StatUtils.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
*
* https://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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.stat;
import java.util.Arrays;
import java.util.List;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.stat.descriptive.DescriptiveStatistics;
import org.hipparchus.stat.descriptive.UnivariateStatistic;
import org.hipparchus.stat.descriptive.moment.GeometricMean;
import org.hipparchus.stat.descriptive.moment.Mean;
import org.hipparchus.stat.descriptive.moment.Variance;
import org.hipparchus.stat.descriptive.rank.Max;
import org.hipparchus.stat.descriptive.rank.Min;
import org.hipparchus.stat.descriptive.rank.Percentile;
import org.hipparchus.stat.descriptive.summary.Product;
import org.hipparchus.stat.descriptive.summary.Sum;
import org.hipparchus.stat.descriptive.summary.SumOfLogs;
import org.hipparchus.stat.descriptive.summary.SumOfSquares;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/**
* StatUtils provides static methods for computing statistics based on data
* stored in double[] arrays.
*/
public final class StatUtils {
/** sum */
private static final UnivariateStatistic SUM = new Sum();
/** sumSq */
private static final UnivariateStatistic SUM_OF_SQUARES = new SumOfSquares();
/** prod */
private static final UnivariateStatistic PRODUCT = new Product();
/** sumLog */
private static final UnivariateStatistic SUM_OF_LOGS = new SumOfLogs();
/** min */
private static final UnivariateStatistic MIN = new Min();
/** max */
private static final UnivariateStatistic MAX = new Max();
/** mean */
private static final UnivariateStatistic MEAN = new Mean();
/** variance */
private static final Variance VARIANCE = new Variance();
/** percentile */
private static final Percentile PERCENTILE = new Percentile();
/** geometric mean */
private static final GeometricMean GEOMETRIC_MEAN = new GeometricMean();
/**
* Private Constructor
*/
private StatUtils() {
}
/**
* Returns the sum of the values in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the input array is null.
*
* @param values array of values to sum
* @return the sum of the values or <code>Double.NaN</code> if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double sum(final double... values) throws MathIllegalArgumentException {
return SUM.evaluate(values);
}
/**
* Returns the sum of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* Throws <code>IllegalArgumentException</code> 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 sum of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double sum(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return SUM.evaluate(values, begin, length);
}
/**
* Returns the sum of the squares of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
*
* @param values input array
* @return the sum of the squared values or <code>Double.NaN</code> if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double sumSq(final double... values) throws MathIllegalArgumentException {
return SUM_OF_SQUARES.evaluate(values);
}
/**
* Returns the sum of the squares of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* Throws <code>IllegalArgumentException</code> 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 sum of the squares of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double sumSq(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return SUM_OF_SQUARES.evaluate(values, begin, length);
}
/**
* Returns the product of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
*
* @param values the input array
* @return the product of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double product(final double... values) throws MathIllegalArgumentException {
return PRODUCT.evaluate(values);
}
/**
* Returns the product of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* Throws <code>IllegalArgumentException</code> 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 product of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double product(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return PRODUCT.evaluate(values, begin, length);
}
/**
* Returns the sum of the natural logs of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.summary.SumOfLogs}.
*
* @param values the input array
* @return the sum of the natural logs of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double sumLog(final double... values) throws MathIllegalArgumentException {
return SUM_OF_LOGS.evaluate(values);
}
/**
* Returns the sum of the natural logs of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.summary.SumOfLogs}.
*
* @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 sum of the natural logs of the values or Double.NaN if
* length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double sumLog(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return SUM_OF_LOGS.evaluate(values, begin, length);
}
/**
* Returns the arithmetic mean of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Mean} for
* details on the computing algorithm.
*
* @param values the input array
* @return the mean of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double mean(final double... values) throws MathIllegalArgumentException {
return MEAN.evaluate(values);
}
/**
* Returns the arithmetic mean of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Mean Mean} for
* details on the computing algorithm.
*
* @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 mean of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double mean(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return MEAN.evaluate(values, begin, length);
}
/**
* Returns the geometric mean of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.GeometricMean GeometricMean}
* for details on the computing algorithm.
*
* @param values the input array
* @return the geometric mean of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double geometricMean(final double... values) throws MathIllegalArgumentException {
return GEOMETRIC_MEAN.evaluate(values);
}
/**
* Returns the geometric mean of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.GeometricMean GeometricMean}
* for details on the computing algorithm.
