/*
    * 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.statistics.distribution;
  
  /**
   * Implementation of the hypergeometric distribution.
   *
   * <p>The probability mass function of \( X \) is:
   *
   * <p>\[ f(k; N, K, n) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}} \]
   *
   * <p>for \( N \in \{0, 1, 2, \dots\} \) the population size,
   * \( K \in \{0, 1, \dots, N\} \) the number of success states,
   * \( n \in \{0, 1, \dots, N\} \) the number of samples,
   * \( k \in \{\max(0, n+K-N), \dots, \min(n, K)\} \) the number of successes, and
   *
   * <p>\[ \binom{a}{b} = \frac{a!}{b! \, (a-b)!} \]
   *
   * <p>is the binomial coefficient.
   *
   * @see <a href="https://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/HypergeometricDistribution.html">Hypergeometric distribution (MathWorld)</a>
   */
  public final class HypergeometricDistribution extends AbstractDiscreteDistribution {
      /** The number of successes in the population. */
      private final int numberOfSuccesses;
      /** The population size. */
      private final int populationSize;
      /** The sample size. */
      private final int sampleSize;
      /** The lower bound of the support (inclusive). */
      private final int lowerBound;
      /** The upper bound of the support (inclusive). */
      private final int upperBound;
      /** Binomial probability of success (sampleSize / populationSize). */
      private final double p;
      /** Binomial probability of failure ((populationSize - sampleSize) / populationSize). */
      private final double q;
  
      /**
       * @param populationSize Population size.
       * @param numberOfSuccesses Number of successes in the population.
       * @param sampleSize Sample size.
       */
      private HypergeometricDistribution(int populationSize,
                                         int numberOfSuccesses,
                                         int sampleSize) {
          this.numberOfSuccesses = numberOfSuccesses;
          this.populationSize = populationSize;
          this.sampleSize = sampleSize;
          lowerBound = getLowerDomain(populationSize, numberOfSuccesses, sampleSize);
          upperBound = getUpperDomain(numberOfSuccesses, sampleSize);
          p = (double) sampleSize / (double) populationSize;
          q = (double) (populationSize - sampleSize) / (double) populationSize;
      }
  
      /**
       * Creates a hypergeometric distribution.
       *
       * @param populationSize Population size.
       * @param numberOfSuccesses Number of successes in the population.
       * @param sampleSize Sample size.
       * @return the distribution
       * @throws IllegalArgumentException if {@code numberOfSuccesses < 0}, or
       * {@code populationSize <= 0} or {@code numberOfSuccesses > populationSize}, or
       * {@code sampleSize > populationSize}.
       */
      public static HypergeometricDistribution of(int populationSize,
                                                  int numberOfSuccesses,
                                                  int sampleSize) {
          if (populationSize <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE,
                                              populationSize);
          }
          if (numberOfSuccesses < 0) {
              throw new DistributionException(DistributionException.NEGATIVE,
                                              numberOfSuccesses);
          }
          if (sampleSize < 0) {
              throw new DistributionException(DistributionException.NEGATIVE,
                                              sampleSize);
          }
  
          if (numberOfSuccesses > populationSize) {
             throw new DistributionException(DistributionException.TOO_LARGE,
                                             numberOfSuccesses, populationSize);
         }
         if (sampleSize > populationSize) {
             throw new DistributionException(DistributionException.TOO_LARGE,
                                             sampleSize, populationSize);
         }
         return new HypergeometricDistribution(populationSize, numberOfSuccesses, sampleSize);
     }
 
     /**
      * Return the lowest domain value for the given hypergeometric distribution
      * parameters.
      *
      * @param nn Population size.
      * @param k Number of successes in the population.
      * @param n Sample size.
      * @return the lowest domain value of the hypergeometric distribution.
      */
     private static int getLowerDomain(int nn, int k, int n) {
         // Avoid overflow given N > n:
         // n + K - N == K - (N - n)
         return Math.max(0, k - (nn - n));
     }
 
     /**
      * Return the highest domain value for the given hypergeometric distribution
      * parameters.
      *
      * @param k Number of successes in the population.
      * @param n Sample size.
      * @return the highest domain value of the hypergeometric distribution.
      */
     private static int getUpperDomain(int k, int n) {
         return Math.min(n, k);
     }
 
