org.drip.spaces.functionclass

Class NormedRxToNormedR1Finite

java.lang.Object

org.drip.spaces.functionclass.NormedRxToNormedRxFinite

org.drip.spaces.functionclass.NormedRxToNormedR1Finite

Direct Known Subclasses:

NormedR1ToNormedR1Finite, NormedRdToNormedR1Finite

public class NormedRxToNormedR1Finite
extends NormedRxToNormedRxFinite

NormedRxToNormedR1Finite implements the Class F with f E f : Normed R^x To Normed R^1 Space 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
NormedRxToNormedR1[]	functionSpaces() Retrieve the Array of Function Spaces in the Class
GeneralizedMetricVectorSpace	inputMetricVectorSpace() Retrieve the Input Vector Space
double	operatorPopulationMetricNorm() Compute the Operator Population Metric Norm
double	operatorPopulationSupremumNorm() Compute the Operator Population Supremum Norm
double	operatorSampleMetricNorm(GeneralizedValidatedVector gvvi) Compute the Operator Sample Metric Norm
double	operatorSampleSupremumNorm(GeneralizedValidatedVector gvvi) Compute the Operator Sample Supremum Norm
R1Normed	outputMetricVectorSpace() Retrieve the Output Vector Space
double	populationCoveringNumber(double dblCover) Estimate for the Function Class Population Covering Number
double	populationSupremumCoveringNumber(double dblCover) Estimate for the Function Class Population Supremum Covering Number
double	sampleCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover) Estimate for the Scale-Sensitive Sample Covering Number for the specified Cover Size
double	sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover) Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

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

agnosticCoveringNumberBounds

public FunctionClassCoveringBounds agnosticCoveringNumberBounds()

Description copied from class: NormedRxToNormedRxFinite

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

Specified by:

agnosticCoveringNumberBounds in class NormedRxToNormedRxFinite

Returns:

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

inputMetricVectorSpace

public GeneralizedMetricVectorSpace inputMetricVectorSpace()

Description copied from class: NormedRxToNormedRxFinite

Retrieve the Input Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedRxFinite

Returns:

The Input Vector Space

outputMetricVectorSpace

public R1Normed outputMetricVectorSpace()

Description copied from class: NormedRxToNormedRxFinite

Retrieve the Output Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedRxFinite

Returns:

The Output Vector Space

functionSpaces

public NormedRxToNormedR1[] functionSpaces()

Retrieve the Array of Function Spaces in the Class

Returns:

The Array of Function Spaces in the Class

populationCoveringNumber

public double populationCoveringNumber(double dblCover)
                                throws java.lang.Exception

Estimate for the Function Class Population Covering Number

Parameters:

dblCover - The Size of the Cover

Returns:

Function Class Population Covering Number Estimate

Throws:

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

populationSupremumCoveringNumber

public double populationSupremumCoveringNumber(double dblCover)
                                        throws java.lang.Exception

Estimate for the Function Class Population Supremum Covering Number

Parameters:

dblCover - The Size of the Cover

Returns:

Function Class Population Supremum Covering Number Estimate

Throws:

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

sampleCoveringNumber

public double sampleCoveringNumber(GeneralizedValidatedVector gvvi,
                                   double dblCover)
                            throws java.lang.Exception

Estimate for the Scale-Sensitive Sample Covering Number for the specified Cover Size

Parameters:

gvvi - The Validated Instance Vector Sequence

dblCover - The Size of the Cover

Returns:

The Scale-Sensitive Sample Covering Number for the specified Cover Size

Throws:

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

sampleSupremumCoveringNumber

public double sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi,
                                           double dblCover)
                                    throws java.lang.Exception

Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

Parameters:

gvvi - The Validated Instance Vector Sequence

dblCover - The Size of the Cover

Returns:

The Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

Throws:

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

operatorPopulationMetricNorm

public double operatorPopulationMetricNorm()
                                    throws java.lang.Exception

Description copied from class: NormedRxToNormedRxFinite

Compute the Operator Population Metric Norm

Specified by:

operatorPopulationMetricNorm in class NormedRxToNormedRxFinite

Returns:

The Operator Population Metric Norm

Throws:

java.lang.Exception - Thrown if the Operator Norm cannot be computed

operatorPopulationSupremumNorm

public double operatorPopulationSupremumNorm()
                                      throws java.lang.Exception

Description copied from class: NormedRxToNormedRxFinite

Compute the Operator Population Supremum Norm

Specified by:

operatorPopulationSupremumNorm in class NormedRxToNormedRxFinite

Returns:

The Operator Population Supremum Norm

Throws:

java.lang.Exception - Thrown if the Operator Population Supremum Norm cannot be computed

operatorSampleMetricNorm

public double operatorSampleMetricNorm(GeneralizedValidatedVector gvvi)
                                throws java.lang.Exception

Description copied from class: NormedRxToNormedRxFinite

Compute the Operator Sample Metric Norm

Specified by:

operatorSampleMetricNorm in class NormedRxToNormedRxFinite

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Operator Sample Metric Norm

Throws:

java.lang.Exception - Thrown if the Operator Norm cannot be computed

operatorSampleSupremumNorm

public double operatorSampleSupremumNorm(GeneralizedValidatedVector gvvi)
                                  throws java.lang.Exception

Description copied from class: NormedRxToNormedRxFinite

Compute the Operator Sample Supremum Norm

Specified by:

operatorSampleSupremumNorm in class NormedRxToNormedRxFinite

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Operator Sample Supremum Norm

Throws:

java.lang.Exception - Thrown if the Operator Sample Supremum Norm cannot be computed