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18 package org.apache.commons.math.analysis;
19
20 import org.apache.commons.math.MathException;
21 import org.apache.commons.math.TestUtils;
22
23 import junit.framework.Test;
24 import junit.framework.TestCase;
25 import junit.framework.TestSuite;
26
27 /***
28 * Test the SplineInterpolator.
29 *
30 * @version $Revision: 1.1 $ $Date: 2004/04/02 20:58:59 $
31 */
32 public class SplineInterpolatorTest extends TestCase {
33
34 /*** error tolerance for spline interpolator value at knot points */
35 protected double knotTolerance = 1E-12;
36
37 /*** error tolerance for interpolating polynomial coefficients */
38 protected double coefficientTolerance = 1E-6;
39
40 /*** error tolerance for interpolated values -- high value is from sin test */
41 protected double interpolationTolerance = 1E-2;
42
43 public SplineInterpolatorTest(String name) {
44 super(name);
45 }
46
47 public static Test suite() {
48 TestSuite suite = new TestSuite(SplineInterpolatorTest.class);
49 suite.setName("UnivariateRealInterpolator Tests");
50 return suite;
51 }
52
53 public void testInterpolateLinearDegenerateTwoSegment()
54 throws Exception {
55 double x[] = { 0.0, 0.5, 1.0 };
56 double y[] = { 0.0, 0.5, 1.0 };
57 UnivariateRealInterpolator i = new SplineInterpolator();
58 UnivariateRealFunction f = i.interpolate(x, y);
59 verifyInterpolation(f, x, y);
60 verifyConsistency((PolynomialSplineFunction) f, x);
61
62
63 PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
64 double target[] = {y[0], 1d, 0d, 0d};
65 TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
66 target = new double[]{y[1], 1d, 0d, 0d};
67 TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
68
69
70 assertEquals(0.4,f.value(0.4), interpolationTolerance);
71 }
72
73 public void testInterpolateLinearDegenerateThreeSegment()
74 throws Exception {
75 double x[] = { 0.0, 0.5, 1.0, 1.5 };
76 double y[] = { 0.0, 0.5, 1.0, 1.5 };
77 UnivariateRealInterpolator i = new SplineInterpolator();
78 UnivariateRealFunction f = i.interpolate(x, y);
79 verifyInterpolation(f, x, y);
80
81
82 PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
83 double target[] = {y[0], 1d, 0d, 0d};
84 TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
85 target = new double[]{y[1], 1d, 0d, 0d};
86 TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
87 target = new double[]{y[2], 1d, 0d, 0d};
88 TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
89
90
91 assertEquals(1.4,f.value(1.4), interpolationTolerance);
92 }
93
94 public void testInterpolateLinear() throws Exception {
95 double x[] = { 0.0, 0.5, 1.0 };
96 double y[] = { 0.0, 0.5, 0.0 };
97 UnivariateRealInterpolator i = new SplineInterpolator();
98 UnivariateRealFunction f = i.interpolate(x, y);
99 verifyInterpolation(f, x, y);
100 verifyConsistency((PolynomialSplineFunction) f, x);
101
102
103 PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
104 double target[] = {y[0], 1.5d, 0d, -2d};
105 TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
106 target = new double[]{y[1], 0d, -3d, 2d};
107 TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
108 }
109
110 public void testInterpolateSin() throws Exception {
111 double x[] =
112 {
113 0.0,
114 Math.PI / 6d,
115 Math.PI / 2d,
116 5d * Math.PI / 6d,
117 Math.PI,
118 7d * Math.PI / 6d,
119 3d * Math.PI / 2d,
120 11d * Math.PI / 6d,
121 2.d * Math.PI };
122 double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
123 UnivariateRealInterpolator i = new SplineInterpolator();
124 UnivariateRealFunction f = i.interpolate(x, y);
125 verifyInterpolation(f, x, y);
126 verifyConsistency((PolynomialSplineFunction) f, x);
127
128
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130
131
132
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135
136
137 PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
138 double target[] = {y[0], 1.002676d, 0d, -0.17415829d};
139 TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
140 target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
141 TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
142 target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
143 TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
144 target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
145 TestUtils.assertEquals(polynomials[3].getCoefficients(), target, coefficientTolerance);
146 target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
147 TestUtils.assertEquals(polynomials[4].getCoefficients(), target, coefficientTolerance);
148 target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
149 TestUtils.assertEquals(polynomials[5].getCoefficients(), target, coefficientTolerance);
150 target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
151 TestUtils.assertEquals(polynomials[6].getCoefficients(), target, coefficientTolerance);
152 target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
153 TestUtils.assertEquals(polynomials[7].getCoefficients(), target, coefficientTolerance);
154
155
156 assertEquals(Math.sqrt(2d) / 2d,f.value(Math.PI/4d),interpolationTolerance);
157 assertEquals(Math.sqrt(2d) / 2d,f.value(3d*Math.PI/4d),interpolationTolerance);
158 }
159
160
161 public void testIllegalArguments() throws MathException {
162
163 UnivariateRealInterpolator i = new SplineInterpolator();
164 try {
165 double xval[] = { 0.0, 1.0 };
166 double yval[] = { 0.0, 1.0, 2.0 };
167 i.interpolate(xval, yval);
168 fail("Failed to detect data set array with different sizes.");
169 } catch (IllegalArgumentException iae) {
170 }
171
172 try {
173 double xval[] = { 0.0, 1.0, 0.5 };
174 double yval[] = { 0.0, 1.0, 2.0 };
175 i.interpolate(xval, yval);
176 fail("Failed to detect unsorted arguments.");
177 } catch (IllegalArgumentException iae) {
178 }
179 }
180
181 /***
182 * verifies that f(x[i]) = y[i] for i = 0..n -1 where n is common length -- skips last point.
183 */
184 protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[])
185 throws Exception{
186 for (int i = 0; i < x.length - 1; i++) {
187 assertEquals(f.value(x[i]), y[i], knotTolerance);
188 }
189 }
190
191 /***
192 * Verifies that interpolating polynomials satisfy consistency requirement:
193 * adjacent polynomials must agree through two derivatives at knot points
194 */
195 protected void verifyConsistency(PolynomialSplineFunction f, double x[])
196 throws Exception {
197 PolynomialFunction polynomials[] = f.getPolynomials();
198 for (int i = 1; i < x.length - 2; i++) {
199
200 assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
201 assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
202 polynomials[i + 1].derivative().value(0), 0.5);
203 assertEquals(polynomials[i].polynomialDerivative().derivative().value(x[i +1] - x[i]),
204 polynomials[i + 1].polynomialDerivative().derivative().value(0), 0.5);
205 }
206 }
207
208 }