org.drip.spaces.cover

Interface FunctionClassCoveringBounds

All Known Implementing Classes:

L1R1CoveringBounds, ScaleSensitiveCoveringBounds

public interface FunctionClassCoveringBounds

FunctionClassCoveringBounds implements the estimate Lower/Upper Bounds and/or Absolute Values of the Covering Number for the Function Class. The Main References are: 1) Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators, Cambridge University Press, Cambridge UK. 2) Bartlett, P. L., S. R. Kulkarni, and S. E. Posner (1997): Covering Numbers for Real-valued Function Classes, IEEE Transactions on Information Theory 43 (5) 1721-1724.

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method and Description
double	logLowerBound(double dblCover) Log of the Lower Bound of the Function Covering Number
double	logUpperBound(double dblCover) Log of the Upper Bound of the Function Covering Number

Method Detail

logLowerBound

double logLowerBound(double dblCover)
              throws java.lang.Exception

Log of the Lower Bound of the Function Covering Number

Parameters:

dblCover - The Size of the Cover

Returns:

Log of the Lower Bound of the Function Covering Number

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

logUpperBound

double logUpperBound(double dblCover)
              throws java.lang.Exception

Log of the Upper Bound of the Function Covering Number

Parameters:

dblCover - The Size of the Cover

Returns:

Log of the Upper Bound of the Function Covering Number

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid