smile.math.kernel.MaternKernel Maven / Gradle / Ivy

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/*******************************************************************************
 * Copyright (c) 2010-2020 Haifeng Li. All rights reserved.
 *
 * Smile is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation, either version 3 of
 * the License, or (at your option) any later version.
 *
 * Smile is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with Smile.  If not, see .
 ******************************************************************************/

package smile.math.kernel;

import smile.math.MathEx;

/**
 * The class of Matérn kernels is a generalization of the Gaussian/RBF.
 * It has an additional parameter nu which controls the smoothness of
 * the kernel function. The smaller nu, the less smooth the approximated
 * function is. As nu -> inf, the kernel becomes equivalent to the
 * Gaussian/RBF kernel. When nu = 1/2, the kernel becomes identical to the
 * Laplacian kernel. The Matern kernel become especially simple
 * when nu is half-integer. Important intermediate values are 3/2
 * (once differentiable functions) and 5/2 (twice differentiable functions).
 *
 * @see GaussianKernel
 * @see LaplacianKernel
 *
 * @author Haifeng Li
 */
public class MaternKernel extends Matern implements MercerKernel {
    /**
     * Constructor.
     * @param sigma The length scale of kernel.
     * @param nu The smoothness of the kernel function. Only 0.5, 1.5, 2.5 and Inf are accepted.
     */
    public MaternKernel(double sigma, double nu) {
        this(sigma, nu, 1E-05, 1E5);
    }

    /**
     * Constructor.
     * @param sigma The length scale of kernel.
     * @param nu The smoothness of the kernel function. Only 0.5, 1.5, 2.5 and Inf are accepted.
     *           The smoothness parameter is fixed during hyperparameter for tuning.
     * @param lo The lower bound of length scale for hyperparameter tuning.
     * @param hi The upper bound of length scale for hyperparameter tuning.
     */
    public MaternKernel(double sigma, double nu, double lo, double hi) {
        super(sigma, nu, lo, hi);
    }

    @Override
    public double k(double[] x, double[] y) {
        return k(MathEx.distance(x, y));
    }

    @Override
    public double[] kg(double[] x, double[] y) {
        return kg(MathEx.distance(x, y));
    }

    @Override
    public MaternKernel of(double[] params) {
        return new MaternKernel(params[0], nu, lo, hi);
    }

    @Override
    public double[] hyperparameters() {
        return new double[] { sigma };
    }

    @Override
    public double[] lo() {
        return new double[] { lo };
    }

    @Override
    public double[] hi() {
        return new double[] { hi };
    }
}