*
* @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 geometric mean of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double geometricMean(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return GEOMETRIC_MEAN.evaluate(values, begin, length);
}
/**
* Returns the variance of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* This method returns the bias-corrected sample variance (using {@code n - 1} in
* the denominator). Use {@link #populationVariance(double[])} for the non-bias-corrected
* population variance.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <p>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
*
* @param values the input array
* @return the variance of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double variance(final double... values) throws MathIllegalArgumentException {
return VARIANCE.evaluate(values);
}
/**
* Returns the variance of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* This method returns the bias-corrected sample variance (using {@code n - 1} in
* the denominator). Use {@link #populationVariance(double[], int, int)} for the non-bias-corrected
* population variance.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <p>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or the
* array index parameters are not valid.
*
* @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 MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double variance(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return VARIANCE.evaluate(values, begin, length);
}
/**
* Returns the variance of the entries in the specified portion of
* the input array, using the precomputed mean value. Returns
* <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* This method returns the bias-corrected sample variance (using {@code n - 1} in
* the denominator). Use {@link #populationVariance(double[], double, int, int)} for
* the non-bias-corrected population variance.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <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>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or the
* array index parameters are not valid.
*
* @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 MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double variance(final double[] values, final double mean, final int begin, final int length)
throws MathIllegalArgumentException {
return VARIANCE.evaluate(values, mean, begin, length);
}
/**
* Returns the variance of the entries in the input array, using the
* precomputed mean value. Returns <code>Double.NaN</code> if the array
* is empty.
* <p>
* This method returns the bias-corrected sample variance (using {@code n - 1} in
* the denominator). Use {@link #populationVariance(double[], double)} for the
* non-bias-corrected population variance.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <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>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
*
* @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 MathIllegalArgumentException if the array is null
*/
public static double variance(final double[] values, final double mean) throws MathIllegalArgumentException {
return VARIANCE.evaluate(values, mean);
}
/**
* Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance">
* population variance</a> of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the formula and computing algorithm.
* <p>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
*
* @param values the input array
* @return the population variance of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double populationVariance(final double... values) throws MathIllegalArgumentException {
return new Variance(false).evaluate(values);
}
/**
* Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance">
* population variance</a> of the entries in the specified portion of
* the input array, or <code>Double.NaN</code> if the designated subarray
* is empty.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <p>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or the
* array index parameters are not valid.
*
* @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 population variance of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double populationVariance(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return new Variance(false).evaluate(values, begin, length);
}
/**
* Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance">
* population variance</a> of the entries in the specified portion of
* the input array, using the precomputed mean value. Returns
* <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <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>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or the
* array index parameters are not valid.
*
* @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 population variance of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double populationVariance(final double[] values, final double mean,
final int begin, final int length)
throws MathIllegalArgumentException {
return new Variance(false).evaluate(values, mean, begin, length);
}
/**
* Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance">
* population variance</a> of the entries in the input array, using the precomputed
* mean value. Returns <code>Double.NaN</code> if the array is empty.
* <p>
* See {@link org.hipparchus.stat.descriptive.moment.Variance Variance} for
* details on the computing algorithm.
* <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>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
*
* @param values the input array
* @param mean the precomputed mean value
* @return the population variance of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double populationVariance(final double[] values, final double mean)
throws MathIllegalArgumentException {
return new Variance(false).evaluate(values, mean);
}
/**
* Returns the maximum of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
* </p>
* <ul>
* <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
* (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
* <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>,
* the result is <code>Double.POSITIVE_INFINITY.</code></li>
* </ul>
*
* @param values the input array
* @return the maximum of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double max(final double... values) throws MathIllegalArgumentException {
return MAX.evaluate(values);
}
/**
* Returns the maximum of the entries in the specified portion of the input array,
* or <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or
* the array index parameters are not valid.
* </p>
* <ul>
* <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
* (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
* <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>,
* the result is <code>Double.POSITIVE_INFINITY.</code></li>
* </ul>
*
* @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 maximum of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double max(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return MAX.evaluate(values, begin, length);
}
/**
* Returns the minimum of the entries in the input array, or
* <code>Double.NaN</code> if the array is empty.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null.
* </p>
* <ul>
* <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
* (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
* <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>,
* the result is <code>Double.NEGATIVE_INFINITY.</code></li>
* </ul>
*
* @param values the input array
* @return the minimum of the values or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if the array is null
*/
public static double min(final double... values) throws MathIllegalArgumentException {
return MIN.evaluate(values);
}
/**
* Returns the minimum of the entries in the specified portion of the input array,
* or <code>Double.NaN</code> if the designated subarray is empty.
