/*
    * 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;
  
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.sampling.distribution.StableSampler;
  
  /**
   * Implementation of the Cauchy distribution.
   *
   * <p>The probability density function of \( X \) is:
   *
   * <p>\[ f(x; x_0, \gamma) = { 1 \over \pi \gamma } \left[ { \gamma^2 \over (x - x_0)^2 + \gamma^2  } \right] \]
   *
   * <p>for \( x_0 \) the location,
   * \( \gamma &gt; 0 \) the scale, and
   * \( x \in (-\infty, \infty) \).
   *
   * @see <a href="https://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/CauchyDistribution.html">Cauchy distribution (MathWorld)</a>
   */
  public final class CauchyDistribution extends AbstractContinuousDistribution {
      /** The location of this distribution. */
      private final double location;
      /** The scale of this distribution. */
      private final double scale;
      /** Density factor (scale / pi). */
      private final double scaleOverPi;
      /** Density factor (scale^2). */
      private final double scale2;
  
      /**
       * @param location Location parameter.
       * @param scale Scale parameter.
       */
      private CauchyDistribution(double location,
                                 double scale) {
          this.scale = scale;
          this.location = location;
          scaleOverPi = scale / Math.PI;
          scale2 = scale * scale;
      }
  
      /**
       * Creates a Cauchy distribution.
       *
       * @param location Location parameter.
       * @param scale Scale parameter.
       * @return the distribution
       * @throws IllegalArgumentException if {@code scale <= 0}.
       */
      public static CauchyDistribution of(double location,
                                          double scale) {
          if (scale <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, scale);
          }
          return new CauchyDistribution(location, scale);
      }
  
      /**
       * Gets the location parameter of this distribution.
       *
       * @return the location parameter.
       */
      public double getLocation() {
          return location;
      }
  
      /**
       * Gets the scale parameter of this distribution.
       *
       * @return the scale parameter.
       */
      public double getScale() {
          return scale;
      }
  
      /** {@inheritDoc} */
      @Override
      public double density(double x) {
          final double dev = x - location;
          return scaleOverPi / (dev * dev + scale2);
      }
  
      /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(double x) {
         return cdf((x - location) / scale);
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x) {
         return cdf(-(x - location) / scale);
     }
 
     /**
      * Compute the CDF of the Cauchy distribution with location 0 and scale 1.
      * @param x Point at which the CDF is evaluated
      * @return CDF(x)
      */
     private static double cdf(double x) {
         return 0.5 + (Math.atan(x) / Math.PI);
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>Returns {@link Double#NEGATIVE_INFINITY} when {@code p == 0}
      * and {@link Double#POSITIVE_INFINITY} when {@code p == 1}.
      */
     @Override
     public double inverseCumulativeProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 0) {
             return Double.NEGATIVE_INFINITY;
         } else  if (p == 1) {
             return Double.POSITIVE_INFINITY;
         }
         return location + scale * Math.tan(Math.PI * (p - 0.5));
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>Returns {@link Double#NEGATIVE_INFINITY} when {@code p == 1}
      * and {@link Double#POSITIVE_INFINITY} when {@code p == 0}.
      */
     @Override
     public double inverseSurvivalProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 1) {
             return Double.NEGATIVE_INFINITY;
         } else  if (p == 0) {
             return Double.POSITIVE_INFINITY;
         }
         return location - scale * Math.tan(Math.PI * (p - 0.5));
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The mean is always undefined.
      *
      * @return {@link Double#NaN NaN}.
      */
     @Override
     public double getMean() {
         return Double.NaN;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The variance is always undefined.
      *
      * @return {@link Double#NaN NaN}.
      */
     @Override
     public double getVariance() {
         return Double.NaN;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The lower bound of the support is always negative infinity.
      *
      * @return {@linkplain Double#NEGATIVE_INFINITY negative infinity}.
      */
     @Override
     public double getSupportLowerBound() {
         return Double.NEGATIVE_INFINITY;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The upper bound of the support is always positive infinity.
      *
      * @return {@linkplain Double#POSITIVE_INFINITY positive infinity}.
      */
     @Override
     public double getSupportUpperBound() {
         return Double.POSITIVE_INFINITY;
     }
 
     /** {@inheritDoc} */
     @Override
     double getMedian() {
         // Overridden for the probability(double, double) method.
         // This is intentionally not a public method.
         return location;
     }
 
     /** {@inheritDoc} */
     @Override
     public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) {
         // Cauchy distribution =
         // Stable distribution with alpha=1, beta=0, gamma=scale, delta=location
         return StableSampler.of(rng, 1, 0, getScale(), getLocation())::sample;
     }
 }