DiagonalScalingOperator.java
package org.drip.learning.kernel;
/*
* -*- 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>DiagonalScalingOperator</i> implements the Scaling Operator that is used to determine the Bounds of the
* R<sup>x</sup> L<sub>2</sub> To R<sup>x</sup> L<sub>2</sub> Kernel Linear Integral Operator defined by:
*
* T_k [f(.)] := Integral Over Input Space {k (., y) * f(y) * d[Prob(y)]}
*
* <br><br>
* The References are:
* <br><br>
* <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>
* </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/kernel">Statistical Learning Banach Mercer Kernels</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class DiagonalScalingOperator implements org.drip.spaces.cover.OperatorClassCoveringBounds {
private double[] _adblDiagonalScaler = null;
private double _dblScalingProductSupremumBound = java.lang.Double.NaN;
/**
* DiagonalScalingOperator Constructor
*
* @param adblDiagonalScaler The Diagonal Scaling Multiplier Array
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public DiagonalScalingOperator (
final double[] adblDiagonalScaler)
throws java.lang.Exception
{
if (null == (_adblDiagonalScaler = adblDiagonalScaler))
throw new java.lang.Exception ("DiagonalScalingOperator Constructor: Invalid Inputs");
double dblScalingProduct = 1.;
int iScalingSize = _adblDiagonalScaler.length;
if (0 == iScalingSize)
throw new java.lang.Exception ("DiagonalScalingOperator Constructor: Invalid Inputs");
for (int i = 0; i < iScalingSize; ++i) {
if (!org.drip.numerical.common.NumberUtil.IsValid (_adblDiagonalScaler[i]) || 0. >
_adblDiagonalScaler[i])
throw new java.lang.Exception ("DiagonalScalingOperator Constructor: Invalid Inputs");
if (0 == i) _dblScalingProductSupremumBound = _adblDiagonalScaler[i];
if (i > 0) {
if (_adblDiagonalScaler[i - 1] < _adblDiagonalScaler[i])
throw new java.lang.Exception ("DiagonalScalingOperator Constructor: Invalid Inputs");
double dblCurrentSupremumBound = java.lang.Math.pow ((dblScalingProduct *=
_adblDiagonalScaler[i]) / iScalingSize, 1. / i);
if (_dblScalingProductSupremumBound < dblCurrentSupremumBound)
_dblScalingProductSupremumBound = dblCurrentSupremumBound;
}
}
}
/**
* Retrieve the Diagonal Scaling Multiplier Array
*
* @return The Diagonal Scaling Multiplier Array
*/
public double[] scaler()
{
return _adblDiagonalScaler;
}
@Override public int entropyNumberIndex()
{
return _adblDiagonalScaler.length;
}
@Override public double entropyNumberLowerBound()
{
return _dblScalingProductSupremumBound;
}
@Override public double entropyNumberUpperBound()
{
return 6. * _dblScalingProductSupremumBound;
}
}