/// <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[] lny = Generate.Map(y, Math.Log);
double[] p = LinearCombination(x, lny, method, t => 1.0, t => t);
return(Tuple.Create(Math.Exp(p[0]), p[1]));
}
/// <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 (double A, double B) Power(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
// Transformation: y_h := ln(y) ~> y_h : x -> ln(a) + b*ln(x);
double[] lny = Generate.Map(y, Math.Log);
double[] p = LinearCombination(x, lny, method, t => 1.0, Math.Log);
return(Math.Exp(p[0]), p[1]);
}
/// <summary>
/// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p0, p1, p2, x),
/// returning its best fitting parameter p0, p1 and p2.
/// </summary>
public static Tuple <double, double, double> Curve(double[] x, double[] y, Func <double, double, double, double, double> f, double initialGuess0, double initialGuess1, double initialGuess2, double tolerance = 1e-8, int maxIterations = 1000)
{
return(FindMinimum.OfFunction((p0, p1, p2) => Distance.Euclidean(Generate.Map(x, t => f(p0, p1, p2, t)), y), initialGuess0, initialGuess1, initialGuess2, tolerance, maxIterations));
}
/// <summary>
/// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p, x),
/// returning its best fitting parameter p.
/// </summary>
public static double Curve(double[] x, double[] y, Func <double, double, double> f, double initialGuess, double tolerance = 1e-8, int maxIterations = 1000)
{
return(FindMinimum.OfScalarFunction(p => Distance.Euclidean(Generate.Map(x, t => f(p, t)), y), initialGuess, tolerance, maxIterations));
}
/// <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 = 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 its best fitting parameters as (a, b) tuple.
/// </summary>
public static (double A, double B) Logarithm(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] lnx = Generate.Map(x, Math.Log);
double[] p = LinearCombination(lnx, y, method, _ => 1.0, t => t);
return(p[0], p[1]);
}