/* 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 static jgpml.covariancefunctions.MatrixOperations.exp;
import static jgpml.covariancefunctions.MatrixOperations.sumRows;

/**
 * Linear covariance function with Automatic Relevance Determination (ARD). The
 * covariance function is parameterized as:
 * <p>
 * k(x^p,x^q) = x^p'*inv(P)*x^q
 * <p>
 * where the P matrix is diagonal with ARD parameters ell_1^2,...,ell_D^2, where
 * D is the dimension of the input space. The hyperparameters are:
 * <p>
 * [ log(ell_1)  <br>
 * log(ell_2)  <br>
 * .          <br>
 * log(ell_D) ] <br>
 * <p>
 * Note that there is no bias term; use covConst to add a bias.
 */

public class CovLINard implements CovarianceFunction {

    private final int D;

    /**
     * Creates a new <code>CovSEard CovarianceFunction</code>
     *
     * @param inputDimension muber of dimension of the input
     */
    public CovLINard(int inputDimension) {
        this.D = inputDimension;
    }

    /**
     * Returns the number of hyperparameters of this<code>CovarianceFunction</code>
     *
     * @return number of hyperparameters
     */
    public int numParameters() {
        return this.D;
    }

    /**
     * Compute covariance matrix of a dataset X
     *
     * @param loghyper column <code>Matrix</code> of hyperparameters
     * @param X        input dataset
     * @return K covariance <code>Matrix</code>
     */
    public Matrix compute(Matrix loghyper, Matrix X) {

        if (X.getColumnDimension() != this.D)
            throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
        if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != numParameters())
            throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + numParameters());

        Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0));                         // characteristic length scales
        Matrix diag = new Matrix(this.D, this.D);
        for (int i = 0; i < this.D; i++)
            diag.set(i, i, 1 / ell.get(i, 0));

        X = X.times(diag);

        return X.times(X.transpose());
    }

    /**
     * Compute compute test set covariances
     *
     * @param loghyper column <code>Matrix</code> 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 (X.getColumnDimension() != this.D)
            throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
        if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != numParameters())
            throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + numParameters());

        Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0));                         // characteristic length scales
        Matrix diag = new Matrix(this.D, this.D);
        for (int i = 0; i < this.D; i++)
            diag.set(i, i, 1 / ell.get(i, 0));

        X = X.times(diag);

        Xstar = Xstar.times(diag);
        Matrix A = sumRows(Xstar.arrayTimes(Xstar));

        Matrix B = X.times(Xstar.transpose());
        return new Matrix[]{A, B};
    }

    /**
     * Coompute the derivatives of this <code>CovarianceFunction</code> with respect
     * to the hyperparameter with index <code>idx</code>
     *
     * @param loghyper hyperparameters
     * @param X        input dataset
     * @param index    hyperparameter index
     * @return <code>Matrix</code> of derivatives
     */
    public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
        if (X.getColumnDimension() != this.D)
            throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
        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));

        Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0));                         // characteristic length scales
        Matrix diag = new Matrix(this.D, this.D);
        for (int i = 0; i < this.D; i++)
            diag.set(i, i, 1 / ell.get(i, 0));

        X = X.times(diag);

        Matrix tmp = X.getMatrix(0, X.getRowDimension() - 1, index, index);
        return tmp.times(tmp.transpose()).times(-2);
    }


    public static void main(String[] args) {

        CovLINard cf = new CovLINard(6);

        Matrix X = Matrix.identity(6, 6);
        Matrix logtheta = new Matrix(new double[][]{{0.1}, {0.2}, {0.3}, {0.4}, {0.5}, {0.6}});

        Matrix z = new Matrix(new double[][]{{1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}});

        System.out.println();

        Matrix d = cf.computeDerivatives(logtheta, X, 5);

        d.print(d.getColumnDimension(), 8);

    }
}
