Package org.drip.spaces.metric

Interface RdNormed

All Superinterfaces:

GeneralizedMetricVectorSpace, GeneralizedVector, RdGeneralizedVector

All Known Implementing Classes:

RdCombinatorialBall, RdCombinatorialBanach, RdCombinatorialHilbert, RdContinuousBall, RdContinuousBanach, RdContinuousHilbert

public interface RdNormed
extends GeneralizedMetricVectorSpace, RdGeneralizedVector

RdNormed Abstract Class implements the Normed, Bounded/Unbounded Continuous/Combinatorial l_p R^d Spaces.

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

It provides the following Functionality:

• Retrieve the Borel Sigma R^d Probability Measure
• Compute the Supremum Norm of the Sample
• Compute the Metric Norm of the Sample
• Retrieve the Population Mode
• Compute the Population Supremum Norm of the Sample
• Compute the Borel Measure Expectation for the specified R^d To R¹ Function over the full Input Space

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

Method Summary

Modifier and Type	Method	Description
double	borelMeasureSpaceExpectation(RdToR1 rdToR1Function)	Compute the Borel Measure Expectation for the specified Rd To R1 Function over the full Input Space
Rd	borelSigmaMeasure()	Retrieve the Borel Sigma Rd Probability Measure
double[]	populationMode()	Retrieve the Population Mode
double	populationSupremumNorm()	Compute the Population Supremum Norm of the Sample
double	sampleMetricNorm(double[] x)	Compute the Metric Norm of the Sample
double	sampleSupremumNorm(double[] x)	Compute the Supremum Norm of the Sample

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

pNorm, populationMetricNorm

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

Method Details

borelSigmaMeasure

Rd borelSigmaMeasure()

Retrieve the Borel Sigma R^d Probability Measure

Returns:

The Borel Sigma R^d Probability Measure

sampleSupremumNorm

double sampleSupremumNorm(double[] x)
                   throws java.lang.Exception

Compute the Supremum Norm of the Sample

Parameters:

x - The Sample

Returns:

The Supremum Norm of the Sample

Throws:

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

sampleMetricNorm

double sampleMetricNorm(double[] x)
                 throws java.lang.Exception

Compute the Metric Norm of the Sample

Parameters:

x - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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

populationMode

double[] populationMode()

Retrieve the Population Mode

Returns:

The Population Mode

populationSupremumNorm

double populationSupremumNorm()
                       throws java.lang.Exception

Compute the Population Supremum Norm of the Sample

Returns:

The Population Supremum Norm of the Sample

Throws:

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

borelMeasureSpaceExpectation

double borelMeasureSpaceExpectation(RdToR1 rdToR1Function)
                             throws java.lang.Exception

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

Parameters:

rdToR1Function - R^d To R¹ Function

Returns:

The Borel Measure Expectation for the specified R^d To R¹ Function over the full Input Space

Throws:

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