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17 package org.apache.commons.math4.legacy.analysis.integration;
18
19 import org.apache.commons.math4.legacy.analysis.QuinticFunction;
20 import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
21 import org.apache.commons.math4.legacy.analysis.function.Sin;
22 import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
23 import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
24 import org.apache.commons.math4.core.jdkmath.JdkMath;
25 import org.junit.Assert;
26 import org.junit.Test;
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35 public final class MidPointIntegratorTest {
36 private static final int NUM_ITER = 30;
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53 private long expectedEvaluations(int iterations) {
54 return (long) JdkMath.pow(3, iterations);
55 }
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58
59
60 @Test
61 public void testLowAccuracy() {
62 UnivariateFunction f = new QuinticFunction();
63 UnivariateIntegrator integrator = new MidPointIntegrator(0.01, 1.0e-10, 2, 4);
64
65 double min = -10;
66 double max = -9;
67 double expected = -3697001.0 / 48.0;
68 double tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
69 double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
70 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
71 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
72 Assert.assertEquals(expectedEvaluations(integrator.getIterations()), integrator.getEvaluations());
73 Assert.assertEquals(expected, result, tolerance);
74 }
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78
79 @Test
80 public void testSinFunction() {
81 UnivariateFunction f = new Sin();
82 UnivariateIntegrator integrator = new MidPointIntegrator();
83
84 double min = 0;
85 double max = JdkMath.PI;
86 double expected = 2;
87 double tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
88 double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
89 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
90 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
91 Assert.assertEquals(expectedEvaluations(integrator.getIterations()), integrator.getEvaluations());
92 Assert.assertEquals(expected, result, tolerance);
93
94 min = -JdkMath.PI/3;
95 max = 0;
96 expected = -0.5;
97 tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
98 result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
99 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
100 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
101 Assert.assertEquals(expectedEvaluations(integrator.getIterations()), integrator.getEvaluations());
102 Assert.assertEquals(expected, result, tolerance);
103 }
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108 @Test
109 public void testQuinticFunction() {
110 UnivariateFunction f = new QuinticFunction();
111 UnivariateIntegrator integrator = new MidPointIntegrator();
112
113 double min = 0;
114 double max = 1;
115 double expected = -1.0 / 48;
116 double tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
117 double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
118 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
119 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
120 Assert.assertEquals(expectedEvaluations(integrator.getIterations()), integrator.getEvaluations());
121 Assert.assertEquals(expected, result, tolerance);
122
123 min = 0;
124 max = 0.5;
125 expected = 11.0 / 768;
126 tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
127 result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
128 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
129 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
130 Assert.assertEquals(expected, result, tolerance);
131
132 min = -1;
133 max = 4;
134 expected = 2048 / 3.0 - 78 + 1.0 / 48;
135 tolerance = JdkMath.abs(expected * integrator.getRelativeAccuracy());
136 result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
137 Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 3);
138 Assert.assertTrue(integrator.getIterations() < NUM_ITER);
139 Assert.assertEquals(expectedEvaluations(integrator.getIterations()), integrator.getEvaluations());
140 Assert.assertEquals(expected, result, tolerance);
141 }
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146 @Test
147 public void testParameters() {
148 UnivariateFunction f = new Sin();
149
150 try {
151
152 new MidPointIntegrator().integrate(1000, f, 1, -1);
153 Assert.fail("Expecting NumberIsTooLargeException - bad interval");
154 } catch (NumberIsTooLargeException ex) {
155
156 }
157 try {
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159 new MidPointIntegrator(5, 4);
160 Assert.fail("Expecting NumberIsTooSmallException - bad iteration limits");
161 } catch (NumberIsTooSmallException ex) {
162
163 }
164 try {
165
166 new MidPointIntegrator(10, 99);
167 Assert.fail("Expecting NumberIsTooLargeException - bad iteration limits");
168 } catch (NumberIsTooLargeException ex) {
169
170 }
171 }
172 }