/*
    * 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.numbers.gamma.ErfDifference;
  import org.apache.commons.numbers.gamma.Erfc;
  import org.apache.commons.numbers.gamma.InverseErfc;
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.sampling.distribution.LogNormalSampler;
  import org.apache.commons.rng.sampling.distribution.ZigguratSampler;
  
  /**
   * Implementation of the log-normal distribution.
   *
   * <p>\( X \) is log-normally distributed if its natural logarithm \( \ln(x) \)
   * is normally distributed. The probability density function of \( X \) is:
   *
   * <p>\[ f(x; \mu, \sigma) = \frac 1 {x\sigma\sqrt{2\pi\,}} e^{-{\frac 1 2}\left( \frac{\ln x-\mu}{\sigma} \right)^2 } \]
   *
   * <p>for \( \mu \) the mean of the normally distributed natural logarithm of this distribution,
   * \( \sigma &gt; 0 \) the standard deviation of the normally distributed natural logarithm of this
   * distribution, and
   * \( x \in (0, \infty) \).
   *
   * @see <a href="https://en.wikipedia.org/wiki/Log-normal_distribution">Log-normal distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/LogNormalDistribution.html">Log-normal distribution (MathWorld)</a>
   */
  public final class LogNormalDistribution extends AbstractContinuousDistribution {
      /** &radic;(2 &pi;). */
      private static final double SQRT2PI = Math.sqrt(2 * Math.PI);
      /** The mu parameter of this distribution. */
      private final double mu;
      /** The sigma parameter of this distribution. */
      private final double sigma;
      /** The value of {@code log(sigma) + 0.5 * log(2*PI)} stored for faster computation. */
      private final double logSigmaPlusHalfLog2Pi;
      /** Sigma multiplied by sqrt(2). */
      private final double sigmaSqrt2;
      /** Sigma multiplied by sqrt(2 * pi). */
      private final double sigmaSqrt2Pi;
  
      /**
       * @param mu Mean of the natural logarithm of the distribution values.
       * @param sigma Standard deviation of the natural logarithm of the distribution values.
       */
      private LogNormalDistribution(double mu,
                                    double sigma) {
          this.mu = mu;
          this.sigma = sigma;
          logSigmaPlusHalfLog2Pi = Math.log(sigma) + Constants.HALF_LOG_TWO_PI;
          sigmaSqrt2 = ExtendedPrecision.sqrt2xx(sigma);
          sigmaSqrt2Pi = sigma * SQRT2PI;
      }
  
      /**
       * Creates a log-normal distribution.
       *
       * @param mu Mean of the natural logarithm of the distribution values.
       * @param sigma Standard deviation of the natural logarithm of the distribution values.
       * @return the distribution
       * @throws IllegalArgumentException if {@code sigma <= 0}.
       */
      public static LogNormalDistribution of(double mu,
                                             double sigma) {
          if (sigma <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, sigma);
          }
          return new LogNormalDistribution(mu, sigma);
      }
  
      /**
       * Gets the {@code mu} parameter of this distribution.
       * This is the mean of the natural logarithm of the distribution values,
       * not the mean of distribution.
       *
       * @return the mu parameter.
       */
      public double getMu() {
          return mu;
      }
  
      /**
       * Gets the {@code sigma} parameter of this distribution.
       * This is the standard deviation of the natural logarithm of the distribution values,
      * not the standard deviation of distribution.
      *
      * @return the sigma parameter.
      */
     public double getSigma() {
         return sigma;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For {@code mu}, and sigma {@code s} of this distribution, the PDF
      * is given by
      * <ul>
      * <li>{@code 0} if {@code x <= 0},</li>
      * <li>{@code exp(-0.5 * ((ln(x) - mu) / s)^2) / (s * sqrt(2 * pi) * x)}
      * otherwise.</li>
      * </ul>
      */
     @Override
     public double density(double x) {
         if (x <= 0) {
             return 0;
         }
         final double x0 = Math.log(x) - mu;
         final double x1 = x0 / sigma;
         return Math.exp(-0.5 * x1 * x1) / (sigmaSqrt2Pi * x);
     }
 
