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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   * @version $Id: MultivariateFunctionMappingAdapter.java 1435539 2013-01-19 13:27:24Z tn $
79   * @since 3.0
80   */
81  public class MultivariateFunctionMappingAdapter
82      implements MultivariateFunction {
83      /** Underlying bounded function. */
84      private final MultivariateFunction bounded;
85      /** Mapping functions. */
86      private final Mapper[] mappers;
87  
88      /** Simple constructor.
89       * @param bounded bounded function
90       * @param lower lower bounds for each element of the input parameters array
91       * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
92       * unbounded values)
93       * @param upper upper bounds for each element of the input parameters array
94       * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
95       * unbounded values)
96       * @exception DimensionMismatchException if lower and upper bounds are not
97       * consistent, either according to dimension or to values
98       */
99      public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded,
100                                               final double[] lower, final double[] upper) {
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      * Maps an array from unbounded to bounded.
139      *
140      * @param point Unbounded values.
141      * @return the bounded values.
142      */
143     public double[] unboundedToBounded(double[] point) {
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      * Maps an array from bounded to unbounded.
155      *
156      * @param point Bounded values.
157      * @return the unbounded values.
158      */
159     public double[] boundedToUnbounded(double[] point) {
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          * Maps a value from unbounded to bounded.
188          *
189          * @param y Unbounded value.
190          * @return the bounded value.
191          */
192         double unboundedToBounded(double y);
193 
194         /**
195          * Maps a value from bounded to unbounded.
196          *
197          * @param x Bounded value.
198          * @return the unbounded value.
199          */
200         double boundedToUnbounded(double x);
201     }
202 
203     /** Local class for no bounds mapping. */
204     private static class NoBoundsMapper implements Mapper {
205         /** {@inheritDoc} */
206         public double unboundedToBounded(final double y) {
207             return y;
208         }
209 
210         /** {@inheritDoc} */
211         public double boundedToUnbounded(final double x) {
212             return x;
213         }
214     }
215 
216     /** Local class for lower bounds mapping. */
217     private static class LowerBoundMapper implements Mapper {
218         /** Low bound. */
219         private final double lower;
220 
221         /**
222          * Simple constructor.
223          *
224          * @param lower lower bound
225          */
226         public LowerBoundMapper(final double lower) {
227             this.lower = lower;
228         }
229 
230         /** {@inheritDoc} */
231         public double unboundedToBounded(final double y) {
232             return lower + FastMath.exp(y);
233         }
234 
235         /** {@inheritDoc} */
236         public double boundedToUnbounded(final double x) {
237             return FastMath.log(x - lower);
238         }
239 
240     }
241 
242     /** Local class for upper bounds mapping. */
243     private static class UpperBoundMapper implements Mapper {
244 
245         /** Upper bound. */
246         private final double upper;
247 
248         /** Simple constructor.
249          * @param upper upper bound
250          */
251         public UpperBoundMapper(final double upper) {
252             this.upper = upper;
253         }
254 
255         /** {@inheritDoc} */
256         public double unboundedToBounded(final double y) {
257             return upper - FastMath.exp(-y);
258         }
259 
260         /** {@inheritDoc} */
261         public double boundedToUnbounded(final double x) {
262             return -FastMath.log(upper - x);
263         }
264 
265     }
266 
267     /** Local class for lower and bounds mapping. */
268     private static class LowerUpperBoundMapper implements Mapper {
269         /** Function from unbounded to bounded. */
270         private final UnivariateFunction boundingFunction;
271         /** Function from bounded to unbounded. */
272         private final UnivariateFunction unboundingFunction;
273 
274         /**
275          * Simple constructor.
276          *
277          * @param lower lower bound
278          * @param upper upper bound
279          */
280         public LowerUpperBoundMapper(final double lower, final double upper) {
281             boundingFunction   = new Sigmoid(lower, upper);
282             unboundingFunction = new Logit(lower, upper);
283         }
284 
285         /** {@inheritDoc} */
286         public double unboundedToBounded(final double y) {
287             return boundingFunction.value(y);
288         }
289 
290         /** {@inheritDoc} */
291         public double boundedToUnbounded(final double x) {
292             return unboundingFunction.value(x);
293         }
294     }
295 }