MultivariateFunctionMappingAdapter.java

  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.  *      https://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.  */

  18. /*
  19.  * This is not the original file distributed by the Apache Software Foundation
  20.  * It has been modified by the Hipparchus project
  21.  */
  22. package org.hipparchus.optim.nonlinear.scalar;

  24. import org.hipparchus.analysis.MultivariateFunction;
  25. import org.hipparchus.analysis.UnivariateFunction;
  26. import org.hipparchus.analysis.function.Logit;
  27. import org.hipparchus.analysis.function.Sigmoid;
  28. import org.hipparchus.exception.LocalizedCoreFormats;
  29. import org.hipparchus.exception.MathIllegalArgumentException;
  30. import org.hipparchus.util.FastMath;
  31. import org.hipparchus.util.MathUtils;

  33. /**
  34.  * <p>Adapter for mapping bounded {@link MultivariateFunction} to unbounded ones.</p>
  35.  *
  36.  * <p>
  37.  * This adapter can be used to wrap functions subject to simple bounds on
  38.  * parameters so they can be used by optimizers that do <em>not</em> directly
  39.  * support simple bounds.
  40.  * </p>
  41.  * <p>
  42.  * The principle is that the user function that will be wrapped will see its
  43.  * parameters bounded as required, i.e when its {@code value} method is called
  44.  * with argument array {@code point}, the elements array will fulfill requirement
  45.  * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
  46.  * may be unbounded or bounded only on one side if the corresponding bound is
  47.  * set to an infinite value. The optimizer will not manage the user function by
  48.  * itself, but it will handle this adapter and it is this adapter that will take
  49.  * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
  50.  * be called by the optimizer with unbound parameters, and the adapter will map
  51.  * the unbounded value to the bounded range using appropriate functions like
  52.  * {@link Sigmoid} for double bounded elements for example.
  53.  * </p>
  54.  * <p>
  55.  * As the optimizer sees only unbounded parameters, it should be noted that the
  56.  * start point or simplex expected by the optimizer should be unbounded, so the
  57.  * user is responsible for converting his bounded point to unbounded by calling
  58.  * {@link #boundedToUnbounded(double[])} before providing them to the optimizer.
  59.  * For the same reason, the point returned by the {@link
  60.  * org.hipparchus.optim.BaseMultivariateOptimizer#optimize(org.hipparchus.optim.OptimizationData[])}
  61.  * method is unbounded. So to convert this point to bounded, users must call
  62.  * {@link #unboundedToBounded(double[])} by themselves!</p>
  63.  * <p>
  64.  * This adapter is only a poor man solution to simple bounds optimization constraints
  65.  * that can be used with simple optimizers like
  66.  * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.SimplexOptimizer
  67.  * SimplexOptimizer}.
  68.  * A better solution is to use an optimizer that directly supports simple bounds like
  69.  * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.CMAESOptimizer
  70.  * CMAESOptimizer} or
  71.  * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
  72.  * BOBYQAOptimizer}.
  73.  * One caveat of this poor-man's solution is that behavior near the bounds may be
  74.  * numerically unstable as bounds are mapped from infinite values.
  75.  * Another caveat is that convergence values are evaluated by the optimizer with
  76.  * respect to unbounded variables, so there will be scales differences when
  77.  * converted to bounded variables.
  78.  * </p>
  79.  *
  80.  * @see MultivariateFunctionPenaltyAdapter
  81.  *
  82.  */
  83. public class MultivariateFunctionMappingAdapter
  84.     implements MultivariateFunction {
  85.     /** Underlying bounded function. */
  86.     private final MultivariateFunction bounded;
  87.     /** Mapping functions. */
  88.     private final Mapper[] mappers;

  90.     /** Simple constructor.
  91.      * @param bounded bounded function
  92.      * @param lower lower bounds for each element of the input parameters array
  93.      * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
  94.      * unbounded values)
  95.      * @param upper upper bounds for each element of the input parameters array
  96.      * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
  97.      * unbounded values)
  98.      * @exception MathIllegalArgumentException if lower and upper bounds are not
  99.      * consistent, either according to dimension or to values
  100.      */
  101.     public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded,
  102.                                               final double[] lower, final double[] upper) {
  103.         // safety checks
  104.         MathUtils.checkNotNull(lower);
  105.         MathUtils.checkNotNull(upper);
  106.         if (lower.length != upper.length) {
  107.             throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
  108.                                                    lower.length, upper.length);
  109.         }
  110.         for (int i = 0; i < lower.length; ++i) {
  111.             if (!(upper[i] >= lower[i])) { // NOPMD - the test is written this way so it also fails for NaN
  112.                 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
  113.                                                        upper[i], lower[i]);
  114.             }
  115.         }

  117.         this.bounded = bounded;
  118.         this.mappers = new Mapper[lower.length];
  119.         for (int i = 0; i < mappers.length; ++i) {
  120.             if (Double.isInfinite(lower[i])) {
  121.                 if (Double.isInfinite(upper[i])) {
  122.                     // element is unbounded, no transformation is needed
  123.                     mappers[i] = new NoBoundsMapper();
  124.                 } else {
  125.                     // element is simple-bounded on the upper side
  126.                     mappers[i] = new UpperBoundMapper(upper[i]);
  127.                 }
  128.             } else {
  129.                 if (Double.isInfinite(upper[i])) {
  130.                     // element is simple-bounded on the lower side
  131.                     mappers[i] = new LowerBoundMapper(lower[i]);
  132.                 } else {
  133.                     // element is double-bounded
  134.                     mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]);
  135.                 }
  136.             }
  137.         }
  138.     }

