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Java example source code file (BrentOptimizer.java)

This example Java source code file (BrentOptimizer.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

baseabstractunivariateoptimizer, brent's, brentoptimizer, convergencechecker, default, deprecated, fit, golden_section, min_relative_tolerance, notstrictlypositiveexception, numberistoosmallexception, override, univariatepointvaluepair

The BrentOptimizer.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.univariate;

import org.apache.commons.math3.util.Precision;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.optimization.ConvergenceChecker;
import org.apache.commons.math3.optimization.GoalType;

/**
 * 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.
 * <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>to ensure that the best point encountered is the one returned.
 * </ul>
 *
 * @deprecated As of 3.1 (to be removed in 4.0).
 * @since 2.0
 */
@Deprecated
public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {
    /**
     * Golden section.
     */
    private static final double GOLDEN_SECTION = 0.5 * (3 - FastMath.sqrt(5));
    /**
     * Minimum relative tolerance.
     */
    private static final double MIN_RELATIVE_TOLERANCE = 2 * FastMath.ulp(1d);
    /**
     * Relative threshold.
     */
    private final double relativeThreshold;
    /**
     * Absolute threshold.
     */
    private final double absoluteThreshold;

    /**
     * The arguments are used implement the original stopping criterion
     * of Brent's algorithm.
     * {@code abs} and {@code rel} define a tolerance
     * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than
     * <em>2 macheps and preferably not much less than sqrt(macheps),
     * where <em>macheps is the relative machine precision. {@code abs} must
     * be positive.
     *
     * @param rel Relative threshold.
     * @param abs Absolute threshold.
     * @param checker Additional, user-defined, convergence checking
     * procedure.
     * @throws NotStrictlyPositiveException if {@code abs <= 0}.
     * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
     */
    public BrentOptimizer(double rel,
                          double abs,
                          ConvergenceChecker<UnivariatePointValuePair> checker) {
        super(checker);

        if (rel < MIN_RELATIVE_TOLERANCE) {
            throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
        }
        if (abs <= 0) {
            throw new NotStrictlyPositiveException(abs);
        }

        relativeThreshold = rel;
        absoluteThreshold = abs;
    }

    /**
     * The arguments are used for implementing the original stopping criterion
     * of Brent's algorithm.
     * {@code abs} and {@code rel} define a tolerance
     * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than
     * <em>2 macheps and preferably not much less than sqrt(macheps),
     * where <em>macheps is the relative machine precision. {@code abs} must
     * be positive.
     *
     * @param rel Relative threshold.
     * @param abs Absolute threshold.
     * @throws NotStrictlyPositiveException if {@code abs <= 0}.
     * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
     */
    public BrentOptimizer(double rel,
                          double abs) {
        this(rel, abs, null);
    }

    /** {@inheritDoc} */
    @Override
    protected UnivariatePointValuePair doOptimize() {
        final boolean isMinim = getGoalType() == GoalType.MINIMIZE;
        final double lo = getMin();
        final double mid = getStartValue();
        final double hi = getMax();

        // Optional additional convergence criteria.
        final ConvergenceChecker<UnivariatePointValuePair> checker
            = getConvergenceChecker();

        double a;
        double b;
        if (lo < hi) {
            a = lo;
            b = hi;
        } else {
            a = hi;
            b = lo;
        }

        double x = mid;
        double v = x;
        double w = x;
        double d = 0;
        double e = 0;
        double fx = computeObjectiveValue(x);
        if (!isMinim) {
            fx = -fx;
        }
        double fv = fx;
        double fw = fx;

        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) {
            final double m = 0.5 * (a + b);
            final double tol1 = relativeThreshold * FastMath.abs(x) + absoluteThreshold;
            final double tol2 = 2 * tol1;

            // Default stopping criterion.
            final boolean stop = FastMath.abs(x - m) <= tol2 - 0.5 * (b - a);
            if (!stop) {
                double p = 0;
                double q = 0;
                double r = 0;
                double u = 0;

                if (FastMath.abs(e) > tol1) { // Fit parabola.
                    r = (x - w) * (fx - fv);
                    q = (x - v) * (fx - fw);
                    p = (x - v) * q - (x - w) * r;
                    q = 2 * (q - r);

                    if (q > 0) {
                        p = -p;
                    } else {
                        q = -q;
                    }

                    r = e;
                    e = d;

                    if (p > q * (a - x) &&
                        p < q * (b - x) &&
                        FastMath.abs(p) < FastMath.abs(0.5 * q * r)) {
                        // Parabolic interpolation step.
                        d = p / q;
                        u = x + d;

                        // f must not be evaluated too close to a or b.
                        if (u - a < tol2 || b - u < tol2) {
                            if (x <= m) {
                                d = tol1;
                            } else {
                                d = -tol1;
                            }
                        }
                    } else {
                        // Golden section step.
                        if (x < m) {
                            e = b - x;
                        } else {
                            e = a - x;
                        }
                        d = GOLDEN_SECTION * e;
                    }
                } else {
                    // Golden section step.
                    if (x < m) {
                        e = b - x;
                    } else {
                        e = a - x;
                    }
                    d = GOLDEN_SECTION * e;
                }

                // Update by at least "tol1".
                if (FastMath.abs(d) < tol1) {
                    if (d >= 0) {
                        u = x + tol1;
                    } else {
                        u = x - tol1;
                    }
                } else {
                    u = x + d;
                }

                double fu = computeObjectiveValue(u);
                if (!isMinim) {
                    fu = -fu;
                }

                // User-defined convergence checker.
                previous = current;
                current = new UnivariatePointValuePair(u, isMinim ? fu : -fu);
                best = best(best,
                            best(previous,
                                 current,
                                 isMinim),
                            isMinim);

                if (checker != null && checker.converged(iter, previous, current)) {
                    return best;
                }

                // Update a, b, v, w and x.
                if (fu <= fx) {
                    if (u < x) {
                        b = x;
                    } else {
                        a = x;
                    }
                    v = w;
                    fv = fw;
                    w = x;
                    fw = fx;
                    x = u;
                    fx = fu;
                } else {
                    if (u < x) {
                        a = u;
                    } else {
                        b = u;
                    }
                    if (fu <= fw ||
                        Precision.equals(w, x)) {
                        v = w;
                        fv = fw;
                        w = u;
                        fw = fu;
                    } else if (fu <= fv ||
                               Precision.equals(v, x) ||
                               Precision.equals(v, w)) {
                        v = u;
                        fv = fu;
                    }
                }
            } else { // Default termination (Brent's criterion).
                return best(best,
                            best(previous,
                                 current,
                                 isMinim),
                            isMinim);
            }
            ++iter;
        }
    }

    /**
     * Selects the best of two points.
     *
     * @param a Point and value.
     * @param b Point and value.
     * @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}. When {@code a} and {@code b} have the same function
     * value, {@code a} is returned.
     */
    private UnivariatePointValuePair best(UnivariatePointValuePair a,
                                          UnivariatePointValuePair b,
                                          boolean isMinim) {
        if (a == null) {
            return b;
        }
        if (b == null) {
            return a;
        }

        if (isMinim) {
            return a.getValue() <= b.getValue() ? a : b;
        } else {
            return a.getValue() >= b.getValue() ? a : b;
        }
    }
}

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