DiagonalOperatorCoveringBound.java
package org.drip.learning.bound;
/*
* -*- 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>DiagonalOperatorCoveringBound</i> implements the Behavior of the Bound on the Covering Number of the
* Diagonal Scaling Operator. The Asymptote is set as either
* <br><br>
* log [e_n(A)] ~ O {(1/log n)^alpha}
* <br><br>
* - OR -
* <br><br>
* e_n(A) ~ O {(1/log n)^alpha}
* <br><br>
* The References are:
* <ul>
* <li>
* Ash, R. (1965): <i>Information Theory</i> <b>Inter-science</b> New York
* </li>
* <li>
* Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and Approximation of Operators</i>
* <b>Cambridge University Press</b> Cambridge UK
* </li>
* <li>
* Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and
* Approximation Numbers of Operators <i>Journal of Approximation Theory</i> <b>49</b> 219-237
* </li>
* <li>
* Konig, H. (1986): <i>Eigenvalue Distribution of Compact Operators</i> <b>Birkhauser</b> Basel,
* Switzerland
* </li>
* <li>
* Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex
* Combinations and mlps, in: <i>Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B.
* Scholkopf, and D. Schuurmans - editors</i> <b>MIT Press</b> Cambridge, MA
* </li>
* <li>
* Williamson, R. C., A. J. Smola, and B. Scholkopf (2001): Generalization Performance of Regularization
* Networks and Support Vector Machines via Entropy Numbers of Compact Operators <i>IEEE
* Transactions on Information Theory</i> <b>47 (6)</b> 2516-2532
* </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</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning">Agnostic Learning Bounds under Empirical Loss Minimization Schemes</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning/bound">Covering Numbers, Concentration, Lipschitz Bounds</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class DiagonalOperatorCoveringBound {
/**
* Asymptote on the Base Diagonal Operator Entropy Number
*/
public static final int BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT = 1;
/**
* Asymptote on the Log of the Diagonal Operator Entropy Number
*/
public static final int LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT = 2;
private double _dblOperatorEntropyAsymptoteExponent = java.lang.Double.NaN;
private int _iOperatorEntropyAsymptoteBase = BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT;
/**
* DiagonalOperatorCoveringBound Constructor
*
* @param iOperatorEntropyAsymptoteBase Indicate the Asymptote is on the Base Value or Log Value
* @param dblOperatorEntropyAsymptoteExponent The Entropy Number Asymptote Exponent
*
* @throws java.lang.Exception Throws if the Inputs are Invalid
*/
public DiagonalOperatorCoveringBound (
final int iOperatorEntropyAsymptoteBase,
final double dblOperatorEntropyAsymptoteExponent)
throws java.lang.Exception
{
if ((BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT != (_iOperatorEntropyAsymptoteBase =
iOperatorEntropyAsymptoteBase) && LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT !=
_iOperatorEntropyAsymptoteBase) || !org.drip.numerical.common.NumberUtil.IsValid
(_dblOperatorEntropyAsymptoteExponent = dblOperatorEntropyAsymptoteExponent))
throw new java.lang.Exception ("DiagonalOperatorCoveringBound ctr => Invalid Inputs");
}
/**
* Retrieve the Entropy Number Asymptote Type
*
* @return The Entropy Number Asymptote Type
*/
public int entropyNumberAsymptoteType()
{
return _iOperatorEntropyAsymptoteBase;
}
/**
* Retrieve the Entropy Number Asymptote Exponent
*
* @return The Entropy Number Asymptote Exponent
*/
public double entropyNumberAsymptoteExponent()
{
return _dblOperatorEntropyAsymptoteExponent;
}
}