org.drip.spaces.functionclass

Class NormedR1ToL1R1Finite

java.lang.Object

org.drip.spaces.functionclass.NormedRxToNormedRxFinite

org.drip.spaces.functionclass.NormedRxToNormedR1Finite

org.drip.spaces.functionclass.NormedR1ToNormedR1Finite

org.drip.spaces.functionclass.NormedR1ToL1R1Finite

public class NormedR1ToL1R1Finite
extends NormedR1ToNormedR1Finite

NormedR1ToL1R1Finite implements the Class f E F : Normed R^1 To L1 R^1 Spaces of Finite Functions. The Reference we've used is: - Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators, Cambridge University Press, Cambridge UK.

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method and Description
FunctionClassCoveringBounds	agnosticCoveringNumberBounds() Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
static NormedR1ToL1R1Finite	BoundedPredictorBoundedResponse(double dblMaureyConstant, R1ToR1[] aR1ToR1, double dblPredictorSupport, double dblResponseBound) Create Bounded R^1 To Bounded L1 R^1 Function Class for the specified Bounded Class of Finite Functions

Methods inherited from class org.drip.spaces.functionclass.NormedR1ToNormedR1Finite

functionR1ToR1Set

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedR1Finite

functionSpaces, inputMetricVectorSpace, operatorPopulationMetricNorm, operatorPopulationSupremumNorm, operatorSampleMetricNorm, operatorSampleSupremumNorm, outputMetricVectorSpace, populationCoveringNumber, populationSupremumCoveringNumber, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedRxFinite

maureyConstant, outputDimension, populationMetricCoveringBounds, populationSupremumCoveringBounds, sampleMetricCoveringBounds, sampleSupremumCoveringBounds, scaleSensitiveCoveringBounds

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

BoundedPredictorBoundedResponse

public static final NormedR1ToL1R1Finite BoundedPredictorBoundedResponse(double dblMaureyConstant,
                                                                         R1ToR1[] aR1ToR1,
                                                                         double dblPredictorSupport,
                                                                         double dblResponseBound)

Create Bounded R^1 To Bounded L1 R^1 Function Class for the specified Bounded Class of Finite Functions

Parameters:

dblMaureyConstant - Maurey Constant

aR1ToR1 - The Bounded R^1 To Bounded R^1 Function Set

dblPredictorSupport - The Set Predictor Support

dblResponseBound - The Set Response Bound

Returns:

The Bounded R^1 To Bounded R^1 Function Class for the specified Function Set

agnosticCoveringNumberBounds

public FunctionClassCoveringBounds agnosticCoveringNumberBounds()

Description copied from class: NormedRxToNormedRxFinite

Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class

Overrides:

agnosticCoveringNumberBounds in class NormedRxToNormedR1Finite

Returns:

The Agnostic Covering Number Upper/Lower Bounds for the Function Class