* <p>
* Throws <code>MathIllegalArgumentException</code> if the array is null or
* the array index parameters are not valid.
* </p>
* <ul>
* <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
* (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
* <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>,
* the result is <code>Double.NEGATIVE_INFINITY.</code></li>
* </ul>
*
* @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 minimum of the values or Double.NaN if length = 0
* @throws MathIllegalArgumentException if the array is null or the array index
* parameters are not valid
*/
public static double min(final double[] values, final int begin, final int length)
throws MathIllegalArgumentException {
return MIN.evaluate(values, begin, length);
}
/**
* Returns an estimate of the <code>p</code>th percentile of the values
* in the <code>values</code> array.
* <ul>
* <li>Returns <code>Double.NaN</code> if <code>values</code> has length
* <code>0</code></li>
* <li>Returns (for any value of <code>p</code>) <code>values[0]</code>
* if <code>values</code> has length <code>1</code></li>
* <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
* is null or p is not a valid quantile value (p must be greater than 0
* and less than or equal to 100)</li>
* </ul>
* <p>
* See {@link org.hipparchus.stat.descriptive.rank.Percentile Percentile}
* for a description of the percentile estimation algorithm used.
*
* @param values input array of values
* @param p the percentile value to compute
* @return the percentile value or Double.NaN if the array is empty
* @throws MathIllegalArgumentException if <code>values</code> is null or p is invalid
*/
public static double percentile(final double[] values, final double p) throws MathIllegalArgumentException {
return PERCENTILE.evaluate(values,p);
}
/**
* Returns an estimate of the <code>p</code>th percentile of the values
* in the <code>values</code> array, starting with the element in (0-based)
* position <code>begin</code> in the array and including <code>length</code>
* values.
* <ul>
* <li>Returns <code>Double.NaN</code> if <code>length = 0</code></li>
* <li>Returns (for any value of <code>p</code>) <code>values[begin]</code>
* if <code>length = 1 </code></li>
* <li>Throws <code>MathIllegalArgumentException</code> if <code>values</code>
* is null, <code>begin</code> or <code>length</code> is invalid, or
* <code>p</code> is not a valid quantile value (p must be greater than 0
* and less than or equal to 100)</li>
* </ul>
* <p>
* See {@link org.hipparchus.stat.descriptive.rank.Percentile Percentile}
* for a description of the percentile estimation algorithm used.
*
* @param values array of input values
* @param p the percentile to compute
* @param begin the first (0-based) element to include in the computation
* @param length the number of array elements to include
* @return the percentile value
* @throws MathIllegalArgumentException if the parameters are not valid or the input array is null
*/
public static double percentile(final double[] values, final int begin, final int length, final double p)
throws MathIllegalArgumentException {
return PERCENTILE.evaluate(values, begin, length, p);
}
/**
* Returns the sum of the (signed) differences between corresponding elements of the
* input arrays -- i.e., sum(sample1[i] - sample2[i]).
*
* @param sample1 the first array
* @param sample2 the second array
* @return sum of paired differences
* @throws MathIllegalArgumentException if the arrays do not have the same (positive) length.
* @throws MathIllegalArgumentException if the sample arrays are empty.
*/
public static double sumDifference(final double[] sample1, final double[] sample2)
throws MathIllegalArgumentException {
int n = sample1.length;
MathArrays.checkEqualLength(sample1, sample2);
if (n <= 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.INSUFFICIENT_DIMENSION);
}
double result = 0;
for (int i = 0; i < n; i++) {
result += sample1[i] - sample2[i];
}
return result;
}
/**
* Returns the mean of the (signed) differences between corresponding elements of the
* input arrays -- i.e., sum(sample1[i] - sample2[i]) / sample1.length.
*
* @param sample1 the first array
* @param sample2 the second array
* @return mean of paired differences
* @throws MathIllegalArgumentException if the arrays do not have the same (positive) length.
* @throws MathIllegalArgumentException if the sample arrays are empty.
*/
public static double meanDifference(final double[] sample1, final double[] sample2)
throws MathIllegalArgumentException {
return sumDifference(sample1, sample2) / sample1.length;
}
/**
* Returns the variance of the (signed) differences between corresponding elements of the
* input arrays -- i.e., var(sample1[i] - sample2[i]).
*
* @param sample1 the first array
* @param sample2 the second array
* @param meanDifference the mean difference between corresponding entries
* @return variance of paired differences
* @throws MathIllegalArgumentException if the arrays do not have the same length.
