Java tutorial
/* * 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.math3.optimization.direct; import java.util.Comparator; import org.apache.commons.math3.optimization.PointValuePair; import org.apache.commons.math3.analysis.MultivariateFunction; /** * This class implements the Nelder-Mead simplex algorithm. * * @version $Id: NelderMeadSimplex.java 1422230 2012-12-15 12:11:13Z erans $ * @deprecated As of 3.1 (to be removed in 4.0). * @since 3.0 */ @Deprecated public class NelderMeadSimplex extends AbstractSimplex { /** Default value for {@link #rho}: {@value}. */ private static final double DEFAULT_RHO = 1; /** Default value for {@link #khi}: {@value}. */ private static final double DEFAULT_KHI = 2; /** Default value for {@link #gamma}: {@value}. */ private static final double DEFAULT_GAMMA = 0.5; /** Default value for {@link #sigma}: {@value}. */ private static final double DEFAULT_SIGMA = 0.5; /** Reflection coefficient. */ private final double rho; /** Expansion coefficient. */ private final double khi; /** Contraction coefficient. */ private final double gamma; /** Shrinkage coefficient. */ private final double sigma; /** * Build a Nelder-Mead simplex with default coefficients. * The default coefficients are 1.0 for rho, 2.0 for khi and 0.5 * for both gamma and sigma. * * @param n Dimension of the simplex. */ public NelderMeadSimplex(final int n) { this(n, 1d); } /** * Build a Nelder-Mead simplex with default coefficients. * The default coefficients are 1.0 for rho, 2.0 for khi and 0.5 * for both gamma and sigma. * * @param n Dimension of the simplex. * @param sideLength Length of the sides of the default (hypercube) * simplex. See {@link AbstractSimplex#AbstractSimplex(int,double)}. */ public NelderMeadSimplex(final int n, double sideLength) { this(n, sideLength, DEFAULT_RHO, DEFAULT_KHI, DEFAULT_GAMMA, DEFAULT_SIGMA); } /** * Build a Nelder-Mead simplex with specified coefficients. * * @param n Dimension of the simplex. See * {@link AbstractSimplex#AbstractSimplex(int,double)}. * @param sideLength Length of the sides of the default (hypercube) * simplex. See {@link AbstractSimplex#AbstractSimplex(int,double)}. * @param rho Reflection coefficient. * @param khi Expansion coefficient. * @param gamma Contraction coefficient. * @param sigma Shrinkage coefficient. */ public NelderMeadSimplex(final int n, double sideLength, final double rho, final double khi, final double gamma, final double sigma) { super(n, sideLength); this.rho = rho; this.khi = khi; this.gamma = gamma; this.sigma = sigma; } /** * Build a Nelder-Mead simplex with specified coefficients. * * @param n Dimension of the simplex. See * {@link AbstractSimplex#AbstractSimplex(int)}. * @param rho Reflection coefficient. * @param khi Expansion coefficient. * @param gamma Contraction coefficient. * @param sigma Shrinkage coefficient. */ public NelderMeadSimplex(final int n, final double rho, final double khi, final double gamma, final double sigma) { this(n, 1d, rho, khi, gamma, sigma); } /** * Build a Nelder-Mead simplex with default coefficients. * The default coefficients are 1.0 for rho, 2.0 for khi and 0.5 * for both gamma and sigma. * * @param steps Steps along the canonical axes representing box edges. * They may be negative but not zero. See */ public NelderMeadSimplex(final double[] steps) { this(steps, DEFAULT_RHO, DEFAULT_KHI, DEFAULT_GAMMA, DEFAULT_SIGMA); } /** * Build a Nelder-Mead simplex with specified coefficients. * * @param steps Steps along the canonical axes representing box edges. * They may be negative but not zero. See * {@link AbstractSimplex#AbstractSimplex(double[])}. * @param rho Reflection coefficient. * @param khi Expansion coefficient. * @param gamma Contraction coefficient. * @param sigma Shrinkage coefficient. * @throws IllegalArgumentException if one of the steps is zero. */ public NelderMeadSimplex(final double[] steps, final double rho, final double khi, final double gamma, final double sigma) { super(steps); this.rho = rho; this.khi = khi; this.gamma = gamma; this.sigma = sigma; } /** * Build a Nelder-Mead simplex