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
018package org.apache.commons.math3.optimization.direct;
019
020import org.apache.commons.math3.analysis.MultivariateFunction;
021import org.apache.commons.math3.analysis.UnivariateFunction;
022import org.apache.commons.math3.analysis.function.Logit;
023import org.apache.commons.math3.analysis.function.Sigmoid;
024import org.apache.commons.math3.exception.DimensionMismatchException;
025import org.apache.commons.math3.exception.NumberIsTooSmallException;
026import org.apache.commons.math3.util.FastMath;
027import org.apache.commons.math3.util.MathUtils;
028
029/**
030 * <p>Adapter for mapping bounded {@link MultivariateFunction} to unbounded ones.</p>
031 *
032 * <p>
033 * This adapter can be used to wrap functions subject to simple bounds on
034 * parameters so they can be used by optimizers that do <em>not</em> directly
035 * support simple bounds.
036 * </p>
037 * <p>
038 * The principle is that the user function that will be wrapped will see its
039 * parameters bounded as required, i.e when its {@code value} method is called
040 * with argument array {@code point}, the elements array will fulfill requirement
041 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
042 * may be unbounded or bounded only on one side if the corresponding bound is
043 * set to an infinite value. The optimizer will not manage the user function by
044 * itself, but it will handle this adapter and it is this adapter that will take
045 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
046 * be called by the optimizer with unbound parameters, and the adapter will map
047 * the unbounded value to the bounded range using appropriate functions like
048 * {@link Sigmoid} for double bounded elements for example.
049 * </p>
050 * <p>
051 * As the optimizer sees only unbounded parameters, it should be noted that the
052 * start point or simplex expected by the optimizer should be unbounded, so the
053 * user is responsible for converting his bounded point to unbounded by calling
054 * {@link #boundedToUnbounded(double[])} before providing them to the optimizer.
055 * For the same reason, the point returned by the {@link
056 * org.apache.commons.math3.optimization.BaseMultivariateOptimizer#optimize(int,
057 * MultivariateFunction, org.apache.commons.math3.optimization.GoalType, double[])}
058 * method is unbounded. So to convert this point to bounded, users must call
059 * {@link #unboundedToBounded(double[])} by themselves!</p>
060 * <p>
061 * This adapter is only a poor man solution to simple bounds optimization constraints
062 * that can be used with simple optimizers like {@link SimplexOptimizer} with {@link
063 * NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use
064 * an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or
065 * {@link BOBYQAOptimizer}. One caveat of this poor man solution is that behavior near
066 * the bounds may be numerically unstable as bounds are mapped from infinite values.
067 * Another caveat is that convergence values are evaluated by the optimizer with respect
068 * to unbounded variables, so there will be scales differences when converted to bounded
069 * variables.
070 * </p>
071 *
072 * @see MultivariateFunctionPenaltyAdapter
073 *
074 * @version $Id: MultivariateFunctionMappingAdapter.java 1422230 2012-12-15 12:11:13Z erans $
075 * @deprecated As of 3.1 (to be removed in 4.0).
076 * @since 3.0
077 */
078
079@Deprecated
080public class MultivariateFunctionMappingAdapter implements MultivariateFunction {
081
082    /** Underlying bounded function. */
083    private final MultivariateFunction bounded;
084
085    /** Mapping functions. */
086    private final Mapper[] mappers;
087
088    /** Simple constructor.
089     * @param bounded bounded function
090     * @param lower lower bounds for each element of the input parameters array
091     * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
092     * unbounded values)
093     * @param upper upper bounds for each element of the input parameters array
094     * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
095     * unbounded values)
096     * @exception DimensionMismatchException if lower and upper bounds are not
097     * consistent, either according to dimension or to values
098     */
099    public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded,
100                                                  final double[] lower, final double[] upper) {
101
102        // safety checks
103        MathUtils.checkNotNull(lower);
104        MathUtils.checkNotNull(upper);
105        if (lower.length != upper.length) {
106            throw new DimensionMismatchException(lower.length, upper.length);
107        }
108        for (int i = 0; i < lower.length; ++i) {
109            // note the following test is written in such a way it also fails for NaN
110            if (!(upper[i] >= lower[i])) {
111                throw new NumberIsTooSmallException(upper[i], lower[i], true);
112            }
113        }
114
115        this.bounded = bounded;
116        this.mappers = new Mapper[lower.length];
117        for (int i = 0; i < mappers.length; ++i) {
118            if (Double.isInfinite(lower[i])) {
119                if (Double.isInfinite(upper[i])) {
120                    // element is unbounded, no transformation is needed
121                    mappers[i] = new NoBoundsMapper();
122                } else {
123                    // element is simple-bounded on the upper side
124                    mappers[i] = new UpperBoundMapper(upper[i]);
125                }
126            } else {
127                if (Double.isInfinite(upper[i])) {
128                    // element is simple-bounded on the lower side
129                    mappers[i] = new LowerBoundMapper(lower[i]);
130                } else {
131                    // element is double-bounded
132                    mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]);
133                }
134            }
135        }
136
137    }
138
139    /** Map an array from unbounded to bounded.
