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* Licensed to the Apache Software Foundation (ASF) under one or more
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* 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,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math3.analysis.solvers;
import org.apache.commons.math3.analysis.QuinticFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Expm1;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for {@link MullerSolver2 Muller} solver.
* <p>
* Muller's method converges almost quadratically near roots, but it can
* be very slow in regions far away from zeros. Test runs show that for
* reasonably good initial values, for a default absolute accuracy of 1E-6,
* it generally takes 5 to 10 iterations for the solver to converge.
* <p>
* Tests for the exponential function illustrate the situations where
* Muller solver performs poorly.
*
*/
public final class MullerSolver2Test {
/**
* Test of solver for the sine function.
*/
@Test
public void testSinFunction() {
UnivariateFunction f = new Sin();
UnivariateSolver solver = new MullerSolver2();
double min, max, expected, result, tolerance;
min = 3.0; max = 4.0; expected = FastMath.PI;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
min = -1.0; max = 1.5; expected = 0.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the quintic function.
*/
@Test
public void testQuinticFunction() {
UnivariateFunction f = new QuinticFunction();
UnivariateSolver solver = new MullerSolver2();
double min, max, expected, result, tolerance;
min = -0.4; max = 0.2; expected = 0.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
min = 0.75; max = 1.5; expected = 1.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
min = -0.9; max = -0.2; expected = -0.5;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the exponential function.
* <p>
* It takes 25 to 50 iterations for the last two tests to converge.
*/
@Test
public void testExpm1Function() {
UnivariateFunction f = new Expm1();
UnivariateSolver solver = new MullerSolver2();
double min, max, expected, result, tolerance;
min = -1.0; max = 2.0; expected = 0.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
min = -20.0; max = 10.0; expected = 0.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
min = -50.0; max = 100.0; expected = 0.0;
tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(100, f, min, max);
Assert.assertEquals(expected, result, tolerance);
}
/**
* Test of parameters for the solver.
*/
@Test
public void testParameters() {
UnivariateFunction f = new Sin();
UnivariateSolver solver = new MullerSolver2();
try {
// bad interval
solver.solve(100, f, 1, -1);
Assert.fail("Expecting NumberIsTooLargeException - bad interval");
} catch (NumberIsTooLargeException ex) {
// expected
}
try {
// no bracketing
solver.solve(100, f, 2, 3);
Assert.fail("Expecting NoBracketingException - no bracketing");
} catch (NoBracketingException ex) {
// expected
}
}
}