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Commons Math example source code file (Variance.java)

This example Commons Math source code file (Variance.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

abstractstorelessunivariatestatistic, io, mean, mean, override, override, secondmoment, secondmoment, serializable, variance, variance, weightedevaluation

The Commons Math Variance.java source code

/*
 * 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.math.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.stat.descriptive.WeightedEvaluation;
import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;

/**
 * Computes the variance of the available values.  By default, the unbiased
 * "sample variance" definitional formula is used:
 * <p>
 * variance = sum((x_i - mean)^2) / (n - 1) </p>
 * <p>
 * where mean is the {@link Mean} and <code>n is the number
 * of sample observations.</p>
 * <p>
 * The definitional formula does not have good numerical properties, so
 * this implementation does not compute the statistic using the definitional
 * formula. <ul>
 * <li> The getResult method computes the variance using
 * updating formulas based on West's algorithm, as described in
 * <a href="http://doi.acm.org/10.1145/359146.359152"> Chan, T. F. and
 * J. G. Lewis 1979, <i>Communications of the ACM,
 * vol. 22 no. 9, pp. 526-531.</a>
 * <li> The evaluate methods leverage the fact that they have the
 * full array of values in memory to execute a two-pass algorithm.
 * Specifically, these methods use the "corrected two-pass algorithm" from
 * Chan, Golub, Levesque, <i>Algorithms for Computing the Sample Variance,
 * American Statistician, vol. 37, no. 3 (1983) pp. 242-247.</li>
 * Note that adding values using <code>increment or
 * <code>incrementAll and then executing getResult will
 * sometimes give a different, less accurate, result than executing
 * <code>evaluate with the full array of values. The former approach
 * should only be used when the full array of values is not available.</p>
 * <p>
 * The "population variance"  ( sum((x_i - mean)^2) / n ) can also
 * be computed using this statistic.  The <code>isBiasCorrected
 * property determines whether the "population" or "sample" value is
 * returned by the <code>evaluate and getResult methods.
 * To compute population variances, set this property to <code>false.
 * </p>
 * <p>
 * <strong>Note that this implementation is not synchronized. If
 * multiple threads access an instance of this class concurrently, and at least
 * one of the threads invokes the <code>increment() or
 * <code>clear() method, it must be synchronized externally.

* * @version $Revision: 908626 $ $Date: 2010-02-10 13:44:42 -0500 (Wed, 10 Feb 2010) $ */ public class Variance extends AbstractStorelessUnivariateStatistic implements Serializable, WeightedEvaluation { /** Serializable version identifier */ private static final long serialVersionUID = -9111962718267217978L; /** SecondMoment is used in incremental calculation of Variance*/ protected SecondMoment moment = null; /** * Boolean test to determine if this Variance should also increment * the second moment, this evaluates to false when this Variance is * constructed with an external SecondMoment as a parameter. */ protected boolean incMoment = true; /** * Determines whether or not bias correction is applied when computing the * value of the statisic. True means that bias is corrected. See * {@link Variance} for details on the formula. */ private boolean isBiasCorrected = true; /** * Constructs a Variance with default (true) <code>isBiasCorrected * property. */ public Variance() { moment = new SecondMoment(); } /** * Constructs a Variance based on an external second moment. * * @param m2 the SecondMoment (Third or Fourth moments work * here as well.) */ public Variance(final SecondMoment m2) { incMoment = false; this.moment = m2; } /** * Constructs a Variance with the specified <code>isBiasCorrected * property * * @param isBiasCorrected setting for bias correction - true means * bias will be corrected and is equivalent to using the argumentless * constructor */ public Variance(boolean isBiasCorrected) { moment = new SecondMoment(); this.isBiasCorrected = isBiasCorrected; } /** * Constructs a Variance with the specified <code>isBiasCorrected * property and the supplied external second moment. * * @param isBiasCorrected setting for bias correction - true means * bias will be corrected * @param m2 the SecondMoment (Third or Fourth moments work * here as well.) */ public Variance(boolean isBiasCorrected, SecondMoment m2) { incMoment = false; this.moment = m2; this.isBiasCorrected = isBiasCorrected; } /** * Copy constructor, creates a new {@code Variance} identical * to the {@code original} * * @param original the {@code Variance} instance to copy */ public Variance(Variance original) { copy(original, this); } /** * {@inheritDoc} * <p>If all values are available, it is more accurate to use * {@link #evaluate(double[])} rather than adding values one at a time * using this method and then executing {@link #getResult}, since * <code>evaluate leverages the fact that is has the full * list of values together to execute a two-pass algorithm. * See {@link Variance}.</p> */ @Override public void increment(final double d) { if (incMoment) { moment.increment(d); } } /** * {@inheritDoc} */ @Override public double getResult() { if (moment.n == 0) { return Double.NaN; } else if (moment.n == 1) { return 0d; } else { if (isBiasCorrected) { return moment.m2 / (moment.n - 1d); } else { return moment.m2 / (moment.n); } } } /** * {@inheritDoc} */ public long getN() { return moment.getN(); } /** * {@inheritDoc} */ @Override public void clear() { if (incMoment) { moment.clear(); } } /** * Returns the variance of the entries in the input array, or * <code>Double.NaN if the array is empty. * <p> * See {@link Variance} for details on the computing algorithm.</p> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if the array is null.

