NormedRxToNormedRxFinite.java
package org.drip.spaces.functionclass;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>NormedRxToNormedRxFinite</i> exposes the Space of Functions that are a Transform from the Normed
* R<sup>x</sup> To Normed R<sup>d</sup> Spaces. The References are:
*
* <br><br>
* <ul>
* <li>
* Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of
* Operators in Banach Spaces <i>Annals of the Fourier Institute</i> <b>35 (3)</b> 79-118
* </li>
* <li>
* Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
* <b>Cambridge University Press</b> Cambridge UK
* </li>
* <li>
* Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function
* Classes, in: <i>Proceedings of the 13th Annual Conference on Computational Learning
* Theory</i> <b>ACM</b> New York
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/README.md">R<sup>1</sup> and R<sup>d</sup> Vector/Tensor Spaces (Validated and/or Normed), and Function Classes</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/functionclass/README.md">Normed Finite Spaces Function Class</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class NormedRxToNormedRxFinite {
private double _dblMaureyConstant = java.lang.Double.NaN;
protected NormedRxToNormedRxFinite (
final double dblMaureyConstant)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblMaureyConstant = dblMaureyConstant) || 0. >=
_dblMaureyConstant)
throw new java.lang.Exception ("NormedRxToNormedRxFinite ctr => Invalid Inputs");
}
/**
* Retrieve the Input Vector Space
*
* @return The Input Vector Space
*/
public abstract org.drip.spaces.metric.GeneralizedMetricVectorSpace inputMetricVectorSpace();
/**
* Retrieve the Output Vector Space
*
* @return The Output Vector Space
*/
public abstract org.drip.spaces.metric.GeneralizedMetricVectorSpace outputMetricVectorSpace();
/**
* Compute the Operator Population Metric Norm
*
* @return The Operator Population Metric Norm
*
* @throws java.lang.Exception Thrown if the Operator Norm cannot be computed
*/
public abstract double operatorPopulationMetricNorm()
throws java.lang.Exception;
/**
* Compute the Operator Population Supremum Norm
*
* @return The Operator Population Supremum Norm
*
* @throws java.lang.Exception Thrown if the Operator Population Supremum Norm cannot be computed
*/
public abstract double operatorPopulationSupremumNorm()
throws java.lang.Exception;
/**
* Compute the Operator Sample Metric Norm
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Operator Sample Metric Norm
*
* @throws java.lang.Exception Thrown if the Operator Norm cannot be computed
*/
public abstract double operatorSampleMetricNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
throws java.lang.Exception;
/**
* Compute the Operator Sample Supremum Norm
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Operator Sample Supremum Norm
*
* @throws java.lang.Exception Thrown if the Operator Sample Supremum Norm cannot be computed
*/
public abstract double operatorSampleSupremumNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
throws java.lang.Exception;
/**
* Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
*
* @return The Agnostic Covering Number Upper/Lower Bounds for the Function Class
*/
public abstract org.drip.spaces.cover.FunctionClassCoveringBounds agnosticCoveringNumberBounds();
/**
* Retrieve the Maurey Constant
*
* @return The Maurey Constant
*/
public double maureyConstant()
{
return _dblMaureyConstant;
}
/**
* Retrieve the Scale-Sensitive Covering Number Upper/Lower Bounds given the Specified Sample for the
* Function Class
*
* @param gvvi The Validated Instance Vector Sequence
* @param funcR1ToR1FatShatter The Cover Fat Shattering Coefficient R^1 To R^1
*
* @return The Scale-Sensitive Covering Number Upper/Lower Bounds given the Specified Sample for the
* Function Class
*/
public org.drip.spaces.cover.FunctionClassCoveringBounds scaleSensitiveCoveringBounds (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
final org.drip.function.definition.R1ToR1 funcR1ToR1FatShatter)
{
if (null == gvvi || null == funcR1ToR1FatShatter) return null;
int iSampleSize = -1;
if (gvvi instanceof org.drip.spaces.instance.ValidatedR1) {
double[] adblInstance = ((org.drip.spaces.instance.ValidatedR1) gvvi).instance();
if (null == adblInstance) return null;
iSampleSize = adblInstance.length;
} else if (gvvi instanceof org.drip.spaces.instance.ValidatedRd) {
double[][] aadblInstance = ((org.drip.spaces.instance.ValidatedRd) gvvi).instance();
if (null == aadblInstance) return null;
iSampleSize = aadblInstance.length;
}
try {
return new org.drip.spaces.cover.ScaleSensitiveCoveringBounds (funcR1ToR1FatShatter,
iSampleSize);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Output Dimension
*
* @return The Output Dimension
*
* @throws java.lang.Exception Thrown if the Output Dimension is Invalid
*/
public int outputDimension()
throws java.lang.Exception
{
org.drip.spaces.metric.GeneralizedMetricVectorSpace gmvsOutput = outputMetricVectorSpace();
if (!(gmvsOutput instanceof org.drip.spaces.metric.R1Continuous) && !(gmvsOutput instanceof
org.drip.spaces.metric.RdContinuousBanach))
throw new java.lang.Exception ("NormedRxToNormedRxFinite::dimension => Invalid Inputs");
return gmvsOutput instanceof org.drip.spaces.metric.R1Continuous ? 1 :
((org.drip.spaces.metric.RdContinuousBanach) gmvsOutput).dimension();
}
/**
* Compute the Maurey Covering Number Upper Bounds for Operator Population Metric Norm
*
* @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator
* Population Metric Norm
*/
public org.drip.spaces.cover.MaureyOperatorCoveringBounds populationMetricCoveringBounds()
{
try {
return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
outputDimension(), operatorPopulationMetricNorm());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Maurey Covering Number Upper Bounds for Operator Population Supremum Norm
*
* @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator
* Population Supremum Norm
*/
public org.drip.spaces.cover.MaureyOperatorCoveringBounds populationSupremumCoveringBounds()
{
try {
return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
outputDimension(), operatorPopulationSupremumNorm());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Maurey Covering Number Upper Bounds for Operator Sample Metric Norm
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator Sample
* Metric Norm
*/
public org.drip.spaces.cover.MaureyOperatorCoveringBounds sampleMetricCoveringBounds (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
{
try {
return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
outputDimension(), operatorSampleMetricNorm (gvvi));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Maurey Covering Number Upper Bounds for Operator Sample Supremum Norm
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator Sample
* Supremum Norm
*/
public org.drip.spaces.cover.MaureyOperatorCoveringBounds sampleSupremumCoveringBounds (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
{
try {
return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
outputDimension(), operatorSampleSupremumNorm (gvvi));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}