001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math3.optimization.direct;
019
020 import org.apache.commons.math3.util.FastMath;
021 import org.apache.commons.math3.util.MathArrays;
022 import org.apache.commons.math3.analysis.UnivariateFunction;
023 import org.apache.commons.math3.analysis.MultivariateFunction;
024 import org.apache.commons.math3.exception.NumberIsTooSmallException;
025 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
026 import org.apache.commons.math3.optimization.GoalType;
027 import org.apache.commons.math3.optimization.PointValuePair;
028 import org.apache.commons.math3.optimization.ConvergenceChecker;
029 import org.apache.commons.math3.optimization.MultivariateOptimizer;
030 import org.apache.commons.math3.optimization.univariate.BracketFinder;
031 import org.apache.commons.math3.optimization.univariate.BrentOptimizer;
032 import org.apache.commons.math3.optimization.univariate.UnivariatePointValuePair;
033 import org.apache.commons.math3.optimization.univariate.SimpleUnivariateValueChecker;
034
035 /**
036 * Powell algorithm.
037 * This code is translated and adapted from the Python version of this
038 * algorithm (as implemented in module {@code optimize.py} v0.5 of
039 * <em>SciPy</em>).
040 * <br/>
041 * The default stopping criterion is based on the differences of the
042 * function value between two successive iterations. It is however possible
043 * to define a custom convergence checker that might terminate the algorithm
044 * earlier.
045 * <br/>
046 * The internal line search optimizer is a {@link BrentOptimizer} with a
047 * convergence checker set to {@link SimpleUnivariateValueChecker}.
048 *
049 * @version $Id: PowellOptimizer.java 1462503 2013-03-29 15:48:27Z luc $
050 * @deprecated As of 3.1 (to be removed in 4.0).
051 * @since 2.2
052 */
053 @Deprecated
054 public class PowellOptimizer
055 extends BaseAbstractMultivariateOptimizer<MultivariateFunction>
056 implements MultivariateOptimizer {
057 /**
058 * Minimum relative tolerance.
059 */
060 private static final double MIN_RELATIVE_TOLERANCE = 2 * FastMath.ulp(1d);
061 /**
062 * Relative threshold.
063 */
064 private final double relativeThreshold;
065 /**
066 * Absolute threshold.
067 */
068 private final double absoluteThreshold;
069 /**
070 * Line search.
071 */
072 private final LineSearch line;
073
074 /**
075 * This constructor allows to specify a user-defined convergence checker,
076 * in addition to the parameters that control the default convergence
077 * checking procedure.
078 * <br/>
079 * The internal line search tolerances are set to the square-root of their
080 * corresponding value in the multivariate optimizer.
081 *
082 * @param rel Relative threshold.
083 * @param abs Absolute threshold.
084 * @param checker Convergence checker.
085 * @throws NotStrictlyPositiveException if {@code abs <= 0}.
086 * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
087 */
088 public PowellOptimizer(double rel,
089 double abs,
090 ConvergenceChecker<PointValuePair> checker) {
091 this(rel, abs, FastMath.sqrt(rel), FastMath.sqrt(abs), checker);
092 }
093
094 /**
095 * This constructor allows to specify a user-defined convergence checker,
096 * in addition to the parameters that control the default convergence
097 * checking procedure and the line search tolerances.
098 *
099 * @param rel Relative threshold for this optimizer.
100 * @param abs Absolute threshold for this optimizer.
101 * @param lineRel Relative threshold for the internal line search optimizer.
102 * @param lineAbs Absolute threshold for the internal line search optimizer.
103 * @param checker Convergence checker.
104 * @throws NotStrictlyPositiveException if {@code abs <= 0}.
