Fixed bugs in "BrentOptimizer".
Renamed "BrentMinimizerTest" to "BrentOptimizerTest". Modified "MultiStartUnivariateRealOptimizerTest" because it uses "BrentOptimizer" as the underlying optimizer, and so was affected by the changes. git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@979257 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Gilles Sadowski
parent
d4b02f6a3a
commit
58f407fc8a
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@ -18,19 +18,20 @@ package org.apache.commons.math.optimization.univariate;
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import org.apache.commons.math.FunctionEvaluationException;
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import org.apache.commons.math.MaxIterationsExceededException;
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import org.apache.commons.math.exception.NotStrictlyPositiveException;
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import org.apache.commons.math.analysis.UnivariateRealFunction;
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import org.apache.commons.math.optimization.GoalType;
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/**
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* Implements Richard Brent's algorithm (from his book "Algorithms for
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* Minimization without Derivatives", p. 79) for finding minima of real
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* univariate functions.
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* univariate functions. This implementation is an adaptation partly
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* based on the Python code from SciPy (module "optimize.py" v0.5).
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*
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* @version $Revision$ $Date$
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* @since 2.0
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*/
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public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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/**
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* Golden section.
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*/
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@ -47,15 +48,16 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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public double optimize(final UnivariateRealFunction f, final GoalType goalType,
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final double min, final double max, final double startValue)
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throws MaxIterationsExceededException, FunctionEvaluationException {
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return optimize(f, goalType, min, max);
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clearResult();
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return localMin(f, goalType, min, startValue, max,
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getRelativeAccuracy(), getAbsoluteAccuracy());
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}
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/** {@inheritDoc} */
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public double optimize(final UnivariateRealFunction f, final GoalType goalType,
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final double min, final double max)
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throws MaxIterationsExceededException, FunctionEvaluationException {
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clearResult();
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return localMin(f, goalType, min, max, relativeAccuracy, absoluteAccuracy);
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return optimize(f, goalType, min, max, min + GOLDEN_SECTION * (max - min));
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}
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/**
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@ -69,23 +71,41 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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* {@code eps} should be no smaller than <em>2 macheps</em> and preferable not
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* much less than <em>sqrt(macheps)</em>, where <em>macheps</em> is the relative
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* machine precision. {@code t} should be positive.
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* @param f the function to solve
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* @param f the function to solve.
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* @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE}
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* or {@link GoalType#MINIMIZE}
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* @param a Lower bound of the interval
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* @param b Higher bound of the interval
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* @param eps Relative accuracy
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* @param t Absolute accuracy
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* @return the point at which the function is minimal.
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* or {@link GoalType#MINIMIZE}.
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* @param lo Lower bound of the interval.
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* @param mid Point inside the interval {@code [lo, hi]}.
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* @param hi Higher bound of the interval.
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* @param eps Relative accuracy.
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* @param t Absolute accuracy.
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* @return the optimum point.
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* @throws MaxIterationsExceededException if the maximum iteration count
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* is exceeded.
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* @throws FunctionEvaluationException if an error occurs evaluating
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* the function.
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*/
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private double localMin(final UnivariateRealFunction f, final GoalType goalType,
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double a, double b, final double eps, final double t)
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private double localMin(UnivariateRealFunction f,
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GoalType goalType,
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double lo, double mid, double hi,
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double eps, double t)
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throws MaxIterationsExceededException, FunctionEvaluationException {
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double x = a + GOLDEN_SECTION * (b - a);
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if (eps <= 0) {
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throw new NotStrictlyPositiveException(eps);
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}
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if (t <= 0) {
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throw new NotStrictlyPositiveException(t);
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}
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double a, b;
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if (lo < hi) {
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a = lo;
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b = hi;
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} else {
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a = hi;
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b = lo;
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}
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double x = mid;
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double v = x;
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double w = x;
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double e = 0;
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@ -99,18 +119,18 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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int count = 0;
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while (count < maximalIterationCount) {
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double m = 0.5 * (a + b);
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double tol = eps * Math.abs(x) + t;
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double t2 = 2 * tol;
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final double tol1 = eps * Math.abs(x) + t;
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final double tol2 = 2 * tol1;
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// Check stopping criterion.
