/* ===========================================================
* 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.]
*
* ---------------
* Regression.java
* ---------------
* (C) Copyright 2002-2014, by Object Refinery Limited.
*
* Original Author: David Gilbert (for Object Refinery Limited);
* Contributor(s): Peter Kolb (patch 2795746);
*
* Changes
* -------
* 30-Sep-2002 : Version 1 (DG);
* 18-Aug-2003 : Added 'abstract' (DG);
* 15-Jul-2004 : Switched getX() with getXValue() and getY() with
* getYValue() (DG);
* 29-May-2009 : Added support for polynomial regression, see patch 2795746
* by Peter Kolb (DG);
*
*/
package org.jfree.data.statistics;
import org.jfree.chart.util.ParamChecks;
import org.jfree.data.xy.XYDataset;
/**
* A utility class for fitting regression curves to data.
*/
public abstract class Regression {
/**
* Returns the parameters 'a' and 'b' for an equation y = a + bx, fitted to
* the data using ordinary least squares regression. The result is
* returned as a double[], where result[0] --> a, and result[1] --> b.
*
* @param data the data.
*
* @return The parameters.
*/
public static double[] getOLSRegression(double[][] data) {
int n = data.length;
if (n < 2) {
throw new IllegalArgumentException("Not enough data.");
}
double sumX = 0;
double sumY = 0;
double sumXX = 0;
double sumXY = 0;
for (double[] aData : data) {
double x = aData[0];
double y = aData[1];
sumX += x;
sumY += y;
double xx = x * x;
sumXX += xx;
double xy = x * y;
sumXY += xy;
}
double sxx = sumXX - (sumX * sumX) / n;
double sxy = sumXY - (sumX * sumY) / n;
double xbar = sumX / n;
double ybar = sumY / n;
double[] result = new double[2];
result[1] = sxy / sxx;
result[0] = ybar - result[1] * xbar;
return result;
}
/**
* Returns the parameters 'a' and 'b' for an equation y = a + bx, fitted to
* the data using ordinary least squares regression. The result is returned
* as a double[], where result[0] --> a, and result[1] --> b.
*
* @param data the data.
* @param series the series (zero-based index).
*
* @return The parameters.
*/
public static double[] getOLSRegression(XYDataset data, int series) {
int n = data.getItemCount(series);
if (n < 2) {
throw new IllegalArgumentException("Not enough data.");
}
double sumX = 0;
double sumY = 0;
double sumXX = 0;
double sumXY = 0;
for (int i = 0; i < n; i++) {
double x = data.getXValue(series, i);
double y = data.getYValue(series, i);
sumX += x;
sumY += y;
double xx = x * x;
sumXX += xx;
double xy = x * y;
sumXY += xy;
}
double sxx = sumXX - (sumX * sumX) / n;
double sxy = sumXY - (sumX * sumY) / n;
double xbar = sumX / n;
double ybar = sumY / n;
double[] result = new double[2];
result[1] = sxy / sxx;
result[0] = ybar - result[1] * xbar;
return result;
}
/**
* Returns the parameters 'a' and 'b' for an equation y = ax^b, fitted to
* the data using a power regression equation. The result is returned as
* an array, where double[0] --> a, and double[1] --> b.
*
* @param data the data.
*
* @return The parameters.
*/
public static double[] getPowerRegression(double[][] data) {
int n = data.length;
if (n < 2) {
throw new IllegalArgumentException("Not enough data.");
}
double sumX = 0;
double sumY = 0;
double sumXX = 0;
double sumXY = 0;
for (double[] aData : data) {
double x = Math.log(aData[0]);
double y = Math.log(aData[1]);
sumX += x;
sumY += y;
double xx = x * x;
sumXX += xx;
double xy = x * y;
sumXY += xy;
}
double sxx = sumXX - (sumX * sumX) / n;
double sxy = sumXY - (sumX * sumY) / n;
double xbar = sumX / n;
double ybar = sumY / n;
double[] result = new double[2];
result[1] = sxy / sxx;
result[0] = Math.pow(Math.exp(1.0), ybar - result[1] * xbar);
return result;
}
/**
* Returns the parameters 'a' and 'b' for an equation y = ax^b, fitted to
* the data using a power regression equation. The result is returned as
* an array, where double[0] --> a, and double[1] --> b.
*
* @param data the data.
* @param series the series to fit the regression line against.
*
* @return The parameters.
*/
public static double[] getPowerRegression(XYDataset data, int series) {
int n = data.getItemCount(series);
if (n < 2) {
throw new IllegalArgumentException("Not enough data.");
}
double sumX = 0;
double sumY = 0;
double sumXX = 0;
double sumXY = 0;
for (int i = 0; i < n; i++) {
double x = Math.log(data.getXValue(series, i));
double y = Math.log(data.getYValue(series, i));
sumX += x;
sumY += y;
double xx = x * x;
sumXX += xx;
double xy = x * y;
sumXY += xy;
}
double sxx = sumXX - (sumX * sumX) / n;
double sxy = sumXY - (sumX * sumY) / n;
double xbar = sumX / n;
double ybar = sumY / n;
double[] result = new double[2];
result[1] = sxy / sxx;
result[0] = Math.pow(Math.exp(1.0), ybar - result[1] * xbar);
return result;
}
/**
* Returns the parameters 'a0', 'a1', 'a2', ..., 'an' for a polynomial
* function of order n, y = a0 + a1 * x + a2 * x^2 + ... + an * x^n,
* fitted to the data using a polynomial regression equation.
