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Java example source code file (HermiteInterpolatorTest.java)

This example Java source code file (HermiteInterpolatorTest.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

derivativestructure, hermiteinterpolator, hermiteinterpolatortest, polynomialfunction, random, test, util

The HermiteInterpolatorTest.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.analysis.interpolation;

import java.util.Random;

import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class HermiteInterpolatorTest {

    @Test
    public void testZero() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(0.0, new double[] { 0.0 });
        for (double x = -10; x < 10; x += 1.0) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals(0.0, y.getValue(), 1.0e-15);
            Assert.assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 0.0 }),
                        interpolator.getPolynomials()[0]);
    }

    @Test
    public void testQuadratic() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(0.0, new double[] { 2.0 });
        interpolator.addSamplePoint(1.0, new double[] { 0.0 });
        interpolator.addSamplePoint(2.0, new double[] { 0.0 });
        for (double x = -10; x < 10; x += 1.0) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15);
            Assert.assertEquals(2 * x - 3.0, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 2.0, -3.0, 1.0 }),
                        interpolator.getPolynomials()[0]);
    }

    @Test
    public void testMixedDerivatives() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(0.0, new double[] { 1.0 }, new double[] { 2.0 });
        interpolator.addSamplePoint(1.0, new double[] { 4.0 });
        interpolator.addSamplePoint(2.0, new double[] { 5.0 }, new double[] { 2.0 });
        Assert.assertEquals(4, interpolator.getPolynomials()[0].degree());
        DerivativeStructure y0 = interpolator.value(new DerivativeStructure(1, 1, 0, 0.0))[0];
        Assert.assertEquals(1.0, y0.getValue(), 1.0e-15);
        Assert.assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15);
        Assert.assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15);
        DerivativeStructure y2 = interpolator.value(new DerivativeStructure(1, 1, 0, 2.0))[0];
        Assert.assertEquals(5.0, y2.getValue(), 1.0e-15);
        Assert.assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15);
        checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }),
                        interpolator.getPolynomials()[0]);
    }

    @Test
    public void testRandomPolynomialsValuesOnly() {

        Random random = new Random(0x42b1e7dbd361a932l);

        for (int i = 0; i < 100; ++i) {

            int maxDegree = 0;
            PolynomialFunction[] p = new PolynomialFunction[5];
            for (int k = 0; k < p.length; ++k) {
                int degree = random.nextInt(7);
                p[k] = randomPolynomial(degree, random);
                maxDegree = FastMath.max(maxDegree, degree);
            }

            HermiteInterpolator interpolator = new HermiteInterpolator();
            for (int j = 0; j < 1 + maxDegree; ++j) {
                double x = 0.1 * j;
                double[] values = new double[p.length];
                for (int k = 0; k < p.length; ++k) {
                    values[k] = p[k].value(x);
                }
                interpolator.addSamplePoint(x, values);
            }

            for (double x = 0; x < 2; x += 0.1) {
                double[] values = interpolator.value(x);
                Assert.assertEquals(p.length, values.length);
                for (int k = 0; k < p.length; ++k) {
                    Assert.assertEquals(p[k].value(x), values[k], 1.0e-8 * FastMath.abs(p[k].value(x)));
                }
            }

            PolynomialFunction[] result = interpolator.getPolynomials();
            for (int k = 0; k < p.length; ++k) {
                checkPolynomial(p[k], result[k]);
            }

        }
    }

    @Test
    public void testRandomPolynomialsFirstDerivative() {

        Random random = new Random(0x570803c982ca5d3bl);

        for (int i = 0; i < 100; ++i) {

            int maxDegree = 0;
            PolynomialFunction[] p      = new PolynomialFunction[5];
            PolynomialFunction[] pPrime = new PolynomialFunction[5];
            for (int k = 0; k < p.length; ++k) {
                int degree = random.nextInt(7);
                p[k]      = randomPolynomial(degree, random);
                pPrime[k] = p[k].polynomialDerivative();
                maxDegree = FastMath.max(maxDegree, degree);
            }

