Tuple<double, double> Exponential(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
// Transformation: y_h := ln(y) ~> y_h : x -> ln(a) + r*x;
double[] y_hat = Generate.Map(y, Math.Log);
double[] p_hat = Fit.LinearCombination(x, y_hat, method, t => 1.0, t => t);
return Tuple.Create(Math.Exp(p_hat[0]), p_hat[1]);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to an exponential y : x -> a*exp(r*x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func<double, double> ExponentialFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Exponential(x, y, method);
var a = parameters.Item1;
var r = parameters.Item2;
return z => a * Math.Exp(r * z);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning its best fitting parameters as (a, b) tuple.
/// </summary>
public static Tuple<double, double> Logarithm(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] lnx = Generate.Map(x, Math.Log);
double[] p = Fit.LinearCombination(lnx, y, method, t => 1.0, t => t);
return Tuple.Create(p[0], p[1]);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func<double, double> LogarithmFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Logarithm(x, y, method);
var a = parameters.Item1;
var b = parameters.Item2;
return z => a + b * Math.Log(z);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a power y : x -> a*x^b,
/// returning its best fitting parameters as (a, b) tuple.
/// </summary>
public static Tuple<double, double> Power(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
// Transformation: y_h := ln(y) ~> y_h : x -> ln(a) + b*ln(x);
double[] y_hat = Generate.Map(y, Math.Log);
double[] p_hat = Fit.LinearCombination(x, y_hat, method, t => 1.0, Math.Log);
return Tuple.Create(Math.Exp(p_hat[0]), p_hat[1]);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a power y : x -> a*x^b,
/// returning a function y' for the best fitting line.
/// </summary>
public static Func<double, double> PowerFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Power(x, y, method);
var a = parameters.Item1;
var b = parameters.Item2;
return z => a * Math.Pow(z, b);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.

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