/*
 * 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.MathRuntimeException;

/**
 * Default implementation of
 * {@link org.apache.commons.math.distribution.CauchyDistribution}.
 *
 * @since 1.1
 * @version $Revision$ $Date$
 */
public class CauchyDistributionImpl extends AbstractContinuousDistribution implements CauchyDistribution, Serializable {

	/** Serializable version identifier */
	private static final long serialVersionUID = 8589540077390120676L;

	/** The median of this distribution. */
	private double median = 0;

	/** The scale of this distribution. */
	private double scale = 1;

	/**
	 * Creates cauchy distribution with the medain equal to zero and scale equal
	 * to one.
	 */
	public CauchyDistributionImpl() {
		this(0.0, 1.0);
	}

	/**
	 * Create a cauchy distribution using the given median and scale.
	 * 
	 * @param median
	 *            median for this distribution
	 * @param s
	 *            scale parameter for this distribution
	 */
	public CauchyDistributionImpl(double median, double s) {
		super();
		setMedian(median);
		setScale(s);
	}

	/**
	 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
	 * 
	 * @param x
	 *            the value at which the CDF is evaluated.
	 * @return CDF evaluted at <code>x</code>.
	 */
	public double cumulativeProbability(double x) {
		return 0.5 + (Math.atan((x - median) / scale) / Math.PI);
	}

	/**
	 * Access the median.
	 * 
	 * @return median for this distribution
	 */
	public double getMedian() {
		return median;
	}

	/**
	 * Access the scale parameter.
	 * 
	 * @return scale parameter for this distribution
	 */
	public double getScale() {
		return scale;
	}

	/**
	 * For this distribution, X, this method returns the critical point x, such
	 * that P(X &lt; x) = <code>p</code>.
	 * <p>
	 * Returns <code>Double.NEGATIVE_INFINITY</code> 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 IllegalArgumentException
	 *             if <code>p</code> is not a valid probability.
	 */
	@Override
	public double inverseCumulativeProbability(double p) {
		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 == 0) {
			ret = Double.NEGATIVE_INFINITY;
		} else if (p == 1) {
			ret = Double.POSITIVE_INFINITY;
		} else {
			ret = median + scale * Math.tan(Math.PI * (p - .5));
		}
		return ret;
	}

	/**
	 * Modify the median.
	 * 
	 * @param median
	 *            for this distribution
	 */
	public void setMedian(double median) {
		this.median = median;
	}

	/**
	 * Modify the scale parameter.
	 * 
	 * @param s
	 *            scale parameter for this distribution
	 * @throws IllegalArgumentException
	 *             if <code>sd</code> is not positive.
	 */
	public void setScale(double s) {
		if (s <= 0.0) {
			throw MathRuntimeException.createIllegalArgumentException("scale must be positive ({0})", s);
		}
		scale = s;
	}

	/**
	 * 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) {
		double ret;

		if (p < .5) {
			ret = -Double.MAX_VALUE;
		} else {
			ret = getMedian();
		}

		return ret;
	}

	/**
	 * 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) {
		double ret;

		if (p < .5) {
			ret = getMedian();
		} else {
			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) {
		double ret;

		if (p < .5) {
			ret = getMedian() - getScale();
		} else if (p > .5) {
			ret = getMedian() + getScale();
		} else {
			ret = getMedian();
		}

		return ret;
	}
}
