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Posted to dev@commons.apache.org by md...@apache.org on 2003/06/24 05:02:28 UTC
cvs commit: jakarta-commons-sandbox/math/src/test/org/apache/commons/math/analysis SinFunction.java QuinticFunction.java RealSolverTest.java
mdiggory 2003/06/23 20:02:28
Added: math/src/test/org/apache/commons/math/analysis
SinFunction.java QuinticFunction.java
RealSolverTest.java
Log:
This is the second half of this pr. Commit of analysis solver tests.
PR: http://nagoya.apache.org/bugzilla/show_bug.cgi?id=20844
Submitted by: J. Pietschman
Revision Changes Path
1.1 jakarta-commons-sandbox/math/src/test/org/apache/commons/math/analysis/SinFunction.java
Index: SinFunction.java
===================================================================
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.analysis;
import org.apache.commons.math.MathException;
/**
* Auxillary class for testing solvers.
*
* The function is extraordinarily well behaved around zero roots: it
* has an inflection point there (second order derivative is zero),
* which means linear approximation (Regula Falsi) will converge
* quadratically.
*
* @author pietsch at apache.org
*
*/
public class SinFunction implements UnivariateRealFunction {
/* Evaluate sinus fuction.
* @see org.apache.commons.math.UnivariateRealFunction#value(double)
*/
public double value(double x) throws MathException {
return Math.sin(x);
}
/* First derivative of sinus function
* @see org.apache.commons.math.UnivariateRealFunction#firstDerivative(double)
*/
public double firstDerivative(double x) throws MathException {
return Math.cos(x);
}
/* Second derivative of sinus function.
* Unsupported.
* @see org.apache.commons.math.UnivariateRealFunction#secondDerivative(double)
*/
public double secondDerivative(double x) throws MathException {
throw new UnsupportedOperationException();
}
}
1.1 jakarta-commons-sandbox/math/src/test/org/apache/commons/math/analysis/QuinticFunction.java
Index: QuinticFunction.java
===================================================================
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.analysis;
import org.apache.commons.math.MathException;
/**
* Auxillary class for testing solvers.
*
* @author pietsch at apache.org
*
*/
public class QuinticFunction implements UnivariateRealFunction {
/* Evaluate quintic.
* @see org.apache.commons.math.UnivariateRealFunction#value(double)
*/
public double value(double x) throws MathException {
return (x-1)*(x-0.5)*x*(x+0.5)*(x+1);
}
/* First derivative of quintic.
* @see org.apache.commons.math.UnivariateRealFunction#firstDerivative(double)
*/
public double firstDerivative(double x) throws MathException {
return (5*x*x-3.75)*x*x+0.25;
}
/* Second order derivative of quintic.
* Unsupported.
* @see org.apache.commons.math.UnivariateRealFunction#secondDerivative(double)
*/
public double secondDerivative(double x) throws MathException {
throw new UnsupportedOperationException();
}
}
1.1 jakarta-commons-sandbox/math/src/test/org/apache/commons/math/analysis/RealSolverTest.java
Index: RealSolverTest.java
===================================================================
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.analysis;
import org.apache.commons.math.MathException;
import junit.framework.Assert;
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.
*
* @author pietsch at apache.org
*
*/
public final class RealSolverTest extends TestCase {
public RealSolverTest(String name) {
super(name);
}
public static Test suite() {
TestSuite suite = new TestSuite(RealSolverTest.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 monotonous.
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);
}
public void testQuinticZero() throws MathException {
// The quintic function has zeroes 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 = UnivariateRealSolverFactory.solve(f, -0.2, 0.2);
assertEquals(result, 0, solver.getAbsoluteAccuracy());
result = UnivariateRealSolverFactory.solve(f, -0.1, 0.3);
Assert.assertEquals(result, 0, 1E-8);
result = UnivariateRealSolverFactory.solve(f, -0.3, 0.45);
Assert.assertEquals(result, 0, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.3, 0.7);
Assert.assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.2, 0.6);
Assert.assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.05, 0.95);
Assert.assertEquals(result, 0.5, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.85, 1.25);
Assert.assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.8, 1.2);
Assert.assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.85, 1.75);
Assert.assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.55, 1.45);
Assert.assertEquals(result, 1.0, 1E-6);
result = UnivariateRealSolverFactory.solve(f, 0.85, 5);
Assert.assertEquals(result, 1.0, 1E-6);
}
}
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