jgpml.covariancefunctions.CovSEiso Maven / Gradle / Ivy
/* This file is part of the jgpml Project.
* http://github.com/renzodenardi/jgpml
*
* Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
package jgpml.covariancefunctions;
import Jama.Matrix;
import org.apache.commons.math3.util.FastMath;
import java.util.Arrays;
import static jgpml.covariancefunctions.MatrixOperations.exp;
/**
* Squared Exponential covariance function with isotropic distance measure. The covariance function is parameterized
* as:
*
* k(x^p,x^q) = sf2 * exp(-(x^p - x^q)'*inv(P)*(x^p - x^q)/2)
*
* where the P matrix is ell^2 times the unit matrix and sf2 is the signal variance. The hyperparameters are:
*
* [ log(ell) log(sqrt(sf2)) ]
*/
public class CovSEiso implements CovarianceFunction {
public CovSEiso() {
}
private static Matrix squareDist(Matrix a) {
return CovSEiso.squareDist(a, a);
}
private static Matrix squareDist(Matrix a, Matrix b) {
Matrix C = new Matrix(a.getColumnDimension(), b.getColumnDimension());
int m = a.getColumnDimension();
int n = b.getColumnDimension();
int d = a.getRowDimension();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
double z = 0.0;
for (int k = 0; k < d; k++) {
double t = a.get(k, i) - b.get(k, j);
z += t * t;
}
C.set(i, j, z);
}
}
return C;
}
public static void main(String[] args) {
CovSEiso cf = new CovSEiso();
Matrix X = Matrix.identity(6, 6);
Matrix logtheta = new Matrix(new double[][]{{0.1}, {0.2}});
Matrix d = cf.computeDerivatives(logtheta, X, 1);
d.print(d.getColumnDimension(), 8);
}
/**
* Returns the number of hyperparameters of thisCovarianceFunction
*
* @return number of hyperparameters
*/
public int numParameters() {
return 2;
}
/**
* Compute covariance matrix of a dataset X
*
* @param loghyper column Matrix of hyperparameters
* @param X input dataset
* @return K covariance Matrix
*/
public Matrix compute(Matrix loghyper, Matrix X) {
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != numParameters())
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + numParameters());
double ell = FastMath.exp(loghyper.get(0, 0));
double sf2 = FastMath.exp(2 * loghyper.get(1, 0));
return exp(CovSEiso.squareDist(X.transpose().times(1 / ell)).times(-0.5)).times(sf2);
}
/**
* Compute compute test set covariances
*
* @param loghyper column Matrix of hyperparameters
* @param X input dataset
* @param Xstar test set
* @return [K(Xstar, Xstar) K(X,Xstar)]
*/
public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != numParameters())
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + numParameters());
double ell = FastMath.exp(loghyper.get(0, 0));
double sf2 = FastMath.exp(2 * loghyper.get(1, 0));
double[] a = new double[Xstar.getRowDimension()];
Arrays.fill(a, sf2);
Matrix A = new Matrix(a, a.length);
Matrix B = exp(CovSEiso.squareDist(X.transpose().times(1 / ell), Xstar.transpose().times(1 / ell)).times(-0.5)).times(sf2);
return new Matrix[]{A, B};
}
/**
* Coompute the derivatives of this CovarianceFunction with respect to the hyperparameter with index
* idx
*
* @param loghyper hyperparameters
* @param X input dataset
* @param index hyperparameter index
* @return Matrix of derivatives
*/
public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != numParameters())
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + numParameters());
if (index > numParameters() - 1)
throw new IllegalArgumentException("Wrong hyperparameters index " + index + " it should be smaller or equal to " + (numParameters() - 1));
double ell = FastMath.exp(loghyper.get(0, 0));
double sf2 = FastMath.exp(2 * loghyper.get(1, 0));
Matrix tmp = CovSEiso.squareDist(X.transpose().times(1 / ell));
Matrix A = null;
if (index == 0) {
A = exp(tmp.times(-0.5)).arrayTimes(tmp).times(sf2);
} else {
A = exp(tmp.times(-0.5)).times(2 * sf2);
}
return A;
}
}
// private static Matrix squareDist(Matrix a, Matrix b, Matrix Q){
//
// if(a.getColumnDimension()!=Q.getRowDimension() || b.getColumnDimension()!=Q.getColumnDimension())
// throw new IllegalArgumentException("Wrong size of for Q "+Q.getRowDimension()+"x"+Q.getColumnDimension()+" instead of "+a.getColumnDimension()+"x"+b.getColumnDimension());
//
// Matrix C = new Matrix(D,1);
//
// for (int i=0; i