/*
 * $Id$
 * 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.Inline;
import org.eclipse.xtext.xbase.lib.Pure;

/**
 * Law that representes a triangular density.
 *
 * <p>Reference:
 * <a href="http://mathworld.wolfram.com/TriangularDistribution.html">Triangular 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
 */
public class TriangularStochasticLaw extends StochasticLaw {

    private final double minX;

    private final double mode;

    private final double maxX;

    private final double dxmode;

    private final double delta1;

    private final double delta2;

    /**
     * Construct a law with the following parameters.
     * <ul>
     * <li><code>minX</code></li>
     * <li><code>mode</code></li>
     * <li><code>maxX</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.
     */
    public TriangularStochasticLaw(Map<String, String> parameters) throws LawParameterNotFoundException {
        this(paramFloat("minX", parameters), //$NON-NLS-1$
                paramFloat("mode", parameters), //$NON-NLS-1$
                paramFloat("maxX", parameters)); //$NON-NLS-1$
    }

    /** Construct the law.
     * @param minX1 is the lower bound where {@code f(minX) = 0}
     * @param mode is the maxima point of the distribution {@code f(mode) = max(f(x))}
     * @param maxX1 is the upper bound where {@code f(maxX) = 0}
     */
    public TriangularStochasticLaw(double minX1, double mode, double maxX1) {
        double i = minX1;
        double a = maxX1;
        double mod = mode;
        if (i > a) {
            final double t = a;
            a = i;
            i = t;
        }
        if (i > mod) {
            final double t = mod;
            mod = i;
            i = t;
        }
        if (mod > a) {
            final double t = a;
            a = mod;
            mod = t;
        }
        this.minX = i;
        this.mode = mod;
        this.maxX = a;


        this.delta1 = (this.maxX - this.minX) * (this.mode - this.minX);
        this.delta2 = (this.maxX - this.minX) * (this.maxX - this.mode);

        this.dxmode = (this.mode - this.minX) / (this.maxX - this.minX);
    }

    /** Replies a random value that respect
     * the current stochastic law.
     *
     * @param minX is the lower bound where {@code f(minX) = 0}
     * @param mode is the maxima point of the distribution {@code f(mode) = max(f(x))}
     * @param maxX is the upper bound where {@code f(maxX) = 0}
     * @return a value depending of the stochastic law parameters
     * @throws MathException when math definition error.
     */
    @Pure
    @Inline(value = "StochasticGenerator.generateRandomValue(new TriangularStochasticLaw(($1), ($2), ($3)))",
            imported = {StochasticGenerator.class, TriangularStochasticLaw.class})
    public static double random(double minX, double mode, double maxX) throws MathException {
        return StochasticGenerator.generateRandomValue(new TriangularStochasticLaw(minX, mode, maxX));
    }

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

    @Pure
    @Override
    public double f(double x)  throws MathException {
        if ((x < this.minX) || (x > this.maxX)) {
            throw new OutsideDomainException(x);
        }

        final double denom = this.maxX - this.minX;

        if (x <= this.mode) {
            final double xm = 2. * (x - this.minX);
            return xm / (denom * (this.mode - this.minX));
        }

        final double xm = 2. * (this.maxX - x);
        return 1.f - (xm / (denom * (this.maxX - this.mode)));

    }

    @Pure
    @Override
    public MathFunctionRange[] getRange() {
        return MathFunctionRange.createSet(this.minX, this.maxX);
    }

    /** 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
    public double inverseF(double u) throws MathException {
        if ((u < 0) || (u > 1)) {
            throw new OutsideDomainException(u);
        }

        if (u < this.dxmode) {
            return Math.sqrt(u * this.delta1) + this.minX;
        }

        return this.maxX - Math.sqrt((1 - u) * this.delta2);
    }

}