/*
 * 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;

/**
 * Implementation for the {@link ZipfDistribution}.
 * 
 * @version $Revision$ $Date$
 */
public class ZipfDistributionImpl extends AbstractIntegerDistribution 
    implements ZipfDistribution, Serializable {

    /** Serializable version identifier. */
    private static final long serialVersionUID = -140627372283420404L;

    /** Number of elements. */
    private int numberOfElements;

    /** Exponent parameter of the distribution. */
    private double exponent;

    /**
     * Create a new Zipf distribution with the given number of elements and 
     * exponent. Both values must be positive; otherwise an 
     * <code>IllegalArgumentException</code> is thrown.
     * 
     * @param numberOfElements the number of elements
     * @param exponent the exponent
     * @exception IllegalArgumentException if n &le; 0 or s &le; 0.0
     */
    public ZipfDistributionImpl(final int numberOfElements, final double exponent)
        throws IllegalArgumentException {
        setNumberOfElements(numberOfElements);
        setExponent(exponent);
    }

    /**
     * Get the number of elements (e.g. corpus size) for the distribution.
     * 
     * @return the number of elements
     */
    public int getNumberOfElements() {
        return numberOfElements;
    }

    /**
     * Set the number of elements (e.g. corpus size) for the distribution.
     * The parameter value must be positive; otherwise an 
     * <code>IllegalArgumentException</code> is thrown.
     * 
     * @param n the number of elements
     * @exception IllegalArgumentException if n &le; 0
     */
    public void setNumberOfElements(final int n)
        throws IllegalArgumentException {
        if (n <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                    "invalid number of elements {0} (must be positive)",
                    n);
        }
        this.numberOfElements = n;
    }
    
    /**
     * Get the exponent characterising the distribution.
     * 
     * @return the exponent
     */
    public double getExponent() {
        return exponent;
    }

    /**
     * Set the exponent characterising the distribution.
     * The parameter value must be positive; otherwise an 
     * <code>IllegalArgumentException</code> is thrown.
     * 
     * @param s the exponent
     * @exception IllegalArgumentException if s &le; 0.0
     */
    public void setExponent(final double s)
        throws IllegalArgumentException {
        if (s <= 0.0) {
            throw MathRuntimeException.createIllegalArgumentException(
                    "invalid exponent {0} (must be positive)",
                    s);
        }
        this.exponent = s;
    }

    /**
     * The probability mass function P(X = x) for a Zipf distribution.
     * 
     * @param x the value at which the probability density function is evaluated.
     * @return the value of the probability mass function at x
     */
    public double probability(final int x) {
        if (x <= 0 || x > getNumberOfElements()) {
            return 0.0;
        }

        return (1.0 / Math.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);

    }
    
    /**
     * The probability distribution function P(X <= x) for a Zipf distribution.
     * 
     * @param x the value at which the PDF is evaluated.
     * @return Zipf distribution function evaluated at x
     */
    @Override
    public double cumulativeProbability(final int x) {
        if (x <= 0) {
            return 0.0;
        } else if (x >= getNumberOfElements()) {
            return 1.0;
        }

        return generalizedHarmonic(x, exponent) / generalizedHarmonic(numberOfElements, exponent);

    }

    /**
     * Access the domain value lower bound, based on <code>p</code>, used to
     * bracket a PDF 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 int getDomainLowerBound(final double p) {
        return 0;
    }

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


    /**
     * Calculates the Nth generalized harmonic number. See 
     * <a href="http://mathworld.wolfram.com/HarmonicSeries.html">Harmonic 
     * Series</a>.
     * 
     * @param n the term in the series to calculate (must be &ge; 1)
     * @param m the exponent; special case m == 1.0 is the harmonic series
     * @return the nth generalized harmonic number
     */
    private double generalizedHarmonic(final int n, final double m) {
        double value = 0;
        for (int k = n; k > 0; --k) {
            value += 1.0 / Math.pow(k, m);
        }
        return value;
    }

}
