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* 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
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*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
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package org.apache.commons.math.optimization.general;
import org.apache.commons.math.exception.MathIllegalStateException;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.solvers.BrentSolver;
import org.apache.commons.math.analysis.solvers.UnivariateRealSolver;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.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>
*
* @version $Id: NonLinearConjugateGradientOptimizer.java 1131229 2011-06-03 20:49:25Z luc $
* @since 2.0
*
*/
public class NonLinearConjugateGradientOptimizer
extends AbstractScalarDifferentiableOptimizer {
/** Update formula for the beta parameter. */
private final ConjugateGradientFormula updateFormula;
/** Preconditioner (may be null). */
private Preconditioner preconditioner;
/** solver to use in the line search (may be null). */
private UnivariateRealSolver solver;
/** Initial step used to bracket the optimum in line search. */
private double initialStep;
/** Current point. */
private double[] point;
/**
* Simple constructor with default settings.
* The convergence check is set to a {@link
* org.apache.commons.math.optimization.SimpleVectorialValueChecker}.
*
* @param updateFormula formula to use for updating the β parameter,
* must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link
* ConjugateGradientFormula#POLAK_RIBIERE}
*/
public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula) {
this.updateFormula = updateFormula;
preconditioner = null;
solver = null;
initialStep = 1.0;
}
/**
* Set the preconditioner.
* @param preconditioner preconditioner to use for next optimization,
* may be null to remove an already registered preconditioner
*/
public void setPreconditioner(final Preconditioner preconditioner) {
this.preconditioner = preconditioner;
}
/**
* Set the solver to use during line search.
* @param lineSearchSolver solver to use during line search, may be null
* to remove an already registered solver and fall back to the
* default {@link BrentSolver Brent solver}.
*/
public void setLineSearchSolver(final UnivariateRealSolver lineSearchSolver) {
solver = lineSearchSolver;
}
/**
* 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 RealPointValuePair doOptimize() {
// Initialization.
if (preconditioner == null) {
preconditioner = new IdentityPreconditioner();
}
if (solver == null) {
solver = new BrentSolver();
}
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];
}
RealPointValuePair current = null;
int iter = 0;
int maxEval = getMaxEvaluations();
while (true) {
++iter;
final double objective = computeObjectiveValue(point);
RealPointValuePair previous = current;
current = new RealPointValuePair(point, objective);
if (previous != null) {
if (getConvergenceChecker().converged(iter, previous, current)) {
// We have found an optimum.
return current;
}
}
double dTd = 0;
for (final double di : searchDirection) {
dTd += di * di;
}
// Find the optimal step in the search direction.
final UnivariateRealFunction lsf = new LineSearchFunction(searchDirection);
final double uB = findUpperBound(lsf, 0, initialStep);
// XXX Last parameters is set to a value clode 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.
* @throws org.apache.commons.math.exception.MathUserException if the
* function throws one.
*/
private double findUpperBound(final UnivariateRealFunction 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. */
private 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 UnivariateRealFunction {
/** Search direction. */
private final double[] searchDirection;
/** Simple constructor.
* @param searchDirection search direction
*/
public 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;
}
}
}