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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.math3.optim.nonlinear.scalar;
18  
19  import org.apache.commons.math3.analysis.MultivariateFunction;
20  import org.apache.commons.math3.analysis.UnivariateFunction;
21  import org.apache.commons.math3.analysis.function.Logit;
22  import org.apache.commons.math3.analysis.function.Sigmoid;
23  import org.apache.commons.math3.exception.DimensionMismatchException;
24  import org.apache.commons.math3.exception.NumberIsTooSmallException;
25  import org.apache.commons.math3.util.FastMath;
26  import org.apache.commons.math3.util.MathUtils;
27  
28  /**
29   * <p>Adapter for mapping bounded {@link MultivariateFunction} to unbounded ones.</p>
30   *
31   * <p>
32   * This adapter can be used to wrap functions subject to simple bounds on
33   * parameters so they can be used by optimizers that do <em>not</em> directly
34   * support simple bounds.
35   * </p>
36   * <p>
37   * The principle is that the user function that will be wrapped will see its
38   * parameters bounded as required, i.e when its {@code value} method is called
39   * with argument array {@code point}, the elements array will fulfill requirement
40   * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
41   * may be unbounded or bounded only on one side if the corresponding bound is
42   * set to an infinite value. The optimizer will not manage the user function by
43   * itself, but it will handle this adapter and it is this adapter that will take
44   * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
45   * be called by the optimizer with unbound parameters, and the adapter will map
46   * the unbounded value to the bounded range using appropriate functions like
47   * {@link Sigmoid} for double bounded elements for example.
48   * </p>
49   * <p>
50   * As the optimizer sees only unbounded parameters, it should be noted that the
51   * start point or simplex expected by the optimizer should be unbounded, so the
52   * user is responsible for converting his bounded point to unbounded by calling
53   * {@link #boundedToUnbounded(double[])} before providing them to the optimizer.
54   * For the same reason, the point returned by the {@link
55   * org.apache.commons.math3.optimization.BaseMultivariateOptimizer#optimize(int,
56   * MultivariateFunction, org.apache.commons.math3.optimization.GoalType, double[])}
57   * method is unbounded. So to convert this point to bounded, users must call
58   * {@link #unboundedToBounded(double[])} by themselves!</p>
59   * <p>
60   * This adapter is only a poor man solution to simple bounds optimization constraints
61   * that can be used with simple optimizers like
62   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
63   * SimplexOptimizer}.
64   * A better solution is to use an optimizer that directly supports simple bounds like
65   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer
66   * CMAESOptimizer} or
67   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
68   * BOBYQAOptimizer}.
69   * One caveat of this poor-man's solution is that behavior near the bounds may be
70   * numerically unstable as bounds are mapped from infinite values.
71   * Another caveat is that convergence values are evaluated by the optimizer with
72   * respect to unbounded variables, so there will be scales differences when
73   * converted to bounded variables.
74   * </p>
75   *
76   * @see MultivariateFunctionPenaltyAdapter
77   *
78   * @since 3.0
79   */
80  public class MultivariateFunctionMappingAdapter
81      implements MultivariateFunction {
82      /** Underlying bounded function. */
83      private final MultivariateFunction bounded;
84      /** Mapping functions. */
85      private final Mapper[] mappers;
86  
87      /** Simple constructor.
88       * @param bounded bounded function
89       * @param lower lower bounds for each element of the input parameters array
90       * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
91       * unbounded values)
92       * @param upper upper bounds for each element of the input parameters array
93       * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
94       * unbounded values)
95       * @exception DimensionMismatchException if lower and upper bounds are not
96       * consistent, either according to dimension or to values
97       */
98      public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded,
99                                                final double[] lower, final double[] upper) {
100         // safety checks
101         MathUtils.checkNotNull(lower);
102         MathUtils.checkNotNull(upper);
103         if (lower.length != upper.length) {
104             throw new DimensionMismatchException(lower.length, upper.length);
105         }
106         for (int i = 0; i < lower.length; ++i) {
107             // note the following test is written in such a way it also fails for NaN
108             if (!(upper[i] >= lower[i])) {
109                 throw new NumberIsTooSmallException(upper[i], lower[i], true);
110             }
111         }
112 
113         this.bounded = bounded;
114         this.mappers = new Mapper[lower.length];
115         for (int i = 0; i < mappers.length; ++i) {
116             if (Double.isInfinite(lower[i])) {
117                 if (Double.isInfinite(upper[i])) {
118                     // element is unbounded, no transformation is needed
119                     mappers[i] = new NoBoundsMapper();
120                 } else {
121                     // element is simple-bounded on the upper side
122                     mappers[i] = new UpperBoundMapper(upper[i]);
123                 }
124             } else {
125                 if (Double.isInfinite(upper[i])) {
126                     // element is simple-bounded on the lower side
127                     mappers[i] = new LowerBoundMapper(lower[i]);
128                 } else {
129                     // element is double-bounded
130                     mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]);
131                 }
132             }
133         }
134     }
135 
136     /**
137      * Maps an array from unbounded to bounded.
