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Diffstat (limited to 'src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/MultivariateFunctionMappingAdapter.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/MultivariateFunctionMappingAdapter.java | 294 |
1 files changed, 294 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/MultivariateFunctionMappingAdapter.java b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/MultivariateFunctionMappingAdapter.java new file mode 100644 index 0000000..3c5127c --- /dev/null +++ b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/MultivariateFunctionMappingAdapter.java @@ -0,0 +1,294 @@ +/* + * 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 + * + * @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); + } + } +} |