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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.math3.stat;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
import org.apache.commons.math3.stat.descriptive.UnivariateStatistic;
import org.apache.commons.math3.stat.descriptive.moment.GeometricMean;
import org.apache.commons.math3.stat.descriptive.moment.Mean;
import org.apache.commons.math3.stat.descriptive.moment.Variance;
import org.apache.commons.math3.stat.descriptive.rank.Max;
import org.apache.commons.math3.stat.descriptive.rank.Min;
import org.apache.commons.math3.stat.descriptive.rank.Percentile;
import org.apache.commons.math3.stat.descriptive.summary.Product;
import org.apache.commons.math3.stat.descriptive.summary.Sum;
import org.apache.commons.math3.stat.descriptive.summary.SumOfLogs;
import org.apache.commons.math3.stat.descriptive.summary.SumOfSquares;
/**
* StatUtils provides static methods for computing statistics based on data
* stored in double[] arrays.
*
* @version $Id: StatUtils.java 1244107 2012-02-14 16:17:55Z erans $
*/
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
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the input array
* is null.
*
* @param values array of values to sum
* @return the sum of the values or Double.NaN if the array
* is empty
* @throws IllegalArgumentException if the array is null
*/
public static double sum(final double[] values) {
return SUM.evaluate(values);
}
/**
* Returns the sum of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws 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 sum 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 static double sum(final double[] values, final int begin,
final int length) {
return SUM.evaluate(values, begin, length);
}
/**
* Returns the sum of the squares of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* @param values input array
* @return the sum of the squared values or Double.NaN if the
* array is empty
* @throws IllegalArgumentException if the array is null
*/
public static double sumSq(final double[] values) {
return SUM_OF_SQUARES.evaluate(values);
}
/**
* Returns the sum of the squares of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws 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 sum of the squares 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 static double sumSq(final double[] values, final int begin,
final int length) {
return SUM_OF_SQUARES.evaluate(values, begin, length);
}
/**
* Returns the product of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException 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 IllegalArgumentException if the array is null
*/
public static double product(final double[] values) {
return PRODUCT.evaluate(values);
}
/**
* Returns the product of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws 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 product 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 static double product(final double[] values, final int begin,
final int length) {
return PRODUCT.evaluate(values, begin, length);
}
/**
* Returns the sum of the natural logs of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.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 IllegalArgumentException if the array is null
*/
public static double sumLog(final double[] values) {
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 Double.NaN if the designated subarray
* is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.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 IllegalArgumentException 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) {
return SUM_OF_LOGS.evaluate(values, begin, length);
}
/**
* Returns the arithmetic mean of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.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 IllegalArgumentException if the array is null
*/
public static double mean(final double[] values) {
return MEAN.evaluate(values);
}
/**
* Returns the arithmetic mean of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.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 IllegalArgumentException 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) {
return MEAN.evaluate(values, begin, length);
}
/**
* Returns the geometric mean of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.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 IllegalArgumentException if the array is null
*/
public static double geometricMean(final double[] values) {
return GEOMETRIC_MEAN.evaluate(values);
}
/**
* Returns the geometric mean of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws IllegalArgumentException if the array is null.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.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 IllegalArgumentException 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) {
return GEOMETRIC_MEAN.evaluate(values, begin, length);
}
/**
* Returns the variance of the entries in the input array, or
* Double.NaN if the array is empty.
*
* 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.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException if the array is null
*/
public static double variance(final double[] values) {
return VARIANCE.evaluate(values);
}
/**
* Returns the variance of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* 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.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException 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) {
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
* Double.NaN if the designated subarray is empty.
*
* 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.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* 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.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException 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) {
return VARIANCE.evaluate(values, mean, begin, length);
}
/**
* Returns the variance of the entries in the input array, using the
* precomputed mean value. Returns Double.NaN if the array
* is empty.
*
* 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.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* 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.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException if the array is null
*/
public static double variance(final double[] values, final double mean) {
return VARIANCE.evaluate(values, mean);
}
/**
* Returns the
* population variance of the entries in the input array, or
* Double.NaN if the array is empty.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the formula and computing algorithm.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException if the array is null
*/
public static double populationVariance(final double[] values) {
return new Variance(false).evaluate(values);
}
/**
* Returns the
* population variance of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException 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) {
return new Variance(false).evaluate(values, begin, length);
}
/**
* Returns the
* population variance of the entries in the specified portion of
* the input array, using the precomputed mean value. Returns
* Double.NaN if the designated subarray is empty.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* 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.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException 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) {
return new Variance(false).evaluate(values, mean, begin, length);
}
/**
* Returns the
* population variance of the entries in the input array, using the
* precomputed mean value. Returns Double.NaN if the array
* is empty.
*
* See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for
* details on the computing algorithm.
*
* 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.
*
* Returns 0 for a single-value (i.e. length = 1) sample.
