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Java example source code file (MultivariateFunctionMappingAdapter.java)

This example Java source code file (MultivariateFunctionMappingAdapter.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

logit, lowerboundmapper, lowerupperboundmapper, mapper, multivariatefunction, multivariatefunctionmappingadapter, noboundsmapper, numberistoosmallexception, sigmoid, univariatefunction, upperboundmapper

The MultivariateFunctionMappingAdapter.java Java example source code

 * 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,
 * See the License for the specific language governing permissions and
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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> * 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 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 * * @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 */ 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 */ 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 */ 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); } } }

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