/*
* 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.math.analysis.solvers;
import junit.framework.TestCase;
import org.apache.commons.math.MathException;
import org.apache.commons.math.analysis.MonitoredFunction;
import org.apache.commons.math.analysis.QuinticFunction;
import org.apache.commons.math.analysis.SinFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
/**
* Testcase for UnivariateRealSolver.
* Because Brent-Dekker is guaranteed to converge in less than the default
* maximum iteration count due to bisection fallback, it is quite hard to
* debug. I include measured iteration counts plus one in order to detect
* regressions. On average Brent-Dekker should use 4..5 iterations for the
* default absolute accuracy of 10E-8 for sinus and the quintic function around
* zero, and 5..10 iterations for the other zeros.
*
* @version $Revision:670469 $ $Date:2008-06-23 10:01:38 +0200 (lun., 23 juin 2008) $
*/
public final class BrentSolverTest extends TestCase {
public BrentSolverTest(String name) {
super(name);
}
@Deprecated
public void testDeprecated() throws MathException {
// The sinus function is behaved well around the root at #pi. The second
// order derivative is zero, which means linar approximating methods will
// still converge quadratically.
UnivariateRealFunction f = new SinFunction();
double result;
UnivariateRealSolver solver = new BrentSolver(f);
// Somewhat benign interval. The function is monotone.
result = solver.solve(3, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 4 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 5);
// Larger and somewhat less benign interval. The function is grows first.
result = solver.solve(1, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
solver = new SecantSolver(f);
result = solver.solve(3, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 4 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 5);
result = solver.solve(1, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
assertEquals(result, solver.getResult(), 0);
}
public void testSinZero() throws MathException {
// The sinus function is behaved well around the root at #pi. The second
// order derivative is zero, which means linar approximating methods will
// still converge quadratically.
UnivariateRealFunction f = new SinFunction();
double result;
UnivariateRealSolver solver = new BrentSolver();
// Somewhat benign interval. The function is monotone.
result = solver.solve(f, 3, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 4 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 5);
// Larger and somewhat less benign interval. The function is grows first.
result = solver.solve(f, 1, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
solver = new SecantSolver();
result = solver.solve(f, 3, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 4 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 5);
result = solver.solve(f, 1, 4);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
assertEquals(result, solver.getResult(), 0);
}
public void testQuinticZero() throws MathException {
// The quintic function has zeros at 0, +-0.5 and +-1.
// Around the root of 0 the function is well behaved, with a second derivative
// of zero a 0.
// The other roots are less well to find, in particular the root at 1, because
// the function grows fast for x>1.
// The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
// intervals containing these values are harder for the solvers.
UnivariateRealFunction f = new QuinticFunction();
double result;
// Brent-Dekker solver.
UnivariateRealSolver solver = new BrentSolver();
// Symmetric bracket around 0. Test whether solvers can handle hitting
// the root in the first iteration.
result = solver.solve(f, -0.2, 0.2);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
assertTrue(solver.getIterationCount() <= 2);
// 1 iterations on i586 JDK 1.4.1.
// Asymmetric bracket around 0, just for fun. Contains extremum.
result = solver.solve(f, -0.1, 0.3);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
// Large bracket around 0. Contains two extrema.
result = solver.solve(f, -0.3, 0.45);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
// 6 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 7);
// Benign bracket around 0.5, function is monotonous.
result = solver.solve(f, 0.3, 0.7);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 6 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 7);
// Less benign bracket around 0.5, contains one extremum.
result = solver.solve(f, 0.2, 0.6);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 6 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 7);
// Large, less benign bracket around 0.5, contains both extrema.
result = solver.solve(f, 0.05, 0.95);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 8 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 9);
// Relatively benign bracket around 1, function is monotonous. Fast growth for x>1
// is still a problem.
result = solver.solve(f, 0.85, 1.25);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 8 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 9);
// Less benign bracket around 1 with extremum.
result = solver.solve(f, 0.8, 1.2);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 8 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 9);
// Large bracket around 1. Monotonous.
result = solver.solve(f, 0.85, 1.75);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 10 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 11);
// Large bracket around 1. Interval contains extremum.
result = solver.solve(f, 0.55, 1.45);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 7 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 8);
// Very large bracket around 1 for testing fast growth behaviour.
result = solver.solve(f, 0.85, 5);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 12 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 13);
// Secant solver.
