MATH-1014
"PolynomialCurveFitter" as replacement of "PolynomialFitter". Some tests have been obsoleted by the refactoring (which hides the optimizer and thus avoids some potential misuses). git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1543906 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Gilles Sadowski
parent
54a7796ff2
commit
c1ba07bb65
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@ -51,6 +51,9 @@ If the output is not quite correct, check for invisible trailing spaces!
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</properties>
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<body>
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<release version="3.3" date="TBD" description="TBD">
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<action dev="erans" type="add" issue="MATH-1014">
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Refactoring of curve fitters (package "o.a.c.m.fitting").
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</action>
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<action dev="tn" type="add" issue="MATH-970">
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Added possibility to retrieve the best found solution of the "SimplexSolver" in case
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the iteration limit has been reached. The "optimize(OptimizationData...)" method now
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@ -0,0 +1,125 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math3.fitting;
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import java.util.Collection;
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import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
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import org.apache.commons.math3.exception.MathInternalError;
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import org.apache.commons.math3.fitting.leastsquares.LevenbergMarquardtOptimizer;
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import org.apache.commons.math3.fitting.leastsquares.WithStartPoint;
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import org.apache.commons.math3.fitting.leastsquares.WithMaxIterations;
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import org.apache.commons.math3.linear.DiagonalMatrix;
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/**
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* Fits points to a {@link
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* org.apache.commons.math3.analysis.polynomials.PolynomialFunction.Parametric polynomial}
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* function.
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* <br/>
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* The size of the {@link #withStartPoint(double[]) initial guess} array defines the
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* degree of the polynomial to be fitted.
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* They must be sorted in increasing order of the polynomial's degree.
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* The optimal values of the coefficients will be returned in the same order.
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*
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* @version $Id$
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* @since 3.3
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*/
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public class PolynomialCurveFitter extends AbstractCurveFitter<LevenbergMarquardtOptimizer>
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implements WithStartPoint<PolynomialCurveFitter>,
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WithMaxIterations<PolynomialCurveFitter> {
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/** Parametric function to be fitted. */
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private static final PolynomialFunction.Parametric FUNCTION = new PolynomialFunction.Parametric();
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/** Initial guess. */
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private final double[] initialGuess;
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/** Maximum number of iterations of the optimization algorithm. */
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private final int maxIter;
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/**
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* Contructor used by the factory methods.
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*
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* @param initialGuess Initial guess.
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* @param maxIter Maximum number of iterations of the optimization algorithm.
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* @throws MathInternalError if {@code initialGuess} is {@code null}.
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*/
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private PolynomialCurveFitter(double[] initialGuess,
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int maxIter) {
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this.initialGuess = initialGuess;
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this.maxIter = maxIter;
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}
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/**
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* Creates a default curve fitter.
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* Zero will be used as initial guess for the coefficients, and the maximum
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* number of iterations of the optimization algorithm is set to
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* {@link Integer#MAX_VALUE}.
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*
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* @param degree Degree of the polynomial to be fitted.
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* @return a curve fitter.
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*
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* @see #withStartPoint(double[])
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* @see #withMaxIterations(int)
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*/
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public static PolynomialCurveFitter create(int degree) {
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return new PolynomialCurveFitter(new double[degree + 1], Integer.MAX_VALUE);
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}
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/** {@inheritDoc} */
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public PolynomialCurveFitter withStartPoint(double[] start) {
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return new PolynomialCurveFitter(start.clone(),
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maxIter);
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}
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/** {@inheritDoc} */
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public PolynomialCurveFitter withMaxIterations(int max) {
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return new PolynomialCurveFitter(initialGuess,
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max);
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}
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/** {@inheritDoc} */
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@Override
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protected LevenbergMarquardtOptimizer getOptimizer(Collection<WeightedObservedPoint> observations) {
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// Prepare least-squares problem.
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final int len = observations.size();
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final double[] target = new double[len];
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final double[] weights = new double[len];
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int i = 0;
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for (WeightedObservedPoint obs : observations) {
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target[i] = obs.getY();
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weights[i] = obs.getWeight();
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++i;
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}
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final AbstractCurveFitter.TheoreticalValuesFunction model
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= new AbstractCurveFitter.TheoreticalValuesFunction(FUNCTION,
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observations);
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if (initialGuess == null) {
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throw new MathInternalError();
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}
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// Return a new optimizer set up to fit a Gaussian curve to the
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// observed points.
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return LevenbergMarquardtOptimizer.create()
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.withMaxEvaluations(Integer.MAX_VALUE)
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.withMaxIterations(maxIter)
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.withStartPoint(initialGuess)
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.withTarget(target)
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.withWeight(new DiagonalMatrix(weights))
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.withModelAndJacobian(model.getModelFunction(),
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model.getModelFunctionJacobian());
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}
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}
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@ -26,7 +26,10 @@ import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimiz
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*
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* @version $Id: PolynomialFitter.java 1416643 2012-12-03 19:37:14Z tn $
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* @since 2.0
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* @deprecated As of 3.3. Please use {@link PolynomialCurveFitter} and
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* {@link WeightedObservedPoints} instead.
