Package 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 R¹ To L₁ R¹ Spaces of Finite Functions. The Reference we've used is:

• Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK

It provides the following Functionality:

• Create Bounded R¹ To Bounded L1 R¹ Function Class for the specified Bounded Class of Finite Functions

• Module = Computational Core Module
• Library = Statistical Learning Library
• Project = R¹ and R^d Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
• Package = Normed Finite Spaces Function Class

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
FunctionClassCoveringBounds	agnosticCoveringNumberBounds()	Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
static NormedR1ToL1R1Finite	BoundedPredictorBoundedResponse(double maureyConstant, R1ToR1[] aR1ToR1, double dblPredictorSupport, double dblResponseBound)	Create Bounded R1 To Bounded L1 R1 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 Details

BoundedPredictorBoundedResponse

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

Create Bounded R¹ To Bounded L1 R¹ Function Class for the specified Bounded Class of Finite Functions

Parameters:

maureyConstant - Maurey Constant

aR1ToR1 - The Bounded R¹ To Bounded R¹ Function Set

dblPredictorSupport - The Set Predictor Support

dblResponseBound - The Set Response Bound

Returns:

The Bounded R¹ To Bounded R¹ 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