solver = new SecantSolver();
result = solver.solve(f, -0.2, 0.2);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
// 1 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 2);
result = solver.solve(f, -0.1, 0.3);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
// 5 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 6);
result = solver.solve(f, -0.3, 0.45);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0, solver.getAbsoluteAccuracy());
// 6 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 7);
result = solver.solve(f, 0.3, 0.7);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 7 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 8);
result = solver.solve(f, 0.2, 0.6);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 6 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 7);
result = solver.solve(f, 0.05, 0.95);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 0.5, solver.getAbsoluteAccuracy());
// 8 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 9);
result = solver.solve(f, 0.85, 1.25);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 10 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 11);
result = solver.solve(f, 0.8, 1.2);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 8 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 9);
result = solver.solve(f, 0.85, 1.75);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 14 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 15);
// The followig is especially slow because the solver first has to reduce
// the bracket to exclude the extremum. After that, convergence is rapide.
result = solver.solve(f, 0.55, 1.45);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 7 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 8);
result = solver.solve(f, 0.85, 5);
//System.out.println(
// "Root: " + result + " Iterations: " + solver.getIterationCount());
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
// 14 iterations on i586 JDK 1.4.1.
assertTrue(solver.getIterationCount() <= 15);
// Static solve method
result = UnivariateRealSolverUtils.solve(f, -0.2, 0.2);
assertEquals(result, 0, solver.getAbsoluteAccuracy());
result = UnivariateRealSolverUtils.solve(f, -0.1, 0.3);
assertEquals(result, 0, 1E-8);
result = UnivariateRealSolverUtils.solve(f, -0.3, 0.45);
assertEquals(result, 0, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.3, 0.7);
assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.2, 0.6);
assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.05, 0.95);
assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.85, 1.25);
assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.8, 1.2);
assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.85, 1.75);
assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.55, 1.45);
assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverUtils.solve(f, 0.85, 5);
assertEquals(result, 1.0, 1E-6);
}
public void testRootEndpoints() throws Exception {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = new BrentSolver();
// endpoint is root
double result = solver.solve(f, Math.PI, 4);
assertEquals(Math.PI, result, solver.getAbsoluteAccuracy());
result = solver.solve(f, 3, Math.PI);
assertEquals(Math.PI, result, solver.getAbsoluteAccuracy());
result = solver.solve(f, Math.PI, 4, 3.5);
assertEquals(Math.PI, result, solver.getAbsoluteAccuracy());
result = solver.solve(f, 3, Math.PI, 3.07);
assertEquals(Math.PI, result, solver.getAbsoluteAccuracy());
}
public void testBadEndpoints() throws Exception {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = new BrentSolver();
try { // bad interval
solver.solve(f, 1, -1);
fail("Expecting IllegalArgumentException - bad interval");
} catch (IllegalArgumentException ex) {
// expected
}
try { // no bracket
solver.solve(f, 1, 1.5);
fail("Expecting IllegalArgumentException - non-bracketing");
} catch (IllegalArgumentException ex) {
// expected
}
try { // no bracket
solver.solve(f, 1, 1.5, 1.2);
fail("Expecting IllegalArgumentException - non-bracketing");
} catch (IllegalArgumentException ex) {
// expected
}
}
public void testInitialGuess() throws MathException {
MonitoredFunction f = new MonitoredFunction(new QuinticFunction());
UnivariateRealSolver solver = new BrentSolver();
double result;
// no guess
result = solver.solve(f, 0.6, 7.0);
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
int referenceCallsCount = f.getCallsCount();
assertTrue(referenceCallsCount >= 13);
// invalid guess (it *is* a root, but outside of the range)
try {
result = solver.solve(f, 0.6, 7.0, 0.0);
fail("an IllegalArgumentException was expected");
} catch (IllegalArgumentException iae) {
// expected behaviour
} catch (Exception e) {
fail("wrong exception caught: " + e.getMessage());
}
// bad guess
f.setCallsCount(0);
result = solver.solve(f, 0.6, 7.0, 0.61);
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
assertTrue(f.getCallsCount() > referenceCallsCount);
// good guess
f.setCallsCount(0);
result = solver.solve(f, 0.6, 7.0, 0.999999);
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
assertTrue(f.getCallsCount() < referenceCallsCount);
// perfect guess
f.setCallsCount(0);
result = solver.solve(f, 0.6, 7.0, 1.0);
assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
assertEquals(0, solver.getIterationCount());
assertEquals(1, f.getCallsCount());
}
}