Commons Math example source code file (SplineInterpolatorTest.java)

This example Commons Math source code file (SplineInterpolatorTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

exception, exception, failed, illegalargumentexception, polynomialfunction, polynomialfunction, polynomialsplinefunction, splineinterpolator, splineinterpolator, splineinterpolatortest, testcase, univariaterealfunction, univariaterealinterpolator, univariaterealinterpolator

The Commons Math SplineInterpolatorTest.java 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.math.analysis.interpolation;

import junit.framework.TestCase;

import org.apache.commons.math.MathException;
import org.apache.commons.math.TestUtils;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;

/**
 * Test the SplineInterpolator.
 *
 * @version $Revision: 902201 $ $Date: 2010-01-22 13:18:16 -0500 (Fri, 22 Jan 2010) $
 */
public class SplineInterpolatorTest extends TestCase {

    /** error tolerance for spline interpolator value at knot points */
    protected double knotTolerance = 1E-12;

    /** error tolerance for interpolating polynomial coefficients */
    protected double coefficientTolerance = 1E-6;

    /** error tolerance for interpolated values -- high value is from sin test */
    protected double interpolationTolerance = 1E-2;

    public SplineInterpolatorTest(String name) {
        super(name);
    }

    public void testInterpolateLinearDegenerateTwoSegment()
        throws Exception {
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 1.0 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction 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
        assertEquals(0.0,f.value(0.0), interpolationTolerance);
        assertEquals(0.4,f.value(0.4), interpolationTolerance);
        assertEquals(1.0,f.value(1.0), interpolationTolerance);
    }

    public void testInterpolateLinearDegenerateThreeSegment()
        throws Exception {
        double x[] = { 0.0, 0.5, 1.0, 1.5 };
        double y[] = { 0.0, 0.5, 1.0, 1.5 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction 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
        assertEquals(0,f.value(0), interpolationTolerance);
        assertEquals(1.4,f.value(1.4), interpolationTolerance);
        assertEquals(1.5,f.value(1.5), interpolationTolerance);
    }

    public void testInterpolateLinear() throws Exception {
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 0.0 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction 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);
    }

    public void testInterpolateSin() throws Exception {
        double x[] =
            {
                0.0,
                Math.PI / 6d,
                Math.PI / 2d,
                5d * Math.PI / 6d,
                Math.PI,
                7d * Math.PI / 6d,
                3d * Math.PI / 2d,
                11d * Math.PI / 6d,
                2.d * Math.PI };
        double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction 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, coefficientTolerance);
        target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
        TestUtils.assertEquals(polynomials[3].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
        TestUtils.assertEquals(polynomials[4].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[5].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[6].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
        TestUtils.assertEquals(polynomials[7].getCoefficients(), target, coefficientTolerance);

        //Check interpolation
        assertEquals(Math.sqrt(2d) / 2d,f.value(Math.PI/4d),interpolationTolerance);
        assertEquals(Math.sqrt(2d) / 2d,f.value(3d*Math.PI/4d),interpolationTolerance);
    }


    public void testIllegalArguments() throws MathException {
        // Data set arrays of different size.
        UnivariateRealInterpolator i = new SplineInterpolator();
        try {
            double xval[] = { 0.0, 1.0 };
            double yval[] = { 0.0, 1.0, 2.0 };
            i.interpolate(xval, yval);
            fail("Failed to detect data set array with different sizes.");
        } catch (IllegalArgumentException iae) {
        }
        // 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);
            fail("Failed to detect unsorted arguments.");
        } catch (IllegalArgumentException iae) {
        }
    }

    /**
     * verifies that f(x[i]) = y[i] for i = 0..n-1 where n is common length.
     */
    protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[])
        throws Exception{
        for (int i = 0; i < x.length; i++) {
            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[])
        throws Exception {
        PolynomialFunction polynomials[] = f.getPolynomials();
        for (int i = 1; i < x.length - 2; i++) {
            // evaluate polynomials and derivatives at x[i + 1]
            assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
            assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
                    polynomials[i + 1].derivative().value(0), 0.5);
            assertEquals(polynomials[i].polynomialDerivative().derivative().value(x[i +1] - x[i]),
                    polynomials[i + 1].polynomialDerivative().derivative().value(0), 0.5);
        }
    }

}