Mega Code Archive
Statistical functions on arrays of numbers, namely, the mean, variance, standard deviation, covariance, min and max
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/*
* 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
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* 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));
}
}
}
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