* The result is returned as an array with a length of n + 2,
* where double[0] --> a0, double[1] --> a1, .., double[n] --> an.
* and double[n + 1] is the correlation coefficient R2
* Reference: J. D. Faires, R. L. Burden, Numerische Methoden (german
* edition), pp. 243ff and 327ff.
*
* @param dataset the dataset (<code>null</code> not permitted).
* @param series the series to fit the regression line against (the series
* must have at least order + 1 non-NaN items).
* @param order the order of the function (> 0).
*
* @return The parameters.
*
* @since 1.0.14
*/
public static double[] getPolynomialRegression(XYDataset dataset,
int series, int order) {
ParamChecks.nullNotPermitted(dataset, "dataset");
int itemCount = dataset.getItemCount(series);
if (itemCount < order + 1) {
throw new IllegalArgumentException("Not enough data.");
}
int validItems = 0;
double[][] data = new double[2][itemCount];
for(int item = 0; item < itemCount; item++){
double x = dataset.getXValue(series, item);
double y = dataset.getYValue(series, item);
if (!Double.isNaN(x) && !Double.isNaN(y)){
data[0][validItems] = x;
data[1][validItems] = y;
validItems++;
}
}
if (validItems < order + 1) {
throw new IllegalArgumentException("Not enough data.");
}
int equations = order + 1;
int coefficients = order + 2;
double[] result = new double[equations + 1];
double[][] matrix = new double[equations][coefficients];
double sumX = 0.0;
double sumY = 0.0;
for(int item = 0; item < validItems; item++){
sumX += data[0][item];
sumY += data[1][item];
for(int eq = 0; eq < equations; eq++){
for(int coe = 0; coe < coefficients - 1; coe++){
matrix[eq][coe] += Math.pow(data[0][item],eq + coe);
}
matrix[eq][coefficients - 1] += data[1][item]
* Math.pow(data[0][item],eq);
}
}
double[][] subMatrix = calculateSubMatrix(matrix);
for (int eq = 1; eq < equations; eq++) {
matrix[eq][0] = 0;
for (int coe = 1; coe < coefficients; coe++) {
matrix[eq][coe] = subMatrix[eq - 1][coe - 1];
}
}
for (int eq = equations - 1; eq > -1; eq--) {
double value = matrix[eq][coefficients - 1];
for (int coe = eq; coe < coefficients -1; coe++) {
value -= matrix[eq][coe] * result[coe];
}
result[eq] = value / matrix[eq][eq];
}
double meanY = sumY / validItems;
double yObsSquare = 0.0;
double yRegSquare = 0.0;
for (int item = 0; item < validItems; item++) {
double yCalc = 0;
for (int eq = 0; eq < equations; eq++) {
yCalc += result[eq] * Math.pow(data[0][item],eq);
}
yRegSquare += Math.pow(yCalc - meanY, 2);
yObsSquare += Math.pow(data[1][item] - meanY, 2);
}
double rSquare = yRegSquare / yObsSquare;
result[equations] = rSquare;
return result;
}
/**
* Returns a matrix with the following features: (1) the number of rows
* and columns is 1 less than that of the original matrix; (2)the matrix
* is triangular, i.e. all elements a (row, column) with column > row are
* zero. This method is used for calculating a polynomial regression.
*
* @param matrix the start matrix.
*
* @return The new matrix.
*/
private static double[][] calculateSubMatrix(double[][] matrix){
int equations = matrix.length;
int coefficients = matrix[0].length;
double[][] result = new double[equations - 1][coefficients - 1];
for (int eq = 1; eq < equations; eq++) {
double factor = matrix[0][0] / matrix[eq][0];
for (int coe = 1; coe < coefficients; coe++) {
result[eq - 1][coe -1] = matrix[0][coe] - matrix[eq][coe]
* factor;
}
}
if (equations == 1) {
return result;
}
// check for zero pivot element
if (result[0][0] == 0) {
boolean found = false;
for (int i = 0; i < result.length; i ++) {
if (result[i][0] != 0) {
found = true;
double[] temp = result[0];
System.arraycopy(result[i], 0, result[0], 0,
result[i].length);
System.arraycopy(temp, 0, result[i], 0, temp.length);
break;
}
}
if (!found) {
return new double[equations - 1][coefficients - 1];
}
}
double[][] subMatrix = calculateSubMatrix(result);
for (int eq = 1; eq < equations - 1; eq++) {
result[eq][0] = 0;
for (int coe = 1; coe < coefficients - 1; coe++) {
result[eq][coe] = subMatrix[eq - 1][coe - 1];
}
}
return result;
}
}