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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
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package org.apache.commons.math.analysis.solvers;
import org.apache.commons.math.MathException;
import org.apache.commons.math.analysis.Expm1Function;
import org.apache.commons.math.analysis.QuinticFunction;
import org.apache.commons.math.analysis.SinFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import junit.framework.TestCase;
/**
* Testcase for 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.
*
* @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
*/
public final class MullerSolverTest extends TestCase {
/**
* Test deprecated APIs.
*/
@Deprecated
public void testDeprecated() throws MathException {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = new MullerSolver(f);
double min, max, expected, result, tolerance;
min = 3.0; max = 4.0; expected = Math.PI;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(min, max);
assertEquals(expected, result, tolerance);
min = -1.0; max = 1.5; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test deprecated APIs.
*/
@Deprecated
public void testDeprecated2() throws MathException {
UnivariateRealFunction f = new QuinticFunction();
MullerSolver solver = new MullerSolver(f);
double min, max, expected, result, tolerance;
min = -0.4; max = 0.2; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(min, max);
assertEquals(expected, result, tolerance);
min = 0.75; max = 1.5; expected = 1.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(min, max);
assertEquals(expected, result, tolerance);
min = -0.9; max = -0.2; expected = -0.5;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the sine function.
*/
public void testSinFunction() throws MathException {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = 3.0; max = 4.0; expected = Math.PI;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
min = -1.0; max = 1.5; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the sine function using solve2().
*/
public void testSinFunction2() throws MathException {
UnivariateRealFunction f = new SinFunction();
MullerSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = 3.0; max = 4.0; expected = Math.PI;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
min = -1.0; max = 1.5; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the quintic function.
*/
public void testQuinticFunction() throws MathException {
UnivariateRealFunction f = new QuinticFunction();
UnivariateRealSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = -0.4; max = 0.2; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
min = 0.75; max = 1.5; expected = 1.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
min = -0.9; max = -0.2; expected = -0.5;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the quintic function using solve2().
*/
public void testQuinticFunction2() throws MathException {
UnivariateRealFunction f = new QuinticFunction();
MullerSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = -0.4; max = 0.2; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
min = 0.75; max = 1.5; expected = 1.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
min = -0.9; max = -0.2; expected = -0.5;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the exponential function.
* <p>
* It takes 10 to 15 iterations for the last two tests to converge.
* In fact, if not for the bisection alternative, the solver would
* exceed the default maximal iteration of 100.
*/
public void testExpm1Function() throws MathException {
UnivariateRealFunction f = new Expm1Function();
UnivariateRealSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = -1.0; max = 2.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
min = -20.0; max = 10.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
min = -50.0; max = 100.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of solver for the exponential function using solve2().
* <p>
* It takes 25 to 50 iterations for the last two tests to converge.
*/
public void testExpm1Function2() throws MathException {
UnivariateRealFunction f = new Expm1Function();
MullerSolver solver = new MullerSolver();
double min, max, expected, result, tolerance;
min = -1.0; max = 2.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
min = -20.0; max = 10.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
min = -50.0; max = 100.0; expected = 0.0;
tolerance = Math.max(solver.getAbsoluteAccuracy(),
Math.abs(expected * solver.getRelativeAccuracy()));
result = solver.solve2(f, min, max);
assertEquals(expected, result, tolerance);
}
/**
* Test of parameters for the solver.
*/
public void testParameters() throws Exception {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = new MullerSolver();
try {
// bad interval
solver.solve(f, 1, -1);
fail("Expecting IllegalArgumentException - bad interval");
} catch (IllegalArgumentException ex) {
// expected
}
try {
// no bracketing
solver.solve(f, 2, 3);
fail("Expecting IllegalArgumentException - no bracketing");
} catch (IllegalArgumentException ex) {
// expected
}
}
}