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 */ 017package org.apache.commons.math4.legacy.optim.nonlinear.scalar; 018 019import org.apache.commons.math4.legacy.analysis.MultivariateFunction; 020import org.apache.commons.math4.legacy.analysis.UnivariateFunction; 021import org.apache.commons.math4.legacy.analysis.function.Logit; 022import org.apache.commons.math4.legacy.analysis.function.Sigmoid; 023import org.apache.commons.math4.legacy.exception.NullArgumentException; 024import org.apache.commons.math4.legacy.exception.DimensionMismatchException; 025import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException; 026import org.apache.commons.math4.core.jdkmath.JdkMath; 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.math4.legacy.optim.BaseMultivariateOptimizer 056 * #optimize(org.apache.commons.math4.legacy.optim.OptimizationData...)} 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.math4.legacy.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.math4.legacy.optim.nonlinear.scalar.noderiv.CMAESOptimizer 066 * CMAESOptimizer} or 067 * {@link org.apache.commons.math4.legacy.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 * @since 3.0 079 */ 080public class MultivariateFunctionMappingAdapter 081 implements MultivariateFunction { 082 /** Underlying bounded function. */ 083 private final MultivariateFunction bounded; 084 /** Mapping functions. */ 085 private final Mapper[] mappers; 086 087 /** Simple constructor. 088 * @param bounded bounded function 089 * @param lower lower bounds for each element of the input parameters array 090 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for 091 * unbounded values) 092 * @param upper upper bounds for each element of the input parameters array 093 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for 094 * unbounded values) 095 * @exception DimensionMismatchException if lower and upper bounds are not 096 * consistent, either according to dimension or to values 097 */ 098 public MultivariateFunctionMappingAdapter(final MultivariateFunction bounded, 099 final double[] lower, final double[] upper) { 100 // safety checks 101 NullArgumentException.check(lower); 102 NullArgumentException.check(upper); 103 if (lower.length != upper.length) { 104 throw new DimensionMismatchException(lower.length, upper.length); 105 } 106 for (int i = 0; i < lower.length; ++i) { 107 // note the following test is written in such a way it also fails for NaN 108 if (!(upper[i] >= lower[i])) { 109 throw new NumberIsTooSmallException(upper[i], lower[i], true); 110 } 111 } 112 113 this.bounded = bounded; 114 this.mappers = new Mapper[lower.length]; 115 for (int i = 0; i < mappers.length; ++i) { 116 if (Double.isInfinite(lower[i])) { 117 if (Double.isInfinite(upper[i])) { 118 // element is unbounded, no transformation is needed 119 mappers[i] = new NoBoundsMapper(); 120 } else { 121 // element is simple-bounded on the upper side 122 mappers[i] = new UpperBoundMapper(upper[i]); 123 } 124 } else { 125 if (Double.isInfinite(upper[i])) { 126 // element is simple-bounded on the lower side 127 mappers[i] = new LowerBoundMapper(lower[i]); 128 } else { 129 // element is double-bounded 130 mappers[i] = new LowerUpperBoundMapper(lower[i], upper[i]); 131 } 132 } 133 } 134 } 135 136 /** 137 * Maps an array from unbounded to bounded. 138 * 139 * @param point Unbounded values. 140 * @return the bounded values. 141 */ 142 public double[] unboundedToBounded(double[] point) { 143 // Map unbounded input point to bounded point. 144 final double[] mapped = new double[mappers.length]; 145 for (int i = 0; i < mappers.length; ++i) { 146 mapped[i] = mappers[i].unboundedToBounded(point[i]); 147 } 148 149 return mapped; 150 } 151 152 /** 153 * Maps an array from bounded to unbounded. 154 * 155 * @param point Bounded values. 156 * @return the unbounded values. 157 */ 158 public double[] boundedToUnbounded(double[] point) { 159 // Map bounded input point to unbounded point. 160 final double[] mapped = new double[mappers.length]; 161 for (int i = 0; i < mappers.length; ++i) { 162 mapped[i] = mappers[i].boundedToUnbounded(point[i]); 163 } 164 165 return mapped; 166 } 167 168 /** 169 * Compute the underlying function value from an unbounded point. 170 * <p> 171 * This method simply bounds the unbounded point using the mappings 172 * set up at construction and calls the underlying function using 173 * the bounded point. 174 * </p> 175 * @param point unbounded value 176 * @return underlying function value 177 * @see #unboundedToBounded(double[]) 178 */ 179 @Override 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 @Override 207 public double unboundedToBounded(final double y) { 208 return y; 209 } 210 211 /** {@inheritDoc} */ 212 @Override 213 public double boundedToUnbounded(final double x) { 214 return x; 215 } 216 } 217 218 /** Local class for lower bounds mapping. */ 219 private static class LowerBoundMapper implements Mapper { 220 /** Low bound. */ 221 private final double lower; 222 223 /** 224 * Simple constructor. 225 * 226 * @param lower lower bound 227 */ 228 LowerBoundMapper(final double lower) { 229 this.lower = lower; 230 } 231 232 /** {@inheritDoc} */ 233 @Override 234 public double unboundedToBounded(final double y) { 235 return lower + JdkMath.exp(y); 236 } 237 238 /** {@inheritDoc} */ 239 @Override 240 public double boundedToUnbounded(final double x) { 241 return JdkMath.log(x - lower); 242 } 243 } 244 245 /** Local class for upper bounds mapping. */ 246 private static class UpperBoundMapper implements Mapper { 247 248 /** Upper bound. */ 249 private final double upper; 250 251 /** Simple constructor. 252 * @param upper upper bound 253 */ 254 UpperBoundMapper(final double upper) { 255 this.upper = upper; 256 } 257 258 /** {@inheritDoc} */ 259 @Override 260 public double unboundedToBounded(final double y) { 261 return upper - JdkMath.exp(-y); 262 } 263 264 /** {@inheritDoc} */ 265 @Override 266 public double boundedToUnbounded(final double x) { 267 return -JdkMath.log(upper - x); 268 } 269 } 270 271 /** Local class for lower and bounds mapping. */ 272 private static class LowerUpperBoundMapper implements Mapper { 273 /** Function from unbounded to bounded. */ 274 private final UnivariateFunction boundingFunction; 275 /** Function from bounded to unbounded. */ 276 private final UnivariateFunction unboundingFunction; 277 278 /** 279 * Simple constructor. 280 * 281 * @param lower lower bound 282 * @param upper upper bound 283 */ 284 LowerUpperBoundMapper(final double lower, final double upper) { 285 boundingFunction = new Sigmoid(lower, upper); 286 unboundingFunction = new Logit(lower, upper); 287 } 288 289 /** {@inheritDoc} */ 290 @Override 291 public double unboundedToBounded(final double y) { 292 return boundingFunction.value(y); 293 } 294 295 /** {@inheritDoc} */ 296 @Override 297 public double boundedToUnbounded(final double x) { 298 return unboundingFunction.value(x); 299 } 300 } 301}