/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  
  package org.hipparchus.distribution.continuous;
  
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.special.Erf;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  
  /**
   * Implementation of the normal (gaussian) distribution.
   *
   * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution (Wikipedia)</a>
   * @see <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal distribution (MathWorld)</a>
   */
  public class NormalDistribution extends AbstractRealDistribution {
      /** Serializable version identifier. */
      private static final long serialVersionUID = 20160320L;
      /** &radic;(2) */
      private static final double SQRT2 = FastMath.sqrt(2.0);
      /** Mean of this distribution. */
      private final double mean;
      /** Standard deviation of this distribution. */
      private final double standardDeviation;
      /** The value of {@code log(sd) + 0.5*log(2*pi)} stored for faster computation. */
      private final double logStandardDeviationPlusHalfLog2Pi;
  
      /**
       * Create a normal distribution with mean equal to zero and standard
       * deviation equal to one.
       */
      public NormalDistribution() {
          this(0, 1);
      }
  
      /**
       * Create a normal distribution using the given mean, standard deviation.
       *
       * @param mean Mean for this distribution.
       * @param sd Standard deviation for this distribution.
       * @throws MathIllegalArgumentException if {@code sd <= 0}.
       */
      public NormalDistribution(double mean, double sd)
          throws MathIllegalArgumentException {
          if (sd <= 0) {
              throw new MathIllegalArgumentException(LocalizedCoreFormats.STANDARD_DEVIATION, sd);
          }
  
          this.mean = mean;
          this.standardDeviation = sd;
          this.logStandardDeviationPlusHalfLog2Pi =
                  FastMath.log(sd) + 0.5 * FastMath.log(2 * FastMath.PI);
      }
  
      /**
       * Access the mean.
       *
       * @return the mean for this distribution.
       */
      public double getMean() {
          return mean;
      }
  
      /**
       * Access the standard deviation.
       *
       * @return the standard deviation for this distribution.
       */
      public double getStandardDeviation() {
          return standardDeviation;
      }
  
      /** {@inheritDoc} */
      @Override
      public double density(double x) {
          return FastMath.exp(logDensity(x));
      }
  
     /** {@inheritDoc} */
     @Override
     public double logDensity(double x) {
         final double x0 = x - mean;
         final double x1 = x0 / standardDeviation;
         return -0.5 * x1 * x1 - logStandardDeviationPlusHalfLog2Pi;
     }
 
     /**
      * {@inheritDoc}
      *
      * If {@code x} is more than 40 standard deviations from the mean, 0 or 1
      * is returned, as in these cases the actual value is within
      * {@code Double.MIN_VALUE} of 0 or 1.
      */
     @Override
     public double cumulativeProbability(double x)  {
         final double dev = x - mean;
         if (FastMath.abs(dev) > 40 * standardDeviation) {
             return dev < 0 ? 0.0d : 1.0d;
         }
         return 0.5 * Erf.erfc(-dev / (standardDeviation * SQRT2));
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseCumulativeProbability(final double p) throws MathIllegalArgumentException {
         MathUtils.checkRangeInclusive(p, 0, 1);
         return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
     }
 
     /** {@inheritDoc} */
     @Override
     public double probability(double x0,
                               double x1)
         throws MathIllegalArgumentException {
         if (x0 > x1) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
                                                 x0, x1, true);
         }
         final double denom = standardDeviation * SQRT2;
         final double v0 = (x0 - mean) / denom;
         final double v1 = (x1 - mean) / denom;
         return 0.5 * Erf.erf(v0, v1);
     }
 
     /**
      * {@inheritDoc}
      *
      * For mean parameter {@code mu}, the mean is {@code mu}.
      */
     @Override
     public double getNumericalMean() {
         return getMean();
     }
 
     /**
      * {@inheritDoc}
      *
      * For standard deviation parameter {@code s}, the variance is {@code s^2}.
      */
     @Override
     public double getNumericalVariance() {
         final double s = getStandardDeviation();
         return s * s;
     }
 
     /**
      * {@inheritDoc}
      *
      * The lower bound of the support is always negative infinity
      * no matter the parameters.
      *
      * @return lower bound of the support (always
      * {@code Double.NEGATIVE_INFINITY})
      */
     @Override
     public double getSupportLowerBound() {
         return Double.NEGATIVE_INFINITY;
     }
 
     /**
      * {@inheritDoc}
      *
      * The upper bound of the support is always positive infinity
      * no matter the parameters.
      *
      * @return upper bound of the support (always
      * {@code Double.POSITIVE_INFINITY})
      */
     @Override
     public double getSupportUpperBound() {
         return Double.POSITIVE_INFINITY;
     }
 
     /**
      * {@inheritDoc}
      *
      * The support of this distribution is connected.
      *
      * @return {@code true}
      */
     @Override
     public boolean isSupportConnected() {
         return true;
     }
 }