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 * @deprecated As of 3.1 (to be removed in 4.0).
075 * @since 3.0
076 */
077
078@Deprecated
079public class MultivariateFunctionMappingAdapter implements MultivariateFunction {
080
081    /** Underlying bounded function. */
082    private final MultivariateFunction bounded;
083
084    /** Mapping functions. */
085    private final Mapper[] mappers;
086
087    /** Simple constructor.
088     * @param bounded bounded function
089     * @param lower lower bounds for each element of the input parameters array
090     * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
091     * unbounded values)
092     * @param upper upper bounds for each element of the input parameters array
093     * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
094     * unbounded values)
095     * @exception DimensionMismatchException if lower and upper bounds are not
096     * consistent, either according to dimension or to values
097     */
098    public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded,
099                                                  final double[] lower, final double[] upper) {
100
101        // safety checks
102        MathUtils.checkNotNull(lower);
103        MathUtils.checkNotNull(upper);
104        if (lower.length != upper.length) {
105            throw new DimensionMismatchException(lower.length, upper.length);
106        }
107        for (int i = 0; i < lower.length; ++i) {
108            // note the following test is written in such a way it also fails for NaN
109            if (!(upper[i] >= lower[i])) {
110                throw new NumberIsTooSmallException(upper[i], lower[i], true);
111            }
112        }
113
114        this.bounded = bounded;
115        this.mappers = new Mapper[lower.length];
116        for (int i = 0; i < mappers.length; ++i) {
117            if (Double.isInfinite(lower[i])) {
118                if (Double.isInfinite(upper[i])) {
119                    // element is unbounded, no transformation is needed
120                    mappers[i] = new NoBoundsMapper();
121                } else {
122                    // element is simple-bounded on the upper side
123                    mappers[i] = new UpperBoundMapper(upper[i]);
124                }
125            } else {
126                if (Double.isInfinite(upper[i])) {
127                    // element is simple-bounded on the lower side
128                    mappers[i] = new LowerBoundMapper(lower[i]);
129                } else {
130                    // element is double-bounded
131                    mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]);
132                }
133            }
134        }
135
136    }
137
138    /** Map an array from unbounded to bounded.
139     * @param point unbounded value
140     * @return bounded value
141     */
142    public double[] unboundedToBounded(double[] point) {
143
144        // map unbounded input point to bounded point
145        final double[] mapped = new double[mappers.length];
146        for (int i = 0; i < mappers.length; ++i) {
147            mapped[i] = mappers[i].unboundedToBounded(point[i]);
148        }
149
150        return mapped;
151
152    }
153
154    /** Map an array from bounded to unbounded.
155     * @param point bounded value
156     * @return unbounded value
157     */
158    public double[] boundedToUnbounded(double[] point) {
159
160        // map bounded input point to unbounded point
161        final double[] mapped = new double[mappers.length];
162        for (int i = 0; i < mappers.length; ++i) {
163            mapped[i] = mappers[i].boundedToUnbounded(point[i]);
164        }
165
166        return mapped;
167
168    }
169
170    /** Compute the underlying function value from an unbounded point.
171     * <p>
172     * This method simply bounds the unbounded point using the mappings
173     * set up at construction and calls the underlying function using
174     * the bounded point.
175     * </p>
176     * @param point unbounded value
177     * @return underlying function value
178     * @see #unboundedToBounded(double[])
179     */
180    public double value(double[] point) {
181        return bounded.value(unboundedToBounded(point));
182    }
183
184    /** Mapping interface. */
185    private interface Mapper {
186
187        /** Map a value from unbounded to bounded.
188         * @param y unbounded value
189         * @return bounded value
190         */
191        double unboundedToBounded(double y);
192
193        /** Map a value from bounded to unbounded.
194         * @param x bounded value
195         * @return unbounded value
196         */
197        double boundedToUnbounded(double x);
198
199    }
200
201    /** Local class for no bounds mapping. */
202    private static class NoBoundsMapper implements Mapper {
203
204        /** Simple constructor.
205         */
206        public NoBoundsMapper() {
207        }
208
209        /** {@inheritDoc} */
210        public double unboundedToBounded(final double y) {
211            return y;
212        }
213
214        /** {@inheritDoc} */
215        public double boundedToUnbounded(final double x) {
216            return x;
217        }
218
219    }
220
221    /** Local class for lower bounds mapping. */
222    private static class LowerBoundMapper implements Mapper {
223
224        /** Low bound. */
225        private final double lower;
226
227        /** Simple constructor.
228         * @param lower lower bound
229         */
230        public LowerBoundMapper(final double lower) {
231            this.lower = lower;
232        }
233
234        /** {@inheritDoc} */
235        public double unboundedToBounded(final double y) {
236            return lower + FastMath.exp(y);
237        }
238
239        /** {@inheritDoc} */
240        public double boundedToUnbounded(final double x) {
241            return FastMath.log(x - lower);
242        }
243
244    }
245
246    /** Local class for upper bounds mapping. */
247    private static class UpperBoundMapper implements Mapper {
248
249        /** Upper bound. */
250        private final double upper;
251
252        /** Simple constructor.
253         * @param upper upper bound
254         */
255        public UpperBoundMapper(final double upper) {
256            this.upper = upper;
257        }
258
259        /** {@inheritDoc} */
260        public double unboundedToBounded(final double y) {
261            return upper - FastMath.exp(-y);
262        }
263
264        /** {@inheritDoc} */
265        public double boundedToUnbounded(final double x) {
266            return -FastMath.log(upper - x);
267        }
268
269    }
270
271    /** Local class for lower and bounds mapping. */
272    private static class LowerUpperBoundMapper implements Mapper {
273
274        /** Function from unbounded to bounded. */
275        private final UnivariateFunction boundingFunction;
276
277        /** Function from bounded to unbounded. */
278        private final UnivariateFunction unboundingFunction;
279
280        /** Simple constructor.
281         * @param lower lower bound
282         * @param upper upper bound
283         */
284        public LowerUpperBoundMapper(final double lower, final double upper) {
285            boundingFunction   = new Sigmoid(lower, upper);
286            unboundingFunction = new Logit(lower, upper);
287        }
288
289        /** {@inheritDoc} */
290        public double unboundedToBounded(final double y) {
291            return boundingFunction.value(y);
292        }
293
294        /** {@inheritDoc} */
295        public double boundedToUnbounded(final double x) {
296            return unboundingFunction.value(x);
297        }
298
299    }
300
301}