LongStandardDeviation.java
/*
* 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.statistics.descriptive;
/**
* Computes the standard deviation of the available values. The default implementation uses the
* following definition of the <em>sample standard deviation</em>:
*
* <p>\[ \sqrt{ \tfrac{1}{n-1} \sum_{i=1}^n (x_i-\overline{x})^2 } \]
*
* <p>where \( \overline{x} \) is the sample mean, and \( n \) is the number of samples.
*
* <ul>
* <li>The result is {@code NaN} if no values are added.
* <li>The result is zero if there is one value in the data set.
* </ul>
*
* <p>The use of the term \( n − 1 \) is called Bessel's correction. Omitting the square root,
* this provides an unbiased estimator of the variance of a hypothetical infinite population. If the
* {@link #setBiased(boolean) biased} option is enabled the normalisation factor is
* changed to \( \frac{1}{n} \) for a biased estimator of the <em>sample variance</em>.
* Note however that square root is a concave function and thus introduces negative bias
* (by Jensen's inequality), which depends on the distribution, and thus the corrected sample
* standard deviation (using Bessel's correction) is less biased, but still biased.
*
* <p>The implementation uses an exact integer sum to compute the scaled (by \( n \))
* sum of squared deviations from the mean; this is normalised by the scaled correction factor.
*
* <p>\[ \frac {n \times \sum_{i=1}^n x_i^2 - (\sum_{i=1}^n x_i)^2}{n \times (n - 1)} \]
*
* <p>Supports up to 2<sup>63</sup> (exclusive) observations.
* This implementation does not check for overflow of the count.
*
* <p>This class is designed to work with (though does not require)
* {@linkplain java.util.stream streams}.
*
* <p><strong>This implementation is not thread safe.</strong>
* If multiple threads access an instance of this class concurrently,
* and at least one of the threads invokes the {@link java.util.function.LongConsumer#accept(long) accept} or
* {@link StatisticAccumulator#combine(StatisticResult) combine} method, it must be synchronized externally.
*
* <p>However, it is safe to use {@link java.util.function.LongConsumer#accept(long) accept}
* and {@link StatisticAccumulator#combine(StatisticResult) combine}
* as {@code accumulator} and {@code combiner} functions of
* {@link java.util.stream.Collector Collector} on a parallel stream,
* because the parallel implementation of {@link java.util.stream.Stream#collect Stream.collect()}
* provides the necessary partitioning, isolation, and merging of results for
* safe and efficient parallel execution.
*
* @see <a href="https://en.wikipedia.org/wiki/Standard_deviation">Standard deviation (Wikipedia)</a>
* @see <a href="https://en.wikipedia.org/wiki/Bessel%27s_correction">Bessel's correction</a>
* @see <a href="https://en.wikipedia.org/wiki/Jensen%27s_inequality">Jensen's inequality</a>
* @see LongVariance
* @since 1.1
*/
public final class LongStandardDeviation implements LongStatistic, StatisticAccumulator<LongStandardDeviation> {
/** Sum of the squared values. */
private final UInt192 sumSq;
/** Sum of the values. */
private final Int128 sum;
/** Count of values that have been added. */
private long n;
/** Flag to control if the statistic is biased, or should use a bias correction. */
private boolean biased;
/**
* Create an instance.
*/
private LongStandardDeviation() {
this(UInt192.create(), Int128.create(), 0);
}
/**
* Create an instance.
*
* @param sumSq Sum of the squared values.
* @param sum Sum of the values.
* @param n Count of values that have been added.
*/
private LongStandardDeviation(UInt192 sumSq, Int128 sum, int n) {
this.sumSq = sumSq;
this.sum = sum;
this.n = n;
}
/**
* Creates an instance.
*
* <p>The initial result is {@code NaN}.
*
* @return {@code LongStandardDeviation} instance.
*/
public static LongStandardDeviation create() {
return new LongStandardDeviation();
}
/**
* Returns an instance populated using the input {@code values}.
*
* @param values Values.
* @return {@code LongStandardDeviation} instance.
*/
public static LongStandardDeviation of(long... values) {
// Note: Arrays could be processed using specialised counts knowing the maximum limit
// for an array is 2^31 values. Requires a UInt160.
final Int128 s = Int128.create();
final UInt192 ss = UInt192.create();
for (final long x : values) {
s.add(x);
ss.addSquare(x);
}
return new LongStandardDeviation(ss, s, values.length);
}
/**
* Updates the state of the statistic to reflect the addition of {@code value}.
*
* @param value Value.
*/
@Override
public void accept(long value) {
sumSq.addSquare(value);
sum.add(value);
n++;
}
/**
* Gets the standard deviation of all input values.
*
* <p>When no values have been added, the result is {@code NaN}.
*
* @return standard deviation of all values.
*/
@Override
public double getAsDouble() {
return LongVariance.computeVarianceOrStd(sumSq, sum, n, biased, true);
}
@Override
public LongStandardDeviation combine(LongStandardDeviation other) {
sumSq.add(other.sumSq);
sum.add(other.sum);
n += other.n;
return this;
}
/**
* Sets the value of the biased flag. The default value is {@code false}. The bias
* term refers to the computation of the variance; the standard deviation is returned
* as the square root of the biased or unbiased <em>sample variance</em>. For further
* details see {@link LongVariance#setBiased(boolean) LongStandardDeviationVariance.setBiased}.
*
* <p>This flag only controls the final computation of the statistic. The value of
* this flag will not affect compatibility between instances during a
* {@link #combine(LongStandardDeviation) combine} operation.
*
* @param v Value.
* @return {@code this} instance
* @see LongStandardDeviation#setBiased(boolean)
*/
public LongStandardDeviation setBiased(boolean v) {
biased = v;
return this;
}
}