* <p> * Does not change the internal state of the statistic.</p> * * @param values the input array * @return the variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException if the array is null */ @Override public double evaluate(final double[] values) { if (values == null) { throw MathRuntimeException.createIllegalArgumentException("input values array is null"); } return evaluate(values, 0, values.length); } /** * Returns the variance of the entries in the specified portion of * the input array, or <code>Double.NaN if the designated subarray * is empty. * <p> * See {@link Variance} for details on the computing algorithm.</p> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Does not change the internal state of the statistic.</p> * <p> * Throws <code>IllegalArgumentException if the array is null.

* * @param values the input array * @param begin index of the first array element to include * @param length the number of elements to include * @return the variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException 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) { double var = Double.NaN; if (test(values, begin, length)) { clear(); if (length == 1) { var = 0.0; } else if (length > 1) { Mean mean = new Mean(); double m = mean.evaluate(values, begin, length); var = evaluate(values, m, begin, length); } } return var; } /** * <p>Returns the weighted variance of the entries in the specified portion of * the input array, or <code>Double.NaN if the designated subarray * is empty.</p> * <p> * Uses the formula <pre> * Σ(weights[i]*(values[i] - weightedMean)<sup>2)/(Σ(weights[i]) - 1) * </pre> * where weightedMean is the weighted mean</p> * <p> * This formula will not return the same result as the unweighted variance when all * weights are equal, unless all weights are equal to 1. The formula assumes that * weights are to be treated as "expansion values," as will be the case if for example * the weights represent frequency counts. To normalize weights so that the denominator * in the variance computation equals the length of the input vector minus one, use <pre> * <code>evaluate(values, MathUtils.normalizeArray(weights, values.length)); * </pre> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if any of the following are true: * <ul>
  • the values array is null
  • * <li>the weights array is null * <li>the weights array does not have the same length as the values array * <li>the weights array contains one or more infinite values * <li>the weights array contains one or more NaN values * <li>the weights array contains negative values * <li>the start and length arguments do not determine a valid array * </ul>

    * <p> * Does not change the internal state of the statistic.</p> * <p> * Throws <code>IllegalArgumentException if either array is null.

