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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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.math4.analysis.integration;
import org.apache.commons.math4.analysis.QuinticFunction;
import org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.analysis.function.Sin;
import org.apache.commons.math4.analysis.integration.MidPointIntegrator;
import org.apache.commons.math4.analysis.integration.UnivariateIntegrator;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for midpoint integrator.
* <p>
* Test runs show that for a default relative accuracy of 1E-6, it generally
* takes 10 to 15 iterations for the integral to converge.
*
*/
public final class MidPointIntegratorTest {
/**
* Test of integrator for the sine function.
*/
@Test
public void testLowAccuracy() {
UnivariateFunction f = new QuinticFunction();
UnivariateIntegrator integrator = new MidPointIntegrator(0.01, 1.0e-10, 2, 4);
double min = -10;
double max = -9;
double expected = -3697001.0 / 48.0;
double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of integrator for the sine function.
*/
@Test
public void testSinFunction() {
UnivariateFunction f = new Sin();
UnivariateIntegrator integrator = new MidPointIntegrator();
double min = 0;
double max = FastMath.PI;
double expected = 2;
double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
min = -FastMath.PI/3;
max = 0;
expected = -0.5;
tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of integrator for the quintic function.
*/
@Test
public void testQuinticFunction() {
UnivariateFunction f = new QuinticFunction();
UnivariateIntegrator integrator = new MidPointIntegrator();
double min = 0;
double max = 1;
double expected = -1.0 / 48;
double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
min = 0;
max = 0.5;
expected = 11.0 / 768;
tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
min = -1;
max = 4;
expected = 2048 / 3.0 - 78 + 1.0 / 48;
tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of parameters for the integrator.
*/
@Test
public void testParameters() {
UnivariateFunction f = new Sin();
try {
// bad interval
new MidPointIntegrator().integrate(1000, f, 1, -1);
Assert.fail("Expecting NumberIsTooLargeException - bad interval");
} catch (NumberIsTooLargeException ex) {
// expected
}
try {
// bad iteration limits
new MidPointIntegrator(5, 4);
Assert.fail("Expecting NumberIsTooSmallException - bad iteration limits");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
// bad iteration limits
new MidPointIntegrator(10, 99);
Assert.fail("Expecting NumberIsTooLargeException - bad iteration limits");
} catch (NumberIsTooLargeException ex) {
// expected
}
}
}