/*
 * $Id$
 * This file is a part of the Arakhne Foundation Classes, http://www.arakhne.org/afc
 *
 * Copyright (c) 2000-2012 Stephane GALLAND.
 * Copyright (c) 2005-10, Multiagent Team, Laboratoire Systemes et Transports,
 *                        Universite de Technologie de Belfort-Montbeliard.
 * Copyright (c) 2013-2016 The original authors, and other authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.arakhne.afc.math.stochastic;

import java.util.Map;
import java.util.Random;

import org.eclipse.xtext.xbase.lib.Pure;


/**
 * Law that representes a Cauchy-Lorentz density.
 *
 * <p>Reference:
 * <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy-Lorentz Distribution</a>.
 *
 * <p>This class uses the uniform random number distribution provided by {@link Random}.
 *
 * @author $Author: cbohrhauer$
 * @version $FullVersion$
 * @mavengroupid $GroupId$
 * @mavenartifactid $ArtifactId$
 * @since 13.0
 */
@SuppressWarnings("checkstyle:parametername")
public class CauchyStochasticLaw extends StochasticLaw {

    private final double x0;

    private final double gamma;

    /**
     * Construct a law with the following parameters.
     * <ul>
     * <li><code>x0</code></li>
     * <li><code>gamma</code></li>
     * </ul>
     *
     * @param parameters is the set of accepted paramters.
     * @throws LawParameterNotFoundException if the list of parameters does not permits to create the law.
     * @throws OutsideDomainException when gamma is outside its domain
     */
    public CauchyStochasticLaw(Map<String, String> parameters) throws OutsideDomainException, LawParameterNotFoundException {
        this.x0 = paramFloat("x0", parameters); //$NON-NLS-1$
        this.gamma = paramFloat("gamma", parameters); //$NON-NLS-1$
        if (this.gamma <= 0) {
            throw new OutsideDomainException(this.gamma);
        }
    }

    /**
     * @param x0 is the location parameter that specifying the location of the peak
     *     of the distribution
     * @param gamma is the scale parameter which specifies the half-width at half-maximum (HWHM).
     * @throws OutsideDomainException when gamma is outside its domain
     */
    public CauchyStochasticLaw(double x0, double gamma) throws OutsideDomainException {
        if (gamma <= 0) {
            throw new OutsideDomainException(gamma);
        }
        this.x0 = x0;
        this.gamma = gamma;
    }

    /** Replies a random value that respect
     * the current stochastic law.
     *
     * @param k represents the shape of the distribution
     * @param xmin is the minimum value of the distribution
     * @return a value depending of the stochastic law parameters
     * @throws MathException when error in the math definition.
     */
    @Pure
    public static double random(double k, double xmin) throws MathException {
        return StochasticGenerator.generateRandomValue(new CauchyStochasticLaw(k, xmin));
    }

    @Pure
    @Override
    public String toString() {
        final StringBuilder b = new StringBuilder();
        b.append("CAUCHY(x0="); //$NON-NLS-1$
        b.append(this.x0);
        b.append(", gamma="); //$NON-NLS-1$
        b.append(this.gamma);
        b.append(')');
        return b.toString();
    }

    @Pure
    @Override
    public double f(double x)  throws MathException {
        final double xm = x - this.x0;
        return 1. / Math.PI * (this.gamma / ((xm * xm) + (this.gamma * this.gamma)));
    }

    @Pure
    @Override
    public MathFunctionRange[] getRange() {
        return MathFunctionRange.createInfinitySet();
    }

    /** Replies the x according to the value of the distribution function.
     *
     * @param u is a value given by the uniform random variable generator {@code U(0, 1)}.
     * @return {@code F<sup>-1</sup>(u)}
     * @throws MathException in case {@code F<sup>-1</sup>(u)} could not be computed
     */
    @Pure
    @Override
    @SuppressWarnings("checkstyle:magicnumber")
    public double inverseF(double u) throws MathException {
        return this.x0 + this.gamma * Math.tan(Math.PI * (u - .5));
    }

}