Java tutorial
/* * 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 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * 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)); } } }