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/*
* 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.optimization.direct;
import java.util.Comparator;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealConvergenceChecker;
import org.apache.commons.math.optimization.RealPointValuePair;
/**
* This class implements the multi-directional direct search method.
*
* @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
* @see NelderMead
* @since 1.2
*/
public class MultiDirectional extends DirectSearchOptimizer {
/** Expansion coefficient. */
private final double khi;
/** Contraction coefficient. */
private final double gamma;
/** Build a multi-directional optimizer with default coefficients.
* <p>The default values are 2.0 for khi and 0.5 for gamma.</p>
*/
public MultiDirectional() {
this.khi = 2.0;
this.gamma = 0.5;
}
/** Build a multi-directional optimizer with specified coefficients.
* @param khi expansion coefficient
* @param gamma contraction coefficient
*/
public MultiDirectional(final double khi, final double gamma) {
this.khi = khi;
this.gamma = gamma;
}
/** {@inheritDoc} */
@Override
protected void iterateSimplex(final Comparator<RealPointValuePair> comparator)
throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {
final RealConvergenceChecker checker = getConvergenceChecker();
while (true) {
incrementIterationsCounter();
// save the original vertex
final RealPointValuePair[] original = simplex;
final RealPointValuePair best = original[0];
// perform a reflection step
final RealPointValuePair reflected = evaluateNewSimplex(original, 1.0, comparator);
if (comparator.compare(reflected, best) < 0) {
// compute the expanded simplex
final RealPointValuePair[] reflectedSimplex = simplex;
final RealPointValuePair expanded = evaluateNewSimplex(original, khi, comparator);
if (comparator.compare(reflected, expanded) <= 0) {
// accept the reflected simplex
simplex = reflectedSimplex;
}
return;
}
// compute the contracted simplex
final RealPointValuePair contracted = evaluateNewSimplex(original, gamma, comparator);
if (comparator.compare(contracted, best) < 0) {
// accept the contracted simplex
return;
}
// check convergence
final int iter = getIterations();
boolean converged = true;
for (int i = 0; i < simplex.length; ++i) {
converged &= checker.converged(iter, original[i], simplex[i]);
}
if (converged) {
return;
}
}
}
/** Compute and evaluate a new simplex.
* @param original original simplex (to be preserved)
* @param coeff linear coefficient
* @param comparator comparator to use to sort simplex vertices from best to poorest
* @return best point in the transformed simplex
* @exception FunctionEvaluationException if the function cannot be evaluated at some point
* @exception OptimizationException if the maximal number of evaluations is exceeded
*/
private RealPointValuePair evaluateNewSimplex(final RealPointValuePair[] original,
final double coeff,
final Comparator<RealPointValuePair> comparator)
throws FunctionEvaluationException, OptimizationException {
final double[] xSmallest = original[0].getPointRef();
final int n = xSmallest.length;
// create the linearly transformed simplex
simplex = new RealPointValuePair[n + 1];
simplex[0] = original[0];
for (int i = 1; i <= n; ++i) {
final double[] xOriginal = original[i].getPointRef();
final double[] xTransformed = new double[n];
for (int j = 0; j < n; ++j) {
xTransformed[j] = xSmallest[j] + coeff * (xSmallest[j] - xOriginal[j]);
}
simplex[i] = new RealPointValuePair(xTransformed, Double.NaN, false);
}
// evaluate it
evaluateSimplex(comparator);
return simplex[0];
}
}
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