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* 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.
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package org.apache.commons.math3.optim.nonlinear.scalar.noderiv;
import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.optim.ConvergenceChecker;
import org.apache.commons.math3.optim.PointValuePair;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.nonlinear.scalar.LineSearch;
import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer;
import org.apache.commons.math3.optim.univariate.UnivariatePointValuePair;
import org.apache.commons.math3.util.Cloner;
import org.apache.commons.math3.util.GWTMath;
import org.apache.commons.math3.util.MathArrays;
/**
* Powell's algorithm.
* This code is translated and adapted from the Python version of this
* algorithm (as implemented in module {@code optimize.py} v0.5 of
* <em>SciPy</em>).
* <br/>
* The default stopping criterion is based on the differences of the
* function value between two successive iterations. It is however possible
* to define a custom convergence checker that might terminate the algorithm
* earlier.
* <br/>
* Line search is performed by the {@link LineSearch} class.
* <br/>
* Constraints are not supported: the call to
* {@link #optimize(OptimizationData[]) optimize} will throw
* {@link MathUnsupportedOperationException} if bounds are passed to it.
* In order to impose simple constraints, the objective function must be
* wrapped in an adapter like
* {@link org.apache.commons.math3.optim.nonlinear.scalar.MultivariateFunctionMappingAdapter
* MultivariateFunctionMappingAdapter} or
* {@link org.apache.commons.math3.optim.nonlinear.scalar.MultivariateFunctionPenaltyAdapter
* MultivariateFunctionPenaltyAdapter}.
*
* @since 2.2
*/
public class PowellOptimizer
extends MultivariateOptimizer {
/**
* Minimum relative tolerance.
*/
private static final double MIN_RELATIVE_TOLERANCE = 2 * GWTMath.ulp(1d);
/**
* Relative threshold.
*/
private final double relativeThreshold;
/**
* Absolute threshold.
*/
private final double absoluteThreshold;
/**
* Line search.
*/
private final LineSearch line;
/**
* This constructor allows to specify a user-defined convergence checker,
* in addition to the parameters that control the default convergence
* checking procedure.
* <br/>
* The internal line search tolerances are set to the square-root of their
* corresponding value in the multivariate optimizer.
*
* @param rel Relative threshold.
* @param abs Absolute threshold.
* @param checker Convergence checker.
* @throws NotStrictlyPositiveException if {@code abs <= 0}.
* @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
*/
public PowellOptimizer(double rel,
double abs,
ConvergenceChecker<PointValuePair> checker) {
this(rel, abs, Math.sqrt(rel), Math.sqrt(abs), checker);
}
/**
* This constructor allows to specify a user-defined convergence checker,
* in addition to the parameters that control the default convergence
* checking procedure and the line search tolerances.
*
* @param rel Relative threshold for this optimizer.
* @param abs Absolute threshold for this optimizer.
* @param lineRel Relative threshold for the internal line search optimizer.
* @param lineAbs Absolute threshold for the internal line search optimizer.
* @param checker Convergence checker.
* @throws NotStrictlyPositiveException if {@code abs <= 0}.
* @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
*/
public PowellOptimizer(double rel,
double abs,
double lineRel,
double lineAbs,
ConvergenceChecker<PointValuePair> 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;
// Create the line search optimizer.
line = new LineSearch(this,
lineRel,
lineAbs,
1d);
}
/**
* The parameters control the default convergence checking procedure.
* <br/>
* The internal line search tolerances are set to the square-root of their
* corresponding value in the multivariate optimizer.
*
* @param rel Relative threshold.
* @param abs Absolute threshold.
* @throws NotStrictlyPositiveException if {@code abs <= 0}.
* @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
*/
public PowellOptimizer(double rel,
double abs) {
this(rel, abs, null);
}
/**
* Builds an instance with the default convergence checking procedure.
*
* @param rel Relative threshold.
* @param abs Absolute threshold.
* @param lineRel Relative threshold for the internal line search optimizer.
