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Java example source code file (FieldHermiteInterpolatorTest.java)

This example Java source code file (FieldHermiteInterpolatorTest.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

bigfraction, dfp, dfpfield, fieldhermiteinterpolator, fieldhermiteinterpolatortest, polynomialfunction, random, test, util

The FieldHermiteInterpolatorTest.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.polynomials.PolynomialFunction;
import org.apache.commons.math3.dfp.Dfp;
import org.apache.commons.math3.dfp.DfpField;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class FieldHermiteInterpolatorTest {

    @Test
    public void testZero() {
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(0) });
        for (int x = -10; x < 10; x++) {
            BigFraction y = interpolator.value(new BigFraction(x))[0];
            Assert.assertEquals(BigFraction.ZERO, y);
            BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 1);
            Assert.assertEquals(BigFraction.ZERO, derivatives[0][0]);
            Assert.assertEquals(BigFraction.ZERO, derivatives[1][0]);
        }
    }

    @Test
    public void testQuadratic() {
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(2) });
        interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(0) });
        interpolator.addSamplePoint(new BigFraction(2), new BigFraction[] { new BigFraction(0) });
        for (double x = -10; x < 10; x += 1.0) {
            BigFraction y = interpolator.value(new BigFraction(x))[0];
            Assert.assertEquals((x - 1) * (x - 2), y.doubleValue(), 1.0e-15);
            BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 3);
            Assert.assertEquals((x - 1) * (x - 2), derivatives[0][0].doubleValue(), 1.0e-15);
            Assert.assertEquals(2 * x - 3, derivatives[1][0].doubleValue(), 1.0e-15);
            Assert.assertEquals(2, derivatives[2][0].doubleValue(), 1.0e-15);
            Assert.assertEquals(0, derivatives[3][0].doubleValue(), 1.0e-15);
        }
    }

    @Test
    public void testMixedDerivatives() {
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(1) }, new BigFraction[] { new BigFraction(2) });
        interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(4) });
        interpolator.addSamplePoint(new BigFraction(2), new BigFraction[] { new BigFraction(5) }, new BigFraction[] { new BigFraction(2) });
        BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(0), 5);
        Assert.assertEquals(new BigFraction(  1), derivatives[0][0]);
        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
        Assert.assertEquals(new BigFraction(  8), derivatives[2][0]);
        Assert.assertEquals(new BigFraction(-24), derivatives[3][0]);
        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
        Assert.assertEquals(new BigFraction(  0), derivatives[5][0]);
        derivatives = interpolator.derivatives(new BigFraction(1), 5);
        Assert.assertEquals(new BigFraction(  4), derivatives[0][0]);
        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
        Assert.assertEquals(new BigFraction( -4), derivatives[2][0]);
        Assert.assertEquals(new BigFraction(  0), derivatives[3][0]);
        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
        Assert.assertEquals(new BigFraction(  0), derivatives[5][0]);
        derivatives = interpolator.derivatives(new BigFraction(2), 5);
        Assert.assertEquals(new BigFraction(  5), derivatives[0][0]);
        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
        Assert.assertEquals(new BigFraction(  8), derivatives[2][0]);
        Assert.assertEquals(new BigFraction( 24), derivatives[3][0]);
        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
        Assert.assertEquals(new BigFraction(  0), derivatives[5][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);
            }

            DfpField field = new DfpField(30);
            Dfp step = field.getOne().divide(field.newDfp(10));
            FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator();
            for (int j = 0; j < 1 + maxDegree; ++j) {
                Dfp x = field.newDfp(j).multiply(step);
                Dfp[] values = new Dfp[p.length];
                for (int k = 0; k < p.length; ++k) {
                    values[k] = field.newDfp(p[k].value(x.getReal()));
                }
                interpolator.addSamplePoint(x, values);
            }

            for (int j = 0; j < 20; ++j) {
                Dfp x = field.newDfp(j).multiply(step);
                Dfp[] values = interpolator.value(x);
                Assert.assertEquals(p.length, values.length);
                for (int k = 0; k < p.length; ++k) {
                    Assert.assertEquals(p[k].value(x.getReal()),
                                        values[k].getReal(),
                                        1.0e-8 * FastMath.abs(p[k].value(x.getReal())));
                }
            }

        }

    }

    @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);
            }

            DfpField field = new DfpField(30);
            Dfp step = field.getOne().divide(field.newDfp(10));
            FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator();
            for (int j = 0; j < 1 + maxDegree / 2; ++j) {
                Dfp x = field.newDfp(j).multiply(step);
                Dfp[] values      = new Dfp[p.length];
                Dfp[] derivatives = new Dfp[p.length];
                for (int k = 0; k < p.length; ++k) {
                    values[k]      = field.newDfp(p[k].value(x.getReal()));
                    derivatives[k] = field.newDfp(pPrime[k].value(x.getReal()));
                }
                interpolator.addSamplePoint(x, values, derivatives);
            }

