Java tutorial
/* =========================================================== * 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); * 03-Jul-2013 : Use ParamChecks (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 (int i = 0; i < n; i++) { double x = data[i][0]; double y = data[i][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 (int i = 0; i < n; i++) { double x = Math.log(data[i][0]); double y = Math.log(data[i][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) { //System.out.println("Equation has no solution!"); 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; } }