* @throws MathIllegalArgumentException if the arrays length is less than 2.
* @see #meanDifference(double[],double[])
*/
public static double varianceDifference(final double[] sample1, final double[] sample2, double meanDifference)
throws MathIllegalArgumentException {
double sum1 = 0d;
double sum2 = 0d;
int n = sample1.length;
MathArrays.checkEqualLength(sample1, sample2);
if (n < 2) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
n, 2);
}
for (int i = 0; i < n; i++) {
final double diff = sample1[i] - sample2[i];
sum1 += (diff - meanDifference) *(diff - meanDifference);
sum2 += diff - meanDifference;
}
return (sum1 - (sum2 * sum2 / n)) / (n - 1);
}
/**
* Normalize (standardize) the sample, so it is has a mean of 0 and a standard deviation of 1.
*
* @param sample Sample to normalize.
* @return normalized (standardized) sample.
*/
public static double[] normalize(final double... sample) {
DescriptiveStatistics stats = new DescriptiveStatistics();
// Add the data from the series to stats
for (int i = 0; i < sample.length; i++) {
stats.addValue(sample[i]);
}
// Compute mean and standard deviation
double mean = stats.getMean();
double standardDeviation = stats.getStandardDeviation();
// initialize the standardizedSample, which has the same length as the sample
double[] standardizedSample = new double[sample.length];
for (int i = 0; i < sample.length; i++) {
// z = (x- mean)/standardDeviation
standardizedSample[i] = (sample[i] - mean) / standardDeviation;
}
return standardizedSample;
}
/**
* Returns the sample mode(s).
* <p>
* The mode is the most frequently occurring value in the sample.
* If there is a unique value with maximum frequency, this value is returned
* as the only element of the output array. Otherwise, the returned array
* contains the maximum frequency elements in increasing order.
* <p>
* For example, if {@code sample} is {0, 12, 5, 6, 0, 13, 5, 17},
* the returned array will have length two, with 0 in the first element and
* 5 in the second.
* <p>
* NaN values are ignored when computing the mode - i.e., NaNs will never
* appear in the output array. If the sample includes only NaNs or has
* length 0, an empty array is returned.
*
* @param sample input data
* @return array of array of the most frequently occurring element(s) sorted in ascending order.
* @throws MathIllegalArgumentException if the indices are invalid or the array is null
*/
public static double[] mode(double... sample) throws MathIllegalArgumentException {
MathUtils.checkNotNull(sample, LocalizedCoreFormats.INPUT_ARRAY);
return getMode(sample, 0, sample.length);
}
/**
* Returns the sample mode(s).
* <p>
* The mode is the most frequently occurring value in the sample.
* If there is a unique value with maximum frequency, this value is returned
* as the only element of the output array. Otherwise, the returned array
* contains the maximum frequency elements in increasing order.
* <p>
* For example, if {@code sample} is {0, 12, 5, 6, 0, 13, 5, 17},
* the returned array will have length two, with 0 in the first element and
* 5 in the second.
* <p>
* NaN values are ignored when computing the mode - i.e., NaNs will never
* appear in the output array. If the sample includes only NaNs or has
* length 0, an empty array is returned.
*
* @param sample input data
* @param begin index (0-based) of the first array element to include
* @param length the number of elements to include
* @return array of array of the most frequently occurring element(s) sorted in ascending order.
* @throws MathIllegalArgumentException if the indices are invalid or the array is null
*/
public static double[] mode(double[] sample, final int begin, final int length) {
MathUtils.checkNotNull(sample, LocalizedCoreFormats.INPUT_ARRAY);
if (begin < 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.START_POSITION, Integer.valueOf(begin));
}
if (length < 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.LENGTH, Integer.valueOf(length));
}
return getMode(sample, begin, length);
}
/**
* Private helper method.
* Assumes parameters have been validated.
* @param values input data
* @param begin index (0-based) of the first array element to include
* @param length the number of elements to include
* @return array of array of the most frequently occurring element(s) sorted in ascending order.
*/
private static double[] getMode(double[] values, final int begin, final int length) {
// Add the values to the frequency table
Frequency<Double> freq = new Frequency<>();
Arrays.stream(values, begin, begin + length)
.filter(d -> !Double.isNaN(d))
.forEach(freq::addValue);
List<Double> list = freq.getMode();
// Convert the list to an array of primitive double
return list.stream()
.mapToDouble(Double::doubleValue)
.toArray();
}
}