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Java example source code file (NevilleInterpolatorTest.java)

This example Java source code file (NevilleInterpolatorTest.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

expecting, expm1, illegalargumentexception, interpolation, nevilleinterpolator, nevilleinterpolatortest, nonmonotonicsequenceexception, sin, test, univariatefunction, univariateinterpolator

The NevilleInterpolatorTest.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 org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Expm1;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;


/**
 * Test case for Neville interpolator.
 * <p>
 * The error of polynomial interpolation is
 *     f(z) - p(z) = f^(n)(zeta) * (z-x[0])(z-x[1])...(z-x[n-1]) / n!
 * where f^(n) is the n-th derivative of the approximated function and
 * zeta is some point in the interval determined by x[] and z.
 * <p>
 * Since zeta is unknown, f^(n)(zeta) cannot be calculated. But we can bound
 * it and use the absolute value upper bound for estimates. For reference,
 * see <b>Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.
 *
 */
public final class NevilleInterpolatorTest {

    /**
     * Test of interpolator for the sine function.
     * <p>
     * |sin^(n)(zeta)| <= 1.0, zeta in [0, 2*PI]
     */
    @Test
    public void testSinFunction() {
        UnivariateFunction f = new Sin();
        UnivariateInterpolator interpolator = new NevilleInterpolator();
        double x[], y[], z, expected, result, tolerance;

        // 6 interpolating points on interval [0, 2*PI]
        int n = 6;
        double min = 0.0, max = 2 * FastMath.PI;
        x = new double[n];
        y = new double[n];
        for (int i = 0; i < n; i++) {
            x[i] = min + i * (max - min) / n;
            y[i] = f.value(x[i]);
        }
        double derivativebound = 1.0;
        UnivariateFunction p = interpolator.interpolate(x, y);

        z = FastMath.PI / 4; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = FastMath.PI * 1.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);
    }

    /**
     * Test of interpolator for the exponential function.
     * <p>
     * |expm1^(n)(zeta)| <= e, zeta in [-1, 1]
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1();
        UnivariateInterpolator interpolator = new NevilleInterpolator();
        double x[], y[], z, expected, result, tolerance;

        // 5 interpolating points on interval [-1, 1]
        int n = 5;
        double min = -1.0, max = 1.0;
        x = new double[n];
        y = new double[n];
        for (int i = 0; i < n; i++) {
            x[i] = min + i * (max - min) / n;
            y[i] = f.value(x[i]);
        }
        double derivativebound = FastMath.E;
        UnivariateFunction p = interpolator.interpolate(x, y);

        z = 0.0; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = 0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = -0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);
    }

    /**
     * Test of parameters for the interpolator.
     */
    @Test
    public void testParameters() {
        UnivariateInterpolator interpolator = new NevilleInterpolator();

        try {
            // bad abscissas array
            double x[] = { 1.0, 2.0, 2.0, 4.0 };
            double y[] = { 0.0, 4.0, 4.0, 2.5 };
            UnivariateFunction p = interpolator.interpolate(x, y);
            p.value(0.0);
            Assert.fail("Expecting NonMonotonicSequenceException - bad abscissas array");
        } catch (NonMonotonicSequenceException ex) {
            // expected
        }
    }

    /**
     * Returns the partial error term (z-x[0])(z-x[1])...(z-x[n-1])/n!
     */
    protected double partialerror(double x[], double z) throws
        IllegalArgumentException {

        if (x.length < 1) {
            throw new IllegalArgumentException
                ("Interpolation array cannot be empty.");
        }
        double out = 1;
        for (int i = 0; i < x.length; i++) {
            out *= (z - x[i]) / (i + 1);
        }
        return out;
    }
}

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