138      *
139      * @param point Unbounded values.
140      * @return the bounded values.
141      */
142     public double[] unboundedToBounded(double[] point) {
143         // Map unbounded input point to bounded point.
144         final double[] mapped = new double[mappers.length];
145         for (int i = 0; i < mappers.length; ++i) {
146             mapped[i] = mappers[i].unboundedToBounded(point[i]);
147         }
148 
149         return mapped;
150     }
151 
152     /**
153      * Maps an array from bounded to unbounded.
154      *
155      * @param point Bounded values.
156      * @return the unbounded values.
157      */
158     public double[] boundedToUnbounded(double[] point) {
159         // Map bounded input point to unbounded point.
160         final double[] mapped = new double[mappers.length];
161         for (int i = 0; i < mappers.length; ++i) {
162             mapped[i] = mappers[i].boundedToUnbounded(point[i]);
163         }
164 
165         return mapped;
166     }
167 
168     /**
169      * Compute the underlying function value from an unbounded point.
170      * <p>
171      * This method simply bounds the unbounded point using the mappings
172      * set up at construction and calls the underlying function using
173      * the bounded point.
174      * </p>
175      * @param point unbounded value
176      * @return underlying function value
177      * @see #unboundedToBounded(double[])
178      */
179     public double value(double[] point) {
180         return bounded.value(unboundedToBounded(point));
181     }
182 
183     /** Mapping interface. */
184     private interface Mapper {
185         /**
186          * Maps a value from unbounded to bounded.
187          *
188          * @param y Unbounded value.
189          * @return the bounded value.
190          */
191         double unboundedToBounded(double y);
192 
193         /**
194          * Maps a value from bounded to unbounded.
195          *
196          * @param x Bounded value.
197          * @return the unbounded value.
198          */
199         double boundedToUnbounded(double x);
200     }
201 
202     /** Local class for no bounds mapping. */
203     private static class NoBoundsMapper implements Mapper {
204         /** {@inheritDoc} */
205         public double unboundedToBounded(final double y) {
206             return y;
207         }
208 
209         /** {@inheritDoc} */
210         public double boundedToUnbounded(final double x) {
211             return x;
212         }
213     }
214 
215     /** Local class for lower bounds mapping. */
216     private static class LowerBoundMapper implements Mapper {
217         /** Low bound. */
218         private final double lower;
219 
220         /**
221          * Simple constructor.
222          *
223          * @param lower lower bound
224          */
225         public LowerBoundMapper(final double lower) {
226             this.lower = lower;
227         }
228 
229         /** {@inheritDoc} */
230         public double unboundedToBounded(final double y) {
231             return lower + FastMath.exp(y);
232         }
233 
234         /** {@inheritDoc} */
235         public double boundedToUnbounded(final double x) {
236             return FastMath.log(x - lower);
237         }
238 
239     }
240 
241     /** Local class for upper bounds mapping. */
242     private static class UpperBoundMapper implements Mapper {
243 
244         /** Upper bound. */
245         private final double upper;
246 
247         /** Simple constructor.
248          * @param upper upper bound
249          */
250         public UpperBoundMapper(final double upper) {
251             this.upper = upper;
252         }
253 
254         /** {@inheritDoc} */
255         public double unboundedToBounded(final double y) {
256             return upper - FastMath.exp(-y);
257         }
258 
259         /** {@inheritDoc} */
260         public double boundedToUnbounded(final double x) {
261             return -FastMath.log(upper - x);
262         }
263 
264     }
265 
266     /** Local class for lower and bounds mapping. */
267     private static class LowerUpperBoundMapper implements Mapper {
268         /** Function from unbounded to bounded. */
269         private final UnivariateFunction boundingFunction;
270         /** Function from bounded to unbounded. */
271         private final UnivariateFunction unboundingFunction;
272 
273         /**
274          * Simple constructor.
275          *
276          * @param lower lower bound
277          * @param upper upper bound
278          */
279         public LowerUpperBoundMapper(final double lower, final double upper) {
280             boundingFunction   = new Sigmoid(lower, upper);
281             unboundingFunction = new Logit(lower, upper);
282         }
283 
284         /** {@inheritDoc} */
285         public double unboundedToBounded(final double y) {
286             return boundingFunction.value(y);
287         }
288 
289         /** {@inheritDoc} */
290         public double boundedToUnbounded(final double x) {
291             return unboundingFunction.value(x);
292         }
293     }
294 }