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    1   /*
    2    * Copyright 2003-2004 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16  package org.apache.commons.math.stat.descriptive.moment;
    17
    18  import java.io.Serializable;
    19
    20  import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
    21
    22  /***
    23   * Computes the variance of the available values.   By default, the unbiased
    24   * "sample variance" definitional formula is used:
    25   * <p>
    26   * variance = sum((x_i - mean)^2) / (n - 1)
    27   * <p>
    28   * where mean is the {@link Mean} and <code>n</code> is the number
    29   * of sample observations.
    30   * <p>
    31   * The definitional formula does not have good numerical properties, so
    32   * this implementation uses updating formulas based on West's algorithm
    33   * as described in <a href="http://doi.acm.org/10.1145/359146.359152">
    34   * Chan, T. F. andJ. G. Lewis 1979, <i>Communications of the ACM</i>,
    35   * vol. 22 no. 9, pp. 526-531.</a>.
    36   * <p>
    37   * The "population variance"  ( sum((x_i - mean)^2) / n ) can also
    38   * be computed using this statistic.  The <code>isBiasCorrected</code>
    39   * property determines whether the "population" or "sample" value is
    40   * returned by the <code>evaluate</code> and <code>getResult</code> methods.
    41   * To compute population variances, set this property to <code>false.</code>
    42   *
    43   * <strong>Note that this implementation is not synchronized.</strong> If
    44   * multiple threads access an instance of this class concurrently, and at least
    45   * one of the threads invokes the <code>increment()</code> or
    46   * <code>clear()</code> method, it must be synchronized externally.
    47   *
    48   * @version $Revision: 1.4 $ $Date: 2004/10/11 06:52:39 $
    49   */
    50  public class Variance extends AbstractStorelessUnivariateStatistic implements Serializable {
    51
    52      /*** Serializable version identifier */
    53      static final long serialVersionUID = -9111962718267217978L;
    54
    55      /*** SecondMoment is used in incremental calculation of Variance*/
    56      protected SecondMoment moment = null;
    57
    58      /***
    59       * Boolean test to determine if this Variance should also increment
    60       * the second moment, this evaluates to false when this Variance is
    61       * constructed with an external SecondMoment as a parameter.
    62       */
    63      protected boolean incMoment = true;
    64
    65      /***
    66       * Determines whether or not bias correction is applied when computing the
    67       * value of the statisic.  True means that bias is corrected.  See
    68       * {@link Variance} for details on the formula.
    69       */
    70      private boolean isBiasCorrected = true;
    71
    72      /***
    73       * Constructs a Variance with default (true) <code>isBiasCorrected</code>
    74       * property.
    75       */
    76      public Variance() {
    77          moment = new SecondMoment();
    78      }
    79
    80      /***
    81       * Constructs a Variance based on an external second moment.
    82       *
    83       * @param m2 the SecondMoment (Thrid or Fourth moments work
    84       * here as well.)
    85       */
    86      public Variance(final SecondMoment m2) {
    87          incMoment = false;
    88          this.moment = m2;
    89      }
    90
    91      /***
    92       * Constructs a Variance with the specified <code>isBiasCorrected</code>
    93       * property
    94       *
    95       * @param isBiasCorrected  setting for bias correction - true means
    96       * bias will be corrected and is equivalent to using the argumentless
    97       * constructor
    98       */
    99      public Variance(boolean isBiasCorrected) {
    100         moment = new SecondMoment();
    101         this.isBiasCorrected = isBiasCorrected;
    102     }
    103
    104     /***
    105      * Constructs a Variance with the specified <code>isBiasCorrected</code>
    106      * property and the supplied external second moment.
    107      *
    108      * @param isBiasCorrected  setting for bias correction - true means
    109      * bias will be corrected
    110      * @param m2 the SecondMoment (Thrid or Fourth moments work
    111      * here as well.)
    112      */
    113     public Variance(boolean isBiasCorrected, SecondMoment m2) {
    114         incMoment = false;
    115         this.moment = m2;
    116         this.isBiasCorrected = isBiasCorrected;
    117     }
    118
    119     /***
    120      * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
    121      */
    122     public void increment(final double d) {
    123         if (incMoment) {
    124             moment.increment(d);
    125         }
    126     }
    127
    128     /***
    129      * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult()
    130      */
    131     public double getResult() {
    132             if (moment.n == 0) {
    133                 return Double.NaN;
    134             } else if (moment.n == 1) {
    135                 return 0d;
    136             } else {
    137                 if (isBiasCorrected) {
    138                     return moment.m2 / ((double) moment.n - 1d);
    139                 } else {
    140                     return moment.m2 / ((double) moment.n);
    141                 }
    142             }
    143     }
    144
    145     /***
    146      * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN()
    147      */
    148     public long getN() {
    149         return moment.getN();
    150     }
    151
    152     /***
    153      * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear()
    154      */
    155     public void clear() {
    156         if (incMoment) {
    157             moment.clear();
    158         }
    159     }
    160
    161     /***
    162      * Returns the variance of the entries in the input array, or
    163      * <code>Double.NaN</code> if the array is empty.
    164      * <p>
    165      * See {@link Variance} for details on the computing algorithm.
    166      * <p>
    167      * Returns 0 for a single-value (i.e. length = 1) sample.
    168      * <p>
    169      * Throws <code>IllegalArgumentException</code> if the array is null.
