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Java example source code file (NonLinearConjugateGradientOptimizer.java)

This example Java source code file (NonLinearConjugateGradientOptimizer.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

brentsolver, conjugategradientformula, convergencechecker, deprecated, goaltype, identitypreconditioner, linesearchfunction, nonlinearconjugategradientoptimizer, override, pointvaluepair, simplevaluechecker, subtract, univariatefunction, univariatesolver

The NonLinearConjugateGradientOptimizer.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.general;

import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.solvers.BrentSolver;
import org.apache.commons.math3.analysis.solvers.UnivariateSolver;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.optimization.PointValuePair;
import org.apache.commons.math3.optimization.SimpleValueChecker;
import org.apache.commons.math3.optimization.ConvergenceChecker;
import org.apache.commons.math3.util.FastMath;

/**
 * Non-linear conjugate gradient optimizer.
 * <p>
 * This class supports both the Fletcher-Reeves and the Polak-Ribière
 * update formulas for the conjugate search directions. It also supports
 * optional preconditioning.
 * </p>
 *
 * @deprecated As of 3.1 (to be removed in 4.0).
 * @since 2.0
 *
 */
@Deprecated
public class NonLinearConjugateGradientOptimizer
    extends AbstractScalarDifferentiableOptimizer {
    /** Update formula for the beta parameter. */
    private final ConjugateGradientFormula updateFormula;
    /** Preconditioner (may be null). */
    private final Preconditioner preconditioner;
    /** solver to use in the line search (may be null). */
    private final UnivariateSolver solver;
    /** Initial step used to bracket the optimum in line search. */
    private double initialStep;
    /** Current point. */
    private double[] point;

    /**
     * Constructor with default {@link SimpleValueChecker checker},
     * {@link BrentSolver line search solver} and
     * {@link IdentityPreconditioner preconditioner}.
     *
     * @param updateFormula formula to use for updating the β parameter,
     * must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link
     * ConjugateGradientFormula#POLAK_RIBIERE}.
     * @deprecated See {@link SimpleValueChecker#SimpleValueChecker()}
     */
    @Deprecated
    public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula) {
        this(updateFormula,
             new SimpleValueChecker());
    }

    /**
     * Constructor with default {@link BrentSolver line search solver} and
     * {@link IdentityPreconditioner preconditioner}.
     *
     * @param updateFormula formula to use for updating the β parameter,
     * must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link
     * ConjugateGradientFormula#POLAK_RIBIERE}.
     * @param checker Convergence checker.
     */
    public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula,
                                               ConvergenceChecker<PointValuePair> checker) {
        this(updateFormula,
             checker,
             new BrentSolver(),
             new IdentityPreconditioner());
    }


    /**
     * Constructor with default {@link IdentityPreconditioner preconditioner}.
     *
     * @param updateFormula formula to use for updating the β parameter,
     * must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link
     * ConjugateGradientFormula#POLAK_RIBIERE}.
     * @param checker Convergence checker.
     * @param lineSearchSolver Solver to use during line search.
     */
    public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula,
                                               ConvergenceChecker<PointValuePair> checker,
                                               final UnivariateSolver lineSearchSolver) {
        this(updateFormula,
             checker,
             lineSearchSolver,
             new IdentityPreconditioner());
    }

    /**
     * @param updateFormula formula to use for updating the β parameter,
     * must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link
     * ConjugateGradientFormula#POLAK_RIBIERE}.
     * @param checker Convergence checker.
     * @param lineSearchSolver Solver to use during line search.
     * @param preconditioner Preconditioner.
     */
    public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula,
                                               ConvergenceChecker<PointValuePair> checker,
                                               final UnivariateSolver lineSearchSolver,
                                               final Preconditioner preconditioner) {
        super(checker);

        this.updateFormula = updateFormula;
        solver = lineSearchSolver;
        this.preconditioner = preconditioner;
        initialStep = 1.0;
    }

    /**
     * Set the initial step used to bracket the optimum in line search.
     * <p>
     * The initial step is a factor with respect to the search direction,
     * which itself is roughly related to the gradient of the function
     * </p>
     * @param initialStep initial step used to bracket the optimum in line search,
     * if a non-positive value is used, the initial step is reset to its
     * default value of 1.0
     */
    public void setInitialStep(final double initialStep) {
        if (initialStep <= 0) {
            this.initialStep = 1.0;
        } else {
            this.initialStep = initialStep;
        }
    }

    /** {@inheritDoc} */
    @Override
    protected PointValuePair doOptimize() {
        final ConvergenceChecker<PointValuePair> checker = getConvergenceChecker();
        point = getStartPoint();
        final GoalType goal = getGoalType();
        final int n = point.length;
        double[] r = computeObjectiveGradient(point);
        if (goal == GoalType.MINIMIZE) {
            for (int i = 0; i < n; ++i) {
                r[i] = -r[i];
            }
        }

