Package 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
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
- Retrieve the Borel Sigma R1 Probability Measure
- Compute the Metric Norm of the Sample
- Retrieve the Population Mode
- Compute the Borel Measure Expectation for the specified R1 To R1 Function over the full Input Space
- Author:
- Lakshmi Krishnamurthy
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Field Summary
Fields inherited from interface org.drip.spaces.metric.GeneralizedMetricVectorSpace
EUCLIDEAN_NORM, L2_NORM, LINFINITITY_NORM
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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 SpaceR1Univariate
borelSigmaMeasure()
Retrieve the Borel Sigma R1 Probability Measuredouble
populationMode()
Retrieve the Population Modedouble
sampleMetricNorm(double x)
Compute the Metric Norm of the SampleMethods 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.R1GeneralizedVector
validateInstance
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Method Details
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borelSigmaMeasure
R1Univariate borelSigmaMeasure()Retrieve the Borel Sigma R1 Probability Measure- Returns:
- The Borel Sigma R1 Probability Measure
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sampleMetricNorm
double sampleMetricNorm(double x) throws java.lang.ExceptionCompute 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
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populationMode
double populationMode() throws java.lang.ExceptionRetrieve the Population Mode- Returns:
- The Population Mode
- Throws:
java.lang.Exception
- Thrown if the Population Mode cannot be calculated
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borelMeasureSpaceExpectation
Compute the Borel Measure Expectation for the specified R1 To R1 Function over the full Input Space- 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
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