// 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.math.optimization.fitting; import static org.junit.Assert.assertEquals; import static org.junit.Assert.assertTrue; import java.util.Random; import org.apache.commons.math.analysis.polynomials.PolynomialFunction; import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer; import org.apache.commons.math.optimization.OptimizationException; import org.apache.commons.math.optimization.general.GaussNewtonOptimizer; import org.apache.commons.math.optimization.general.LevenbergMarquardtOptimizer; import org.junit.Test; public class PolynomialFitterTest { @Test public void testNoError() throws OptimizationException { Random randomizer = new Random(64925784252l); for (int degree = 1; degree < 10; ++degree) { PolynomialFunction p = buildRandomPolynomial(degree, randomizer); PolynomialFitter fitter = new PolynomialFitter(degree, new LevenbergMarquardtOptimizer()); for (int i = 0; i <= degree; ++i) { fitter.addObservedPoint(1.0, i, p.value(i)); } PolynomialFunction fitted = fitter.fit(); for (double x = -1.0; x < 1.0; x += 0.01) { double error = Math.abs(p.value(x) - fitted.value(x)) / (1.0 + Math.abs(p.value(x))); assertEquals(0.0, error, 1.0e-6); } } } @Test public void testSmallError() throws OptimizationException { Random randomizer = new Random(53882150042l); double maxError = 0; for (int degree = 0; degree < 10; ++degree) { PolynomialFunction p = buildRandomPolynomial(degree, randomizer); PolynomialFitter fitter = new PolynomialFitter(degree, new LevenbergMarquardtOptimizer()); for (double x = -1.0; x < 1.0; x += 0.01) { fitter.addObservedPoint(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian()); } PolynomialFunction fitted = fitter.fit(); for (double x = -1.0; x < 1.0; x += 0.01) { double error = Math.abs(p.value(x) - fitted.value(x)) / (1.0 + Math.abs(p.value(x))); maxError = Math.max(maxError, error); assertTrue(Math.abs(error) < 0.1); } } assertTrue(maxError > 0.01); } @Test public void testRedundantSolvable() { // Levenberg-Marquardt should handle redundant information gracefully checkUnsolvableProblem(new LevenbergMarquardtOptimizer(), true); } @Test public void testRedundantUnsolvable() { // Gauss-Newton should not be able to solve redundant information DifferentiableMultivariateVectorialOptimizer optimizer = new GaussNewtonOptimizer(true); checkUnsolvableProblem(optimizer, false); } private void checkUnsolvableProblem(DifferentiableMultivariateVectorialOptimizer optimizer, boolean solvable) { Random randomizer = new Random(1248788532l); for (int degree = 0; degree < 10; ++degree) { PolynomialFunction p = buildRandomPolynomial(degree, randomizer); PolynomialFitter fitter = new PolynomialFitter(degree, optimizer); // reusing the same point over and over again does not bring // information, the problem cannot be solved in this case for // degrees greater than 1 (but one point is sufficient for // degree 0) for (double x = -1.0; x < 1.0; x += 0.01) { fitter.addObservedPoint(1.0, 0.0, p.value(0.0)); } try { fitter.fit(); assertTrue(solvable || (degree == 0)); } catch(OptimizationException e) { assertTrue((! solvable) && (degree > 0)); } } } private PolynomialFunction buildRandomPolynomial(int degree, Random randomizer) { final double[] coefficients = new double[degree + 1]; for (int i = 0; i <= degree; ++i) { coefficients[i] = randomizer.nextGaussian(); } return new PolynomialFunction(coefficients); } }