Package org.drip.spaces.metric

Class RdCombinatorialBanach

java.lang.Object

org.drip.spaces.tensor.RdAggregate

org.drip.spaces.tensor.RdCombinatorialVector

org.drip.spaces.metric.RdCombinatorialBanach

All Implemented Interfaces:

GeneralizedMetricVectorSpace, RdNormed, GeneralizedVector, RdGeneralizedVector

Direct Known Subclasses:

RdCombinatorialBall, RdCombinatorialHilbert

public class RdCombinatorialBanach
extends RdCombinatorialVector
implements RdNormed

RdCombinatorialBanach implements the Bounded/Unbounded Combinatorial l_p R^d Spaces. The Reference we've used is:

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

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

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
RdCombinatorialBanach(R1CombinatorialVector[] aR1CV, Rd distRd, int iPNorm)	RdCombinatorialBanach Space Constructor

Method Summary

Modifier and Type	Method	Description
double	borelMeasureSpaceExpectation(RdToR1 funcRdToR1)	Compute the Borel Measure Expectation for the specified R^d To R^1 Function over the full Input Space
Rd	borelSigmaMeasure()	Retrieve the Borel Sigma R^d Probability Measure
int	pNorm()	Retrieve the P-Norm Index of the Metric Space
double	populationMetricNorm()	Retrieve the Population Metric Norm
double[]	populationMode()	Retrieve the Population Mode
double	populationSupremumNorm()	Compute the Population Supremum Norm of the Sample
double	sampleMetricNorm(double[] adblX)	Compute the Metric Norm of the Sample
double	sampleSupremumNorm(double[] adblX)	Compute the Supremum Norm of the Sample

Methods inherited from class org.drip.spaces.tensor.RdCombinatorialVector

cardinality, hyperVolume, iterator, leftDimensionEdge, leftEdge, rightDimensionEdge, rightEdge

Methods inherited from class org.drip.spaces.tensor.RdAggregate

dimension, isPredictorBounded, match, subset, validateInstance, vectorSpaces

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.drip.spaces.tensor.GeneralizedVector

cardinality, hyperVolume, isPredictorBounded, leftEdge, match, rightEdge, subset

Methods inherited from interface org.drip.spaces.tensor.RdGeneralizedVector

dimension, leftDimensionEdge, rightDimensionEdge, validateInstance, vectorSpaces

Constructor Details

RdCombinatorialBanach

public RdCombinatorialBanach(R1CombinatorialVector[] aR1CV,
Rd distRd,
int iPNorm)
                      throws java.lang.Exception

RdCombinatorialBanach Space Constructor

Parameters:

aR1CV - Array of Combinatorial R^1 Vector Spaces

distRd - The R^d Borel Sigma Measure

iPNorm - The p-norm of the Space

Throws:

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

Method Details

pNorm

public int pNorm()

Description copied from interface: GeneralizedMetricVectorSpace

Retrieve the P-Norm Index of the Metric Space

Specified by:

pNorm in interface GeneralizedMetricVectorSpace

Returns:

The P-Norm Index of the Metric Space

borelSigmaMeasure

public Rd borelSigmaMeasure()

Description copied from interface: RdNormed

Retrieve the Borel Sigma R^d Probability Measure

Specified by:

borelSigmaMeasure in interface RdNormed

Returns:

The Borel Sigma R^d Probability Measure

sampleSupremumNorm

public double sampleSupremumNorm(double[] adblX)
                          throws java.lang.Exception

Description copied from interface: RdNormed

Compute the Supremum Norm of the Sample

Specified by:

sampleSupremumNorm in interface RdNormed

Parameters:

adblX - The Sample

Returns:

The Supremum Norm of the Sample

Throws:

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

sampleMetricNorm

public double sampleMetricNorm(double[] adblX)
                        throws java.lang.Exception

Description copied from interface: RdNormed

Compute the Metric Norm of the Sample

Specified by:

sampleMetricNorm in interface RdNormed

Parameters:

adblX - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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

populationMode

public double[] populationMode()

Description copied from interface: RdNormed

Retrieve the Population Mode

Specified by:

populationMode in interface RdNormed

Returns:

The Population Mode

populationSupremumNorm

public double populationSupremumNorm()
                              throws java.lang.Exception

Description copied from interface: RdNormed

Compute the Population Supremum Norm of the Sample

Specified by:

populationSupremumNorm in interface RdNormed

Returns:

The Population Supremum Norm of the Sample

Throws:

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

populationMetricNorm

public double populationMetricNorm()
                            throws java.lang.Exception

Description copied from interface: GeneralizedMetricVectorSpace

Retrieve the Population Metric Norm

Specified by:

populationMetricNorm in interface GeneralizedMetricVectorSpace

Returns:

The Population Metric Norm

Throws:

java.lang.Exception - The Population Metric Norm cannot be computed

borelMeasureSpaceExpectation

public double borelMeasureSpaceExpectation(RdToR1 funcRdToR1)
                                    throws java.lang.Exception

Description copied from interface: RdNormed

Compute the Borel Measure Expectation for the specified R^d To R^1 Function over the full Input Space

Specified by:

borelMeasureSpaceExpectation in interface RdNormed

Parameters:

funcRdToR1 - R^d To R^1 Function

Returns:

The Borel Measure Expectation for the specified R^d To R^1 Function over the full Input Space

Throws:

java.lang.Exception - Thrown if the Population Mode cannot be calculated