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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,
* 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.
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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.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for {@link BracketingNthOrderBrentSolver bracketing n<sup>th</sup> order Brent} solver.
*
*/
public final class BracketingNthOrderBrentSolverTest extends BaseSecantSolverAbstractTest {
/** {@inheritDoc} */
@Override
protected UnivariateSolver getSolver() {
return new BracketingNthOrderBrentSolver();
}
/** {@inheritDoc} */
@Override
protected int[] getQuinticEvalCounts() {
return new int[] {1, 3, 8, 1, 9, 4, 8, 1, 12, 1, 16};
}
@Test(expected=NumberIsTooSmallException.class)
public void testInsufficientOrder1() {
new BracketingNthOrderBrentSolver(1.0e-10, 1);
}
@Test(expected=NumberIsTooSmallException.class)
public void testInsufficientOrder2() {
new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1);
}
@Test(expected=NumberIsTooSmallException.class)
public void testInsufficientOrder3() {
new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1.0e-10, 1);
}
@Test
public void testConstructorsOK() {
Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 2).getMaximalOrder());
Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 2).getMaximalOrder());
Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1.0e-10, 2).getMaximalOrder());
}
@Test
public void testConvergenceOnFunctionAccuracy() {
BracketingNthOrderBrentSolver solver =
new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 0.001, 3);
QuinticFunction f = new QuinticFunction();
double result = solver.solve(20, f, 0.2, 0.9, 0.4, AllowedSolution.BELOW_SIDE);
Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
Assert.assertTrue(f.value(result) <= 0);
Assert.assertTrue(result - 0.5 > solver.getAbsoluteAccuracy());
result = solver.solve(20, f, -0.9, -0.2, -0.4, AllowedSolution.ABOVE_SIDE);
Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
Assert.assertTrue(f.value(result) >= 0);
Assert.assertTrue(result + 0.5 < -solver.getAbsoluteAccuracy());
}
@Test
public void testIssue716() {
BracketingNthOrderBrentSolver solver =
new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 1.0e-22, 5);
UnivariateFunction sharpTurn = new UnivariateFunction() {
public double value(double x) {
return (2 * x + 1) / (1.0e9 * (x + 1));
}
};
double result = solver.solve(100, sharpTurn, -0.9999999, 30, 15, AllowedSolution.RIGHT_SIDE);
Assert.assertEquals(0, sharpTurn.value(result), solver.getFunctionValueAccuracy());
Assert.assertTrue(sharpTurn.value(result) >= 0);
Assert.assertEquals(-0.5, result, 1.0e-10);
}
@Test
public void testFasterThanNewton() {
// the following test functions come from Beny Neta's paper:
// "Several New Methods for solving Equations"
// intern J. Computer Math Vol 23 pp 265-282
// available here: http://www.math.nps.navy.mil/~bneta/SeveralNewMethods.PDF
// the reference roots have been computed by the Dfp solver to more than
// 80 digits and checked with emacs (only the first 20 digits are reproduced here)
compare(new TestFunction(0.0, -2, 2) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.sin().subtract(x.multiply(0.5));
}
});
compare(new TestFunction(6.3087771299726890947, -5, 10) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.pow(5).add(x).subtract(10000);
}
});
compare(new TestFunction(9.6335955628326951924, 0.001, 10) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.sqrt().subtract(x.reciprocal()).subtract(3);
}
});
compare(new TestFunction(2.8424389537844470678, -5, 5) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.exp().add(x).subtract(20);
}
});
compare(new TestFunction(8.3094326942315717953, 0.001, 10) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.log().add(x.sqrt()).subtract(5);
}
});
compare(new TestFunction(1.4655712318767680266, -0.5, 1.5) {
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.subtract(1).multiply(x).multiply(x).subtract(1);
}
});
}
private void compare(TestFunction f) {
compare(f, f.getRoot(), f.getMin(), f.getMax());
}
private void compare(final UnivariateDifferentiableFunction f,
double root, double min, double max) {
NewtonRaphsonSolver newton = new NewtonRaphsonSolver(1.0e-12);
BracketingNthOrderBrentSolver bracketing =
new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-12, 1.0e-18, 5);
double resultN;
try {
resultN = newton.solve(100, f, min, max);
} catch (TooManyEvaluationsException tmee) {
resultN = Double.NaN;
}
double resultB;
try {
resultB = bracketing.solve(100, f, min, max);
} catch (TooManyEvaluationsException tmee) {
resultB = Double.NaN;
}
Assert.assertEquals(root, resultN, newton.getAbsoluteAccuracy());
Assert.assertEquals(root, resultB, bracketing.getAbsoluteAccuracy());
// bracketing solver evaluates only function value, we set the weight to 1
final int weightedBracketingEvaluations = bracketing.getEvaluations();
// Newton-Raphson solver evaluates both function value and derivative, we set the weight to 2
final int weightedNewtonEvaluations = 2 * newton.getEvaluations();
Assert.assertTrue(weightedBracketingEvaluations < weightedNewtonEvaluations);
}
private static abstract class TestFunction implements UnivariateDifferentiableFunction {
private final double root;
private final double min;
private final double max;
protected TestFunction(final double root, final double min, final double max) {
this.root = root;
this.min = min;
this.max = max;
}
public double getRoot() {
return root;
}
public double getMin() {
return min;
}
public double getMax() {
return max;
}
public double value(final double x) {
return value(new DerivativeStructure(0, 0, x)).getValue();
}
public abstract DerivativeStructure value(final DerivativeStructure t);
}
}