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Java > Open Source Codes > org > apache > commons > math > analysis > PolynomialSplineFunctionTest


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 JavaDoc;
21 import junit.framework.TestCase;
22
23 import org.apache.commons.math.FunctionEvaluationException;
24
25 /**
26  * Tests the PolynomialSplineFunction implementation.
27  *
28  * @version $Revision$
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 JavaDoc 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 JavaDoc 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 JavaDoc ex) {
87             // expected
88 }
89     }
90     
91     public void testValues() throws Exception JavaDoc {
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 JavaDoc("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 JavaDoc("x is out of range");
149      }
150 }
151     
152
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