* @param lineAbs Absolute threshold for the internal line search optimizer.
* @throws NotStrictlyPositiveException if {@code abs <= 0}.
* @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
*/
public PowellOptimizer(double rel,
double abs,
double lineRel,
double lineAbs) {
this(rel, abs, lineRel, lineAbs, null);
}
/** {@inheritDoc} */
@Override
protected PointValuePair doOptimize() {
checkParameters();
final GoalType goal = getGoalType();
final double[] guess = getStartPoint();
final int n = guess.length;
final double[][] direc = new double[n][n];
for (int i = 0; i < n; i++) {
direc[i][i] = 1;
}
final ConvergenceChecker<PointValuePair> checker
= getConvergenceChecker();
double[] x = guess;
double fVal = computeObjectiveValue(x);
double[] x1 = Cloner.clone(x);
while (true) {
incrementIterationCount();
double fX = fVal;
double fX2 = 0;
double delta = 0;
int bigInd = 0;
double alphaMin = 0;
for (int i = 0; i < n; i++) {
final double[] d = MathArrays.copyOf(direc[i]);
fX2 = fVal;
final UnivariatePointValuePair optimum = line.search(x, d);
fVal = optimum.getValue();
alphaMin = optimum.getPoint();
final double[][] result = newPointAndDirection(x, d, alphaMin);
x = result[0];
if ((fX2 - fVal) > delta) {
delta = fX2 - fVal;
bigInd = i;
}
}
// Default convergence check.
boolean stop = 2 * (fX - fVal) <=
(relativeThreshold * (Math.abs(fX) + Math.abs(fVal)) +
absoluteThreshold);
final PointValuePair previous = new PointValuePair(x1, fX);
final PointValuePair current = new PointValuePair(x, fVal);
if (!stop && checker != null) { // User-defined stopping criteria.
stop = checker.converged(getIterations(), previous, current);
}
if (stop) {
if (goal == GoalType.MINIMIZE) {
return (fVal < fX) ? current : previous;
} else {
return (fVal > fX) ? current : previous;
}
}
final double[] d = new double[n];
final double[] x2 = new double[n];
for (int i = 0; i < n; i++) {
d[i] = x[i] - x1[i];
x2[i] = 2 * x[i] - x1[i];
}
x1 = Cloner.clone(x);
fX2 = computeObjectiveValue(x2);
if (fX > fX2) {
double t = 2 * (fX + fX2 - 2 * fVal);
double temp = fX - fVal - delta;
t *= temp * temp;
temp = fX - fX2;
t -= delta * temp * temp;
if (t < 0.0) {
final UnivariatePointValuePair optimum = line.search(x, d);
fVal = optimum.getValue();
alphaMin = optimum.getPoint();
final double[][] result = newPointAndDirection(x, d, alphaMin);
x = result[0];
final int lastInd = n - 1;
direc[bigInd] = direc[lastInd];
direc[lastInd] = result[1];
}
}
}
}
/**
* Compute a new point (in the original space) and a new direction
* vector, resulting from the line search.
*
* @param p Point used in the line search.
* @param d Direction used in the line search.
* @param optimum Optimum found by the line search.
* @return a 2-element array containing the new point (at index 0) and
* the new direction (at index 1).
*/
private double[][] newPointAndDirection(double[] p,
double[] d,
double optimum) {
final int n = p.length;
final double[] nP = new double[n];
final double[] nD = new double[n];
for (int i = 0; i < n; i++) {
nD[i] = d[i] * optimum;
nP[i] = p[i] + nD[i];
}
final double[][] result = new double[2][];
result[0] = nP;
result[1] = nD;
return result;
}
/**
* @throws MathUnsupportedOperationException if bounds were passed to the
* {@link #optimize(OptimizationData[]) optimize} method.
*/
private void checkParameters() {
if (getLowerBound() != null ||
getUpperBound() != null) {
throw new MathUnsupportedOperationException(LocalizedFormats.CONSTRAINT);
}
}
}