/*
 * 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;

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

	/** Serializable version identifier */
	private static final long serialVersionUID = -8352658048349159782L;

	/** Internal Gamma distribution. */
	private GammaDistribution gamma;

	/**
	 * Create a Chi-Squared distribution with the given degrees of freedom.
	 * 
	 * @param df
	 *            degrees of freedom.
	 */
	public ChiSquaredDistributionImpl(double df) {
		this(df, new GammaDistributionImpl(df / 2.0, 2.0));
	}

	/**
	 * Create a Chi-Squared distribution with the given degrees of freedom.
	 * 
	 * @param df
	 *            degrees of freedom.
	 * @param g
	 *            the underlying gamma distribution used to compute
	 *            probabilities.
	 * @since 1.2
	 */
	public ChiSquaredDistributionImpl(double df, GammaDistribution g) {
		super();
		setGamma(g);
		setDegreesOfFreedom(df);
	}

	/**
	 * Modify the degrees of freedom.
	 * 
	 * @param degreesOfFreedom
	 *            the new degrees of freedom.
	 */
	public void setDegreesOfFreedom(double degreesOfFreedom) {
		getGamma().setAlpha(degreesOfFreedom / 2.0);
	}

	/**
	 * Access the degrees of freedom.
	 * 
	 * @return the degrees of freedom.
	 */
	public double getDegreesOfFreedom() {
		return getGamma().getAlpha() * 2.0;
	}

	/**
	 * 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) {
		return gamma.density(x);
	}

	/**
	 * For this distribution, X, this method returns P(X &lt; x).
	 * 
	 * @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 {
		return getGamma().cumulativeProbability(x);
	}

	/**
	 * 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 <code>p</code> is not a valid probability.
	 */
	@Override
	public double inverseCumulativeProbability(final double p) throws MathException {
		if (p == 0) {
			return 0d;
		}
		if (p == 1) {
			return Double.POSITIVE_INFINITY;
		}
		return super.inverseCumulativeProbability(p);
	}

	/**
	 * Access the domain value lower bound, based on <code>p</code>, used to
	 * bracket a CDF root. This method is used by
	 * {@link #inverseCumulativeProbability(double)} to find critical values.
	 * 
	 * @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 Double.MIN_VALUE * getGamma().getBeta();
	}

	/**
	 * Access the domain value upper bound, based on <code>p</code>, used to
	 * bracket a CDF root. This method is used by
	 * {@link #inverseCumulativeProbability(double)} to find critical values.
	 * 
	 * @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: chi squared is skewed to the left
		// NOTE: therefore, P(X < &mu;) > .5

		double ret;

		if (p < .5) {
			// use mean
			ret = getDegreesOfFreedom();
		} else {
			// use max
			ret = Double.MAX_VALUE;
		}

		return ret;
	}

	/**
	 * Access the initial domain value, based on <code>p</code>, used to bracket
	 * a CDF root. This method is used by
	 * {@link #inverseCumulativeProbability(double)} to find critical values.
	 * 
	 * @param p
	 *            the desired probability for the critical value
	 * @return initial domain value
	 */
	@Override
	protected double getInitialDomain(double p) {
		// NOTE: chi squared is skewed to the left
		// NOTE: therefore, P(X < &mu;) > .5

		double ret;

		if (p < .5) {
			// use 1/2 mean
			ret = getDegreesOfFreedom() * .5;
		} else {
			// use mean
			ret = getDegreesOfFreedom();
		}

		return ret;
	}

	/**
	 * Modify the underlying gamma distribution. The caller is responsible for
	 * insuring the gamma distribution has the proper parameter settings.
	 * 
	 * @param g
	 *            the new distribution.
	 * @since 1.2 made public
	 */
	public void setGamma(GammaDistribution g) {
		this.gamma = g;

	}

	/**
	 * Access the Gamma distribution.
	 * 
	 * @return the internal Gamma distribution.
	 */
	private GammaDistribution getGamma() {
		return gamma;
	}
}
