content: /*
   * 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.asterix.runtime.aggregates.utils;
  
  /**
  The central moments of a data sample are useful for calculating statistics (such as stddev and
  variance) in a single pass.
  
  This class is based on a paper written by Philippe Pébay: Formulas for Robust, One-Pass Parallel
  Computation of Covariances and Arbitrary-Order Statistical Moments, 2008, Technical Report
  SAND2008-6212, Sandia National Laboratories.
  */
  public class SingleVarFunctionsUtil {
      private double m1;
      private double m2;
      private double m3;
      private double m4;
      private long count;
      private boolean m3Flag;
      private boolean m4Flag;
  
      public SingleVarFunctionsUtil() {
          m1 = 0.0;
          m2 = 0.0;
          count = 0;
      }
  
      /**
       * Set the central moments of your current data sample
       *
       * @param  moment1  first moment (mean) of the data sample
       * @param  moment2  second moment of the data sample
       * @param  moment3  third moment of the data sample
       * @param  moment4  fourth moment of the data sample
       * @param  cnt      number of samples
       * @param  moment3Flag   boolean flag to update the value of the third moment when adding values to the data sample
       * @param  moment4Flag   boolean flag to update the value of the fourth moment when adding values to the data sample
       */
      public void set(double moment1, double moment2, double moment3, double moment4, long cnt, boolean moment3Flag,
              boolean moment4Flag) {
          m1 = moment1;
          m2 = moment2;
          m3 = moment3;
          m4 = moment4;
          count = cnt;
          m3Flag = moment3Flag;
          m4Flag = moment4Flag;
      }
  
      /**
       * Update the central moments after adding val to your data sample
       *
       * @param  val      value to add to the data sample
       */
      public void push(double val) {
          count++;
          double delta = val - m1;
          double delta_n = delta / count;
          double term1 = delta * delta_n * (count - 1);
          m1 += delta / count;
          if (m4Flag) {
              m4 += term1 * delta_n * delta_n * (count * count - 3 * count + 3);
              m4 += 6 * delta_n * delta_n * m2 - 4 * delta_n * m3;
          }
          if (m3Flag) {
              m3 += term1 * delta_n * (count - 2) - 3 * delta_n * m2;
          }
          m2 += term1;
      }
  
      /**
       * Combine two sets of central moments into one.
       *
       * @param  moment1  first moment (mean) of the data sample
       * @param  moment2  second moment of the data sample
       * @param  moment3  third moment of the data sample
       * @param  moment4  fourth moment of the data sample
       * @param  cnt      number of samples
       */
      public void combine(double moment1, double moment2, double moment3, double moment4, long cnt) {
          double delta = moment1 - m1;
          long combined_count = count + cnt;
          if (m3Flag) {
              double delta3 = delta * delta * delta;
              if (m4Flag) {
                  m4 += moment4 + delta3 * delta * count * cnt * (count * count - count * cnt + cnt * cnt)
                          / (combined_count * combined_count * combined_count);
                  m4 += 6 * delta * delta * (count * count * moment2 + cnt * cnt * m2) / (combined_count * combined_count)
                          + 4 * delta * (count * moment3 - cnt * m3) / combined_count;
              }
              m3 += moment3 + delta3 * count * cnt * (count - cnt) / (combined_count * combined_count);
              m3 += 3 * delta * (count * moment2 - cnt * m2) / combined_count;
          }
          m1 = (count * m1 + cnt * moment1) / combined_count;
          m2 += moment2 + delta * delta * count * cnt / combined_count;
          count = combined_count;
      }
  
      public double getM1() {
          return m1;
      }
  
      public double getM2() {
          return m2;
      }
  
      public double getM3() {
          return m3;
      }
  
      public double getM4() {
          return m4;
      }
  
      public long getCount() {
          return count;
      }
  }
  