org.apache.commons.statistics.descriptive.IntSumOfSquares Maven / Gradle / Ivy
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* 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;
import java.math.BigInteger;
/**
* Returns the sum of the squares of the available values. Uses the following definition:
*
* \[ \sum_{i=1}^n x_i^2 \]
*
*
where \( n \) is the number of samples.
*
*
* - The result is zero if no values are observed.
*
*
* The implementation uses an exact integer sum to compute the sum of squared values.
* The exact sum is returned using {@link #getAsBigInteger()}. Methods that return {@code int} or
* {@code long} primitives will raise an exception if the result overflows.
*
*
Note that the implementation does not use {@code BigInteger} arithmetic; for
* performance the sum is computed using primitives to create an unsigned 128-bit integer.
* Support is provided for at least 263 observations.
*
*
This class is designed to work with (though does not require)
* {@linkplain java.util.stream streams}.
*
*
This implementation is not thread safe.
* If multiple threads access an instance of this class concurrently,
* and at least one of the threads invokes the {@link java.util.function.IntConsumer#accept(int) accept} or
* {@link StatisticAccumulator#combine(StatisticResult) combine} method, it must be synchronized externally.
*
*
However, it is safe to use {@link java.util.function.IntConsumer#accept(int) 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.
*
* @since 1.1
*/
public final class IntSumOfSquares implements IntStatistic, StatisticAccumulator {
/** Small array sample size.
* Used to avoid computing with UInt96 then converting to UInt128. */
private static final int SMALL_SAMPLE = 10;
/** Sum of the squared values. */
private final UInt128 sumSq;
/**
* Create an instance.
*/
private IntSumOfSquares() {
this(UInt128.create());
}
/**
* Create an instance.
*
* @param sumSq Sum of the squared values.
*/
private IntSumOfSquares(UInt128 sumSq) {
this.sumSq = sumSq;
}
/**
* Creates an instance.
*
* The initial result is zero.
*
* @return {@code IntSumOfSquares} instance.
*/
public static IntSumOfSquares create() {
return new IntSumOfSquares();
}
/**
* Returns an instance populated using the input {@code values}.
*
* @param values Values.
* @return {@code IntSumOfSquares} instance.
*/
public static IntSumOfSquares of(int... values) {
// Small arrays can be processed using the object
if (values.length < SMALL_SAMPLE) {
final IntSumOfSquares stat = new IntSumOfSquares();
for (final int x : values) {
stat.accept(x);
}
return stat;
}
// Arrays can be processed using specialised counts knowing the maximum limit
// for an array is 2^31 values.
final UInt96 ss = UInt96.create();
// Process pairs as we know two maximum value int^2 will not overflow
// an unsigned long.
final int end = values.length & ~0x1;
for (int i = 0; i < end; i += 2) {
final long x = values[i];
final long y = values[i + 1];
ss.addPositive(x * x + y * y);
}
if (end < values.length) {
final long x = values[end];
ss.addPositive(x * x);
}
// Convert
return new IntSumOfSquares(UInt128.of(ss));
}
/**
* Gets the sum of squares.
*
*
This is package private for use in {@link IntStatistics}.
*
* @return the sum of squares
*/
UInt128 getSumOfSquares() {
return sumSq;
}
/**
* Updates the state of the statistic to reflect the addition of {@code value}.
*
* @param value Value.
*/
@Override
public void accept(int value) {
sumSq.addPositive((long) value * value);
}
/**
* Gets the sum of squares of all input values.
*
*
When no values have been added, the result is zero.
*
*
Warning: This will raise an {@link ArithmeticException}
* if the result is not within the range {@code [0, 2^31)}.
*
* @return sum of all values.
* @throws ArithmeticException if the {@code result} overflows an {@code int}
* @see #getAsBigInteger()
*/
@Override
public int getAsInt() {
return sumSq.toIntExact();
}
/**
* Gets the sum of squares of all input values.
*
*
When no values have been added, the result is zero.
*
*
Warning: This will raise an {@link ArithmeticException}
* if the result is not within the range {@code [0, 2^63)}.
*
* @return sum of all values.
* @throws ArithmeticException if the {@code result} overflows a {@code long}
* @see #getAsBigInteger()
*/
@Override
public long getAsLong() {
return sumSq.toLongExact();
}
/**
* Gets the sum of squares of all input values.
*
*
When no values have been added, the result is zero.
*
*
Note that this conversion can lose information about the precision of the
* {@code BigInteger} value.
*
* @return sum of squares of all values.
* @see #getAsBigInteger()
*/
@Override
public double getAsDouble() {
return sumSq.toDouble();
}
/**
* Gets the sum of squares of all input values.
*
*
When no values have been added, the result is zero.
*
* @return sum of squares of all values.
*/
@Override
public BigInteger getAsBigInteger() {
return sumSq.toBigInteger();
}
@Override
public IntSumOfSquares combine(IntSumOfSquares other) {
sumSq.add(other.sumSq);
return this;
}
}