src/test/org/apache/commons/math/analysis/BrentSolverTest.java - commons-math - Git at Google

 /*
  * 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;

 import org.apache.commons.math.MathException;

 import junit.framework.Test;
 import junit.framework.TestCase;
 import junit.framework.TestSuite;

 /**
  * 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);
     }

     public static Test suite() {
         TestSuite suite = new TestSuite(BrentSolverTest.class);
         suite.setName("UnivariateRealSolver Tests");
         return suite;
     }

     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(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 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(f);
         // Symmetric bracket around 0. Test whether solvers can handle hitting
         // the root in the first iteration.
         result = solver.solve(-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(-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(-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(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(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(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(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(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(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(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(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(f);
         result = solver.solve(-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(-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(-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(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(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(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(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(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(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(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(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(f);

         // endpoint is root
         double result = solver.solve(Math.PI, 4);
         assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());

         result = solver.solve(3, Math.PI);
         assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
     }

     public void testBadEndpoints() throws Exception {
         UnivariateRealFunction f = new SinFunction();
         UnivariateRealSolver solver = new BrentSolver(f);
         try {  // bad interval
             solver.solve(1, -1);
             fail("Expecting IllegalArgumentException - bad interval");
         } catch (IllegalArgumentException ex) {
             // expected
         }
         try {  // no bracket
             solver.solve(1, 1.5);
             fail("Expecting IllegalArgumentException - non-bracketing");
         } catch (IllegalArgumentException ex) {
             // expected
         }
     }

     public void testInitialGuess() throws MathException {

         MonitoredFunction f = new MonitoredFunction(new QuinticFunction());
         UnivariateRealSolver solver = new BrentSolver(f);
         double result;

         // no guess
         result = solver.solve(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(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(0.6, 7.0, 0.61);
         assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
         assertTrue(f.getCallsCount() > referenceCallsCount);

         // good guess
         f.setCallsCount(0);
         result = solver.solve(0.6, 7.0, 0.999999);
         assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
         assertTrue(f.getCallsCount() < referenceCallsCount);

         // perfect guess
         f.setCallsCount(0);
         result = solver.solve(0.6, 7.0, 1.0);
         assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
         assertEquals(0, solver.getIterationCount());
         assertEquals(1, f.getCallsCount());

     }

 }
	/*
	* 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;

	import org.apache.commons.math.MathException;

	import junit.framework.Test;
	import junit.framework.TestCase;
	import junit.framework.TestSuite;

	/**
	* 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);
	}

	public static Test suite() {
	TestSuite suite = new TestSuite(BrentSolverTest.class);
	suite.setName("UnivariateRealSolver Tests");
	return suite;
	}

	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(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 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(f);
	// Symmetric bracket around 0. Test whether solvers can handle hitting
	// the root in the first iteration.
	result = solver.solve(-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(-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(-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(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(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(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(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(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(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(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(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(f);
	result = solver.solve(-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(-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(-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(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(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(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(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(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(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(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(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(f);

	// endpoint is root
	double result = solver.solve(Math.PI, 4);
	assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());

	result = solver.solve(3, Math.PI);
	assertEquals(result, Math.PI, solver.getAbsoluteAccuracy());
	}

	public void testBadEndpoints() throws Exception {
	UnivariateRealFunction f = new SinFunction();
	UnivariateRealSolver solver = new BrentSolver(f);
	try { // bad interval
	solver.solve(1, -1);
	fail("Expecting IllegalArgumentException - bad interval");
	} catch (IllegalArgumentException ex) {
	// expected
	}
	try { // no bracket
	solver.solve(1, 1.5);
	fail("Expecting IllegalArgumentException - non-bracketing");
	} catch (IllegalArgumentException ex) {
	// expected
	}
	}

	public void testInitialGuess() throws MathException {

	MonitoredFunction f = new MonitoredFunction(new QuinticFunction());
	UnivariateRealSolver solver = new BrentSolver(f);
	double result;

	// no guess
	result = solver.solve(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(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(0.6, 7.0, 0.61);
	assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
	assertTrue(f.getCallsCount() > referenceCallsCount);

	// good guess
	f.setCallsCount(0);
	result = solver.solve(0.6, 7.0, 0.999999);
	assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
	assertTrue(f.getCallsCount() < referenceCallsCount);

	// perfect guess
	f.setCallsCount(0);
	result = solver.solve(0.6, 7.0, 1.0);
	assertEquals(result, 1.0, solver.getAbsoluteAccuracy());
	assertEquals(0, solver.getIterationCount());
	assertEquals(1, f.getCallsCount());

	}

	}