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MATH-855 (second take). 

Best point must be returned.


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1382070 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Gilles Sadowski 2012-09-07 15:43:40 +00:00
parent ad923872f3
commit ac597cc172
2 changed files with 69 additions and 12 deletions
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40
src/main/java/org/apache/commons/math3/optimization/univariate/BrentOptimizer.java
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@ -24,13 +24,19 @@ import org.apache.commons.math3.optimization.ConvergenceChecker;
import org.apache.commons.math3.optimization.GoalType;
/**
* Implements Richard Brent's algorithm (from his book "Algorithms for
* For a function defined on some interval {@code (lo, hi)}, this class
* finds an approximation {@code x} to the point at which the function
* attains its minimum.
* It implements Richard Brent's algorithm (from his book "Algorithms for
* Minimization without Derivatives", p. 79) for finding minima of real
* univariate functions. This implementation is an adaptation partly
* based on the Python code from SciPy (module "optimize.py" v0.5).
* If the function is defined on some interval {@code (lo, hi)}, then
* this method finds an approximation {@code x} to the point at which
* the function attains its minimum.
* univariate functions.
* <br/>
* This code is an adaptation, partly based on the Python code from SciPy
* (module "optimize.py" v0.5); the original algorithm is also modified
* <ul>
* <li>to use an initial guess provided by the user,</li>
* <li>to ensure that the best point encountered is the one returned.</li>
* </ul>
*
* @version $Id$
* @since 2.0
@ -141,6 +147,8 @@ public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
UnivariatePointValuePair previous = null;
UnivariatePointValuePair current
= new UnivariatePointValuePair(x, isMinim ? fx : -fx);
// Best point encountered so far (which is the initial guess).
UnivariatePointValuePair best = current;
int iter = 0;
while (true) {
@ -224,10 +232,15 @@ public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
// User-defined convergence checker.
previous = current;
current = new UnivariatePointValuePair(u, isMinim ? fu : -fu);
best = best(best,
best(current,
previous,
isMinim),
isMinim);
if (checker != null) {
if (checker.converged(iter, previous, current)) {
return best(current, previous, isMinim);
return best;
}
}
@ -264,7 +277,11 @@ public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
}
}
} else { // Default termination (Brent's criterion).
return best(current, previous, isMinim);
return best(best,
best(current,
previous,
isMinim),
isMinim);
}
++iter;
}
@ -278,7 +295,8 @@ public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
* @param isMinim {@code true} if the selected point must be the one with
* the lowest value.
* @return the best point, or {@code null} if {@code a} and {@code b} are
* both {@code null}.
* both {@code null}. When {@code a} and {@code b} have the same function
* value, {@code a} is returned.
*/
private UnivariatePointValuePair best(UnivariatePointValuePair a,
UnivariatePointValuePair b,
@ -291,9 +309,9 @@ public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
}
if (isMinim) {
return a.getValue() < b.getValue() ? a : b;
return a.getValue() <= b.getValue() ? a : b;
} else {
return a.getValue() > b.getValue() ? a : b;
return a.getValue() >= b.getValue() ? a : b;
}
}
}

41
src/test/java/org/apache/commons/math3/optimization/univariate/BrentOptimizerTest.java
View File

@ -184,6 +184,43 @@ public final class BrentOptimizerTest {
Assert.assertEquals(804.9355825, result, 1e-6);
}
/**
* Contrived example showing that prior to the resolution of MATH-855
* (second revision), the algorithm would not return the best point if
* it happened to be the initial guess.
*/
@Test
public void testKeepInitIfBest() {
final double minSin = 3 * Math.PI / 2;
final double offset = 1e-8;
final double delta = 1e-7;
final UnivariateFunction f1 = new Sin();
final UnivariateFunction f2 = new StepFunction(new double[] { minSin, minSin + offset, minSin + 2 * offset},
new double[] { 0, -1, 0 });
final UnivariateFunction f = FunctionUtils.add(f1, f2);
// A slightly less stringent tolerance would make the test pass
// even with the previous implementation.
final double relTol = 1e-8;
final UnivariateOptimizer optimizer = new BrentOptimizer(relTol, 1e-100);
final double init = minSin + 1.5 * offset;
final UnivariatePointValuePair result
= optimizer.optimize(200, f, GoalType.MINIMIZE,
minSin - 6.789 * delta,
minSin + 9.876 * delta,
init);
final int numEval = optimizer.getEvaluations();
final double sol = result.getPoint();
final double expected = init;
// System.out.println("numEval=" + numEval);
// System.out.println("min=" + init + " f=" + f.value(init));
// System.out.println("sol=" + sol + " f=" + f.value(sol));
// System.out.println("exp=" + expected + " f=" + f.value(expected));
Assert.assertTrue("Best point not reported", f.value(sol) <= f.value(expected));
}
/**
* Contrived example showing that prior to the resolution of MATH-855,
* the algorithm, by always returning the last evaluated point, would
@ -200,7 +237,9 @@ public final class BrentOptimizerTest {
final UnivariateFunction f = FunctionUtils.add(f1, f2);
final UnivariateOptimizer optimizer = new BrentOptimizer(1e-8, 1e-100);
final UnivariatePointValuePair result
= optimizer.optimize(200, f, GoalType.MINIMIZE, minSin - 6.789 * delta, minSin + 9.876 * delta);
= optimizer.optimize(200, f, GoalType.MINIMIZE,
minSin - 6.789 * delta,
minSin + 9.876 * delta);
final int numEval = optimizer.getEvaluations();
final double sol = result.getPoint();