    * * @param values the input array * @param weights the weights array * @param begin index of the first array element to include * @param length the number of elements to include * @return the weighted variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException if the parameters are not valid * @since 2.1 */ public double evaluate(final double[] values, final double[] weights, final int begin, final int length) { double var = Double.NaN; if (test(values, weights,begin, length)) { clear(); if (length == 1) { var = 0.0; } else if (length > 1) { Mean mean = new Mean(); double m = mean.evaluate(values, weights, begin, length); var = evaluate(values, weights, m, begin, length); } } return var; } /** * <p> * Returns the weighted variance of the entries in the the input array.</p> * <p> * Uses the formula <pre> * Σ(weights[i]*(values[i] - weightedMean)<sup>2)/(Σ(weights[i]) - 1) * </pre> * where weightedMean is the weighted mean</p> * <p> * This formula will not return the same result as the unweighted variance when all * weights are equal, unless all weights are equal to 1. The formula assumes that * weights are to be treated as "expansion values," as will be the case if for example * the weights represent frequency counts. To normalize weights so that the denominator * in the variance computation equals the length of the input vector minus one, use <pre> * <code>evaluate(values, MathUtils.normalizeArray(weights, values.length)); * </pre> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if any of the following are true: * <ul>
  • the values array is null
  • * <li>the weights array is null * <li>the weights array does not have the same length as the values array * <li>the weights array contains one or more infinite values * <li>the weights array contains one or more NaN values * <li>the weights array contains negative values * </ul>

    * <p> * Does not change the internal state of the statistic.</p> * <p> * Throws <code>IllegalArgumentException if either array is null.

    * * @param values the input array * @param weights the weights array * @return the weighted variance of the values * @throws IllegalArgumentException if the parameters are not valid * @since 2.1 */ public double evaluate(final double[] values, final double[] weights) { return evaluate(values, weights, 0, values.length); } /** * Returns the variance of the entries in the specified portion of * the input array, using the precomputed mean value. Returns * <code>Double.NaN if the designated subarray is empty. * <p> * See {@link Variance} for details on the computing algorithm.</p> * <p> * The formula used assumes that the supplied mean value is the arithmetic * mean of the sample data, not a known population parameter. This method * is supplied only to save computation when the mean has already been * computed.</p> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if the array is null.

    * <p> * Does not change the internal state of the statistic.</p> * * @param values the input array * @param mean the precomputed mean value * @param begin index of the first array element to include * @param length the number of elements to include * @return the variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException if the array is null or the array index * parameters are not valid */ public double evaluate(final double[] values, final double mean, final int begin, final int length) { double var = Double.NaN; if (test(values, begin, length)) { if (length == 1) { var = 0.0; } else if (length > 1) { double accum = 0.0; double dev = 0.0; double accum2 = 0.0; for (int i = begin; i < begin + length; i++) { dev = values[i] - mean; accum += dev * dev; accum2 += dev; } double len = length; if (isBiasCorrected) { var = (accum - (accum2 * accum2 / len)) / (len - 1.0); } else { var = (accum - (accum2 * accum2 / len)) / len; } } } return var; } /** * Returns the variance of the entries in the input array, using the * precomputed mean value. Returns <code>Double.NaN if the array * is empty. * <p> * See {@link Variance} for details on the computing algorithm.</p> * <p> * If <code>isBiasCorrected is true the formula used * assumes that the supplied mean value is the arithmetic mean of the * sample data, not a known population parameter. If the mean is a known * population parameter, or if the "population" version of the variance is * desired, set <code>isBiasCorrected to false before * invoking this method.</p> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if the array is null.

    * <p> * Does not change the internal state of the statistic.</p> * * @param values the input array * @param mean the precomputed mean value * @return the variance of the values or Double.NaN if the array is empty * @throws IllegalArgumentException if the array is null */ public double evaluate(final double[] values, final double mean) { return evaluate(values, mean, 0, values.length); } /** * Returns the weighted variance of the entries in the specified portion of * the input array, using the precomputed weighted mean value. Returns * <code>Double.NaN if the designated subarray is empty. * <p> * Uses the formula <pre> * Σ(weights[i]*(values[i] - mean)<sup>2)/(Σ(weights[i]) - 1) * </pre>

