    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    package org.apache.commons.math3.optim.nonlinear.scalar;
    018
    019    import org.apache.commons.math3.analysis.MultivariateFunction;
    020    import org.apache.commons.math3.analysis.UnivariateFunction;
    021    import org.apache.commons.math3.analysis.function.Logit;
    022    import org.apache.commons.math3.analysis.function.Sigmoid;
    023    import org.apache.commons.math3.exception.DimensionMismatchException;
    024    import org.apache.commons.math3.exception.NumberIsTooSmallException;
    025    import org.apache.commons.math3.util.FastMath;
    026    import org.apache.commons.math3.util.MathUtils;
    027
    028    /**
    029     * <p>Adapter for mapping bounded {@link MultivariateFunction} to unbounded ones.</p>
    030     *
    031     * <p>
    032     * This adapter can be used to wrap functions subject to simple bounds on
    033     * parameters so they can be used by optimizers that do <em>not</em> directly
    034     * support simple bounds.
    035     * </p>
    036     * <p>
    037     * The principle is that the user function that will be wrapped will see its
    038     * parameters bounded as required, i.e when its {@code value} method is called
    039     * with argument array {@code point}, the elements array will fulfill requirement
    040     * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
    041     * may be unbounded or bounded only on one side if the corresponding bound is
    042     * set to an infinite value. The optimizer will not manage the user function by
    043     * itself, but it will handle this adapter and it is this adapter that will take
    044     * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
    045     * be called by the optimizer with unbound parameters, and the adapter will map
    046     * the unbounded value to the bounded range using appropriate functions like
    047     * {@link Sigmoid} for double bounded elements for example.
    048     * </p>
    049     * <p>
    050     * As the optimizer sees only unbounded parameters, it should be noted that the
    051     * start point or simplex expected by the optimizer should be unbounded, so the
    052     * user is responsible for converting his bounded point to unbounded by calling
    053     * {@link #boundedToUnbounded(double[])} before providing them to the optimizer.
    054     * For the same reason, the point returned by the {@link
    055     * org.apache.commons.math3.optimization.BaseMultivariateOptimizer#optimize(int,
    056     * MultivariateFunction, org.apache.commons.math3.optimization.GoalType, double[])}
    057     * method is unbounded. So to convert this point to bounded, users must call
    058     * {@link #unboundedToBounded(double[])} by themselves!</p>
    059     * <p>
    060     * This adapter is only a poor man solution to simple bounds optimization constraints
    061     * that can be used with simple optimizers like
    062     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
    063     * SimplexOptimizer}.
    064     * A better solution is to use an optimizer that directly supports simple bounds like
    065     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer
    066     * CMAESOptimizer} or
    067     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
    068     * BOBYQAOptimizer}.
    069     * One caveat of this poor-man's solution is that behavior near the bounds may be
    070     * numerically unstable as bounds are mapped from infinite values.
    071     * Another caveat is that convergence values are evaluated by the optimizer with
    072     * respect to unbounded variables, so there will be scales differences when
    073     * converted to bounded variables.
    074     * </p>
    075     *
    076     * @see MultivariateFunctionPenaltyAdapter
    077     *
    078     * @version $Id: MultivariateFunctionMappingAdapter.java 1416643 2012-12-03 19:37:14Z tn $
    079     * @since 3.0
    080     */
    081    public class MultivariateFunctionMappingAdapter
    082        implements MultivariateFunction {
    083        /** Underlying bounded function. */
    084        private final MultivariateFunction bounded;
    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            // 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    }