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 lp Rd
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 Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
- Package = Hilbert/Banach Normed Metric Spaces
- Author:
- Lakshmi Krishnamurthy
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Constructor Summary
Constructors Constructor Description R1Combinatorial(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm)
R1Combinatorial Space Constructor -
Method Summary
Modifier and Type Method Description double
borelMeasureSpaceExpectation(R1ToR1 funcR1ToR1)
Compute the Borel Measure Expectation for the specified R^1 To R^1 Function over the full Input SpaceR1Univariate
borelSigmaMeasure()
Retrieve the Borel Sigma R^1 Probability Measureint
pNorm()
Retrieve the P-Norm Index of the Metric Spacedouble
populationMetricNorm()
Retrieve the Population Metric Normdouble
populationMode()
Retrieve the Population Modedouble
sampleMetricNorm(double dblX)
Compute the Metric Norm of the Samplestatic R1Combinatorial
Standard(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm)
Construct the Standard l^p R^1 Combinatorial Space Instancestatic R1Combinatorial
Supremum(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1)
Construct the Supremum (i.e., l^Infinity) R^1 Combinatorial Space InstanceMethods 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
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Constructor Details
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R1Combinatorial
public R1Combinatorial(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm) throws java.lang.ExceptionR1Combinatorial Space Constructor- Parameters:
lsElementSpace
- The List Space of ElementsdistR1
- The R^1 Borel Sigma MeasureiPNorm
- The p-norm of the Space- Throws:
java.lang.Exception
- Thrown if the Inputs are Invalid
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Method Details
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Standard
public static final R1Combinatorial Standard(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm)Construct the Standard l^p R^1 Combinatorial Space Instance- Parameters:
lsElementSpace
- The List Space of ElementsdistR1
- The R^1 Borel Sigma MeasureiPNorm
- The p-norm of the Space- Returns:
- The Standard l^p R^1 Combinatorial Space Instance
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Supremum
public static final R1Combinatorial Supremum(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1)Construct the Supremum (i.e., l^Infinity) R^1 Combinatorial Space Instance- Parameters:
lsElementSpace
- The List Space of ElementsdistR1
- The R^1 Borel Sigma Measure- Returns:
- The Supremum (i.e., l^Infinity) R^1 Combinatorial Space Instance
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pNorm
public int pNorm()Description copied from interface:GeneralizedMetricVectorSpace
Retrieve the P-Norm Index of the Metric Space- Specified by:
pNorm
in interfaceGeneralizedMetricVectorSpace
- Returns:
- The P-Norm Index of the Metric Space
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borelSigmaMeasure
Description copied from interface:R1Normed
Retrieve the Borel Sigma R^1 Probability Measure- Specified by:
borelSigmaMeasure
in interfaceR1Normed
- Returns:
- The Borel Sigma R^1 Probability Measure
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sampleMetricNorm
public double sampleMetricNorm(double dblX) throws java.lang.ExceptionDescription copied from interface:R1Normed
Compute the Metric Norm of the Sample- Specified by:
sampleMetricNorm
in interfaceR1Normed
- Parameters:
dblX
- The Sample- Returns:
- The Metric Norm of the Sample
- Throws:
java.lang.Exception
- Thrown if the Inputs are Invalid
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populationMode
public double populationMode() throws java.lang.ExceptionDescription copied from interface:R1Normed
Retrieve the Population Mode- Specified by:
populationMode
in interfaceR1Normed
- Returns:
- The Population Mode
- Throws:
java.lang.Exception
- Thrown if the Population Mode cannot be calculated
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populationMetricNorm
public double populationMetricNorm() throws java.lang.ExceptionDescription copied from interface:GeneralizedMetricVectorSpace
Retrieve the Population Metric Norm- Specified by:
populationMetricNorm
in interfaceGeneralizedMetricVectorSpace
- Returns:
- The Population Metric Norm
- Throws:
java.lang.Exception
- The Population Metric Norm cannot be computed
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borelMeasureSpaceExpectation
Description copied from interface:R1Normed
Compute the Borel Measure Expectation for the specified R^1 To R^1 Function over the full Input Space- Specified by:
borelMeasureSpaceExpectation
in interfaceR1Normed
- 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
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