    170      * <p>
    171      * Does not change the internal state of the statistic.
    172      *
    173      * @param values the input array
    174      * @return the variance of the values or Double.NaN if length = 0
    175      * @throws IllegalArgumentException if the array is null
    176      */
    177     public double evaluate(final double[] values) {
    178         if (values == null) {
    179             throw new IllegalArgumentException("input values array is null");
    180         }
    181         return evaluate(values, 0, values.length);
    182     }
    183
    184     /***
    185      * Returns the variance of the entries in the specified portion of
    186      * the input array, or <code>Double.NaN</code> if the designated subarray
    187      * is empty.
    188      * <p>
    189      * See {@link Variance} for details on the computing algorithm.
    190      * <p>
    191      * Returns 0 for a single-value (i.e. length = 1) sample.
    192      * <p>
    193      * Does not change the internal state of the statistic.
    194      * <p>
    195      * Throws <code>IllegalArgumentException</code> if the array is null.
    196      *
    197      * @param values the input array
    198      * @param begin index of the first array element to include
    199      * @param length the number of elements to include
    200      * @return the variance of the values or Double.NaN if length = 0
    201      * @throws IllegalArgumentException if the array is null or the array index
    202      *  parameters are not valid
    203      */
    204     public double evaluate(final double[] values, final int begin, final int length) {
    205
    206         double var = Double.NaN;
    207
    208         if (test(values, begin, length)) {
    209             clear();
    210             if (length == 1) {
    211                 var = 0.0;
    212             } else if (length > 1) {
    213                 Mean mean = new Mean();
    214                 double m = mean.evaluate(values, begin, length);
    215                 var = evaluate(values, m, begin, length);
    216             }
    217         }
    218         return var;
    219     }
    220
    221     /***
    222      * Returns the variance of the entries in the specified portion of
    223      * the input array, using the precomputed mean value.  Returns
    224      * <code>Double.NaN</code> if the designated subarray is empty.
    225      * <p>
    226      * See {@link Variance} for details on the computing algorithm.
    227      * <p>
    228      * The formula used assumes that the supplied mean value is the arithmetic
    229      * mean of the sample data, not a known population parameter.  This method
    230      * is supplied only to save computation when the mean has already been
    231      * computed.
    232      * <p>
    233      * Returns 0 for a single-value (i.e. length = 1) sample.
    234      * <p>
    235      * Throws <code>IllegalArgumentException</code> if the array is null.
    236      * <p>
    237      * Does not change the internal state of the statistic.
    238      *
    239      * @param values the input array
    240      * @param mean the precomputed mean value
    241      * @param begin index of the first array element to include
    242      * @param length the number of elements to include
    243      * @return the variance of the values or Double.NaN if length = 0
    244      * @throws IllegalArgumentException if the array is null or the array index
    245      *  parameters are not valid
    246      */
    247     public double evaluate(final double[] values, final double mean,
    248             final int begin, final int length) {
    249
    250         double var = Double.NaN;
    251
    252         if (test(values, begin, length)) {
    253             if (length == 1) {
    254                 var = 0.0;
    255             } else if (length > 1) {
    256                 double accum = 0.0;
    257                 double accum2 = 0.0;
    258                 for (int i = begin; i < begin + length; i++) {
    259                     accum += Math.pow((values[i] - mean), 2.0);
    260                     accum2 += (values[i] - mean);
    261                 }
    262                 if (isBiasCorrected) {
    263                     var = (accum - (Math.pow(accum2, 2) / ((double) length))) /
    264                     (double) (length - 1);
    265                 } else {
    266                     var = (accum - (Math.pow(accum2, 2) / ((double) length))) /
    267                     (double) length;
    268                 }
    269             }
    270         }
    271         return var;
    272     }
    273
    274     /***
    275      * Returns the variance of the entries in the input array, using the
    276      * precomputed mean value.  Returns <code>Double.NaN</code> if the array
    277      * is empty.
    278      * <p>
    279      * See {@link Variance} for details on the computing algorithm.
    280      * <p>
    281      * If <code>isBiasCorrected</code> is <code>true</code> the formula used
    282      * assumes that the supplied mean value is the arithmetic mean of the
    283      * sample data, not a known population parameter.  If the mean is a known
    284      * population parameter, or if the "population" version of the variance is
    285      * desired, set <code>isBiasCorrected</code> to <code>false</code> before
    286      * invoking this method.
    287      * <p>
    288      * Returns 0 for a single-value (i.e. length = 1) sample.
    289      * <p>
    290      * Throws <code>IllegalArgumentException</code> if the array is null.
    291      * <p>
    292      * Does not change the internal state of the statistic.
    293      *
    294      * @param values the input array
    295      * @param mean the precomputed mean value
    296      * @return the variance of the values or Double.NaN if the array is empty
    297      * @throws IllegalArgumentException if the array is null
    298      */
    299     public double evaluate(final double[] values, final double mean) {
    300         return evaluate(values, mean, 0, values.length);
    301     }
    302
    303     /***
    304      * @return Returns the isBiasCorrected.
    305      */
    306     public boolean isBiasCorrected() {
    307         return isBiasCorrected;
    308     }
    309
    310     /***
    311      * @param isBiasCorrected The isBiasCorrected to set.
    312      */
    313     public void setBiasCorrected(boolean isBiasCorrected) {
    314         this.isBiasCorrected = isBiasCorrected;
    315     }
    316
    317 }