105 * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
106 */
107 public PowellOptimizer(double rel,
108 double abs,
109 double lineRel,
110 double lineAbs,
111 ConvergenceChecker<PointValuePair> checker) {
112 super(checker);
113
114 if (rel < MIN_RELATIVE_TOLERANCE) {
115 throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
116 }
117 if (abs <= 0) {
118 throw new NotStrictlyPositiveException(abs);
119 }
120 relativeThreshold = rel;
121 absoluteThreshold = abs;
122
123 // Create the line search optimizer.
124 line = new LineSearch(lineRel,
125 lineAbs);
126 }
127
128 /**
129 * The parameters control the default convergence checking procedure.
130 * <br/>
131 * The internal line search tolerances are set to the square-root of their
132 * corresponding value in the multivariate optimizer.
133 *
134 * @param rel Relative threshold.
135 * @param abs Absolute threshold.
136 * @throws NotStrictlyPositiveException if {@code abs <= 0}.
137 * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
138 */
139 public PowellOptimizer(double rel,
140 double abs) {
141 this(rel, abs, null);
142 }
143
144 /**
145 * Builds an instance with the default convergence checking procedure.
146 *
147 * @param rel Relative threshold.
148 * @param abs Absolute threshold.
149 * @param lineRel Relative threshold for the internal line search optimizer.
150 * @param lineAbs Absolute threshold for the internal line search optimizer.
151 * @throws NotStrictlyPositiveException if {@code abs <= 0}.
152 * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
153 * @since 3.1
154 */
155 public PowellOptimizer(double rel,
156 double abs,
157 double lineRel,
158 double lineAbs) {
159 this(rel, abs, lineRel, lineAbs, null);
160 }
161
162 /** {@inheritDoc} */
163 @Override
164 protected PointValuePair doOptimize() {
165 final GoalType goal = getGoalType();
166 final double[] guess = getStartPoint();
167 final int n = guess.length;
168
169 final double[][] direc = new double[n][n];
170 for (int i = 0; i < n; i++) {
171 direc[i][i] = 1;
172 }
173
174 final ConvergenceChecker<PointValuePair> checker
175 = getConvergenceChecker();
176
177 double[] x = guess;
178 double fVal = computeObjectiveValue(x);
179 double[] x1 = x.clone();
180 int iter = 0;
181 while (true) {
182 ++iter;
183
184 double fX = fVal;
185 double fX2 = 0;
186 double delta = 0;
187 int bigInd = 0;
188 double alphaMin = 0;
189
190 for (int i = 0; i < n; i++) {
191 final double[] d = MathArrays.copyOf(direc[i]);
192
193 fX2 = fVal;
194
195 final UnivariatePointValuePair optimum = line.search(x, d);
196 fVal = optimum.getValue();
197 alphaMin = optimum.getPoint();
198 final double[][] result = newPointAndDirection(x, d, alphaMin);
199 x = result[0];
200
201 if ((fX2 - fVal) > delta) {
202 delta = fX2 - fVal;
203 bigInd = i;
204 }
205 }
206
207 // Default convergence check.
208 boolean stop = 2 * (fX - fVal) <=
209 (relativeThreshold * (FastMath.abs(fX) + FastMath.abs(fVal)) +
210 absoluteThreshold);
211
212 final PointValuePair previous = new PointValuePair(x1, fX);
213 final PointValuePair current = new PointValuePair(x, fVal);
214 if (!stop && checker != null) {
215 stop = checker.converged(iter, previous, current);
216 }
217 if (stop) {
218 if (goal == GoalType.MINIMIZE) {
219 return (fVal < fX) ? current : previous;
220 } else {
221 return (fVal > fX) ? current : previous;
222 }
223 }
224
225 final double[] d = new double[n];
226 final double[] x2 = new double[n];
227 for (int i = 0; i < n; i++) {
228 d[i] = x[i] - x1[i];
229 x2[i] = 2 * x[i] - x1[i];
230 }
231
232 x1 = x.clone();
233 fX2 = computeObjectiveValue(x2);
234
235 if (fX > fX2) {
236 double t = 2 * (fX + fX2 - 2 * fVal);
237 double temp = fX - fVal - delta;
238 t *= temp * temp;
239 temp = fX - fX2;
240 t -= delta * temp * temp;
241
242 if (t < 0.0) {
243 final UnivariatePointValuePair optimum = line.search(x, d);
244 fVal = optimum.getValue();
245 alphaMin = optimum.getPoint();
246 final double[][] result = newPointAndDirection(x, d, alphaMin);
247 x = result[0];
248
249 final int lastInd = n - 1;
250 direc[bigInd] = direc[lastInd];
251 direc[lastInd] = result[1];
252 }
253 }
254 }
255 }
256
257 /**
258 * Compute a new point (in the original space) and a new direction
259 * vector, resulting from the line search.