*
* Throws IllegalArgumentException 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 IllegalArgumentException if the array is null
*/
public static double populationVariance(final double[] values, final double mean) {
return new Variance(false).evaluate(values, mean);
}
/**
* Returns the maximum of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
*
* - The result is
NaN iff all values are NaN
* (i.e. NaN values have no impact on the value of the statistic).
* - If any of the values equals
Double.POSITIVE_INFINITY,
* the result is Double.POSITIVE_INFINITY.
*
*
* @param values the input array
* @return the maximum of the values or Double.NaN if the array is empty
* @throws IllegalArgumentException if the array is null
*/
public static double max(final double[] values) {
return MAX.evaluate(values);
}
/**
* Returns the maximum of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws IllegalArgumentException if the array is null or
* the array index parameters are not valid.
*
*
* - The result is
NaN iff all values are NaN
* (i.e. NaN values have no impact on the value of the statistic).
* - If any of the values equals
Double.POSITIVE_INFINITY,
* the result is Double.POSITIVE_INFINITY.
*
*
* @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 IllegalArgumentException 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) {
return MAX.evaluate(values, begin, length);
}
/**
* Returns the minimum of the entries in the input array, or
* Double.NaN if the array is empty.
*
* Throws IllegalArgumentException if the array is null.
*
*
* - The result is
NaN iff all values are NaN
* (i.e. NaN values have no impact on the value of the statistic).
* - If any of the values equals
Double.NEGATIVE_INFINITY,
* the result is Double.NEGATIVE_INFINITY.
*
*
* @param values the input array
* @return the minimum of the values or Double.NaN if the array is empty
* @throws IllegalArgumentException if the array is null
*/
public static double min(final double[] values) {
return MIN.evaluate(values);
}
/**
* Returns the minimum of the entries in the specified portion of
* the input array, or Double.NaN if the designated subarray
* is empty.
*
* Throws IllegalArgumentException if the array is null or
* the array index parameters are not valid.
*
*
* - The result is
NaN iff all values are NaN
* (i.e. NaN values have no impact on the value of the statistic).
* - If any of the values equals
Double.NEGATIVE_INFINITY,
* the result is Double.NEGATIVE_INFINITY.
*
*
* @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 IllegalArgumentException 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) {
return MIN.evaluate(values, begin, length);
}
/**
* Returns an estimate of the pth percentile of the values
* in the values array.
*
*
* - Returns
Double.NaN if values has length
* 0
* - Returns (for any value of
p) values[0]
* if values has length 1
* - Throws
IllegalArgumentException if values
* is null or p is not a valid quantile value (p must be greater than 0
* and less than or equal to 100)
*
*
* See {@link org.apache.commons.math3.stat.descriptive.rank.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 IllegalArgumentException if values is null
* or p is invalid
*/
public static double percentile(final double[] values, final double p) {
return PERCENTILE.evaluate(values,p);
}
/**
* Returns an estimate of the pth percentile of the values
* in the values array, starting with the element in (0-based)
* position begin in the array and including length
* values.
*
*
* - Returns
Double.NaN if length = 0
* - Returns (for any value of
p) values[begin]
* if length = 1
* - Throws
IllegalArgumentException if values
* is null , begin or length is invalid, or
* p is not a valid quantile value (p must be greater than 0
* and less than or equal to 100)
*
*
* See {@link org.apache.commons.math3.stat.descriptive.rank.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 IllegalArgumentException 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) {
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 DimensionMismatchException if the arrays do not have the same
* (positive) length.
* @throws NoDataException if the sample arrays are empty.
*/
public static double sumDifference(final double[] sample1, final double[] sample2) {
int n = sample1.length;
if (n != sample2.length) {
throw new DimensionMismatchException(n, sample2.length);
}
if (n <= 0) {
throw new NoDataException(LocalizedFormats.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 DimensionMismatchException if the arrays do not have the same
* (positive) length.
* @throws NoDataException if the sample arrays are empty.
*/
public static double meanDifference(final double[] sample1, final double[] sample2) {
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
* @see #meanDifference(double[],double[])
* @return variance of paired differences
* @throws DimensionMismatchException if the arrays do not have the same
* length.
* @throws NumberIsTooSmallException if the arrays length is less than 2.
*/
public static double varianceDifference(final double[] sample1,
final double[] sample2,
double meanDifference) {
double sum1 = 0d;
double sum2 = 0d;
double diff = 0d;
int n = sample1.length;
if (n != sample2.length) {
throw new DimensionMismatchException(n, sample2.length);
}
if (n < 2) {
throw new NumberIsTooSmallException(n, 2, true);
}
for (int i = 0; i < n; i++) {
diff = sample1[i] - sample2[i];
sum1 += (diff - meanDifference) *(diff - meanDifference);
sum2 += diff - meanDifference;
}
return (sum1 - (sum2 * sum2 / n)) / (n - 1);
}
/**
* Normalize (standardize) the series, so in the end it is having a mean of 0 and a standard deviation of 1.
*
* @param sample Sample to normalize.
* @return normalized (standardized) sample.
* @since 2.2
*/
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;
}
}