org.apache.commons.math3.optim.nonlinear.scalar
Class MultivariateFunctionMappingAdapter

java.lang.Object
  extended by org.apache.commons.math3.optim.nonlinear.scalar.MultivariateFunctionMappingAdapter
All Implemented Interfaces:
MultivariateFunction

public class MultivariateFunctionMappingAdapter
extends Object
implements MultivariateFunction

Adapter for mapping bounded MultivariateFunction to unbounded ones.

This adapter can be used to wrap functions subject to simple bounds on parameters so they can be used by optimizers that do not directly support simple bounds.

The principle is that the user function that will be wrapped will see its parameters bounded as required, i.e when its value method is called with argument array point, the elements array will fulfill requirement 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 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 Sigmoid for double bounded elements for example.

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 boundedToUnbounded(double[]) before providing them to the optimizer. For the same reason, the point returned by the BaseMultivariateOptimizer.optimize(int, MultivariateFunction, org.apache.commons.math3.optimization.GoalType, double[]) method is unbounded. So to convert this point to bounded, users must call unboundedToBounded(double[]) by themselves!

This adapter is only a poor man solution to simple bounds optimization constraints that can be used with simple optimizers like SimplexOptimizer. A better solution is to use an optimizer that directly supports simple bounds like CMAESOptimizer or 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.

Since:
3.0
Version:
$Id: MultivariateFunctionMappingAdapter.java 1435539 2013-01-19 13:27:24Z tn $
See Also:
MultivariateFunctionPenaltyAdapter

Constructor Summary
MultivariateFunctionMappingAdapter(MultivariateFunction bounded, double[] lower, double[] upper)
          Simple constructor.
 
Method Summary
 double[] boundedToUnbounded(double[] point)
          Maps an array from bounded to unbounded.
 double[] unboundedToBounded(double[] point)
          Maps an array from unbounded to bounded.
 double value(double[] point)
          Compute the underlying function value from an unbounded point.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

MultivariateFunctionMappingAdapter

public MultivariateFunctionMappingAdapter(MultivariateFunction bounded,
                                          double[] lower,
                                          double[] upper)
Simple constructor.

Parameters:
bounded - bounded function
lower - lower bounds for each element of the input parameters array (some elements may be set to Double.NEGATIVE_INFINITY for unbounded values)
upper - upper bounds for each element of the input parameters array (some elements may be set to Double.POSITIVE_INFINITY for unbounded values)
Throws:
DimensionMismatchException - if lower and upper bounds are not consistent, either according to dimension or to values
Method Detail

unboundedToBounded

public double[] unboundedToBounded(double[] point)
Maps an array from unbounded to bounded.

Parameters:
point - Unbounded values.
Returns:
the bounded values.

boundedToUnbounded

public double[] boundedToUnbounded(double[] point)
Maps an array from bounded to unbounded.

Parameters:
point - Bounded values.
Returns:
the unbounded values.

value

public double value(double[] point)
Compute the underlying function value from an unbounded point.

This method simply bounds the unbounded point using the mappings set up at construction and calls the underlying function using the bounded point.

Specified by:
value in interface MultivariateFunction
Parameters:
point - unbounded value
Returns:
underlying function value
See Also:
unboundedToBounded(double[])


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