            HermiteInterpolator interpolator = new HermiteInterpolator();
            for (int j = 0; j < 1 + maxDegree / 2; ++j) {
                double x = 0.1 * j;
                double[] values      = new double[p.length];
                double[] derivatives = new double[p.length];
                for (int k = 0; k < p.length; ++k) {
                    values[k]      = p[k].value(x);
                    derivatives[k] = pPrime[k].value(x);
                }
                interpolator.addSamplePoint(x, values, derivatives);
            }

            for (double x = 0; x < 2; x += 0.1) {
                DerivativeStructure[] y = interpolator.value(new DerivativeStructure(1, 1, 0, x));
                Assert.assertEquals(p.length, y.length);
                for (int k = 0; k < p.length; ++k) {
                    Assert.assertEquals(p[k].value(x), y[k].getValue(), 1.0e-8 * FastMath.abs(p[k].value(x)));
                    Assert.assertEquals(pPrime[k].value(x), y[k].getPartialDerivative(1), 4.0e-8 * FastMath.abs(p[k].value(x)));
                }
            }

            PolynomialFunction[] result = interpolator.getPolynomials();
            for (int k = 0; k < p.length; ++k) {
                checkPolynomial(p[k], result[k]);
            }

        }
    }

    @Test
    public void testSine() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        for (double x = 0; x < FastMath.PI; x += 0.5) {
            interpolator.addSamplePoint(x, new double[] { FastMath.sin(x) });
        }
        for (double x = 0.1; x <= 2.9; x += 0.01) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 2, 0, x))[0];
            Assert.assertEquals( FastMath.sin(x), y.getValue(), 3.5e-5);
            Assert.assertEquals( FastMath.cos(x), y.getPartialDerivative(1), 1.3e-4);
            Assert.assertEquals(-FastMath.sin(x), y.getPartialDerivative(2), 2.9e-3);
        }
    }

    @Test
    public void testSquareRoot() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        for (double x = 1.0; x < 3.6; x += 0.5) {
            interpolator.addSamplePoint(x, new double[] { FastMath.sqrt(x) });
        }
        for (double x = 1.1; x < 3.5; x += 0.01) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals(FastMath.sqrt(x), y.getValue(), 1.5e-4);
            Assert.assertEquals(0.5 / FastMath.sqrt(x), y.getPartialDerivative(1), 8.5e-4);
        }
    }

    @Test
    public void testWikipedia() {
        // this test corresponds to the example from Wikipedia page:
        // http://en.wikipedia.org/wiki/Hermite_interpolation
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(-1, new double[] { 2 }, new double[] { -8 }, new double[] { 56 });
        interpolator.addSamplePoint( 0, new double[] { 1 }, new double[] {  0 }, new double[] {  0 });
        interpolator.addSamplePoint( 1, new double[] { 2 }, new double[] {  8 }, new double[] { 56 });
        for (double x = -1.0; x <= 1.0; x += 0.125) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            double x2 = x * x;
            double x4 = x2 * x2;
            double x8 = x4 * x4;
            Assert.assertEquals(x8 + 1, y.getValue(), 1.0e-15);
            Assert.assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }),
                        interpolator.getPolynomials()[0]);
    }

    @Test
    public void testOnePointParabola() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(0, new double[] { 1 }, new double[] { 1 }, new double[] { 2 });
        for (double x = -1.0; x <= 1.0; x += 0.125) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals(1 + x * (1 + x), y.getValue(), 1.0e-15);
            Assert.assertEquals(1 + 2 * x, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 1, 1, 1 }),
                        interpolator.getPolynomials()[0]);
    }

    private PolynomialFunction randomPolynomial(int degree, Random random) {
        double[] coeff = new double[ 1 + degree];
        for (int j = 0; j < degree; ++j) {
            coeff[j] = random.nextDouble();
        }
        return new PolynomialFunction(coeff);
    }

    @Test(expected=NoDataException.class)
    public void testEmptySample() {
        new HermiteInterpolator().value(0.0);
    }

    @Test(expected=IllegalArgumentException.class)
    public void testDuplicatedAbscissa() {
        HermiteInterpolator interpolator = new HermiteInterpolator();
        interpolator.addSamplePoint(1.0, new double[] { 0.0 });
        interpolator.addSamplePoint(1.0, new double[] { 1.0 });
    }

    private void checkPolynomial(PolynomialFunction expected, PolynomialFunction result) {
        Assert.assertTrue(result.degree() >= expected.degree());
        double[] cE = expected.getCoefficients();
        double[] cR = result.getCoefficients();
        for (int i = 0; i < cE.length; ++i) {
            Assert.assertEquals(cE[i], cR[i], 1.0e-8 * FastMath.abs(cE[i]));
        }
        for (int i = cE.length; i < cR.length; ++i) {
            Assert.assertEquals(0.0, cR[i], 1.0e-9);
        }
    }

}

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