    * <p> * The formula used assumes that the supplied mean value is the weighted arithmetic * mean of the sample data, not a known population parameter. This method * is supplied only to save computation when the mean has already been * computed.</p> * <p> * This formula will not return the same result as the unweighted variance when all * weights are equal, unless all weights are equal to 1. The formula assumes that * weights are to be treated as "expansion values," as will be the case if for example * the weights represent frequency counts. To normalize weights so that the denominator * in the variance computation equals the length of the input vector minus one, use <pre> * <code>evaluate(values, MathUtils.normalizeArray(weights, values.length), mean); * </pre> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if any of the following are true: * <ul>
  • the values array is null
  • * <li>the weights array is null * <li>the weights array does not have the same length as the values array * <li>the weights array contains one or more infinite values * <li>the weights array contains one or more NaN values * <li>the weights array contains negative values * <li>the start and length arguments do not determine a valid array * </ul>

    * <p> * Does not change the internal state of the statistic.</p> * * @param values the input array * @param weights the weights array * @param mean the precomputed weighted mean value * @param begin index of the first array element to include * @param length the number of elements to include * @return the variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException if the parameters are not valid * @since 2.1 */ public double evaluate(final double[] values, final double[] weights, final double mean, final int begin, final int length) { double var = Double.NaN; if (test(values, weights, begin, length)) { if (length == 1) { var = 0.0; } else if (length > 1) { double accum = 0.0; double dev = 0.0; double accum2 = 0.0; for (int i = begin; i < begin + length; i++) { dev = values[i] - mean; accum += weights[i] * (dev * dev); accum2 += weights[i] * dev; } double sumWts = 0; for (int i = 0; i < weights.length; i++) { sumWts += weights[i]; } if (isBiasCorrected) { var = (accum - (accum2 * accum2 / sumWts)) / (sumWts - 1.0); } else { var = (accum - (accum2 * accum2 / sumWts)) / sumWts; } } } return var; } /** * <p>Returns the weighted variance of the values in the input array, using * the precomputed weighted mean value.</p> * <p> * Uses the formula <pre> * Σ(weights[i]*(values[i] - mean)<sup>2)/(Σ(weights[i]) - 1) * </pre>

    * <p> * The formula used assumes that the supplied mean value is the weighted arithmetic * mean of the sample data, not a known population parameter. This method * is supplied only to save computation when the mean has already been * computed.</p> * <p> * This formula will not return the same result as the unweighted variance when all * weights are equal, unless all weights are equal to 1. The formula assumes that * weights are to be treated as "expansion values," as will be the case if for example * the weights represent frequency counts. To normalize weights so that the denominator * in the variance computation equals the length of the input vector minus one, use <pre> * <code>evaluate(values, MathUtils.normalizeArray(weights, values.length), mean); * </pre> * <p> * Returns 0 for a single-value (i.e. length = 1) sample.</p> * <p> * Throws <code>IllegalArgumentException if any of the following are true: * <ul>
  • the values array is null
  • * <li>the weights array is null * <li>the weights array does not have the same length as the values array * <li>the weights array contains one or more infinite values * <li>the weights array contains one or more NaN values * <li>the weights array contains negative values * </ul>

    * <p> * Does not change the internal state of the statistic.</p> * * @param values the input array * @param weights the weights array * @param mean the precomputed weighted mean value * @return the variance of the values or Double.NaN if length = 0 * @throws IllegalArgumentException if the parameters are not valid * @since 2.1 */ public double evaluate(final double[] values, final double[] weights, final double mean) { return evaluate(values, weights, mean, 0, values.length); } /** * @return Returns the isBiasCorrected. */ public boolean isBiasCorrected() { return isBiasCorrected; } /** * @param biasCorrected The isBiasCorrected to set. */ public void setBiasCorrected(boolean biasCorrected) { this.isBiasCorrected = biasCorrected; } /** * {@inheritDoc} */ @Override public Variance copy() { Variance result = new Variance(); copy(this, result); return result; } /** * Copies source to dest. * <p>Neither source nor dest can be null.

    * * @param source Variance to copy * @param dest Variance to copy to * @throws NullPointerException if either source or dest is null */ public static void copy(Variance source, Variance dest) { dest.moment = source.moment.copy(); dest.isBiasCorrected = source.isBiasCorrected; dest.incMoment = source.incMoment; } }

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