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if (Math.abs(x - m) > t2 - 0.5 * (b - a)) {
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if (Math.abs(x - m) > tol2 - 0.5 * (b - a)) {
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double p = 0;
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double q = 0;
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double r = 0;
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double d = 0;
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double u = 0;
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if (Math.abs(e) > tol) { // Fit parabola.
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if (Math.abs(e) > tol1) { // Fit parabola.
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r = (x - w) * (fx - fv);
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q = (x - v) * (fx - fw);
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p = (x - v) * q - (x - w) * r;
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@ -124,24 +144,53 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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r = e;
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e = d;
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}
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if (Math.abs(p) < Math.abs(0.5 * q * r) &&
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(p < q * (a - x)) && (p < q * (b - x))) { // Parabolic interpolation step.
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d = p / q;
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u = x + d;
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if (p > q * (a - x)
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&& p < q * (b - x)
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&& Math.abs(p) < Math.abs(0.5 * q * r)) {
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// Parabolic interpolation step.
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d = p / q;
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u = x + d;
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// f must not be evaluated too close to a or b.
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if (((u - a) < t2) || ((b - u) < t2)) {
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d = (x < m) ? tol : -tol;
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// f must not be evaluated too close to a or b.
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if (u - a < tol2
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|| b - u < tol2) {
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if (x <= m) {
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d = tol1;
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} else {
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d = -tol1;
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}
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}
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} else {
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// Golden section step.
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if (x < m) {
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e = b - x;
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} else {
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e = a - x;
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}
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d = GOLDEN_SECTION * e;
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}
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} else {
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// Golden section step.
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if (x < m) {
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e = b - x;
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} else {
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e = a - x;
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}
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} else { // Golden section step.
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e = ((x < m) ? b : a) - x;
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d = GOLDEN_SECTION * e;
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}
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// f must not be evaluated too close to a or b.
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u = x + ((Math.abs(d) > tol) ? d : ((d > 0) ? tol : -tol));
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// Update by at least "tol1".
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if (Math.abs(d) < tol1) {
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if (d >= 0) {
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u = x + tol1;
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} else {
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u = x - tol1;
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}
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} else {
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u = x + d;
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}
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double fu = computeObjectiveValue(f, u);
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if (goalType == GoalType.MAXIMIZE) {
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fu = -fu;
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@ -166,12 +215,15 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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} else {
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b = u;
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}
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if ((fu <= fw) || (w == x)) {
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if (fu <= fw
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|| w == x) {
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v = w;
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fv = fw;
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w = u;
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fw = fu;
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} else if ((fu <= fv) || (v == x) || (v == w)) {
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} else if (fu <= fv
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|| v == x
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|| v == w) {
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v = u;
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fv = fu;
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}
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@ -180,12 +232,8 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
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setResult(x, (goalType == GoalType.MAXIMIZE) ? -fx : fx, count);
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return x;
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}
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++count;
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}
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throw new MaxIterationsExceededException(maximalIterationCount);
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}
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}
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@ -52,6 +52,9 @@ The <action> type attribute can be add,update,fix,remove.
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If the output is not quite correct, check for invisible trailing spaces!
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-->
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<release version="2.2" date="TBD" description="TBD">
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<action dev="erans" type="fix" issue="MATH-395">
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Fixed several bugs in "BrentOptimizer".
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</action>
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<action dev="erans" type="fix" issue="MATH-393">
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Fixed inconsistency in return values in "MultiStartUnivariateRealOptimizer".
