Java tutorial
/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math3.optim.nonlinear.scalar; import org.apache.commons.math3.analysis.MultivariateFunction; import org.apache.commons.math3.analysis.UnivariateFunction; import org.apache.commons.math3.analysis.function.Logit; import org.apache.commons.math3.analysis.function.Sigmoid; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.util.MathUtils; /** * <p>Adapter for mapping bounded {@link MultivariateFunction} to unbounded ones.</p> * * <p> * This adapter can be used to wrap functions subject to simple bounds on * parameters so they can be used by optimizers that do <em>not</em> directly * support simple bounds. * </p> * <p> * The principle is that the user function that will be wrapped will see its * parameters bounded as required, i.e when its {@code value} method is called * with argument array {@code point}, the elements array will fulfill requirement * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components * may be unbounded or bounded only on one side if the corresponding bound is * set to an infinite value. The optimizer will not manage the user function by * itself, but it will handle this adapter and it is this adapter that will take * care the bounds are fulfilled. The adapter {@link #value(double[])} method will * be called by the optimizer with unbound parameters, and the adapter will map * the unbounded value to the bounded range using appropriate functions like * {@link Sigmoid} for double bounded elements for example. * </p> * <p> * As the optimizer sees only unbounded parameters, it should be noted that the * start point or simplex expected by the optimizer should be unbounded, so the * user is responsible for converting his bounded point to unbounded by calling * {@link #boundedToUnbounded(double[])} before providing them to the optimizer. * For the same reason, the point returned by the {@link * org.apache.commons.math3.optimization.BaseMultivariateOptimizer#optimize(int, * MultivariateFunction, org.apache.commons.math3.optimization.GoalType, double[])} * method is unbounded. So to convert this point to bounded, users must call * {@link #unboundedToBounded(double[])} by themselves!</p> * <p> * This adapter is only a poor man solution to simple bounds optimization constraints * that can be used with simple optimizers like * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer * SimplexOptimizer}. * A better solution is to use an optimizer that directly supports simple bounds like * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer * CMAESOptimizer} or * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer * BOBYQAOptimizer}. * One caveat of this poor-man's solution is that behavior near the bounds may be * numerically unstable as bounds are mapped from infinite values. * Another caveat is that convergence values are evaluated by the optimizer with * respect to unbounded variables, so there will be scales differences when * converted to bounded variables. * </p> * * @see MultivariateFunctionPenaltyAdapter * * @version $Id: MultivariateFunctionMappingAdapter.java 1416643 2012-12-03 19:37:14Z tn $ * @since 3.0 */ public class MultivariateFunctionMappingAdapter implements MultivariateFunction { /** Underlying bounded function. */ private final MultivariateFunction bounded; /** Mapping functions. */ private final Mapper[] mappers; /** Simple constructor. * @param bounded bounded function * @param lower lower bounds for each element of the input parameters array * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for * unbounded values) * @param upper upper bounds for each element of the input parameters array * (some elements may be set to {@code Double.POSITIVE_INFINITY} for * unbounded values) * @exception DimensionMismatchException if lower and upper bounds are not * consistent, either according to dimension or to values */ public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded, final double[] lower, final double[] upper) { // safety checks MathUtils.checkNotNull(lower); MathUtils.checkNotNull(upper); if (lower.length != upper.length) { throw new DimensionMismatchException(lower.length, upper.length); } for (int i = 0; i < lower.length; ++i) { // note the following test is written in such a way it also fails for NaN if (!(upper[i] >= lower[i])) { throw new NumberIsTooSmallException(upper[i], lower[i], true); } } this.bounded = bounded; this.mappers = new Mapper[lower.length]; for (int i = 0; i < mappers.length; ++i) { if (Double.isInfinite(lower[i])) { if (Double.isInfinite(upper[i])) { // element is unbounded, no transformation is needed mappers[i] = new NoBoundsMapper(); } else { // element is simple-bounded on the upper side mappers[i] = new UpperBoundMapper(upper[i]); } } else { if (Double.isInfinite(upper[i])) { // element is simple-bounded on the lower side mappers[i] = new LowerBoundMapper(lower[i]); } else { // element is double-bounded mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]); } } } } /** * Maps an array from unbounded to bounded. * * @param point Unbounded values. * @return the bounded values. */ public double[] unboundedToBounded(double[] point) { // Map unbounded input point to bounded point. final double[] mapped = new double[mappers.length]; for (int i = 0; i < mappers.length; ++i) { mapped[i] = mappers[i].unboundedToBounded(point[i]); } return mapped; } /** * Maps an array from bounded to unbounded. * * @param point Bounded values. * @return the unbounded values. */ public double[] boundedToUnbounded(double[] point) { // Map bounded input point to unbounded point. final double[] mapped = new double[mappers.length]; for (int i = 0; i < mappers.length; ++i) { mapped[i] = mappers[i].boundedToUnbounded(point[i]); } return mapped; } /** * Compute the underlying function value from an unbounded point. * <p> * This method simply bounds the unbounded point using the mappings * set up at construction and calls the underlying function using * the bounded point. * </p> * @param point unbounded value * @return underlying function value * @see #unboundedToBounded(double[]) */ public double value(double[] point) { return bounded.value(unboundedToBounded(point)); } /** Mapping interface. */ private interface Mapper { /** * Maps a value from unbounded to bounded. * * @param y Unbounded value. * @return the bounded value. */ double unboundedToBounded(double y); /** * Maps a value from bounded to unbounded. * * @param x Bounded value. * @return the unbounded value. */ double boundedToUnbounded(double x); } /** Local class for no bounds mapping. */ private static class NoBoundsMapper implements Mapper { /** {@inheritDoc} */ public double unboundedToBounded(final double y) { return y; } /** {@inheritDoc} */ public double boundedToUnbounded(final double x) { return x; } } /** Local class for lower bounds mapping. */ private static class LowerBoundMapper implements Mapper { /** Low bound. */ private final double lower; /** * Simple constructor. * * @param lower lower bound */ public LowerBoundMapper(final double lower) { this.lower = lower; } /** {@inheritDoc} */ public double unboundedToBounded(final double y) { return lower + FastMath.exp(y); } /** {@inheritDoc} */ public double boundedToUnbounded(final double x) { return FastMath.log(x - lower); } } /** Local class for upper bounds mapping. */ private static class UpperBoundMapper implements Mapper { /** Upper bound. */ private final double upper; /** Simple constructor. * @param upper upper bound */ public UpperBoundMapper(final double upper) { this.upper = upper; } /** {@inheritDoc} */ public double unboundedToBounded(final double y) { return upper - FastMath.exp(-y); } /** {@inheritDoc} */ public double boundedToUnbounded(final double x) { return -FastMath.log(upper - x); } } /** Local class for lower and bounds mapping. */ private static class LowerUpperBoundMapper implements Mapper { /** Function from unbounded to bounded. */ private final UnivariateFunction boundingFunction; /** Function from bounded to unbounded. */ private final UnivariateFunction unboundingFunction; /** * Simple constructor. * * @param lower lower bound * @param upper upper bound */ public LowerUpperBoundMapper(final double lower, final double upper) { boundingFunction = new Sigmoid(lower, upper); unboundingFunction = new Logit(lower, upper); } /** {@inheritDoc} */ public double unboundedToBounded(final double y) { return boundingFunction.value(y); } /** {@inheritDoc} */ public double boundedToUnbounded(final double x) { return unboundingFunction.value(x); } } }