L1R1CoveringBounds.java
package org.drip.spaces.cover;
/*
* -*- 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>L1R1CoveringBounds</i> implements the Lower/Upper Bounds for the Class of Non-decreasing R<sup>1</sup>
* To L<sub>1</sub> R<sup>1</sup> for Functions that are:
*
* <br><br>
* <ul>
* <li>
* Absolutely Bounded
* </li>
* <li>
* Have Bounded Variation
* </li>
* </ul>
*
* The References are:
*
* <br><br>
* <ul>
* <li>
* P. L. Bartlett, S. R. Kulkarni, and S. E. Posner (1997): Covering Numbers for Real-valued
* Function Classes <i>IEEE Transactions on Information Theory</i> <b>45 (5)</b> 1721-1724
* </li>
* <li>
* L. Birge (1987): Estimating a Density Under Order Restrictions: Non-asymptotic Minimax Risk
* <i>Annals of Statistics</i> <b>15</b> 995-1012
* </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/cover/README.md">Vector Spaces Covering Number Estimator</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class L1R1CoveringBounds implements org.drip.spaces.cover.FunctionClassCoveringBounds {
private double _dblBound = java.lang.Double.NaN;
private double _dblSupport = java.lang.Double.NaN;
private double _dblVariation = java.lang.Double.NaN;
/**
* L1R1CoveringBounds Constructor
*
* @param dblSupport The Ordinate Support
* @param dblVariation The Function Variation
* @param dblBound The Function Bound
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public L1R1CoveringBounds (
final double dblSupport,
final double dblVariation,
final double dblBound)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblSupport = dblSupport) || 0. >= _dblSupport ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblVariation = dblVariation) || 0. >= _dblVariation)
throw new java.lang.Exception ("L1R1CoveringBounds ctr: Invalid Inputs");
if (org.drip.numerical.common.NumberUtil.IsValid (_dblBound = dblBound) && _dblBound <= 0.5 *
_dblVariation)
throw new java.lang.Exception ("L1R1CoveringBounds ctr: Invalid Inputs");
}
/**
* Retrieve the Ordinate Support
*
* @return The Ordinate Support
*/
public double support()
{
return _dblSupport;
}
/**
* Retrieve the Function Variation
*
* @return The Function Variation
*/
public double variation()
{
return _dblVariation;
}
/**
* Retrieve the Function Bound
*
* @return The Function Bound
*/
public double bound()
{
return _dblBound;
}
@Override public double logLowerBound (
final double dblCover)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. == dblCover)
throw new java.lang.Exception ("L1R1CoveringBounds::logLowerBound => Invalid Inputs");
double dblVariationCoverScale = dblCover / (_dblSupport * _dblVariation);
double dblVariationLogLowerBound = 1. / (54. * dblVariationCoverScale);
if (1. < 12. * dblVariationCoverScale)
throw new java.lang.Exception ("L1R1CoveringBounds::logLowerBound => Invalid Inputs");
return !org.drip.numerical.common.NumberUtil.IsValid (_dblBound) ? dblVariationLogLowerBound : 1. +
dblVariationLogLowerBound * java.lang.Math.log (2.) + java.lang.Math.log (_dblSupport * _dblBound
/ (6. * dblCover));
}
@Override public double logUpperBound (
final double dblCover)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover))
throw new java.lang.Exception ("L1R1CoveringBounds::logUpperBound => Invalid Inputs");
double dblVariationCoverScale = dblCover / (_dblSupport * _dblVariation);
if (1. < 12. * dblVariationCoverScale)
throw new java.lang.Exception ("L1R1CoveringBounds::logUpperBound => Invalid Inputs");
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblBound))
return java.lang.Math.log (2.) * 12. / dblVariationCoverScale;
return java.lang.Math.log (2.) * 18. / dblVariationCoverScale + 3. * _dblSupport * (2. * _dblBound -
_dblVariation) / (8. * dblCover);
}
}