commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/HarmonicCurveFitterTest.java

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 * 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
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 *      http://www.apache.org/licenses/LICENSE-2.0
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 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math4.legacy.fitting;

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

import org.apache.commons.numbers.angle.Angle;
import org.apache.commons.math4.legacy.analysis.function.HarmonicOscillator;
import org.apache.commons.math4.legacy.exception.MathIllegalStateException;
import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
import org.apache.commons.math4.core.jdkmath.JdkMath;
import org.junit.Assert;
import org.junit.Test;

public class HarmonicCurveFitterTest {
    /**
     * Zero points is not enough observed points.
     */
    @Test(expected=NumberIsTooSmallException.class)
    public void testPreconditions1() {
        HarmonicCurveFitter.create().fit(new WeightedObservedPoints().toList());
    }

    @Test
    public void testNoError() {
        final double a = 0.2;
        final double w = 3.4;
        final double p = 4.1;
        final HarmonicOscillator f = new HarmonicOscillator(a, w, p);

        final WeightedObservedPoints points = new WeightedObservedPoints();
        for (double x = 0.0; x < 1.3; x += 0.01) {
            points.add(1, x, f.value(x));
        }

        final SimpleCurveFitter fitter = HarmonicCurveFitter.create();
        final double[] fitted = fitter.fit(points.toList());
        Assert.assertEquals(a, fitted[0], 1.0e-13);
        Assert.assertEquals(w, fitted[1], 1.0e-13);
        Assert.assertEquals(p, Angle.Rad.WITHIN_0_AND_2PI.applyAsDouble(fitted[2]), 1e-13);

        final HarmonicOscillator ff = new HarmonicOscillator(fitted[0], fitted[1], fitted[2]);
        for (double x = -1.0; x < 1.0; x += 0.01) {
            Assert.assertTrue(JdkMath.abs(f.value(x) - ff.value(x)) < 1e-13);
        }
    }

    @Test
    public void test1PercentError() {
        final Random randomizer = new Random(64925784252L);
        final double a = 0.2;
        final double w = 3.4;
        final double p = 4.1;
        final HarmonicOscillator f = new HarmonicOscillator(a, w, p);

        final WeightedObservedPoints points = new WeightedObservedPoints();
        for (double x = 0.0; x < 10.0; x += 0.1) {
            points.add(1, x, f.value(x) + 0.01 * randomizer.nextGaussian());
        }

        final SimpleCurveFitter fitter = HarmonicCurveFitter.create();
        final double[] fitted = fitter.fit(points.toList());
        Assert.assertEquals(a, fitted[0], 7.6e-4);
        Assert.assertEquals(w, fitted[1], 2.7e-3);
        Assert.assertEquals(p, Angle.Rad.WITHIN_0_AND_2PI.applyAsDouble(fitted[2]), 1.3e-2);
    }

    @Test
    public void testTinyVariationsData() {
        final Random randomizer = new Random(64925784252L);

        final WeightedObservedPoints points = new WeightedObservedPoints();
        for (double x = 0.0; x < 10.0; x += 0.1) {
            points.add(1, x, 1e-7 * randomizer.nextGaussian());
        }

        final SimpleCurveFitter fitter = HarmonicCurveFitter.create();
        fitter.fit(points.toList());

        // This test serves to cover the part of the code of "guessAOmega"
        // when the algorithm using integrals fails.
    }

    @Test
    public void testInitialGuess() {
        final Random randomizer = new Random(45314242L);
        final double a = 0.2;
        final double w = 3.4;
        final double p = 4.1;
        final HarmonicOscillator f = new HarmonicOscillator(a, w, p);

        final WeightedObservedPoints points = new WeightedObservedPoints();
        for (double x = 0.0; x < 10.0; x += 0.1) {
            points.add(1, x, f.value(x) + 0.01 * randomizer.nextGaussian());
        }

        final SimpleCurveFitter fitter = HarmonicCurveFitter.create()
            .withStartPoint(new double[] { 0.15, 3.6, 4.5 });
        final double[] fitted = fitter.fit(points.toList());
        Assert.assertEquals(a, fitted[0], 1.2e-3);
        Assert.assertEquals(w, fitted[1], 3.3e-3);
        Assert.assertEquals(p, Angle.Rad.WITHIN_0_AND_2PI.applyAsDouble(fitted[2]), 1.7e-2);
    }

    @Test
    public void testUnsorted() {
        Random randomizer = new Random(64925784252L);
        final double a = 0.2;
        final double w = 3.4;
        final double p = 4.1;
        final HarmonicOscillator f = new HarmonicOscillator(a, w, p);

        // Build a regularly spaced array of measurements.
        final int size = 100;
        final double[] xTab = new double[size];
        final double[] yTab = new double[size];
        for (int i = 0; i < size; i++) {
            xTab[i] = 0.1 * i;
            yTab[i] = f.value(xTab[i]) + 0.01 * randomizer.nextGaussian();
        }

        // shake it
        for (int i = 0; i < size; i++) {
            int i1 = randomizer.nextInt(size);
            int i2 = randomizer.nextInt(size);
            double xTmp = xTab[i1];
            double yTmp = yTab[i1];
            xTab[i1] = xTab[i2];
            yTab[i1] = yTab[i2];
            xTab[i2] = xTmp;
            yTab[i2] = yTmp;
        }

        // Pass it to the fitter.
        final WeightedObservedPoints points = new WeightedObservedPoints();
        for (int i = 0; i < size; ++i) {
            points.add(1, xTab[i], yTab[i]);
        }

        final SimpleCurveFitter fitter = HarmonicCurveFitter.create();
        final double[] fitted = fitter.fit(points.toList());
        Assert.assertEquals(a, fitted[0], 7.6e-4);
        Assert.assertEquals(w, fitted[1], 3.5e-3);
        Assert.assertEquals(p, Angle.Rad.WITHIN_0_AND_2PI.applyAsDouble(fitted[2]), 1.5e-2);
    }

    @Test(expected=MathIllegalStateException.class)
    public void testMath844() {
        final double[] y = { 0, 1, 2, 3, 2, 1,
                             0, -1, -2, -3, -2, -1,
                             0, 1, 2, 3, 2, 1,
                             0, -1, -2, -3, -2, -1,
                             0, 1, 2, 3, 2, 1, 0 };
        final List<WeightedObservedPoint> points = new ArrayList<>();
        for (int i = 0; i < y.length; i++) {
            points.add(new WeightedObservedPoint(1, i, y[i]));
        }

        // The guesser fails because the function is far from an harmonic
        // function: It is a triangular periodic function with amplitude 3
        // and period 12, and all sample points are taken at integer abscissae
        // so function values all belong to the integer subset {-3, -2, -1, 0,
        // 1, 2, 3}.
        new HarmonicCurveFitter.ParameterGuesser().guess(points);
    }
}