Package org.drip.spaces.functionclass

Class NormedRxToNormedRdFinite

java.lang.Object
org.drip.spaces.functionclass.NormedRxToNormedRxFinite
org.drip.spaces.functionclass.NormedRxToNormedRdFinite
Direct Known Subclasses:
HilbertRxToSupremumRdFinite
public class NormedRxToNormedRdFinite
extends NormedRxToNormedRxFinite
NormedRxToNormedRdFinite implements the Class F with f E f : Normed Rx To Normed Rd Space of Finite Functions. The References are:

  • Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operators in Banach Spaces Annals of the Fourier Institute 35 (3) 79-118
  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK
  • Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory ACM New York
It provides the following Functionality:
  • NormedRxToNormedRdFinite Constructor
  • Retrieve the Array of Function Spaces in the Class
  • Estimate for the Function Class Population Covering Number Array, one for each dimension
  • Estimate for the Function Class Population Supremum Covering Number Array, one for each dimension
  • Estimate for the Scale-Sensitive Sample Covering Number Array for the specified Cover Size
  • Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size
  • Compute the Population Rd Metric Norm
  • Compute the Population Rd Supremum Norm
  • Compute the Sample Rd Metric Norm
  • Compute the Sample Rd Supremum Norm




Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • NormedRxToNormedRdFinite

      public NormedRxToNormedRdFinite​(double maureyConstant, NormedRxToNormedRd[] normedRxToNormedRdArray) throws java.lang.Exception
      NormedRxToNormedRdFinite Constructor
      Parameters:
      maureyConstant - Maurey Constant
      normedRxToNormedRdArray - Array of the Normed Rx To Normed Rd Spaces
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • agnosticCoveringNumberBounds

      public FunctionClassCoveringBounds agnosticCoveringNumberBounds()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
      Specified by:
      agnosticCoveringNumberBounds in class NormedRxToNormedRxFinite
      Returns:
      The Agnostic Covering Number Upper/Lower Bounds for the Function Class

    • inputMetricVectorSpace

      public GeneralizedMetricVectorSpace inputMetricVectorSpace()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Input Vector Space
      Specified by:
      inputMetricVectorSpace in class NormedRxToNormedRxFinite
      Returns:
      The Input Vector Space

    • outputMetricVectorSpace

      public RdNormed outputMetricVectorSpace()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Output Vector Space
      Specified by:
      outputMetricVectorSpace in class NormedRxToNormedRxFinite
      Returns:
      The Output Vector Space

    • functionSpaces

      public NormedRxToNormedRd[] functionSpaces()
      Retrieve the Array of Function Spaces in the Class
      Returns:
      The Array of Function Spaces in the Class

    • populationCoveringNumber

      public double[] populationCoveringNumber​(double[] coverArray)
      Estimate for the Function Class Population Covering Number Array, one for each dimension
      Parameters:
      coverArray - The Size of the Cover Array
      Returns:
      Function Class Population Covering Number Estimate Array, one for each dimension

    • populationCoveringNumber

      public double[] populationCoveringNumber​(double cover)
      Estimate for the Function Class Population Covering Number Array, one for each dimension
      Parameters:
      cover - The Cover
      Returns:
      Function Class Population Covering Number Estimate Array, one for each dimension

    • populationSupremumCoveringNumber

      public double[] populationSupremumCoveringNumber​(double[] coverArray)
      Estimate for the Function Class Population Supremum Covering Number Array, one for each dimension
      Parameters:
      coverArray - The Size of the Cover Array
      Returns:
      Function Class Population Supremum Covering Number Estimate Array, one for each dimension

    • populationSupremumCoveringNumber

      public double[] populationSupremumCoveringNumber​(double cover)
      Estimate for the Function Class Population Supremum Covering Number Array, one for each dimension
      Parameters:
      cover - The Cover
      Returns:
      Function Class Population Covering Supremum Number Estimate Array, one for each dimension

    • sampleCoveringNumber

      public double[] sampleCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double[] coverArray)
      Estimate for the Scale-Sensitive Sample Covering Number Array for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      coverArray - The Size of the Cover Array
      Returns:
      The Scale-Sensitive Sample Covering Number Array for the specified Cover Size

    • sampleCoveringNumber

      public double[] sampleCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover)
      Estimate for the Scale-Sensitive Sample Covering Number Array for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      cover - The Size of the Cover Array
      Returns:
      The Scale-Sensitive Sample Covering Number Array for the specified Cover Size

    • sampleSupremumCoveringNumber

      public double[] sampleSupremumCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double[] coverArray)
      Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      coverArray - The Cover Array
      Returns:
      The Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

    • sampleSupremumCoveringNumber

      public double[] sampleSupremumCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover)
      Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      cover - The Cover
      Returns:
      The Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

    • populationRdMetricNorm

      public double[] populationRdMetricNorm()
      Compute the Population Rd Metric Norm
      Returns:
      The Population Rd Metric Norm

    • populationRdSupremumNorm

      public double[] populationRdSupremumNorm()
      Compute the Population Rd Supremum Norm
      Returns:
      The Population Rd Supremum Norm

    • sampleRdMetricNorm

      public double[] sampleRdMetricNorm​(GeneralizedValidatedVector generalizedValidatedVector)
      Compute the Sample Rd Metric Norm
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Rd Metric Norm

    • sampleRdSupremumNorm

      public double[] sampleRdSupremumNorm​(GeneralizedValidatedVector generalizedValidatedVector)
      Compute the Sample Rd Supremum Norm
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Rd Supremum Norm

    • operatorPopulationMetricNorm

      public double operatorPopulationMetricNorm() throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Population Metric Norm
      Specified by:
      operatorPopulationMetricNorm in class NormedRxToNormedRxFinite
      Returns:
      The Operator Population Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Norm cannot be computed

    • operatorPopulationSupremumNorm

      public double operatorPopulationSupremumNorm() throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Population Supremum Norm
      Specified by:
      operatorPopulationSupremumNorm in class NormedRxToNormedRxFinite
      Returns:
      The Operator Population Supremum Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Population Supremum Norm cannot be computed

    • operatorSampleMetricNorm

      public double operatorSampleMetricNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Sample Metric Norm
      Specified by:
      operatorSampleMetricNorm in class NormedRxToNormedRxFinite
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Operator Sample Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Norm cannot be computed

    • operatorSampleSupremumNorm

      public double operatorSampleSupremumNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Sample Supremum Norm
      Specified by:
      operatorSampleSupremumNorm in class NormedRxToNormedRxFinite
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Operator Sample Supremum Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Sample Supremum Norm cannot be computed