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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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.
*
* This class supports both the Fletcher-Reeves and the Polak-Ribière
* update formulas for the conjugate search directions. It also supports
* optional preconditioning.
*
*
* @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 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 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 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.
*
* The initial step is a factor with respect to the search direction,
* which itself is roughly related to the gradient of the function
*
* @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 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.
*
* 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.
*
*/
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;
}
}
}