260 *
261 * @param p Point used in the line search.
262 * @param d Direction used in the line search.
263 * @param optimum Optimum found by the line search.
264 * @return a 2-element array containing the new point (at index 0) and
265 * the new direction (at index 1).
266 */
267 private double[][] newPointAndDirection(double[] p,
268 double[] d,
269 double optimum) {
270 final int n = p.length;
271 final double[] nP = new double[n];
272 final double[] nD = new double[n];
273 for (int i = 0; i < n; i++) {
274 nD[i] = d[i] * optimum;
275 nP[i] = p[i] + nD[i];
276 }
277
278 final double[][] result = new double[2][];
279 result[0] = nP;
280 result[1] = nD;
281
282 return result;
283 }
284
285 /**
286 * Class for finding the minimum of the objective function along a given
287 * direction.
288 */
289 private class LineSearch extends BrentOptimizer {
290 /**
291 * Value that will pass the precondition check for {@link BrentOptimizer}
292 * but will not pass the convergence check, so that the custom checker
293 * will always decide when to stop the line search.
294 */
295 private static final double REL_TOL_UNUSED = 1e-15;
296 /**
297 * Value that will pass the precondition check for {@link BrentOptimizer}
298 * but will not pass the convergence check, so that the custom checker
299 * will always decide when to stop the line search.
300 */
301 private static final double ABS_TOL_UNUSED = Double.MIN_VALUE;
302 /**
303 * Automatic bracketing.
304 */
305 private final BracketFinder bracket = new BracketFinder();
306
307 /**
308 * The "BrentOptimizer" default stopping criterion uses the tolerances
309 * to check the domain (point) values, not the function values.
310 * We thus create a custom checker to use function values.
311 *
312 * @param rel Relative threshold.
313 * @param abs Absolute threshold.
314 */
315 LineSearch(double rel,
316 double abs) {
317 super(REL_TOL_UNUSED,
318 ABS_TOL_UNUSED,
319 new SimpleUnivariateValueChecker(rel, abs));
320 }
321
322 /**
323 * Find the minimum of the function {@code f(p + alpha * d)}.
324 *
325 * @param p Starting point.
326 * @param d Search direction.
327 * @return the optimum.
328 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
329 * if the number of evaluations is exceeded.
330 */
331 public UnivariatePointValuePair search(final double[] p, final double[] d) {
332 final int n = p.length;
333 final UnivariateFunction f = new UnivariateFunction() {
334 public double value(double alpha) {
335 final double[] x = new double[n];
336 for (int i = 0; i < n; i++) {
337 x[i] = p[i] + alpha * d[i];
338 }
339 final double obj = PowellOptimizer.this.computeObjectiveValue(x);
340 return obj;
341 }
342 };
343
344 final GoalType goal = PowellOptimizer.this.getGoalType();
345 bracket.search(f, goal, 0, 1);
346 // Passing "MAX_VALUE" as a dummy value because it is the enclosing
347 // class that counts the number of evaluations (and will eventually
348 // generate the exception).
349 return optimize(Integer.MAX_VALUE, f, goal,
350 bracket.getLo(), bracket.getHi(), bracket.getMid());
351 }
352 }
353 }