     /** {@inheritDoc} */
     @Override
     public double probability(double x0,
                               double x1) {
         if (x0 > x1) {
             throw new DistributionException(DistributionException.INVALID_RANGE_LOW_GT_HIGH,
                                             x0, x1);
         }
         if (x0 <= 0) {
             return cumulativeProbability(x1);
         }
         // Assumes x1 >= x0 && x0 > 0
         final double v0 = (Math.log(x0) - mu) / sigmaSqrt2;
         final double v1 = (Math.log(x1) - mu) / sigmaSqrt2;
         return 0.5 * ErfDifference.value(v0, v1);
     }
 
     /** {@inheritDoc}
      *
      * <p>See documentation of {@link #density(double)} for computation details.
      */
     @Override
     public double logDensity(double x) {
         if (x <= 0) {
             return Double.NEGATIVE_INFINITY;
         }
         final double logX = Math.log(x);
         final double x0 = logX - mu;
         final double x1 = x0 / sigma;
         return -0.5 * x1 * x1 - (logSigmaPlusHalfLog2Pi + logX);
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For {@code mu}, and sigma {@code s} of this distribution, the CDF
      * is given by
      * <ul>
      * <li>{@code 0} if {@code x <= 0},</li>
      * <li>{@code 0} if {@code ln(x) - mu < 0} and {@code mu - ln(x) > 40 * s}, as
      * in these cases the actual value is within {@link Double#MIN_VALUE} of 0,
      * <li>{@code 1} if {@code ln(x) - mu >= 0} and {@code ln(x) - mu > 40 * s},
      * as in these cases the actual value is within {@link Double#MIN_VALUE} of
      * 1,</li>
      * <li>{@code 0.5 + 0.5 * erf((ln(x) - mu) / (s * sqrt(2))} otherwise.</li>
      * </ul>
      */
     @Override
     public double cumulativeProbability(double x)  {
         if (x <= 0) {
             return 0;
         }
         final double dev = Math.log(x) - mu;
         return 0.5 * Erfc.value(-dev / sigmaSqrt2);
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x)  {
         if (x <= 0) {
             return 1;
         }
         final double dev = Math.log(x) - mu;
         return 0.5 * Erfc.value(dev / sigmaSqrt2);
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseCumulativeProbability(double p) {
         ArgumentUtils.checkProbability(p);
         return Math.exp(mu - sigmaSqrt2 * InverseErfc.value(2 * p));
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseSurvivalProbability(double p) {
         ArgumentUtils.checkProbability(p);
         return Math.exp(mu + sigmaSqrt2 * InverseErfc.value(2 * p));
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For \( \mu \) the mean of the normally distributed natural logarithm of
      * this distribution, \( \sigma &gt; 0 \) the standard deviation of the normally
      * distributed natural logarithm of this distribution, the mean is:
      *
      * <p>\[ \exp(\mu + \frac{\sigma^2}{2}) \]
      */
     @Override
     public double getMean() {
         final double s = sigma;
         return Math.exp(mu + (s * s / 2));
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For \( \mu \) the mean of the normally distributed natural logarithm of
      * this distribution, \( \sigma &gt; 0 \) the standard deviation of the normally
      * distributed natural logarithm of this distribution, the variance is:
      *
      * <p>\[ [\exp(\sigma^2) - 1)] \exp(2 \mu + \sigma^2) \]
      */
     @Override
     public double getVariance() {
         final double s = sigma;
         final double ss = s * s;
         return Math.expm1(ss) * Math.exp(2 * mu + ss);
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The lower bound of the support is always 0.
      *
      * @return 0.
      */
     @Override
     public double getSupportLowerBound() {
         return 0;
     }
 
     /**
      * {@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
     public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) {
         // Log normal distribution sampler.
         final ZigguratSampler.NormalizedGaussian gaussian = ZigguratSampler.NormalizedGaussian.of(rng);
         return LogNormalSampler.of(gaussian, mu, sigma)::sample;
     }
 }