/*
    * 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.math4.legacy.stat.descriptive.moment;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.NullArgumentException;
  import org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  /**
   * Computes the skewness of the available values.
   * <p>
   * We use the following (unbiased) formula to define skewness:</p>
   * <p>
   * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
   * <p>
   * where n is the number of values, mean is the {@link Mean} and std is the
   * {@link StandardDeviation} </p>
   * <p>
   * Note that this statistic is undefined for {@code n < 3}.  <code>Double.Nan</code>
   * is returned when there is not sufficient data to compute the statistic.
   * Double.NaN may also be returned if the input includes NaN and / or
   * infinite values.</p>
   * <p>
   * <strong>Note that this implementation is not synchronized.</strong> If
   * multiple threads access an instance of this class concurrently, and at least
   * one of the threads invokes the <code>increment()</code> or
   * <code>clear()</code> method, it must be synchronized externally. </p>
   */
  public class Skewness extends AbstractStorelessUnivariateStatistic {
      /** The value below which the variance is considered zero and thus skewness is zero. */
      private static final double ZERO_VARIANCE_THRESHOLD = 10E-20;
  
      /** Third moment on which this statistic is based. */
      protected ThirdMoment moment;
  
       /**
       * Determines whether or not this statistic can be incremented or cleared.
       * <p>
       * Statistics based on (constructed from) external moments cannot
       * be incremented or cleared.</p>
      */
      protected boolean incMoment;
  
      /**
       * Constructs a Skewness.
       */
      public Skewness() {
          incMoment = true;
          moment = new ThirdMoment();
      }
  
      /**
       * Constructs a Skewness with an external moment.
       * @param m3 external moment
       */
      public Skewness(final ThirdMoment m3) {
          incMoment = false;
          this.moment = m3;
      }
  
      /**
       * Copy constructor, creates a new {@code Skewness} identical
       * to the {@code original}.
       *
       * @param original the {@code Skewness} instance to copy
       * @throws NullArgumentException if original is null
       */
      public Skewness(Skewness original) throws NullArgumentException {
          copy(original, this);
      }
  
      /**
       * {@inheritDoc}
       * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
       * create a Skewness, this method does nothing. In that case, the
       * ThirdMoment should be incremented directly.</p>
       */
      @Override
      public void increment(final double d) {
          if (incMoment) {
              moment.increment(d);
          }
      }
 
     /**
      * Returns the value of the statistic based on the values that have been added.
      * <p>
      * See {@link Skewness} for the definition used in the computation.</p>
      *
      * @return the skewness of the available values.
      */
     @Override
     public double getResult() {
 
         if (moment.n < 3) {
             return Double.NaN;
         }
         double variance = moment.m2 / (moment.n - 1);
         if (variance < ZERO_VARIANCE_THRESHOLD) {
             return 0.0d;
         } else {
             double n0 = moment.getN();
             return  (n0 * moment.m3) /
             ((n0 - 1) * (n0 -2) * JdkMath.sqrt(variance) * variance);
         }
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public long getN() {
         return moment.getN();
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public void clear() {
         if (incMoment) {
             moment.clear();
         }
     }
 
     /**
      * Returns the Skewness of the entries in the specified portion of the
      * input array.
      * <p>
      * See {@link Skewness} for the definition used in the computation.</p>
      * <p>
      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
      *
      * @param values the input array
      * @param begin the index of the first array element to include
      * @param length the number of elements to include
      * @return the skewness of the values or Double.NaN if length is less than 3
      * @throws MathIllegalArgumentException if the array is null or the array index
      *  parameters are not valid
      */
     @Override
     public double evaluate(final double[] values,final int begin, final int length)
         throws MathIllegalArgumentException {
 
         // Initialize the skewness
         double skew = Double.NaN;
 
         if (MathArrays.verifyValues(values, begin, length) && length > 2 ) {
             Mean mean = new Mean();
             // Get the mean and the standard deviation
             double m = mean.evaluate(values, begin, length);
 
             // Calc the std, this is implemented here instead
             // of using the standardDeviation method eliminate
             // a duplicate pass to get the mean
             double accum = 0.0;
             double accum2 = 0.0;
             for (int i = begin; i < begin + length; i++) {
                 final double d = values[i] - m;
                 accum  += d * d;
                 accum2 += d;
             }
             final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
             if (variance < ZERO_VARIANCE_THRESHOLD) {
                 skew = 0.0d;
             } else {
                 double accum3 = 0.0;
                 for (int i = begin; i < begin + length; i++) {
                     final double d = values[i] - m;
                     accum3 += d * d * d;
                 }
                 accum3 /= variance * JdkMath.sqrt(variance);
 
                 // Get N
                 double n0 = length;
 
                 // Calculate skewness
                 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
             }
         }
         return skew;
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public Skewness copy() {
         Skewness result = new Skewness();
         // No try-catch or advertised exception because args are guaranteed non-null
         copy(this, result);
         return result;
     }
 
     /**
      * Copies source to dest.
      * <p>Neither source nor dest can be null.</p>
      *
      * @param source Skewness to copy
      * @param dest Skewness to copy to
      * @throws NullArgumentException if either source or dest is null
      */
     public static void copy(Skewness source, Skewness dest)
         throws NullArgumentException {
         NullArgumentException.check(source);
         NullArgumentException.check(dest);
         dest.moment = new ThirdMoment(source.moment.copy());
         dest.incMoment = source.incMoment;
     }
 }