            Dfp h = step.divide(field.newDfp(100000));
            for (int j = 0; j < 20; ++j) {
                Dfp x = field.newDfp(j).multiply(step);
                Dfp[] y  = interpolator.value(x);
                Dfp[] yP = interpolator.value(x.add(h));
                Dfp[] yM = interpolator.value(x.subtract(h));
                Assert.assertEquals(p.length, y.length);
                for (int k = 0; k < p.length; ++k) {
                    Assert.assertEquals(p[k].value(x.getReal()),
                                        y[k].getReal(),
                                        1.0e-8 * FastMath.abs(p[k].value(x.getReal())));
                    Assert.assertEquals(pPrime[k].value(x.getReal()),
                                        yP[k].subtract(yM[k]).divide(h.multiply(2)).getReal(),
                                        4.0e-8 * FastMath.abs(p[k].value(x.getReal())));
                }
            }

        }
    }

    @Test
    public void testSine() {
        DfpField field = new DfpField(30);
        FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator();
        for (Dfp x = field.getZero(); x.getReal() < FastMath.PI; x = x.add(0.5)) {
            interpolator.addSamplePoint(x, new Dfp[] { x.sin() });
        }
        for (Dfp x = field.newDfp(0.1); x.getReal() < 2.9; x = x.add(0.01)) {
            Dfp y = interpolator.value(x)[0];
            Assert.assertEquals( x.sin().getReal(), y.getReal(), 3.5e-5);
        }
    }

    @Test
    public void testSquareRoot() {
        DfpField field = new DfpField(30);
        FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator();
        for (Dfp x = field.getOne(); x.getReal() < 3.6; x = x.add(0.5)) {
            interpolator.addSamplePoint(x, new Dfp[] { x.sqrt() });
        }
        for (Dfp x = field.newDfp(1.1); x.getReal() < 3.5; x = x.add(0.01)) {
            Dfp y = interpolator.value(x)[0];
            Assert.assertEquals(x.sqrt().getReal(), y.getReal(), 1.5e-4);
        }
    }

    @Test
    public void testWikipedia() {
        // this test corresponds to the example from Wikipedia page:
        // http://en.wikipedia.org/wiki/Hermite_interpolation
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(-1),
                                    new BigFraction[] { new BigFraction( 2) },
                                    new BigFraction[] { new BigFraction(-8) },
                                    new BigFraction[] { new BigFraction(56) });
        interpolator.addSamplePoint(new BigFraction( 0),
                                    new BigFraction[] { new BigFraction( 1) },
                                    new BigFraction[] { new BigFraction( 0) },
                                    new BigFraction[] { new BigFraction( 0) });
        interpolator.addSamplePoint(new BigFraction( 1),
                                    new BigFraction[] { new BigFraction( 2) },
                                    new BigFraction[] { new BigFraction( 8) },
                                    new BigFraction[] { new BigFraction(56) });
        for (BigFraction x = new BigFraction(-1); x.doubleValue() <= 1.0; x = x.add(new BigFraction(1, 8))) {
            BigFraction y = interpolator.value(x)[0];
            BigFraction x2 = x.multiply(x);
            BigFraction x4 = x2.multiply(x2);
            BigFraction x8 = x4.multiply(x4);
            Assert.assertEquals(x8.add(new BigFraction(1)), y);
        }
    }

    @Test
    public void testOnePointParabola() {
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(0),
                                    new BigFraction[] { new BigFraction(1) },
                                    new BigFraction[] { new BigFraction(1) },
                                    new BigFraction[] { new BigFraction(2) });
        for (BigFraction x = new BigFraction(-1); x.doubleValue() <= 1.0; x = x.add(new BigFraction(1, 8))) {
            BigFraction y = interpolator.value(x)[0];
            Assert.assertEquals(BigFraction.ONE.add(x.multiply(BigFraction.ONE.add(x))), y);
        }
    }

    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 testEmptySampleValue() {
        new FieldHermiteInterpolator<BigFraction>().value(BigFraction.ZERO);
    }

    @Test(expected=NoDataException.class)
    public void testEmptySampleDerivative() {
        new FieldHermiteInterpolator<BigFraction>().derivatives(BigFraction.ZERO, 1);
    }

    @Test(expected=IllegalArgumentException.class)
    public void testDuplicatedAbscissa() {
        FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator();
        interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(0) });
        interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(1) });
    }

}

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