140     * @param point unbounded value
141     * @return bounded value
142     */
143    public double[] unboundedToBounded(double[] point) {
144
145        // map unbounded input point to bounded point
146        final double[] mapped = new double[mappers.length];
147        for (int i = 0; i < mappers.length; ++i) {
148            mapped[i] = mappers[i].unboundedToBounded(point[i]);
149        }
150
151        return mapped;
152
153    }
154
155    /** Map an array from bounded to unbounded.
156     * @param point bounded value
157     * @return unbounded value
158     */
159    public double[] boundedToUnbounded(double[] point) {
160
161        // map bounded input point to unbounded point
162        final double[] mapped = new double[mappers.length];
163        for (int i = 0; i < mappers.length; ++i) {
164            mapped[i] = mappers[i].boundedToUnbounded(point[i]);
165        }
166
167        return mapped;
168
169    }
170
171    /** Compute the underlying function value from an unbounded point.
172     * <p>
173     * This method simply bounds the unbounded point using the mappings
174     * set up at construction and calls the underlying function using
175     * the bounded point.
176     * </p>
177     * @param point unbounded value
178     * @return underlying function value
179     * @see #unboundedToBounded(double[])
180     */
181    public double value(double[] point) {
182        return bounded.value(unboundedToBounded(point));
183    }
184
185    /** Mapping interface. */
186    private interface Mapper {
187
188        /** Map a value from unbounded to bounded.
189         * @param y unbounded value
190         * @return bounded value
191         */
192        double unboundedToBounded(double y);
193
194        /** Map a value from bounded to unbounded.
195         * @param x bounded value
196         * @return unbounded value
197         */
198        double boundedToUnbounded(double x);
199
200    }
201
202    /** Local class for no bounds mapping. */
203    private static class NoBoundsMapper implements Mapper {
204
205        /** Simple constructor.
206         */
207        public NoBoundsMapper() {
208        }
209
210        /** {@inheritDoc} */
211        public double unboundedToBounded(final double y) {
212            return y;
213        }
214
215        /** {@inheritDoc} */
216        public double boundedToUnbounded(final double x) {
217            return x;
218        }
219
220    }
221
222    /** Local class for lower bounds mapping. */
223    private static class LowerBoundMapper implements Mapper {
224
225        /** Low bound. */
226        private final double lower;
227
228        /** Simple constructor.
229         * @param lower lower bound
230         */
231        public LowerBoundMapper(final double lower) {
232            this.lower = lower;
233        }
234
235        /** {@inheritDoc} */
236        public double unboundedToBounded(final double y) {
237            return lower + FastMath.exp(y);
238        }
239
240        /** {@inheritDoc} */
241        public double boundedToUnbounded(final double x) {
242            return FastMath.log(x - lower);
243        }
244
245    }
246
247    /** Local class for upper bounds mapping. */
248    private static class UpperBoundMapper implements Mapper {
249
250        /** Upper bound. */
251        private final double upper;
252
253        /** Simple constructor.
254         * @param upper upper bound
255         */
256        public UpperBoundMapper(final double upper) {
257            this.upper = upper;
258        }
259
260        /** {@inheritDoc} */
261        public double unboundedToBounded(final double y) {
262            return upper - FastMath.exp(-y);
263        }
264
265        /** {@inheritDoc} */
266        public double boundedToUnbounded(final double x) {
267            return -FastMath.log(upper - x);
268        }
269
270    }
271
272    /** Local class for lower and bounds mapping. */
273    private static class LowerUpperBoundMapper implements Mapper {
274
275        /** Function from unbounded to bounded. */
276        private final UnivariateFunction boundingFunction;
277
278        /** Function from bounded to unbounded. */
279        private final UnivariateFunction unboundingFunction;
280
281        /** Simple constructor.
282         * @param lower lower bound
283         * @param upper upper bound
284         */
285        public LowerUpperBoundMapper(final double lower, final double upper) {
286            boundingFunction   = new Sigmoid(lower, upper);
287            unboundingFunction = new Logit(lower, upper);
288        }
289
290        /** {@inheritDoc} */
291        public double unboundedToBounded(final double y) {
292            return boundingFunction.value(y);
293        }
294
295        /** {@inheritDoc} */
296        public double boundedToUnbounded(final double x) {
297            return unboundingFunction.value(x);
298        }
299
300    }
301
302}