/* ===========================================================
* JFreeChart : a free chart library for the Java(tm) platform
* ===========================================================
*
* (C) Copyright 2000-2014, by Object Refinery Limited and Contributors.
*
* Project Info: http://www.jfree.org/jfreechart/index.html
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
* USA.
*
* [Oracle and Java are registered trademarks of Oracle and/or its affiliates.
* Other names may be trademarks of their respective owners.]
*
* ---------------
* Statistics.java
* ---------------
* (C) Copyright 2000-2014, by Matthew Wright and Contributors.
*
* Original Author: Matthew Wright;
* Contributor(s): David Gilbert (for Object Refinery Limited);
*
* Changes (from 08-Nov-2001)
* --------------------------
* 08-Nov-2001 : Added standard header and tidied Javadoc comments (DG);
* Moved from JFreeChart to package com.jrefinery.data.* in
* JCommon class library (DG);
* 24-Jun-2002 : Removed unnecessary local variable (DG);
* 07-Oct-2002 : Fixed errors reported by Checkstyle (DG);
* 26-May-2004 : Moved calculateMean() method from BoxAndWhiskerCalculator (DG);
* 02-Jun-2004 : Fixed bug in calculateMedian() method (DG);
* 11-Jan-2005 : Removed deprecated code in preparation for the 1.0.0
* release (DG);
*
*/
package org.jfree.data.statistics;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import org.jfree.chart.util.ParamChecks;
/**
* A utility class that provides some common statistical functions.
*/
public abstract class Statistics {
/**
* Returns the mean of an array of numbers. This is equivalent to calling
* {@code calculateMean(values, true)}.
*
* @param values the values ({@code null} not permitted).
*
* @return The mean.
*/
public static double calculateMean(Number[] values) {
return calculateMean(values, true);
}
/**
* Returns the mean of an array of numbers.
*
* @param values the values ({@code null} not permitted).
* @param includeNullAndNaN a flag that controls whether or not
* {@code null} and {@code Double.NaN} values are included
* in the calculation (if either is present in the array, the result is
* {@link Double#NaN}).
*
* @return The mean.
*
* @since 1.0.3
*/
public static double calculateMean(Number[] values,
boolean includeNullAndNaN) {
ParamChecks.nullNotPermitted(values, "values");
double sum = 0.0;
double current;
int counter = 0;
for (Number value : values) {
// treat nulls the same as NaNs
if (value != null) {
current = value.doubleValue();
} else {
current = Double.NaN;
}
// calculate the sum and count
if (includeNullAndNaN || !Double.isNaN(current)) {
sum = sum + current;
counter++;
}
}
double result = (sum / counter);
return result;
}
/**
* Returns the mean of a collection of {@code Number} objects.
*
* @param values the values ({@code null} not permitted).
*
* @return The mean.
*/
public static double calculateMean(Collection<Number> values) {
return calculateMean(values, true);
}
/**
* Returns the mean of a collection of {@code Number} objects.
*
* @param values the values ({@code null} not permitted).
* @param includeNullAndNaN a flag that controls whether or not
* {@code null} and {@code Double.NaN} values are included
* in the calculation (if either is present in the array, the result is
* {@link Double#NaN}).
*
* @return The mean.
*
* @since 1.0.3
*/
public static double calculateMean(Collection<Number> values,
boolean includeNullAndNaN) {
ParamChecks.nullNotPermitted(values, "values");
int count = 0;
double total = 0.0;
for (Number n : values) {
if (n == null) {
if (includeNullAndNaN) {
return Double.NaN;
}
else {
continue;
}
}
double value = n.doubleValue();
if (Double.isNaN(value)) {
if (includeNullAndNaN) {
return Double.NaN;
}
else {
continue;
}
}
total = total + value;
count = count + 1;
}
return total / count;
}
/**
* Calculates the median for a list of values ({@code Number} objects).
* The list of values will be copied, and the copy sorted, before
* calculating the median. To avoid this step (if your list of values
* is already sorted), use the {@link #calculateMedian(List, boolean)}
* method.
