| /* |
| * 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.math4.fitting; |
| |
| import java.util.Random; |
| |
| import org.apache.commons.math4.TestUtils; |
| import org.apache.commons.math4.analysis.polynomials.PolynomialFunction; |
| import org.apache.commons.statistics.distribution.ContinuousDistribution; |
| import org.apache.commons.statistics.distribution.UniformContinuousDistribution; |
| import org.apache.commons.math4.exception.ConvergenceException; |
| import org.apache.commons.math4.util.FastMath; |
| import org.apache.commons.rng.simple.RandomSource; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| /** |
| * Test for class {@link PolynomialCurveFitter}. |
| */ |
| public class PolynomialCurveFitterTest { |
| @Test |
| public void testFit() { |
| final ContinuousDistribution.Sampler rng |
| = new UniformContinuousDistribution(-100, 100).createSampler(RandomSource.create(RandomSource.WELL_512_A, |
| 64925784252L)); |
| final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2 |
| final PolynomialFunction f = new PolynomialFunction(coeff); |
| |
| // Collect data from a known polynomial. |
| final WeightedObservedPoints obs = new WeightedObservedPoints(); |
| for (int i = 0; i < 100; i++) { |
| final double x = rng.sample(); |
| obs.add(x, f.value(x)); |
| } |
| |
| // Start fit from initial guesses that are far from the optimal values. |
| final PolynomialCurveFitter fitter |
| = PolynomialCurveFitter.create(0).withStartPoint(new double[] { -1e-20, 3e15, -5e25 }); |
| final double[] best = fitter.fit(obs.toList()); |
| |
| TestUtils.assertEquals("best != coeff", coeff, best, 1e-12); |
| } |
| |
| @Test |
| public void testNoError() { |
| final Random randomizer = new Random(64925784252l); |
| for (int degree = 1; degree < 10; ++degree) { |
| final PolynomialFunction p = buildRandomPolynomial(degree, randomizer); |
| final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree); |
| |
| final WeightedObservedPoints obs = new WeightedObservedPoints(); |
| for (int i = 0; i <= degree; ++i) { |
| obs.add(1.0, i, p.value(i)); |
| } |
| |
| final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList())); |
| |
| for (double x = -1.0; x < 1.0; x += 0.01) { |
| final double error = FastMath.abs(p.value(x) - fitted.value(x)) / |
| (1.0 + FastMath.abs(p.value(x))); |
| Assert.assertEquals(0.0, error, 1.0e-6); |
| } |
| } |
| } |
| |
| @Test |
| public void testSmallError() { |
| final Random randomizer = new Random(53882150042l); |
| double maxError = 0; |
| for (int degree = 0; degree < 10; ++degree) { |
| final PolynomialFunction p = buildRandomPolynomial(degree, randomizer); |
| final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree); |
| |
| final WeightedObservedPoints obs = new WeightedObservedPoints(); |
| for (double x = -1.0; x < 1.0; x += 0.01) { |
| obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian()); |
| } |
| |
| final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList())); |
| |
| for (double x = -1.0; x < 1.0; x += 0.01) { |
| final double error = FastMath.abs(p.value(x) - fitted.value(x)) / |
| (1.0 + FastMath.abs(p.value(x))); |
| maxError = FastMath.max(maxError, error); |
| Assert.assertTrue(FastMath.abs(error) < 0.1); |
| } |
| } |
| Assert.assertTrue(maxError > 0.01); |
| } |
| |
| @Test |
| public void testRedundantSolvable() { |
| // Levenberg-Marquardt should handle redundant information gracefully |
| checkUnsolvableProblem(true); |
| } |
| |
| @Test |
| public void testLargeSample() { |
| final Random randomizer = new Random(0x5551480dca5b369bl); |
| double maxError = 0; |
| for (int degree = 0; degree < 10; ++degree) { |
| final PolynomialFunction p = buildRandomPolynomial(degree, randomizer); |
| final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree); |
| |
| final WeightedObservedPoints obs = new WeightedObservedPoints(); |
| for (int i = 0; i < 40000; ++i) { |
| final double x = -1.0 + i / 20000.0; |
| obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian()); |
| } |
| |
| final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList())); |
| for (double x = -1.0; x < 1.0; x += 0.01) { |
| final double error = FastMath.abs(p.value(x) - fitted.value(x)) / |
| (1.0 + FastMath.abs(p.value(x))); |
| maxError = FastMath.max(maxError, error); |
| Assert.assertTrue(FastMath.abs(error) < 0.01); |
| } |
| } |
| Assert.assertTrue(maxError > 0.001); |
| } |
| |
| private void checkUnsolvableProblem(boolean solvable) { |
| final Random randomizer = new Random(1248788532l); |
| |
| for (int degree = 0; degree < 10; ++degree) { |
| final PolynomialFunction p = buildRandomPolynomial(degree, randomizer); |
| final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree); |
| final WeightedObservedPoints obs = new WeightedObservedPoints(); |
| // 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) { |
| obs.add(1.0, 0.0, p.value(0.0)); |
| } |
| |
| try { |
| fitter.fit(obs.toList()); |
| Assert.assertTrue(solvable || (degree == 0)); |
| } catch(ConvergenceException e) { |
| Assert.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); |
| } |
| } |