Statistical functions on arrays of numbers, namely, the mean, variance, standard deviation, covariance, min and max : Math « Development Class « Java






  1. Java
  2. Development Class
  3. Math

Statistical functions on arrays of numbers, namely, the mean, variance, standard deviation, covariance, min and max

       

/*
 * Copyright (c) 2009-2010, Sergey Karakovskiy and Julian Togelius
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *     * Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright
 *       notice, this list of conditions and the following disclaimer in the
 *       documentation and/or other materials provided with the distribution.
 *     * Neither the name of the Mario AI nor the
 *       names of its contributors may be used to endorse or promote products
 *       derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
 * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

//package ch.idsia.utils.statistics;

import java.io.IOException;
import java.io.PrintStream;
import java.util.Enumeration;
import java.util.Vector;

/**
 * This class implements some simple statistical functions on arrays of numbers,
 * namely, the mean, variance, standard deviation, covariance, min and max.
 */

public class Stats {

  /**
   * Converts a vector of Numbers into an array of double. This function does
   * not necessarily belong here, but is commonly required in order to apply
   * the statistical functions conveniently, since they only deal with arrays
   * of double. (Note that a Number of the common superclass of all the Object
   * versions of the primitives, such as Integer, Double etc.).
   */
  // package that at present just provides average and sd of a
  // vector of doubles

  // also enables writing the
  // Gnuplot comments begin with #

  // next need to find out how to select a particular line style
  // found it :
  // This plots sin(x) and cos(x) with linespoints, using the same line type
  // but different point types:
  // plot sin(x) with linesp lt 1 pt 3, cos(x) with linesp lt 1 pt 4
  public static double[] v2a(Vector v) {
    double[] d = new double[v.size()];
    int i = 0;
    for (Enumeration e = v.elements(); e.hasMoreElements();)
      d[i++] = ((Number) e.nextElement()).doubleValue();
    return d;
  }

  /**
   * Calculates the square of a double.
   * 
   * @return Returns x*x
   */

  public static double sqr(double x) {
    return x * x;
  }

  /**
   * Returns the average of an array of double.
   */

  public static double mean(double[] v) {
    double tot = 0.0;
    for (int i = 0; i < v.length; i++)
      tot += v[i];
    return tot / v.length;
  }

  /**
   * @param v
   *            - sample
   * @return the average of an array of int.
   */

  public static double mean(int[] v) {
    double tot = 0.0;
    for (int i = 0; i < v.length; i++)
      tot += v[i];
    return tot / v.length;
  }

  /**
   * Returns the sample standard deviation of an array of double.
   */

  public static double sdev(double[] v) {
    return Math.sqrt(variance(v));
  }

  /**
   * Returns the standard error of an array of double, where this is defined
   * as the standard deviation of the sample divided by the square root of the
   * sample size.
   */

  public static double stderr(double[] v) {
    return sdev(v) / Math.sqrt(v.length);
  }

  /**
   * Returns the variance of the array of double.
   */

  public static double variance(double[] v) {
    double mu = mean(v);
    double sumsq = 0.0;
    for (int i = 0; i < v.length; i++)
      sumsq += sqr(mu - v[i]);
    return sumsq / (v.length);
    // return 1.12; this was done to test a discrepancy with Business
    // Statistics
  }

  /**
   * this alternative version was used to check correctness
   */

  private static double variance2(double[] v) {
    double mu = mean(v);
    double sumsq = 0.0;
    for (int i = 0; i < v.length; i++)
      sumsq += sqr(v[i]);
    System.out.println(sumsq + " : " + mu);
    double diff = (sumsq - v.length * sqr(mu));
    System.out.println("Diff = " + diff);
    return diff / (v.length);
  }

  /**
   * Returns the covariance of the paired arrays of double.
   */

  public static double covar(double[] v1, double[] v2) {
    double m1 = mean(v1);
    double m2 = mean(v2);
    double sumsq = 0.0;
    for (int i = 0; i < v1.length; i++)
      sumsq += (m1 - v1[i]) * (m2 - v2[i]);
    return sumsq / (v1.length);
  }

  public static double correlation(double[] v1, double[] v2) {
    // an inefficient implementation!!!
    return covar(v1, v2) / (sdev(v1) * sdev(v2));
  }

  public static double correlation2(double[] v1, double[] v2) {
    // an inefficient implementation!!!
    return sqr(covar(v1, v2)) / (covar(v1, v1) * covar(v2, v2));
  }

  /**
   * Returns the maximum value in the array.
   */

  public static double max(double[] v) {
    double m = v[0];
    for (int i = 1; i < v.length; i++)
      m = Math.max(m, v[i]);
    return m;
  }

  /**
   * Returns the minimum value in the array.
   */

  public static double min(double[] v) {
    double m = v[0];
    for (int i = 1; i < v.length; i++)
      m = Math.min(m, v[i]);
    return m;
  }

  /**
   * Prints the means and standard deviation of the data to the standard
   * output.
   */

  public static void analyse(double[] v) {
    analyse(v, System.out);
    // System.out.println("Average = " + mean(v) + "  sd = " + sdev(v));
  }

  /**
   * Prints the means and standard deviation of the data to the specified
   * PrintStream
   * 
   * @param v
   *            contains the data
   * @param s
   *            is the corresponding PrintStream
   */

  public static void analyse(double[] v, PrintStream s) {
    s.println("Average = " + mean(v) + "  sd = " + sdev(v));
  }

  /**
   * @param v
   *            contains the data
   * @return A String summary of the with the mean and standard deviation of
   *         the data.
   */

  public static String analysisString(double[] v) {
    return "Average = " + mean(v) + "  sd = " + sdev(v) + "  min = "
        + min(v) + "  max = " + max(v);
  }

  /**
   * Returns a string that compares the root mean square of the data with the
   * standard deviation of the data. This is probably too specialised to be of
   * much general use.
   * 
   * @param v
   *            contains the data
   * @return root mean square = <...> standard deviation = <...>
   */
  public static String rmsString(double[] v) {
    double[] tv = new double[v.length];
    for (int i = 0; i < v.length; i++)
      tv[i] = v[i] * v[i];
    return "rms = " + mean(tv) + " sd = " + sdev(v) + "\n";
  }

  /**
   * Runs through some utils using the functions defined in this class.
   * 
   * @throws java.io.IOException
   */

  public static void main(String[] args) throws IOException {

    double[] d = new double[0];

    double dd = mean(d);

    System.out.println(dd + "\t" + Double.isNaN(dd));

    for (int i = 0; i < 3; i++) {
      double[] x = new double[i];
      System.out.println(mean(x) + "\t " + stderr(x) + "\t " + sdev(x));
    }
  }

}








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