Package org.drip.spaces.metric

Class R1Combinatorial

java.lang.Object

org.drip.spaces.tensor.R1CombinatorialVector

org.drip.spaces.metric.R1Combinatorial

All Implemented Interfaces:

GeneralizedMetricVectorSpace, R1Normed, GeneralizedVector, R1GeneralizedVector

Direct Known Subclasses:

R1CombinatorialBall

public class R1Combinatorial
extends R1CombinatorialVector
implements R1Normed

R1Combinatorial implements the Normed, 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

It provides the following Functionality:

• Construct the Standard l_p R₁ Combinatorial Space Instance
• Construct the Supremum (i.e., l_Infinity) R₁ Combinatorial Space Instance
• R1Combinatorial Space Constructor

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

Author:

Lakshmi Krishnamurthy

Field Summary

Fields inherited from interface org.drip.spaces.metric.GeneralizedMetricVectorSpace

EUCLIDEAN_NORM, L2_NORM, LINFINITITY_NORM

Constructor Summary

Constructors

Constructor	Description
R1Combinatorial(java.util.List<java.lang.Double> elementSpaceList, R1Univariate r1Distribution, int pNorm)	R1Combinatorial Space Constructor

Method Summary

Modifier and Type	Method	Description
double	borelMeasureSpaceExpectation(R1ToR1 r1ToR1Function)	Compute the Borel Measure Expectation for the specified R1 To R1 Function over the full Input Space
R1Univariate	borelSigmaMeasure()	Retrieve the Borel Sigma R1 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	sampleMetricNorm(double x)	Compute the Metric Norm of the Sample
static R1Combinatorial	Standard(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm)	Construct the Standard lp R1 Combinatorial Space Instance
static R1Combinatorial	Supremum(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1)	Construct the Supremum (i.e., lInfinity) R1 Combinatorial Space Instance

Methods inherited from class org.drip.spaces.tensor.R1CombinatorialVector

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

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.R1GeneralizedVector

validateInstance

Constructor Details

R1Combinatorial

public R1Combinatorial(java.util.List<java.lang.Double> elementSpaceList,
R1Univariate r1Distribution,
int pNorm)
                throws java.lang.Exception

R1Combinatorial Space Constructor

Parameters:

elementSpaceList - The List Space of Elements

r1Distribution - The R₁ Borel Sigma Measure

pNorm - The p-norm of the Space

Throws:

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

Method Details

Standard

public static final R1Combinatorial Standard(java.util.List<java.lang.Double> lsElementSpace,
R1Univariate distR1,
int iPNorm)

Construct the Standard l_p R₁ Combinatorial Space Instance

Parameters:

lsElementSpace - The List Space of Elements

distR1 - The R₁ Borel Sigma Measure

iPNorm - The p-norm of the Space

Returns:

The Standard l_p R₁ Combinatorial Space Instance

Supremum

public static final R1Combinatorial Supremum(java.util.List<java.lang.Double> lsElementSpace,
R1Univariate distR1)

Construct the Supremum (i.e., l_Infinity) R₁ Combinatorial Space Instance

Parameters:

lsElementSpace - The List Space of Elements

distR1 - The R₁ Borel Sigma Measure

Returns:

The Supremum (i.e., l_Infinity) R₁ Combinatorial Space Instance

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 R1Univariate borelSigmaMeasure()

Description copied from interface: R1Normed

Retrieve the Borel Sigma R¹ Probability Measure

Specified by:

borelSigmaMeasure in interface R1Normed

Returns:

The Borel Sigma R¹ Probability Measure

sampleMetricNorm

public double sampleMetricNorm(double x)
                        throws java.lang.Exception

Description copied from interface: R1Normed

Compute the Metric Norm of the Sample

Specified by:

sampleMetricNorm in interface R1Normed

Parameters:

x - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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

populationMode

public double populationMode()
                      throws java.lang.Exception

Description copied from interface: R1Normed

Retrieve the Population Mode

Specified by:

populationMode in interface R1Normed

Returns:

The Population Mode

Throws:

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

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(R1ToR1 r1ToR1Function)
                                    throws java.lang.Exception

Description copied from interface: R1Normed

Compute the Borel Measure Expectation for the specified R¹ To R¹ Function over the full Input Space

Specified by:

borelMeasureSpaceExpectation in interface R1Normed

Parameters:

r1ToR1Function - R¹ To R¹ Function Instance

Returns:

The Borel Measure Expectation for the specified R¹ To R¹ Function over `the full Input Space

Throws:

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