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Java example source code file (PolynomialFitterTest.java)

This example Java source code file (PolynomialFitterTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

curvefitter, deprecated, gaussnewtonoptimizer, levenbergmarquardtoptimizer, polynomialfitter, polynomialfittertest, polynomialfunction, random, simplevectorvaluechecker, suppresswarnings, test, trying, uniformrealdistribution, util

The PolynomialFitterTest.java Java example source code

/*
 * 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.math3.fitting;

import java.util.Random;

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction.Parametric;
import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer;
import org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer;
import org.apache.commons.math3.optim.nonlinear.vector.jacobian.GaussNewtonOptimizer;
import org.apache.commons.math3.optim.SimpleVectorValueChecker;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.distribution.RealDistribution;
import org.apache.commons.math3.distribution.UniformRealDistribution;
import org.apache.commons.math3.TestUtils;
import org.junit.Test;
import org.junit.Assert;

/**
 * Test for class {@link CurveFitter} where the function to fit is a
 * polynomial.
 */
@Deprecated
public class PolynomialFitterTest {
    @Test
    public void testFit() {
        final RealDistribution rng = new UniformRealDistribution(-100, 100);
        rng.reseedRandomGenerator(64925784252L);

        final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
        final PolynomialFitter fitter = new PolynomialFitter(optim);
        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.
        for (int i = 0; i < 100; i++) {
            final double x = rng.sample();
            fitter.addObservedPoint(x, f.value(x));
        }

        // Start fit from initial guesses that are far from the optimal values.
        final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

        TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
    }

    @Test
    public void testNoError() {
        Random randomizer = new Random(64925784252l);
        for (int degree = 1; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (int i = 0; i <= degree; ++i) {
                fitter.addObservedPoint(1.0, i, p.value(i));
            }

            final double[] init = new double[degree + 1];
            PolynomialFunction fitted = new PolynomialFunction(fitter.fit(init));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                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() {
        Random randomizer = new Random(53882150042l);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(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());
            }

            final double[] init = new double[degree + 1];
            PolynomialFunction fitted = new PolynomialFunction(fitter.fit(init));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                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 testMath798() {
        final double tol = 1e-14;
        final SimpleVectorValueChecker checker = new SimpleVectorValueChecker(tol, tol);
        final double[] init = new double[] { 0, 0 };
        final int maxEval = 3;

        final double[] lm = doMath798(new LevenbergMarquardtOptimizer(checker), maxEval, init);
        final double[] gn = doMath798(new GaussNewtonOptimizer(checker), maxEval, init);

        for (int i = 0; i <= 1; i++) {
            Assert.assertEquals(lm[i], gn[i], tol);
        }
    }

    /**
     * This test shows that the user can set the maximum number of iterations
     * to avoid running for too long.
     * But in the test case, the real problem is that the tolerance is way too
     * stringent.
     */
    @Test(expected=TooManyEvaluationsException.class)
    public void testMath798WithToleranceTooLow() {
        final double tol = 1e-100;
        final SimpleVectorValueChecker checker = new SimpleVectorValueChecker(tol, tol);
        final double[] init = new double[] { 0, 0 };
        final int maxEval = 10000; // Trying hard to fit.

        @SuppressWarnings("unused")
        final double[] gn = doMath798(new GaussNewtonOptimizer(checker), maxEval, init);
    }

    /**
     * This test shows that the user can set the maximum number of iterations
     * to avoid running for too long.
     * Even if the real problem is that the tolerance is way too stringent, it
     * is possible to get the best solution so far, i.e. a checker will return
     * the point when the maximum iteration count has been reached.
     */
    @Test
    public void testMath798WithToleranceTooLowButNoException() {
        final double tol = 1e-100;
        final double[] init = new double[] { 0, 0 };
        final int maxEval = 10000; // Trying hard to fit.
        final SimpleVectorValueChecker checker = new SimpleVectorValueChecker(tol, tol, maxEval);

        final double[] lm = doMath798(new LevenbergMarquardtOptimizer(checker), maxEval, init);
        final double[] gn = doMath798(new GaussNewtonOptimizer(checker), maxEval, init);

        for (int i = 0; i <= 1; i++) {
            Assert.assertEquals(lm[i], gn[i], 1e-15);
        }
    }

    /**
     * @param optimizer Optimizer.
     * @param maxEval Maximum number of function evaluations.
     * @param init First guess.
     * @return the solution found by the given optimizer.
     */
    private double[] doMath798(MultivariateVectorOptimizer optimizer,
                               int maxEval,
                               double[] init) {
        final CurveFitter<Parametric> fitter = new CurveFitter(optimizer);

        fitter.addObservedPoint(-0.2, -7.12442E-13);
        fitter.addObservedPoint(-0.199, -4.33397E-13);
        fitter.addObservedPoint(-0.198, -2.823E-13);
        fitter.addObservedPoint(-0.197, -1.40405E-13);
        fitter.addObservedPoint(-0.196, -7.80821E-15);
        fitter.addObservedPoint(-0.195, 6.20484E-14);
        fitter.addObservedPoint(-0.194, 7.24673E-14);
        fitter.addObservedPoint(-0.193, 1.47152E-13);
        fitter.addObservedPoint(-0.192, 1.9629E-13);
        fitter.addObservedPoint(-0.191, 2.12038E-13);
        fitter.addObservedPoint(-0.19, 2.46906E-13);
        fitter.addObservedPoint(-0.189, 2.77495E-13);
        fitter.addObservedPoint(-0.188, 2.51281E-13);
        fitter.addObservedPoint(-0.187, 2.64001E-13);
        fitter.addObservedPoint(-0.186, 2.8882E-13);
        fitter.addObservedPoint(-0.185, 3.13604E-13);
        fitter.addObservedPoint(-0.184, 3.14248E-13);
        fitter.addObservedPoint(-0.183, 3.1172E-13);
        fitter.addObservedPoint(-0.182, 3.12912E-13);
        fitter.addObservedPoint(-0.181, 3.06761E-13);
        fitter.addObservedPoint(-0.18, 2.8559E-13);
        fitter.addObservedPoint(-0.179, 2.86806E-13);
        fitter.addObservedPoint(-0.178, 2.985E-13);
        fitter.addObservedPoint(-0.177, 2.67148E-13);
        fitter.addObservedPoint(-0.176, 2.94173E-13);
        fitter.addObservedPoint(-0.175, 3.27528E-13);
        fitter.addObservedPoint(-0.174, 3.33858E-13);
        fitter.addObservedPoint(-0.173, 2.97511E-13);
        fitter.addObservedPoint(-0.172, 2.8615E-13);
        fitter.addObservedPoint(-0.171, 2.84624E-13);

        final double[] coeff = fitter.fit(maxEval,
                                          new PolynomialFunction.Parametric(),
                                          init);
        return coeff;
    }

    @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
        checkUnsolvableProblem(new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-15, 1e-15)), false);
    }

    @Test
    public void testLargeSample() {
        Random randomizer = new Random(0x5551480dca5b369bl);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (int i = 0; i < 40000; ++i) {
                double x = -1.0 + i / 20000.0;
                fitter.addObservedPoint(1.0, x,
                                        p.value(x) + 0.1 * randomizer.nextGaussian());
            }

            final double[] init = new double[degree + 1];
            PolynomialFunction fitted = new PolynomialFunction(fitter.fit(init));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                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(MultivariateVectorOptimizer optimizer,
                                        boolean solvable) {
        Random randomizer = new Random(1248788532l);
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(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 {
                final double[] init = new double[degree + 1];
                fitter.fit(init);
                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);
    }
}

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