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Java example source code file (PolynomialSplineFunctionTest.java)

This example Java source code file (PolynomialSplineFunctionTest.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, mathillegalargumentexception, mathillegalstateexception, outofrangeexception, polynomialfunction, polynomialsplinefunction, polynomialsplinefunctiontest, test, univariatefunction, util

The PolynomialSplineFunctionTest.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.polynomials;

import java.util.Arrays;

import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.junit.Assert;
import org.junit.Test;

/**
 * Tests the PolynomialSplineFunction implementation.
 *
 */
public class PolynomialSplineFunctionTest {

    /** Error tolerance for tests */
    protected double tolerance = 1.0e-12;

    /**
     * Quadratic polynomials used in tests:
     *
     * x^2 + x            [-1, 0)
     * x^2 + x + 2        [0, 1)
     * x^2 + x + 4        [1, 2)
     *
     * Defined so that evaluation using PolynomialSplineFunction evaluation
     * algorithm agrees at knot point boundaries.
     */
    protected PolynomialFunction[] polynomials = {
        new PolynomialFunction(new double[] {0d, 1d, 1d}),
        new PolynomialFunction(new double[] {2d, 1d, 1d}),
        new PolynomialFunction(new double[] {4d, 1d, 1d})
    };

    /** Knot points  */
    protected double[] knots = {-1, 0, 1, 2};

    /** Derivative of test polynomials -- 2x + 1  */
    protected PolynomialFunction dp =
        new PolynomialFunction(new double[] {1d, 2d});


    @Test
    public void testConstructor() {
        PolynomialSplineFunction spline =
            new PolynomialSplineFunction(knots, polynomials);
        Assert.assertTrue(Arrays.equals(knots, spline.getKnots()));
        Assert.assertEquals(1d, spline.getPolynomials()[0].getCoefficients()[2], 0);
        Assert.assertEquals(3, spline.getN());

        try { // too few knots
            new PolynomialSplineFunction(new double[] {0}, polynomials);
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }

        try { // too many knots
            new PolynomialSplineFunction(new double[] {0,1,2,3,4}, polynomials);
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }

        try { // knots not increasing
            new PolynomialSplineFunction(new double[] {0,1, 3, 2}, polynomials);
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testValues() {
        PolynomialSplineFunction spline =
            new PolynomialSplineFunction(knots, polynomials);
        UnivariateFunction dSpline = spline.derivative();

        /**
         * interior points -- spline value at x should equal p(x - knot)
         * where knot is the largest knot point less than or equal to x and p
         * is the polynomial defined over the knot segment to which x belongs.
         */
        double x = -1;
        int index = 0;
        for (int i = 0; i < 10; i++) {
           x+=0.25;
           index = findKnot(knots, x);
           Assert.assertEquals("spline function evaluation failed for x=" + x,
                   polynomials[index].value(x - knots[index]), spline.value(x), tolerance);
           Assert.assertEquals("spline derivative evaluation failed for x=" + x,
                   dp.value(x - knots[index]), dSpline.value(x), tolerance);
        }

        // knot points -- centering should zero arguments
        for (int i = 0; i < 3; i++) {
            Assert.assertEquals("spline function evaluation failed for knot=" + knots[i],
                    polynomials[i].value(0), spline.value(knots[i]), tolerance);
            Assert.assertEquals("spline function evaluation failed for knot=" + knots[i],
                    dp.value(0), dSpline.value(knots[i]), tolerance);
        }

        try { //outside of domain -- under min
            x = spline.value(-1.5);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }

        try { //outside of domain -- over max
            x = spline.value(2.5);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testIsValidPoint() {
        final PolynomialSplineFunction spline =
            new PolynomialSplineFunction(knots, polynomials);
        final double xMin = knots[0];
        final double xMax = knots[knots.length - 1];

        double x;

        x = xMin;
        Assert.assertTrue(spline.isValidPoint(x));
        // Ensure that no exception is thrown.
        spline.value(x);

        x = xMax;
        Assert.assertTrue(spline.isValidPoint(x));
        // Ensure that no exception is thrown.
        spline.value(x);

        final double xRange = xMax - xMin;
        x = xMin + xRange / 3.4;
        Assert.assertTrue(spline.isValidPoint(x));
        // Ensure that no exception is thrown.
        spline.value(x);

        final double small = 1e-8;
        x = xMin - small;
        Assert.assertFalse(spline.isValidPoint(x));
        // Ensure that an exception would have been thrown.
        try {
            spline.value(x);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException expected) {}
    }

    /**
     *  Do linear search to find largest knot point less than or equal to x.
     *  Implementation does binary search.
     */
     protected int findKnot(double[] knots, double x) {
         if (x < knots[0] || x >= knots[knots.length -1]) {
             throw new OutOfRangeException(x, knots[0], knots[knots.length -1]);
         }
         for (int i = 0; i < knots.length; i++) {
             if (knots[i] > x) {
                 return i - 1;
             }
         }
         throw new MathIllegalStateException();
     }
}

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