Package org.drip.spaces.metric

Class RdHilbert

java.lang.Object

org.drip.spaces.tensor.RdAggregate

org.drip.spaces.tensor.RdContinuousVector

org.drip.spaces.metric.RdBanach

org.drip.spaces.metric.RdHilbert

All Implemented Interfaces:

GeneralizedMetricVectorSpace, RdNormed, GeneralizedVector, RdGeneralizedVector

public class RdHilbert
extends RdBanach

RdHilbert implements the Bounded/Unbounded, Continuous l₂ 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 R² Hilbert Space Instance
• RdHilbert 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
RdHilbert(R1ContinuousVector[] r1ContinuousVectorArray, RdContinuous rd)	RdHilbert Space Constructor

Method Summary

Modifier and Type	Method	Description
double	sampleMetricNorm(double[] xArray)	Compute the Metric Norm of the Sample
static RdHilbert	StandardHilbert(int iDimension, RdContinuous distRd)	Construct the Standard l2 Rd Hilbert Space Instance

Methods inherited from class org.drip.spaces.metric.RdBanach

borelMeasureSpaceExpectation, borelSigmaMeasure, pNorm, populationMetricNorm, populationMode, populationSupremumNorm, sampleSupremumNorm, StandardBanach, SupremumBanach

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

cardinality, hyperVolume, leftDimensionEdge, leftEdge, rightDimensionEdge, rightEdge, Standard

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

RdHilbert

public RdHilbert(R1ContinuousVector[] r1ContinuousVectorArray,
RdContinuous rd)
          throws java.lang.Exception

RdHilbert Space Constructor

Parameters:

r1ContinuousVectorArray - Array of R¹ Continuous Vector Spaces

rd - The Multivariate Borel Sigma Measure

Throws:

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

Method Details

StandardHilbert

public static final RdHilbert StandardHilbert(int iDimension,
RdContinuous distRd)

Construct the Standard l² R^d Hilbert Space Instance

Parameters:

iDimension - The Space Dimension

distRd - The R^d Borel Sigma Measure

Returns:

The Standard l² R^d Hilbert Space Instance

sampleMetricNorm

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

Description copied from interface: RdNormed

Compute the Metric Norm of the Sample

Specified by:

sampleMetricNorm in interface RdNormed

Overrides:

sampleMetricNorm in class RdBanach

Parameters:

xArray - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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