src/test/org/apache/commons/math/analysis/PolynomialSplineFunctionTest.java

/*
 * 
 * Copyright (c) 2004 The Apache Software Foundation. All rights reserved.
 * 
 * Licensed 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;

import java.util.Arrays;
import junit.framework.TestCase;

import org.apache.commons.math.FunctionEvaluationException;

/**
 * Tests the PolynomialSplineFunction implementation.
 *
 * @version $Revision$
 */
public class PolynomialSplineFunctionTest extends TestCase {

    /** 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});
    
    
    public void testConstructor() {
        PolynomialSplineFunction spline = 
            new PolynomialSplineFunction(knots, polynomials);
        assertTrue(Arrays.equals(knots, spline.getKnots()));
        assertEquals(1d, spline.getPolynomials()[0].getCoefficients()[2], 0);
        assertEquals(3, spline.getN());
        
        try { // too few knots
            spline = 
                new PolynomialSplineFunction(new double[] {0}, polynomials);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // expected
        }
        
        try { // too many knots
            spline = 
                new PolynomialSplineFunction(new double[] {0,1,2,3,4}, polynomials);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // expected
        }
        
        try { // knots not increasing
            spline = 
                new PolynomialSplineFunction(new double[] {0,1, 3, 2}, polynomials);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // expected
        }
    }
    
    public void testValues() throws Exception {
        PolynomialSplineFunction spline = 
            new PolynomialSplineFunction(knots, polynomials);
        UnivariateRealFunction 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);
           assertEquals("spline function evaluation failed for x=" + x, 
                   polynomials[index].value(x - knots[index]), spline.value(x), tolerance);
           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++) {
            assertEquals("spline function evaluation failed for knot=" + knots[i],
                    polynomials[i].value(0), spline.value(knots[i]), tolerance);
            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);
            fail("Expecting IllegalArgumentException");
        } catch (FunctionEvaluationException ex) {
            // expected
        }
        
        try { //outside of domain -- over max
            x = spline.value(2.5);
            fail("Expecting IllegalArgumentException");
        } catch (FunctionEvaluationException ex) {
            // 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 IllegalArgumentException("x is out of range");
         }
         for (int i = 0; i < knots.length; i++) {
             if (knots[i] > x) {
                 return i -1;
             }
         }
         throw new IllegalArgumentException("x is out of range");
     }
}