home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (NelderMeadSimplex.java)

This example Java source code file (NelderMeadSimplex.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractsimplex, comparator, default_gamma, default_khi, default_rho, default_sigma, deprecated, multivariatefunction, neldermeadsimplex, override, pointvaluepair, util

The NelderMeadSimplex.java Java example source code

/*
 * 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.
 *
 * @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);
        }
    }
}

Other Java examples (source code examples)

Here is a short list of links related to this Java NelderMeadSimplex.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2019 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.