/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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.apache.commons.math.distribution;

import java.io.Serializable;

import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;

/**
 * The default implementation of {@link ExponentialDistribution}.
 *
 * @version $Revision$ $Date$
 */
public class ExponentialDistributionImpl extends AbstractContinuousDistribution
		implements ExponentialDistribution, Serializable {

	/** Serializable version identifier */
	private static final long serialVersionUID = 2401296428283614780L;

	/** The mean of this distribution. */
	private double mean;

	/**
	 * Create a exponential distribution with the given mean.
	 * 
	 * @param mean
	 *            mean of this distribution.
	 */
	public ExponentialDistributionImpl(double mean) {
		super();
		setMean(mean);
	}

	/**
	 * Modify the mean.
	 * 
	 * @param mean
	 *            the new mean.
	 * @throws IllegalArgumentException
	 *             if <code>mean</code> is not positive.
	 */
	public void setMean(double mean) {
		if (mean <= 0.0) {
			throw MathRuntimeException.createIllegalArgumentException("mean must be positive ({0})", mean);
		}
		this.mean = mean;
	}

	/**
	 * Access the mean.
	 * 
	 * @return the mean.
	 */
	public double getMean() {
		return mean;
	}

	/**
	 * Return the probability density for a particular point.
	 *
	 * @param x
	 *            The point at which the density should be computed.
	 * @return The pdf at point x.
	 */
	public double density(Double x) {
		if (x < 0) {
			return 0;
		}
		return Math.exp(-x / getMean()) / getMean();
	}

	/**
	 * For this distribution, X, this method returns P(X &lt; x).
	 * 
	 * The implementation of this method is based on:
	 * <ul>
	 * <li><a href="http://mathworld.wolfram.com/ExponentialDistribution.html">
	 * Exponential Distribution</a>, equation (1).</li>
	 * </ul>
	 * 
	 * @param x
	 *            the value at which the CDF is evaluated.
	 * @return CDF for this distribution.
	 * @throws MathException
	 *             if the cumulative probability can not be computed due to
	 *             convergence or other numerical errors.
	 */
	public double cumulativeProbability(double x) throws MathException {
		double ret;
		if (x <= 0.0) {
			ret = 0.0;
		} else {
			ret = 1.0 - Math.exp(-x / getMean());
		}
		return ret;
	}

	/**
	 * For this distribution, X, this method returns the critical point x, such
	 * that P(X &lt; x) = <code>p</code>.
	 * <p>
	 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.
	 * </p>
	 * 
	 * @param p
	 *            the desired probability
	 * @return x, such that P(X &lt; x) = <code>p</code>
	 * @throws MathException
	 *             if the inverse cumulative probability can not be computed due
	 *             to convergence or other numerical errors.
	 * @throws IllegalArgumentException
	 *             if p < 0 or p > 1.
	 */
	@Override
	public double inverseCumulativeProbability(double p) throws MathException {
		double ret;

		if (p < 0.0 || p > 1.0) {
			throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range", p, 0.0, 1.0);
		} else if (p == 1.0) {
			ret = Double.POSITIVE_INFINITY;
		} else {
			ret = -getMean() * Math.log(1.0 - p);
		}

		return ret;
	}

	/**
	 * Access the domain value lower bound, based on <code>p</code>, used to
	 * bracket a CDF root.
	 * 
	 * @param p
	 *            the desired probability for the critical value
	 * @return domain value lower bound, i.e. P(X &lt; <i>lower bound</i>) &lt;
	 *         <code>p</code>
	 */
	@Override
	protected double getDomainLowerBound(double p) {
		return 0;
	}

	/**
	 * Access the domain value upper bound, based on <code>p</code>, used to
	 * bracket a CDF root.
	 * 
	 * @param p
	 *            the desired probability for the critical value
	 * @return domain value upper bound, i.e. P(X &lt; <i>upper bound</i>) &gt;
	 *         <code>p</code>
	 */
	@Override
	protected double getDomainUpperBound(double p) {
		// NOTE: exponential is skewed to the left
		// NOTE: therefore, P(X < &mu;) > .5

		if (p < .5) {
			// use mean
			return getMean();
		} else {
			// use max
			return Double.MAX_VALUE;
		}
	}

	/**
	 * Access the initial domain value, based on <code>p</code>, used to bracket
	 * a CDF root.
	 * 
	 * @param p
	 *            the desired probability for the critical value
	 * @return initial domain value
	 */
	@Override
	protected double getInitialDomain(double p) {
		// TODO: try to improve on this estimate
		// TODO: what should really happen here is not derive from
		// AbstractContinuousDistribution
		// TODO: because the inverse cumulative distribution is simple.
		// Exponential is skewed to the left, therefore, P(X < &mu;) > .5
		if (p < .5) {
			// use 1/2 mean
			return getMean() * .5;
		} else {
			// use mean
			return getMean();
		}
	}
}
