    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.analysis.MultivariateFunction;
    021    import org.apache.commons.math3.analysis.UnivariateFunction;
    022    import org.apache.commons.math3.analysis.function.Logit;
    023    import org.apache.commons.math3.analysis.function.Sigmoid;
    024    import org.apache.commons.math3.exception.DimensionMismatchException;
    025    import org.apache.commons.math3.exception.NumberIsTooSmallException;
    026    import org.apache.commons.math3.util.FastMath;
    027    import 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
    080    public 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    }