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</action>
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@ -19,7 +19,7 @@ package org.apache.commons.math.analysis;
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import org.apache.commons.math.FunctionEvaluationException;
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/**
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* Auxillary class for testing solvers.
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* Auxiliary class for testing solvers.
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*
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* @version $Revision$ $Date$
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*/
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@ -48,8 +48,8 @@ public class MultiStartUnivariateRealOptimizerTest {
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assertEquals(-1.0, f.value(optima[i]), 1.0e-10);
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assertEquals(f.value(optima[i]), optimaValues[i], 1.0e-10);
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}
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assertTrue(minimizer.getEvaluations() > 2900);
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assertTrue(minimizer.getEvaluations() < 3100);
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assertTrue(minimizer.getEvaluations() > 1500);
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assertTrue(minimizer.getEvaluations() < 1700);
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}
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@Test
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@ -58,8 +58,9 @@ public class MultiStartUnivariateRealOptimizerTest {
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// The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
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UnivariateRealFunction f = new QuinticFunction();
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UnivariateRealOptimizer underlying = new BrentOptimizer();
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underlying.setRelativeAccuracy(1e-15);
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JDKRandomGenerator g = new JDKRandomGenerator();
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g.setSeed(4312000053l);
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g.setSeed(4312000053L);
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MultiStartUnivariateRealOptimizer minimizer =
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new MultiStartUnivariateRealOptimizer(underlying, 5, g);
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minimizer.setAbsoluteAccuracy(10 * minimizer.getAbsoluteAccuracy());
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@ -82,9 +83,10 @@ public class MultiStartUnivariateRealOptimizerTest {
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fail("wrong exception caught");
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}
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assertEquals(-0.27195612846834, minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2), 1.0e-13);
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assertEquals(-0.27195612846834, minimizer.getResult(), 1.0e-13);
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assertEquals(-0.04433426954946, minimizer.getFunctionValue(), 1.0e-13);
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double result = minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2);
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assertEquals(-0.27195612525275803, result, 1.0e-13);
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assertEquals(-0.27195612525275803, minimizer.getResult(), 1.0e-13);
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assertEquals(-0.04433426954946637, minimizer.getFunctionValue(), 1.0e-13);
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double[] optima = minimizer.getOptima();
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double[] optimaValues = minimizer.getOptimaValues();
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@ -92,11 +94,9 @@ public class MultiStartUnivariateRealOptimizerTest {
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assertEquals(f.value(optima[i]), optimaValues[i], 1.0e-10);
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}
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assertTrue(minimizer.getEvaluations() >= 510);
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assertTrue(minimizer.getEvaluations() <= 530);
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assertTrue(minimizer.getIterationCount() >= 150);
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assertTrue(minimizer.getIterationCount() <= 170);
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assertTrue(minimizer.getEvaluations() >= 300);
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assertTrue(minimizer.getEvaluations() <= 420);
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assertTrue(minimizer.getIterationCount() >= 100);
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assertTrue(minimizer.getIterationCount() <= 140);
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}
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}
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@ -25,15 +25,16 @@ import org.apache.commons.math.MathException;
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import org.apache.commons.math.MaxIterationsExceededException;
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import org.apache.commons.math.analysis.QuinticFunction;
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import org.apache.commons.math.analysis.SinFunction;
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import org.apache.commons.math.analysis.SincFunction;
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import org.apache.commons.math.analysis.UnivariateRealFunction;
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import org.apache.commons.math.optimization.GoalType;
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import org.apache.commons.math.optimization.UnivariateRealOptimizer;
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import org.junit.Test;
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/**
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* @version $Revision$ $Date$
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* @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (Sat, 05 Sep 2009) $
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*/
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public final class BrentMinimizerTest {
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public final class BrentOptimizerTest {
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@Test
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public void testSinMin() throws MathException {
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@ -54,7 +55,7 @@ public final class BrentMinimizerTest {
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assertEquals(3 * Math.PI / 2, minimizer.optimize(f, GoalType.MINIMIZE, 1, 5), 70 * minimizer.getAbsoluteAccuracy());
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assertTrue(minimizer.getIterationCount() <= 50);
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assertTrue(minimizer.getEvaluations() <= 100);
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assertTrue(minimizer.getEvaluations() >= 90);
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assertTrue(minimizer.getEvaluations() >= 30);
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minimizer.setMaxEvaluations(50);
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try {
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minimizer.optimize(f, GoalType.MINIMIZE, 4, 5);
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@ -68,8 +69,7 @@ public final class BrentMinimizerTest {
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@Test
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public void testQuinticMin() throws MathException {
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// The quintic function has zeros at 0, +-0.5 and +-1.