with default coefficients. * The default coefficients are 1.0 for rho, 2.0 for khi and 0.5 * for both gamma and sigma. * * @param referenceSimplex Reference simplex. See * {@link AbstractSimplex#AbstractSimplex(double[][])}. */ public NelderMeadSimplex(final double[][] referenceSimplex) { this(referenceSimplex, DEFAULT_RHO, DEFAULT_KHI, DEFAULT_GAMMA, DEFAULT_SIGMA); } /** * Build a Nelder-Mead simplex with specified coefficients. * * @param referenceSimplex Reference simplex. See * {@link AbstractSimplex#AbstractSimplex(double[][])}. * @param rho Reflection coefficient. * @param khi Expansion coefficient. * @param gamma Contraction coefficient. * @param sigma Shrinkage coefficient. * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException * if the reference simplex does not contain at least one point. * @throws org.apache.commons.math3.exception.DimensionMismatchException * if there is a dimension mismatch in the reference simplex. */ public NelderMeadSimplex(final double[][] referenceSimplex, final double rho, final double khi, final double gamma, final double sigma) { super(referenceSimplex); this.rho = rho; this.khi = khi; this.gamma = gamma; this.sigma = sigma; } /** {@inheritDoc} */ @Override public void iterate(final MultivariateFunction evaluationFunction, final Comparator<PointValuePair> comparator) { // The simplex has n + 1 points if dimension is n. final int n = getDimension(); // Interesting values. final PointValuePair best = getPoint(0); final PointValuePair secondBest = getPoint(n - 1); final PointValuePair worst = getPoint(n); final double[] xWorst = worst.getPointRef(); // Compute the centroid of the best vertices (dismissing the worst // point at index n). final double[] centroid = new double[n]; for (int i = 0; i < n; i++) { final double[] x = getPoint(i).getPointRef(); for (int j = 0; j < n; j++) { centroid[j] += x[j]; } } final double scaling = 1.0 / n; for (int j = 0; j < n; j++) { centroid[j] *= scaling; } // compute the reflection point final double[] xR = new double[n]; for (int j = 0; j < n; j++) { xR[j] = centroid[j] + rho * (centroid[j] - xWorst[j]); } final PointValuePair reflected = new PointValuePair(xR, evaluationFunction.value(xR), false); if (comparator.compare(best, reflected) <= 0 && comparator.compare(reflected, secondBest) < 0) { // Accept the reflected point. replaceWorstPoint(reflected, comparator); } else if (comparator.compare(reflected, best) < 0) { // Compute the expansion point. final double[] xE = new double[n]; for (int j = 0; j < n; j++) { xE[j] = centroid[j] + khi * (xR[j] - centroid[j]); } final PointValuePair expanded = new PointValuePair(xE, evaluationFunction.value(xE), false); if (comparator.compare(expanded, reflected) < 0) { // Accept the expansion point. replaceWorstPoint(expanded, comparator); } else { // Accept the reflected point. replaceWorstPoint(reflected, comparator); } } else { if (comparator.compare(reflected, worst) < 0) { // Perform an outside contraction. final double[] xC = new double[n]; for (int j = 0; j < n; j++) { xC[j] = centroid[j] + gamma * (xR[j] - centroid[j]); } final PointValuePair outContracted = new PointValuePair(xC, evaluationFunction.value(xC), false); if (comparator.compare(outContracted, reflected) <= 0) { // Accept the contraction point. replaceWorstPoint(outContracted, comparator); return; } } else { // Perform an inside contraction. final double[] xC = new double[n]; for (int j = 0; j < n; j++) { xC[j] = centroid[j] - gamma * (centroid[j] - xWorst[j]); } final PointValuePair inContracted = new PointValuePair(xC, evaluationFunction.value(xC), false); if (comparator.compare(inContracted, worst) < 0) { // Accept the contraction point. replaceWorstPoint(inContracted, comparator); return; } } // Perform a shrink. final double[] xSmallest = getPoint(0).getPointRef(); for (int i = 1; i <= n; i++) { final double[] x = getPoint(i).getPoint(); for (int j = 0; j < n; j++) { x[j] = xSmallest[j] + sigma * (x[j] - xSmallest[j]); } setPoint(i, new PointValuePair(x, Double.NaN, false)); } evaluate(evaluationFunction, comparator); } } }