1   /*
2    * 
3    * Copyright (c) 2004 The Apache Software Foundation. All rights reserved.
4    * 
5    * Licensed under the Apache License, Version 2.0 (the "License"); you may not
6    * use this file except in compliance with the License. You may obtain a copy
7    * of the License at
8    * 
9    * http://www.apache.org/licenses/LICENSE-2.0
10   * 
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
13   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
14   * License for the specific language governing permissions and limitations
15   * under the License.
16   *  
17   */
18  package org.apache.commons.math.analysis;
19  
20  import java.util.Arrays;
21  import junit.framework.TestCase;
22  
23  import org.apache.commons.math.FunctionEvaluationException;
24  
25  /**
26   * Tests the PolynomialSplineFunction implementation.
27   *
28   * @version $Revision: 155427 $
29   */
30  public class PolynomialSplineFunctionTest extends TestCase {
31  
32      /** Error tolerance for tests */
33      protected double tolerance = 1.0e-12;
34      
35      /** 
36       * Quadratic polynomials used in tests: 
37       * 
38       * x^2 + x            [-1, 0)
39       * x^2 + x + 2        [0, 1)
40       * x^2 + x + 4        [1, 2)
41       * 
42       * Defined so that evaluation using PolynomialSplineFunction evaluation
43       * algorithm agrees at knot point boundaries.
44       */
45      protected PolynomialFunction[] polynomials = {
46          new PolynomialFunction(new double[] {0d, 1d, 1d}), 
47          new PolynomialFunction(new double[] {2d, 1d, 1d}),
48          new PolynomialFunction(new double[] {4d, 1d, 1d})
49      };
50      
51      /** Knot points  */
52      protected double[] knots = {-1, 0, 1, 2};
53      
54      /** Derivative of test polynomials -- 2x + 1  */
55      protected PolynomialFunction dp = 
56          new PolynomialFunction(new double[] {1d, 2d});
57      
58      
59      public void testConstructor() {
60          PolynomialSplineFunction spline = 
61              new PolynomialSplineFunction(knots, polynomials);
62          assertTrue(Arrays.equals(knots, spline.getKnots()));
63          assertEquals(1d, spline.getPolynomials()[0].getCoefficients()[2], 0);
64          assertEquals(3, spline.getN());
65          
66          try { // too few knots
67              spline = 
68                  new PolynomialSplineFunction(new double[] {0}, polynomials);
69              fail("Expecting IllegalArgumentException");
70          } catch (IllegalArgumentException ex) {
71              // expected
72          }
73          
74          try { // too many knots
75              spline = 
76                  new PolynomialSplineFunction(new double[] {0,1,2,3,4}, polynomials);
77              fail("Expecting IllegalArgumentException");
78          } catch (IllegalArgumentException ex) {
79              // expected
80          }
81          
82          try { // knots not increasing
83              spline = 
84                  new PolynomialSplineFunction(new double[] {0,1, 3, 2}, polynomials);
85              fail("Expecting IllegalArgumentException");
86          } catch (IllegalArgumentException ex) {
87              // expected
88          }
89      }
90      
91      public void testValues() throws Exception {
92          PolynomialSplineFunction spline = 
93              new PolynomialSplineFunction(knots, polynomials);
94          UnivariateRealFunction dSpline = spline.derivative();
95          
96          /**
97           * interior points -- spline value at x should equal p(x - knot)
98           * where knot is the largest knot point less than or equal to x and p 
99           * is the polynomial defined over the knot segment to which x belongs.
100          */
101         double x = -1;
102         int index = 0;
103         for (int i = 0; i < 10; i++) {
104            x+=0.25;
105            index = findKnot(knots, x);
106            assertEquals("spline function evaluation failed for x=" + x, 
107                    polynomials[index].value(x - knots[index]), spline.value(x), tolerance);
108            assertEquals("spline derivative evaluation failed for x=" + x,
109                    dp.value(x - knots[index]), dSpline.value(x), tolerance);
110         }
111         
112         // knot points -- centering should zero arguments
113         for (int i = 0; i < 3; i++) {
114             assertEquals("spline function evaluation failed for knot=" + knots[i],
115                     polynomials[i].value(0), spline.value(knots[i]), tolerance);
116             assertEquals("spline function evaluation failed for knot=" + knots[i],
117                     dp.value(0), dSpline.value(knots[i]), tolerance);
118         }
119         
120         try { //outside of domain -- under min
121             x = spline.value(-1.5);
122             fail("Expecting IllegalArgumentException");
123         } catch (FunctionEvaluationException ex) {
124             // expected
125         }
126         
127         try { //outside of domain -- over max
128             x = spline.value(2.5);
129             fail("Expecting IllegalArgumentException");
130         } catch (FunctionEvaluationException ex) {
131             // expected
132         }         
133     }  
134     
135     /**
136      *  Do linear search to find largest knot point less than or equal to x.
137      *  Implementation does binary search.
138      */
139      protected int findKnot(double[] knots, double x) {
140          if (x < knots[0] || x >= knots[knots.length -1]) {
141              throw new IllegalArgumentException("x is out of range");
142          }
143          for (int i = 0; i < knots.length; i++) {
144              if (knots[i] > x) {
145                  return i -1;
146              }
147          }
148          throw new IllegalArgumentException("x is out of range");
149      }
150 }
151