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// The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
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// The function has local minima at -0.27195613 and 0.82221643.
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UnivariateRealFunction f = new QuinticFunction();
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UnivariateRealOptimizer minimizer = new BrentOptimizer();
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assertEquals(-0.27195613, minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2), 1.0e-8);
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@ -79,17 +79,48 @@ public final class BrentMinimizerTest {
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// search in a large interval
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assertEquals(-0.27195613, minimizer.optimize(f, GoalType.MINIMIZE, -1.0, 0.2), 1.0e-8);
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assertTrue(minimizer.getIterationCount() <= 50);
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}
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@Test
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public void testQuinticMinPythonComparison() throws MathException {
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// The function has local minima at -0.27195613 and 0.82221643.
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UnivariateRealFunction f = new QuinticFunction();
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UnivariateRealOptimizer minimizer = new BrentOptimizer();
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minimizer.setRelativeAccuracy(1e-12);
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minimizer.setAbsoluteAccuracy(1e-11);
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double result;
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int nIter, nEval;
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result = minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2, -0.25);
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nIter = minimizer.getIterationCount();
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nEval = minimizer.getEvaluations();
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// XXX Python: -0.27195612805911351 (instead of -0.2719561279558559).
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assertEquals(-0.2719561279558559, result, 1e-12);
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// XXX Python: 15 (instead of 18).
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assertEquals(18, nEval);
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// XXX Python: 11 (instead of 17).
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assertEquals(17, nIter);
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result = minimizer.optimize(f, GoalType.MINIMIZE, 0.7, 0.9, 0.8);
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nIter = minimizer.getIterationCount();
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nEval = minimizer.getEvaluations();
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// XXX Python: 0.82221643488363705 (instead of 0.8222164326561908).
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assertEquals(0.8222164326561908, result, 1e-12);
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// XXX Python: 25 (instead of 43).
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assertEquals(43, nEval);
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// XXX Python: 21 (instead of 24).
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assertEquals(24, nIter);
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}
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@Test
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public void testQuinticMax() throws MathException {
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// The quintic function has zeros at 0, +-0.5 and +-1.
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// The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
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// The function has a local maximum at 0.27195613.
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UnivariateRealFunction f = new QuinticFunction();
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UnivariateRealOptimizer minimizer = new BrentOptimizer();
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assertEquals(0.27195613, minimizer.optimize(f, GoalType.MAXIMIZE, 0.2, 0.3), 1.0e-8);
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minimizer.setMaximalIterationCount(30);
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minimizer.setMaximalIterationCount(20);
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try {
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minimizer.optimize(f, GoalType.MAXIMIZE, 0.2, 0.3);
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fail("an exception should have been thrown");
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@ -110,8 +141,6 @@ public final class BrentMinimizerTest {
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assertEquals(3 * Math.PI / 2, result, 70 * solver.getAbsoluteAccuracy());
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result = solver.optimize(f, GoalType.MINIMIZE, 4, 3 * Math.PI / 2);
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assertEquals(3 * Math.PI / 2, result, 70 * solver.getAbsoluteAccuracy());
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assertEquals(3 * Math.PI / 2, result, 80 * solver.getAbsoluteAccuracy());
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}
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}
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