     /**
      * Gets the population size parameter of this distribution.
      *
      * @return the population size.
      */
     public int getPopulationSize() {
         return populationSize;
     }
 
     /**
      * Gets the number of successes parameter of this distribution.
      *
      * @return the number of successes.
      */
     public int getNumberOfSuccesses() {
         return numberOfSuccesses;
     }
 
     /**
      * Gets the sample size parameter of this distribution.
      *
      * @return the sample size.
      */
     public int getSampleSize() {
         return sampleSize;
     }
 
     /** {@inheritDoc} */
     @Override
     public double probability(int x) {
         return Math.exp(logProbability(x));
     }
 
     /** {@inheritDoc} */
     @Override
     public double logProbability(int x) {
         if (x < lowerBound || x > upperBound) {
             return Double.NEGATIVE_INFINITY;
         }
         return computeLogProbability(x);
     }
 
     /**
      * Compute the log probability.
      *
      * @param x Value.
      * @return log(P(X = x))
      */
     private double computeLogProbability(int x) {
         final double p1 =
                 SaddlePointExpansionUtils.logBinomialProbability(x, numberOfSuccesses, p, q);
         final double p2 =
                 SaddlePointExpansionUtils.logBinomialProbability(sampleSize - x,
                         populationSize - numberOfSuccesses, p, q);
         final double p3 =
                 SaddlePointExpansionUtils.logBinomialProbability(sampleSize, populationSize, p, q);
         return p1 + p2 - p3;
     }
 
     /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(int x) {
         if (x < lowerBound) {
             return 0.0;
         } else if (x >= upperBound) {
             return 1.0;
         }
         return innerCumulativeProbability(lowerBound, x);
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(int x) {
         if (x < lowerBound) {
             return 1.0;
         } else if (x >= upperBound) {
             return 0.0;
         }
         return innerCumulativeProbability(upperBound, x + 1);
     }
 
     /**
      * For this distribution, {@code X}, this method returns
      * {@code P(x0 <= X <= x1)}.
      * This probability is computed by summing the point probabilities for the
      * values {@code x0, x0 + dx, x0 + 2 * dx, ..., x1}; the direction {@code dx} is determined
      * using a comparison of the input bounds.
      * This should be called by using {@code x0} as the domain limit and {@code x1}
      * as the internal value. This will result in an initial sum of increasing larger magnitudes.
      *
      * @param x0 Inclusive domain bound.
      * @param x1 Inclusive internal bound.
      * @return {@code P(x0 <= X <= x1)}.
      */
     private double innerCumulativeProbability(int x0, int x1) {
         // Assume the range is within the domain.
         // Reuse the computation for probability(x) but avoid checking the domain for each call.
         int x = x0;
         double ret = Math.exp(computeLogProbability(x));
         if (x0 < x1) {
             while (x != x1) {
                 x++;
                 ret += Math.exp(computeLogProbability(x));
             }
         } else {
             while (x != x1) {
                 x--;
                 ret += Math.exp(computeLogProbability(x));
             }
         }
         return ret;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For population size \( N \), number of successes \( K \), and sample
      * size \( n \), the mean is:
      *
      * <p>\[ n \frac{K}{N} \]
      */
     @Override
     public double getMean() {
         return getSampleSize() * (getNumberOfSuccesses() / (double) getPopulationSize());
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For population size \( N \), number of successes \( K \), and sample
      * size \( n \), the variance is:
      *
      * <p>\[ n \frac{K}{N} \frac{N-K}{N} \frac{N-n}{N-1} \]
      */
     @Override
     public double getVariance() {
         final double N = getPopulationSize();
         final double K = getNumberOfSuccesses();
         final double n = getSampleSize();
         return (n * K * (N - K) * (N - n)) / (N * N * (N - 1));
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For population size \( N \), number of successes \( K \), and sample
      * size \( n \), the lower bound of the support is \( \max \{ 0, n + K - N \} \).
      *
      * @return lower bound of the support
      */
     @Override
     public int getSupportLowerBound() {
         return lowerBound;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For number of successes \( K \), and sample
      * size \( n \), the upper bound of the support is \( \min \{ n, K \} \).
      *
      * @return upper bound of the support
      */
     @Override
     public int getSupportUpperBound() {
         return upperBound;
     }
 }