org.drip.spaces.metric

Interface R1Normed

All Superinterfaces:

GeneralizedMetricVectorSpace, GeneralizedVector, R1GeneralizedVector

All Known Implementing Classes:

R1Combinatorial, R1CombinatorialBall, R1Continuous, R1ContinuousBall

public interface R1Normed
extends GeneralizedMetricVectorSpace, R1GeneralizedVector

R1Normed Abstract Class implements the Normed, Bounded/Unbounded Continuous/Combinatorial l^p R^1 Spaces. 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
double	borelMeasureSpaceExpectation(R1ToR1 funcR1ToR1) Compute the Borel Measure Expectation for the specified R^1 To R^1 Function over the full Input Space
R1	borelSigmaMeasure() Retrieve the Borel Sigma R^1 Probability Measure
double	populationMode() Retrieve the Population Mode
double	sampleMetricNorm(double dblX) Compute the Metric Norm of the Sample

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

pNorm, populationMetricNorm

Methods inherited from interface org.drip.spaces.tensor.R1GeneralizedVector

validateInstance

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

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

Method Detail

borelSigmaMeasure

R1 borelSigmaMeasure()

Retrieve the Borel Sigma R^1 Probability Measure

Returns:

The Borel Sigma R^1 Probability Measure

sampleMetricNorm

double sampleMetricNorm(double dblX)
                 throws java.lang.Exception

Compute the Metric Norm of the Sample

Parameters:

dblX - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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

populationMode

double populationMode()
               throws java.lang.Exception

Retrieve the Population Mode

Returns:

The Population Mode

Throws:

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

borelMeasureSpaceExpectation

double borelMeasureSpaceExpectation(R1ToR1 funcR1ToR1)
                             throws java.lang.Exception

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

Parameters:

funcR1ToR1 - R^1 To R^1 Function Instance

Returns:

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

Throws:

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