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+package de.lmu.ifi.dbs.elki.math.statistics;
+/*
+This file is part of ELKI:
+Environment for Developing KDD-Applications Supported by Index-Structures
+
+Copyright (C) 2011
+Ludwig-Maximilians-Universität München
+Lehr- und Forschungseinheit für Datenbanksysteme
+ELKI Development Team
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU Affero General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program 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 Affero General Public License for more details.
+
+You should have received a copy of the GNU Affero General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+
+import de.lmu.ifi.dbs.elki.math.linearalgebra.Matrix;
+import de.lmu.ifi.dbs.elki.math.linearalgebra.Vector;
+
+/**
+ * A polynomial fit is a specific type of multiple regression. The simple
+ * regression model (a first-order polynomial) can be trivially extended to
+ * higher orders.
+ * <p/>
+ * The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of
+ * polynomial equations of order p with polynomial coefficients { b0 ... bp}.
+ * The model can be expressed using data matrix x, target vector y and parameter
+ * vector ?. The ith row of X and Y will contain the x and y value for the ith
+ * data sample.
+ * <p/>
+ * The variables will be transformed in the following way: x => x1, ..., x^p =>
+ * xp Then the model can be written as a multiple linear equation model: y = b0
+ * + b1*x1 + b2*x2 + ... + bp*xp + e
+ *
+ * @author Elke Achtert
+ */
+public class PolynomialRegression extends MultipleLinearRegression {
+ /**
+ * The order of the polynom.
+ */
+ public final int p;
+
+ /**
+ * Provides a new polynomial regression model with the specified parameters.
+ *
+ * @param y the (n x 1) - vector holding the response values (y1, ..., yn)^T.
+ * @param x the (n x 1)-vector holding the x-values (x1, ..., xn)^T.
+ * @param p the order of the polynom.
+ */
+ public PolynomialRegression(Vector y, Vector x, int p) {
+ super(y, xMatrix(x, p));
+ this.p = p;
+ }
+
+ private static Matrix xMatrix(Vector x, int p) {
+ int n = x.getRowDimensionality();
+
+ Matrix result = new Matrix(n, p + 1);
+ for(int i = 0; i < n; i++) {
+ for(int j = 0; j < p + 1; j++) {
+ result.set(i, j, Math.pow(x.get(i), j));
+ }
+ }
+ return result;
+ }
+
+ /**
+ * Returns the adapted coefficient of determination
+ *
+ * @return the adapted coefficient of determination
+ */
+ public double adaptedCoefficientOfDetermination() {
+ int n = getEstimatedResiduals().getRowDimensionality();
+ return 1.0 - ((n - 1.0) / (n * 1.0 - p)) * (1 - coefficientOfDetermination());
+ }
+
+ /**
+ * Performs an estimation of y on the specified x value.
+ *
+ * @param x the x-value for which y is estimated
+ * @return the estimation of y
+ */
+ public double estimateY(double x) {
+ return super.estimateY(xMatrix(new Vector(new double[] { x }), p));
+ }
+} \ No newline at end of file