        // Initial search direction.
        double[] steepestDescent = preconditioner.precondition(point, r);
        double[] searchDirection = steepestDescent.clone();

        double delta = 0;
        for (int i = 0; i < n; ++i) {
            delta += r[i] * searchDirection[i];
        }

        PointValuePair current = null;
        int iter = 0;
        int maxEval = getMaxEvaluations();
        while (true) {
            ++iter;

            final double objective = computeObjectiveValue(point);
            PointValuePair previous = current;
            current = new PointValuePair(point, objective);
            if (previous != null && checker.converged(iter, previous, current)) {
                // We have found an optimum.
                return current;
            }

            // Find the optimal step in the search direction.
            final UnivariateFunction lsf = new LineSearchFunction(searchDirection);
            final double uB = findUpperBound(lsf, 0, initialStep);
            // XXX Last parameters is set to a value close to zero in order to
            // work around the divergence problem in the "testCircleFitting"
            // unit test (see MATH-439).
            final double step = solver.solve(maxEval, lsf, 0, uB, 1e-15);
            maxEval -= solver.getEvaluations(); // Subtract used up evaluations.

            // Validate new point.
            for (int i = 0; i < point.length; ++i) {
                point[i] += step * searchDirection[i];
            }

            r = computeObjectiveGradient(point);
            if (goal == GoalType.MINIMIZE) {
                for (int i = 0; i < n; ++i) {
                    r[i] = -r[i];
                }
            }

            // Compute beta.
            final double deltaOld = delta;
            final double[] newSteepestDescent = preconditioner.precondition(point, r);
            delta = 0;
            for (int i = 0; i < n; ++i) {
                delta += r[i] * newSteepestDescent[i];
            }

            final double beta;
            if (updateFormula == ConjugateGradientFormula.FLETCHER_REEVES) {
                beta = delta / deltaOld;
            } else {
                double deltaMid = 0;
                for (int i = 0; i < r.length; ++i) {
                    deltaMid += r[i] * steepestDescent[i];
                }
                beta = (delta - deltaMid) / deltaOld;
            }
            steepestDescent = newSteepestDescent;

            // Compute conjugate search direction.
            if (iter % n == 0 ||
                beta < 0) {
                // Break conjugation: reset search direction.
                searchDirection = steepestDescent.clone();
            } else {
                // Compute new conjugate search direction.
                for (int i = 0; i < n; ++i) {
                    searchDirection[i] = steepestDescent[i] + beta * searchDirection[i];
                }
            }
        }
    }

    /**
     * Find the upper bound b ensuring bracketing of a root between a and b.
     *
     * @param f function whose root must be bracketed.
     * @param a lower bound of the interval.
     * @param h initial step to try.
     * @return b such that f(a) and f(b) have opposite signs.
     * @throws MathIllegalStateException if no bracket can be found.
     */
    private double findUpperBound(final UnivariateFunction f,
                                  final double a, final double h) {
        final double yA = f.value(a);
        double yB = yA;
        for (double step = h; step < Double.MAX_VALUE; step *= FastMath.max(2, yA / yB)) {
            final double b = a + step;
            yB = f.value(b);
            if (yA * yB <= 0) {
                return b;
            }
        }
        throw new MathIllegalStateException(LocalizedFormats.UNABLE_TO_BRACKET_OPTIMUM_IN_LINE_SEARCH);
    }

    /** Default identity preconditioner. */
    public static class IdentityPreconditioner implements Preconditioner {

        /** {@inheritDoc} */
        public double[] precondition(double[] variables, double[] r) {
            return r.clone();
        }
    }

    /** Internal class for line search.
     * <p>
     * The function represented by this class is the dot product of
     * the objective function gradient and the search direction. Its
     * value is zero when the gradient is orthogonal to the search
     * direction, i.e. when the objective function value is a local
     * extremum along the search direction.
     * </p>
     */
    private class LineSearchFunction implements UnivariateFunction {
        /** Search direction. */
        private final double[] searchDirection;

        /** Simple constructor.
         * @param searchDirection search direction
         */
        LineSearchFunction(final double[] searchDirection) {
            this.searchDirection = searchDirection;
        }

        /** {@inheritDoc} */
        public double value(double x) {
            // current point in the search direction
            final double[] shiftedPoint = point.clone();
            for (int i = 0; i < shiftedPoint.length; ++i) {
                shiftedPoint[i] += x * searchDirection[i];
            }

            // gradient of the objective function
            final double[] gradient = computeObjectiveGradient(shiftedPoint);

            // dot product with the search direction
            double dotProduct = 0;
            for (int i = 0; i < gradient.length; ++i) {
                dotProduct += gradient[i] * searchDirection[i];
            }

            return dotProduct;
        }
    }
}

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