source: src/main/java/agents/uk/ac/soton/ecs/gp4j/util/MathUtils.java

package agents.uk.ac.soton.ecs.gp4j.util;

import agents.Jama.Matrix;
import agents.org.apache.commons.lang.Validate;

public class MathUtils {
        public static double normPDF(double x, double mean, double standardDeviation) {
                return Math.exp(-(Math.pow((x - mean) / standardDeviation, 2)) / 2)
                                / (Math.sqrt(2 * Math.PI) * standardDeviation);
        }

        public static double mvnPDF(double[] x, double[] mu, double[][] sigma) {
                double N = x.length;

                Validate.isTrue(N == mu.length);
                Validate.isTrue(N == sigma.length);

                Matrix sigmaMat = new Matrix(sigma);
                Matrix xMat = new Matrix(x, 1);
                Matrix muMat = new Matrix(mu, 1);

                double constant = 1 / Math.sqrt(Math.pow(2 * Math.PI, N)
                                * sigmaMat.det());

                Matrix xMinMu = xMat.minus(muMat);

                double d = xMinMu.times(sigmaMat.inverse()).times(xMinMu.transpose())
                                .get(0, 0);

                return constant * Math.exp(-0.5 * d);
        }
}