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diff --git a/src/main/java/org/apache/commons/math/optimization/direct/MultiDirectional.java b/src/main/java/org/apache/commons/math/optimization/direct/MultiDirectional.java
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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];
+
+    }
+
+}