*
* @param values the values ({@code null} permitted).
*
* @return The median.
*/
public static double calculateMedian(List<Number> values) {
return calculateMedian(values, true);
}
/**
* Calculates the median for a list of values ({@code Number} objects).
* If {@code copyAndSort} is {@code false}, the list is assumed
* to be presorted in ascending order by value.
*
* @param values the values ({@code null} permitted).
* @param copyAndSort a flag that controls whether the list of values is
* copied and sorted.
*
* @return The median.
*/
public static double calculateMedian(List<Number> values,
boolean copyAndSort) {
if (values == null) {
return Double.NaN;
}
double result = Double.NaN;
if (copyAndSort) {
List<Number> copy = new ArrayList<Number>(values);
Collections.sort((List) copy);
values = copy;
}
int count = values.size();
if (count > 0) {
if (count % 2 == 1) {
if (count > 1) {
Number value = values.get((count - 1) / 2);
result = value.doubleValue();
}
else {
Number value = values.get(0);
result = value.doubleValue();
}
}
else {
Number value1 = values.get(count / 2 - 1);
Number value2 = values.get(count / 2);
result = (value1.doubleValue() + value2.doubleValue()) / 2.0;
}
}
return result;
}
/**
* Calculates the median for a sublist within a list of values
* ({@code Number} objects).
*
* @param values the values, in any order ({@code null} not permitted).
* @param start the start index.
* @param end the end index.
*
* @return The median.
*/
public static double calculateMedian(List<Number> values, int start, int end) {
return calculateMedian(values, start, end, true);
}
/**
* Calculates the median for a sublist within a list of values
* ({@code Number} objects). The entire list will be sorted if the
* {@code ascending} argument is {@code false}.
*
* @param values the values ({@code null} not permitted).
* @param start the start index.
* @param end the end index.
* @param copyAndSort a flag that that controls whether the list of values
* is copied and sorted.
*
* @return The median.
*/
public static double calculateMedian(List<Number> values,
int start, int end, boolean copyAndSort) {
double result = Double.NaN;
if (copyAndSort) {
List<Number> working = new ArrayList<Number>(end - start + 1);
for (int i = start; i <= end; i++) {
working.add(values.get(i));
}
Collections.sort((List) working);
result = calculateMedian(working, false);
}
else {
int count = end - start + 1;
if (count > 0) {
if (count % 2 == 1) {
if (count > 1) {
Number value = values.get(start + (count - 1) / 2);
result = value.doubleValue();
}
else {
Number value = values.get(start);
result = value.doubleValue();
}
}
else {
Number v1 = values.get(start + count / 2 - 1);
Number v2 = values.get(start + count / 2);
result = (v1.doubleValue() + v2.doubleValue()) / 2.0;
}
}
}
return result;
}
/**
* Returns the standard deviation of a set of numbers.
*
* @param data the data ({@code null} or zero length array not
* permitted).
*
* @return The standard deviation of a set of numbers.
*/
public static double getStdDev(Number[] data) {
ParamChecks.nullNotPermitted(data, "data");
if (data.length == 0) {
throw new IllegalArgumentException("Zero length 'data' array.");
}
double avg = calculateMean(data);
double sum = 0.0;
for (Number aData : data) {
double diff = aData.doubleValue() - avg;
sum = sum + diff * diff;
}
return Math.sqrt(sum / (data.length - 1));
}
/**
* Fits a straight line to a set of (x, y) data, returning the slope and
* intercept.
*
* @param xData the x-data ({@code null} not permitted).
* @param yData the y-data ({@code null} not permitted).
*
* @return A double array with the intercept in [0] and the slope in [1].
