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* 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 1435539 2013-01-19 13:27:24Z 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);
}
}
}