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finmath lib is a Mathematical Finance Library in Java.
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/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 26.08.2018
*/
package net.finmath.montecarlo.conditionalexpectation;
import net.finmath.functions.LinearAlgebra;
import net.finmath.stochastic.RandomVariable;
/**
* Performs a linear regression on random variables implementing RandomVariable.
*
* @author Christian Fries
*/
public class LinearRegression {
private final RandomVariable[] basisFunctions;
/**
* Create the linear regression with a set of basis functions.
*
* @param basisFunctions A vector of (independent) random variables to be used as basis functions.
*/
public LinearRegression(final RandomVariable[] basisFunctions) {
super();
this.basisFunctions = basisFunctions;
}
/**
* Get the vector of regression coefficients.
*
* @param value The random variable to regress.
* @return The vector of regression coefficients.
*/
public double[] getRegressionCoefficients(final RandomVariable value) {
if(basisFunctions.length == 0) {
return new double[] { };
}
else if(basisFunctions.length == 1) {
/*
* Regression with one basis function is just a projection on that vector. /
*/
return new double[] { value.mult(basisFunctions[0]).getAverage() / basisFunctions[0].squared().getAverage() };
}
else if(basisFunctions.length == 2) {
/*
* Regression with two basis functions can be solved explicitly if determinant != 0 (otherwise we will fallback to SVD)
*/
final double a = basisFunctions[0].squared().getAverage();
final double b = basisFunctions[0].mult(basisFunctions[1]).average().squared().doubleValue();
final double c = b;
final double d = basisFunctions[1].squared().getAverage();
final double determinant = (a * d - b * c);
if(determinant != 0) {
final double x = value.mult(basisFunctions[0]).getAverage();
final double y = value.mult(basisFunctions[1]).getAverage();
final double alpha0 = (d * x - b * y) / determinant;
final double alpha1 = (a * y - c * x) / determinant;
return new double[] { alpha0, alpha1 };
}
}
/*
* General case
*/
// Build regression matrix
final double[][] BTB = new double[basisFunctions.length][basisFunctions.length];
for(int i=0; i