/*
 * 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;

/**
 * Base class for integer-valued discrete distributions. Default implementations
 * are provided for some of the methods that do not vary from distribution to
 * distribution.
 * 
 * @version $Revision$ $Date$
 */
public abstract class AbstractIntegerDistribution extends AbstractDistribution
		implements IntegerDistribution, Serializable {

	/** Serializable version identifier */
	private static final long serialVersionUID = -1146319659338487221L;

	/**
	 * Default constructor.
	 */
	protected AbstractIntegerDistribution() {
		super();
	}

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns P(X &le; x). In other words, this
	 * method represents the (cumulative) distribution function, or CDF, for
	 * this distribution.
	 * <p>
	 * If <code>x</code> does not represent an integer value, the CDF is
	 * evaluated at the greatest integer less than x.
	 * 
	 * @param x
	 *            the value at which the distribution function is evaluated.
	 * @return cumulative probability that a random variable with this
	 *         distribution takes a value less than or equal to <code>x</code>
	 * @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 cumulativeProbability((int) Math.floor(x));
	}

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns P(x0 &le; X &le; x1).
	 * 
	 * @param x0
	 *            the (inclusive) lower bound
	 * @param x1
	 *            the (inclusive) upper bound
	 * @return the probability that a random variable with this distribution
	 *         will take a value between <code>x0</code> and <code>x1</code>,
	 *         including the endpoints.
	 * @throws MathException
	 *             if the cumulative probability can not be computed due to
	 *             convergence or other numerical errors.
	 * @throws IllegalArgumentException
	 *             if <code>x0 > x1</code>
	 */
	@Override
	public double cumulativeProbability(double x0, double x1) throws MathException {
		if (x0 > x1) {
			throw MathRuntimeException.createIllegalArgumentException(
					"lower endpoint ({0}) must be less than or equal to upper endpoint ({1})", x0, x1);
		}
		if (Math.floor(x0) < x0) {
			return cumulativeProbability(((int) Math.floor(x0)) + 1, (int) Math.floor(x1)); // don't
																							// want
																							// to
																							// count
																							// mass
																							// below
																							// x0
		} else { // x0 is mathematical integer, so use as is
			return cumulativeProbability((int) Math.floor(x0), (int) Math.floor(x1));
		}
	}

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns P(X &le; x). In other words, this
	 * method represents the probability distribution function, or PDF, for this
	 * distribution.
	 * 
	 * @param x
	 *            the value at which the PDF is evaluated.
	 * @return PDF for this distribution.
	 * @throws MathException
	 *             if the cumulative probability can not be computed due to
	 *             convergence or other numerical errors.
	 */
	abstract public double cumulativeProbability(int x) throws MathException;

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns P(X = x). In other words, this method
	 * represents the probability mass function, or PMF, for the distribution.
	 * <p>
	 * If <code>x</code> does not represent an integer value, 0 is returned.
	 * 
	 * @param x
	 *            the value at which the probability density function is
	 *            evaluated
	 * @return the value of the probability density function at x
	 */
	public double probability(double x) {
		double fl = Math.floor(x);
		if (fl == x) {
			return this.probability((int) x);
		} else {
			return 0;
		}
	}

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns P(x0 &le; X &le; x1).
	 * 
	 * @param x0
	 *            the inclusive, lower bound
	 * @param x1
	 *            the inclusive, upper bound
	 * @return the cumulative probability.
	 * @throws MathException
	 *             if the cumulative probability can not be computed due to
	 *             convergence or other numerical errors.
	 * @throws IllegalArgumentException
	 *             if x0 > x1
	 */
	public double cumulativeProbability(int x0, int x1) throws MathException {
		if (x0 > x1) {
			throw MathRuntimeException.createIllegalArgumentException(
					"lower endpoint ({0}) must be less than or equal to upper endpoint ({1})", x0, x1);
		}
		return cumulativeProbability(x1) - cumulativeProbability(x0 - 1);
	}

	/**
	 * For a random variable X whose values are distributed according to this
	 * distribution, this method returns the largest x, such that P(X &le; x)
	 * &le; <code>p</code>.
	 *
	 * @param p
	 *            the desired probability
	 * @return the largest x such that P(X &le; x) <= p
	 * @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
	 */
	public int inverseCumulativeProbability(final double p) throws MathException {
		if (p < 0.0 || p > 1.0) {
			throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range", p, 0.0, 1.0);
		}

		// by default, do simple bisection.
		// subclasses can override if there is a better method.
		int x0 = getDomainLowerBound(p);
		int x1 = getDomainUpperBound(p);
		double pm;
		while (x0 < x1) {
			int xm = x0 + (x1 - x0) / 2;
			pm = cumulativeProbability(xm);
			if (pm > p) {
				// update x1
				if (xm == x1) {
					// this can happen with integer division
					// simply decrement x1
					--x1;
				} else {
					// update x1 normally
					x1 = xm;
				}
			} else {
				// update x0
				if (xm == x0) {
					// this can happen with integer division
					// simply increment x0
					++x0;
				} else {
					// update x0 normally
					x0 = xm;
				}
			}
		}

		// insure x0 is the correct critical point
		pm = cumulativeProbability(x0);
		while (pm > p) {
			--x0;
			pm = cumulativeProbability(x0);
		}

		return x0;
	}

	/**
	 * Access the domain value lower bound, based on <code>p</code>, used to
	 * bracket a PDF 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>
	 */
	protected abstract int getDomainLowerBound(double p);

	/**
	 * Access the domain value upper bound, based on <code>p</code>, used to
	 * bracket a PDF 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>
	 */
	protected abstract int getDomainUpperBound(double p);
}