  140.     /**
  141.      * Maps an array from unbounded to bounded.
  142.      *
  143.      * @param point Unbounded values.
  144.      * @return the bounded values.
  145.      */
  146.     public double[] unboundedToBounded(double[] point) {
  147.         // Map unbounded input point to bounded point.
  148.         final double[] mapped = new double[mappers.length];
  149.         for (int i = 0; i < mappers.length; ++i) {
  150.             mapped[i] = mappers[i].unboundedToBounded(point[i]);
  151.         }

  153.         return mapped;
  154.     }

  156.     /**
  157.      * Maps an array from bounded to unbounded.
  158.      *
  159.      * @param point Bounded values.
  160.      * @return the unbounded values.
  161.      */
  162.     public double[] boundedToUnbounded(double[] point) {
  163.         // Map bounded input point to unbounded point.
  164.         final double[] mapped = new double[mappers.length];
  165.         for (int i = 0; i < mappers.length; ++i) {
  166.             mapped[i] = mappers[i].boundedToUnbounded(point[i]);
  167.         }

  169.         return mapped;
  170.     }

  172.     /**
  173.      * Compute the underlying function value from an unbounded point.
  174.      * <p>
  175.      * This method simply bounds the unbounded point using the mappings
  176.      * set up at construction and calls the underlying function using
  177.      * the bounded point.
  178.      * </p>
  179.      * @param point unbounded value
  180.      * @return underlying function value
  181.      * @see #unboundedToBounded(double[])
  182.      */
  183.     @Override
  184.     public double value(double[] point) {
  185.         return bounded.value(unboundedToBounded(point));
  186.     }

  188.     /** Mapping interface. */
  189.     private interface Mapper {
  190.         /**
  191.          * Maps a value from unbounded to bounded.
  192.          *
  193.          * @param y Unbounded value.
  194.          * @return the bounded value.
  195.          */
  196.         double unboundedToBounded(double y);

  198.         /**
  199.          * Maps a value from bounded to unbounded.
  200.          *
  201.          * @param x Bounded value.
  202.          * @return the unbounded value.
  203.          */
  204.         double boundedToUnbounded(double x);
  205.     }

  207.     /** Local class for no bounds mapping. */
  208.     private static class NoBoundsMapper implements Mapper {
  209.         /** {@inheritDoc} */
  210.         @Override
  211.         public double unboundedToBounded(final double y) {
  212.             return y;
  213.         }

  215.         /** {@inheritDoc} */
  216.         @Override
  217.         public double boundedToUnbounded(final double x) {
  218.             return x;
  219.         }
  220.     }

  222.     /** Local class for lower bounds mapping. */
  223.     private static class LowerBoundMapper implements Mapper {
  224.         /** Low bound. */
  225.         private final double lower;

  227.         /**
  228.          * Simple constructor.
  229.          *
  230.          * @param lower lower bound
  231.          */
  232.         LowerBoundMapper(final double lower) {
  233.             this.lower = lower;
  234.         }

  236.         /** {@inheritDoc} */
  237.         @Override
  238.         public double unboundedToBounded(final double y) {
  239.             return lower + FastMath.exp(y);
  240.         }

  242.         /** {@inheritDoc} */
  243.         @Override
  244.         public double boundedToUnbounded(final double x) {
  245.             return FastMath.log(x - lower);
  246.         }

  248.     }

  250.     /** Local class for upper bounds mapping. */
  251.     private static class UpperBoundMapper implements Mapper {

  253.         /** Upper bound. */
  254.         private final double upper;

  256.         /** Simple constructor.
  257.          * @param upper upper bound
  258.          */
  259.         UpperBoundMapper(final double upper) {
  260.             this.upper = upper;
  261.         }

  263.         /** {@inheritDoc} */
  264.         @Override
  265.         public double unboundedToBounded(final double y) {
  266.             return upper - FastMath.exp(-y);
  267.         }

  269.         /** {@inheritDoc} */
  270.         @Override
  271.         public double boundedToUnbounded(final double x) {
  272.             return -FastMath.log(upper - x);
  273.         }

  275.     }

  277.     /** Local class for lower and bounds mapping. */
  278.     private static class LowerUpperBoundMapper implements Mapper {
  279.         /** Function from unbounded to bounded. */
  280.         private final UnivariateFunction boundingFunction;
  281.         /** Function from bounded to unbounded. */
  282.         private final UnivariateFunction unboundingFunction;

  284.         /**
  285.          * Simple constructor.
  286.          *
  287.          * @param lower lower bound
  288.          * @param upper upper bound
  289.          */
  290.         LowerUpperBoundMapper(final double lower, final double upper) {
  291.             boundingFunction   = new Sigmoid(lower, upper);
  292.             unboundingFunction = new Logit(lower, upper);
  293.         }

  295.         /** {@inheritDoc} */
  296.         @Override
  297.         public double unboundedToBounded(final double y) {
  298.             return boundingFunction.value(y);
  299.         }

  301.         /** {@inheritDoc} */
  302.         @Override
  303.         public double boundedToUnbounded(final double x) {
  304.             return unboundingFunction.value(x);
  305.         }
  306.     }
  307. }
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