*/
public static double[] getLinearFit(Number[] xData, Number[] yData) {
ParamChecks.nullNotPermitted(xData, "xData");
ParamChecks.nullNotPermitted(yData, "yData");
if (xData.length != yData.length) {
throw new IllegalArgumentException(
"Statistics.getLinearFit(): array lengths must be equal.");
}
double[] result = new double[2];
// slope
result[1] = getSlope(xData, yData);
// intercept
result[0] = calculateMean(yData) - result[1] * calculateMean(xData);
return result;
}
/**
* Finds the slope of a regression line using least squares.
*
* @param xData the x-values ({@code null} not permitted).
* @param yData the y-values ({@code null} not permitted).
*
* @return The slope.
*/
public static double getSlope(Number[] xData, Number[] yData) {
ParamChecks.nullNotPermitted(xData, "xData");
ParamChecks.nullNotPermitted(yData, "yData");
if (xData.length != yData.length) {
throw new IllegalArgumentException("Array lengths must be equal.");
}
// ********* stat function for linear slope ********
// y = a + bx
// a = ybar - b * xbar
// sum(x * y) - (sum (x) * sum(y)) / n
// b = ------------------------------------
// sum (x^2) - (sum(x)^2 / n
// *************************************************
// sum of x, x^2, x * y, y
double sx = 0.0, sxx = 0.0, sxy = 0.0, sy = 0.0;
int counter;
for (counter = 0; counter < xData.length; counter++) {
sx = sx + xData[counter].doubleValue();
sxx = sxx + Math.pow(xData[counter].doubleValue(), 2);
sxy = sxy + yData[counter].doubleValue()
* xData[counter].doubleValue();
sy = sy + yData[counter].doubleValue();
}
return (sxy - (sx * sy) / counter) / (sxx - (sx * sx) / counter);
}
/**
* Calculates the correlation between two datasets. Both arrays should
* contain the same number of items. Null values are treated as zero.
* <P>
* Information about the correlation calculation was obtained from:
*
* http://trochim.human.cornell.edu/kb/statcorr.htm
*
* @param data1 the first dataset.
* @param data2 the second dataset.
*
* @return The correlation.
*/
public static double getCorrelation(Number[] data1, Number[] data2) {
ParamChecks.nullNotPermitted(data1, "data1");
ParamChecks.nullNotPermitted(data2, "data2");
if (data1.length != data2.length) {
throw new IllegalArgumentException(
"'data1' and 'data2' arrays must have same length.");
}
int n = data1.length;
double sumX = 0.0;
double sumY = 0.0;
double sumX2 = 0.0;
double sumY2 = 0.0;
double sumXY = 0.0;
for (int i = 0; i < n; i++) {
double x = 0.0;
if (data1[i] != null) {
x = data1[i].doubleValue();
}
double y = 0.0;
if (data2[i] != null) {
y = data2[i].doubleValue();
}
sumX = sumX + x;
sumY = sumY + y;
sumXY = sumXY + (x * y);
sumX2 = sumX2 + (x * x);
sumY2 = sumY2 + (y * y);
}
return (n * sumXY - sumX * sumY) / Math.pow((n * sumX2 - sumX * sumX)
* (n * sumY2 - sumY * sumY), 0.5);
}
/**
* Returns a data set for a moving average on the data set passed in.
*
* @param xData an array of the x data.
* @param yData an array of the y data.
* @param period the number of data points to average
*
* @return A double[][] the length of the data set in the first dimension,
* with two doubles for x and y in the second dimension
*/
public static double[][] getMovingAverage(Number[] xData, Number[] yData,
int period) {
// check arguments...
if (xData.length != yData.length) {
throw new IllegalArgumentException("Array lengths must be equal.");
}
if (period > xData.length) {
throw new IllegalArgumentException(
"Period can't be longer than dataset.");
}
double[][] result = new double[xData.length - period][2];
for (int i = 0; i < result.length; i++) {
result[i][0] = xData[i + period].doubleValue();
// holds the moving average sum
double sum = 0.0;
for (int j = 0; j < period; j++) {
sum += yData[i + j].doubleValue();
}
sum = sum / period;
result[i][1] = sum;
}
return result;
}
}