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*/
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@Deprecated
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public class PolynomialFitter extends CurveFitter<PolynomialFunction.Parametric> {
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/**
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* Simple constructor.
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@ -0,0 +1,166 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math3.fitting;
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import java.util.Random;
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import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
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import org.apache.commons.math3.exception.ConvergenceException;
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import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer;
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import org.apache.commons.math3.util.FastMath;
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import org.apache.commons.math3.distribution.RealDistribution;
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import org.apache.commons.math3.distribution.UniformRealDistribution;
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import org.apache.commons.math3.TestUtils;
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import org.junit.Test;
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import org.junit.Assert;
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/**
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* Test for class {@link PolynomialCurveFitter}.
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*/
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public class PolynomialCurveFitterTest {
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@Test
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public void testFit() {
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final RealDistribution rng = new UniformRealDistribution(-100, 100);
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rng.reseedRandomGenerator(64925784252L);
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final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
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final PolynomialFunction f = new PolynomialFunction(coeff);
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// Collect data from a known polynomial.
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final WeightedObservedPoints obs = new WeightedObservedPoints();
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for (int i = 0; i < 100; i++) {
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final double x = rng.sample();
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obs.add(x, f.value(x));
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}
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// Start fit from initial guesses that are far from the optimal values.
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final PolynomialCurveFitter fitter
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= PolynomialCurveFitter.create(0).withStartPoint(new double[] { -1e-20, 3e15, -5e25 });
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final double[] best = fitter.fit(obs.toList());
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TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
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}
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@Test
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public void testNoError() {
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final Random randomizer = new Random(64925784252l);
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for (int degree = 1; degree < 10; ++degree) {
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final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
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final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
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final WeightedObservedPoints obs = new WeightedObservedPoints();
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for (int i = 0; i <= degree; ++i) {
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obs.add(1.0, i, p.value(i));
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}
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final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));
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for (double x = -1.0; x < 1.0; x += 0.01) {
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final double error = FastMath.abs(p.value(x) - fitted.value(x)) /
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(1.0 + FastMath.abs(p.value(x)));
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Assert.assertEquals(0.0, error, 1.0e-6);
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}
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}
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}
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@Test
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public void testSmallError() {
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final Random randomizer = new Random(53882150042l);
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double maxError = 0;
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for (int degree = 0; degree < 10; ++degree) {
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final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
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final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
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final WeightedObservedPoints obs = new WeightedObservedPoints();
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for (double x = -1.0; x < 1.0; x += 0.01) {
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obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian());
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}
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final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));
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for (double x = -1.0; x < 1.0; x += 0.01) {
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final double error = FastMath.abs(p.value(x) - fitted.value(x)) /
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(1.0 + FastMath.abs(p.value(x)));
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maxError = FastMath.max(maxError, error);
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Assert.assertTrue(FastMath.abs(error) < 0.1);
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}
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}
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Assert.assertTrue(maxError > 0.01);
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}
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@Test
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public void testRedundantSolvable() {
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// Levenberg-Marquardt should handle redundant information gracefully
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checkUnsolvableProblem(true);
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}
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@Test
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public void testLargeSample() {
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final Random randomizer = new Random(0x5551480dca5b369bl);
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double maxError = 0;
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for (int degree = 0; degree < 10; ++degree) {
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final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
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final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
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final WeightedObservedPoints obs = new WeightedObservedPoints();
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for (int i = 0; i < 40000; ++i) {
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final double x = -1.0 + i / 20000.0;
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obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian());
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}
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final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));
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for (double x = -1.0; x < 1.0; x += 0.01) {
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final double error = FastMath.abs(p.value(x) - fitted.value(x)) /
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(1.0 + FastMath.abs(p.value(x)));
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maxError = FastMath.max(maxError, error);
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Assert.assertTrue(FastMath.abs(error) < 0.01);
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}
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}
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Assert.assertTrue(maxError > 0.001);
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}
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private void checkUnsolvableProblem(boolean solvable) {
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final Random randomizer = new Random(1248788532l);
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for (int degree = 0; degree < 10; ++degree) {
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final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
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final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
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final WeightedObservedPoints obs = new WeightedObservedPoints();
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// reusing the same point over and over again does not bring
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// information, the problem cannot be solved in this case for
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// degrees greater than 1 (but one point is sufficient for
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// degree 0)
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for (double x = -1.0; x < 1.0; x += 0.01) {
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obs.add(1.0, 0.0, p.value(0.0));
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}
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try {
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fitter.fit(obs.toList());
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Assert.assertTrue(solvable || (degree == 0));
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} catch(ConvergenceException e) {
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Assert.assertTrue((! solvable) && (degree > 0));
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}
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}
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}
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private PolynomialFunction buildRandomPolynomial(int degree, Random randomizer) {
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final double[] coefficients = new double[degree + 1];
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for (int i = 0; i <= degree; ++i) {
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coefficients[i] = randomizer.nextGaussian();
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}
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return new PolynomialFunction(coefficients);
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}
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}
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