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Java example source code file (SplineInterpolatorTest.java)

This example Java source code file (SplineInterpolatorTest.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

dimensionmismatchexception, failed, nonmonotonicsequenceexception, numberistoosmallexception, polynomialfunction, polynomialsplinefunction, splineinterpolator, splineinterpolatortest, test, univariatefunction, univariateinterpolator

The SplineInterpolatorTest.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.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test the SplineInterpolator.
 *
 */
public class SplineInterpolatorTest {

    /** error tolerance for spline interpolator value at knot points */
    protected double knotTolerance = 1E-14;

    /** error tolerance for interpolating polynomial coefficients */
    protected double coefficientTolerance = 1E-14;

    /** error tolerance for interpolated values -- high value is from sin test */
    protected double interpolationTolerance = 1E-14;

    @Test
    public void testInterpolateLinearDegenerateTwoSegment()
        {
        double tolerance = 1e-15;
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 1.0 };
        UnivariateInterpolator i = new SplineInterpolator();
        UnivariateFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 1d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);

        // Check interpolation
        Assert.assertEquals(0.0,f.value(0.0), tolerance);
        Assert.assertEquals(0.4,f.value(0.4), tolerance);
        Assert.assertEquals(1.0,f.value(1.0), tolerance);
    }

    @Test
    public void testInterpolateLinearDegenerateThreeSegment()
        {
        double tolerance = 1e-15;
        double x[] = { 0.0, 0.5, 1.0, 1.5 };
        double y[] = { 0.0, 0.5, 1.0, 1.5 };
        UnivariateInterpolator i = new SplineInterpolator();
        UnivariateFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 1d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[2], 1d};
        TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);

        // Check interpolation
        Assert.assertEquals(0,f.value(0), tolerance);
        Assert.assertEquals(1.4,f.value(1.4), tolerance);
        Assert.assertEquals(1.5,f.value(1.5), tolerance);
    }

    @Test
    public void testInterpolateLinear() {
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 0.0 };
        UnivariateInterpolator i = new SplineInterpolator();
        UnivariateFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1.5d, 0d, -2d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 0d, -3d, 2d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    }

    @Test
    public void testInterpolateSin() {
        double sineCoefficientTolerance = 1e-6;
        double sineInterpolationTolerance = 0.0043;
        double x[] =
            {
                0.0,
                FastMath.PI / 6d,
                FastMath.PI / 2d,
                5d * FastMath.PI / 6d,
                FastMath.PI,
                7d * FastMath.PI / 6d,
                3d * FastMath.PI / 2d,
                11d * FastMath.PI / 6d,
                2.d * FastMath.PI };
        double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
        UnivariateInterpolator i = new SplineInterpolator();
        UnivariateFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        /* Check coefficients against values computed using R (version 1.8.1, Red Hat Linux 9)
         *
         * To replicate in R:
         *     x[1] <- 0
         *     x[2] <- pi / 6, etc, same for y[] (could use y <- scan() for y values)
         *     g <- splinefun(x, y, "natural")
         *     splinecoef <- eval(expression(z), envir = environment(g))
         *     print(splinecoef)
         */
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1.002676d, 0d, -0.17415829d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[2].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
        TestUtils.assertEquals(polynomials[3].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
        TestUtils.assertEquals(polynomials[4].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[5].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[6].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
        TestUtils.assertEquals(polynomials[7].getCoefficients(), target, sineCoefficientTolerance);

        //Check interpolation
        Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(FastMath.PI/4d),sineInterpolationTolerance);
        Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(3d*FastMath.PI/4d),sineInterpolationTolerance);
    }

    @Test
    public void testIllegalArguments() {
        // Data set arrays of different size.
        UnivariateInterpolator i = new SplineInterpolator();
        try {
            double xval[] = { 0.0, 1.0 };
            double yval[] = { 0.0, 1.0, 2.0 };
            i.interpolate(xval, yval);
            Assert.fail("Failed to detect data set array with different sizes.");
        } catch (DimensionMismatchException iae) {
            // Expected.
        }
        // X values not sorted.
        try {
            double xval[] = { 0.0, 1.0, 0.5 };
            double yval[] = { 0.0, 1.0, 2.0 };
            i.interpolate(xval, yval);
            Assert.fail("Failed to detect unsorted arguments.");
        } catch (NonMonotonicSequenceException iae) {
            // Expected.
        }
        // Not enough data to interpolate.
        try {
            double xval[] = { 0.0, 1.0 };
            double yval[] = { 0.0, 1.0 };
            i.interpolate(xval, yval);
            Assert.fail("Failed to detect unsorted arguments.");
        } catch (NumberIsTooSmallException iae) {
            // Expected.
        }
    }

    /**
     * verifies that f(x[i]) = y[i] for i = 0..n-1 where n is common length.
     */
    protected void verifyInterpolation(UnivariateFunction f, double x[], double y[])
       {
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(f.value(x[i]), y[i], knotTolerance);
        }
    }

    /**
     * Verifies that interpolating polynomials satisfy consistency requirement:
     *    adjacent polynomials must agree through two derivatives at knot points
     */
    protected void verifyConsistency(PolynomialSplineFunction f, double x[])
        {
        PolynomialFunction polynomials[] = f.getPolynomials();
        for (int i = 1; i < x.length - 2; i++) {
            // evaluate polynomials and derivatives at x[i + 1]
            Assert.assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
            Assert.assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
                                polynomials[i + 1].derivative().value(0), 0.5);
            Assert.assertEquals(polynomials[i].polynomialDerivative().derivative().value(x[i +1] - x[i]),
                                polynomials[i + 1].polynomialDerivative().derivative().value(0), 0.5);
        }
    }

}

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