IntegralOperatorEigenContainer.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>IntegralOperatorEigenContainer</i> holds the Group of Eigen-Components that result from the
* Eigenization 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 class IntegralOperatorEigenContainer {
private org.drip.learning.kernel.IntegralOperatorEigenComponent[] _aIOEC = null;
/**
* IntegralOperatorEigenContainer Constructor
*
* @param aIOEC Array of the Integral Operator Eigen-Components
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public IntegralOperatorEigenContainer (
final org.drip.learning.kernel.IntegralOperatorEigenComponent[] aIOEC)
throws java.lang.Exception
{
if (null == (_aIOEC = aIOEC) || 0 == _aIOEC.length)
throw new java.lang.Exception ("IntegralOperatorEigenContainer ctr: Invalid Inputs");
}
/**
* Retrieve the Array of the Integral Operator Eigen-Components
*
* @return The Array of the Integral Operator Eigen-Components
*/
public org.drip.learning.kernel.IntegralOperatorEigenComponent[] eigenComponents()
{
return _aIOEC;
}
/**
* Retrieve the Eigen Input Space
*
* @return The Eigen Input Space
*/
public org.drip.spaces.metric.RdNormed inputMetricVectorSpace()
{
return _aIOEC[0].eigenFunction().inputMetricVectorSpace();
}
/**
* Retrieve the Eigen Output Space
*
* @return The Eigen Output Space
*/
public org.drip.spaces.metric.R1Normed outputMetricVectorSpace()
{
return _aIOEC[0].eigenFunction().outputMetricVectorSpace();
}
/**
* Generate the Diagonally Scaled Normed Vector Space of the RKHS Feature Space Bounds that results on
* applying the Diagonal Scaling Operator
*
* @param dso The Diagonal Scaling Operator
*
* @return The Diagonally Scaled Normed Vector Space of the RKHS Feature Space
*/
public org.drip.spaces.metric.R1Combinatorial diagonallyScaledFeatureSpace (
final org.drip.learning.kernel.DiagonalScalingOperator dso)
{
if (null == dso) return null;
double[] adblDiagonalScalingOperator = dso.scaler();
int iDimension = adblDiagonalScalingOperator.length;
if (iDimension != _aIOEC.length) return null;
java.util.List<java.lang.Double> lsElementSpace = new java.util.ArrayList<java.lang.Double>();
for (int i = 0; i < iDimension; ++i)
lsElementSpace.add (0.5 * _aIOEC[i].rkhsFeatureParallelepipedLength() /
adblDiagonalScalingOperator[i]);
try {
return new org.drip.spaces.metric.R1Combinatorial (lsElementSpace, null, 2);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Generate the Operator Class Covering Number Bounds of the RKHS Feature Space Bounds that result on the
* Application of the Diagonal Scaling Operator
*
* @param dso The Diagonal Scaling Operator
*
* @return The Operator Class Covering Number Bounds of the RKHS Feature Space
*/
public org.drip.spaces.cover.OperatorClassCoveringBounds scaledCoveringNumberBounds (
final org.drip.learning.kernel.DiagonalScalingOperator dso)
{
final org.drip.spaces.metric.R1Combinatorial r1ContinuousScaled = diagonallyScaledFeatureSpace (dso);
if (null == r1ContinuousScaled) return null;
try {
final double dblPopulationMetricNorm = r1ContinuousScaled.populationMetricNorm();
org.drip.spaces.cover.OperatorClassCoveringBounds occb = new
org.drip.spaces.cover.OperatorClassCoveringBounds() {
@Override public double entropyNumberLowerBound()
throws java.lang.Exception
{
return dso.entropyNumberLowerBound() * dblPopulationMetricNorm;
}
@Override public double entropyNumberUpperBound()
throws java.lang.Exception
{
return dso.entropyNumberUpperBound() * dblPopulationMetricNorm;
}
@Override public int entropyNumberIndex()
{
return dso.entropyNumberIndex();
}
@Override public double norm()
throws java.lang.Exception
{
return dso.norm() * dblPopulationMetricNorm;
}
@Override public org.drip.learning.bound.DiagonalOperatorCoveringBound
entropyNumberAsymptote()
{
return dso.entropyNumberAsymptote();
}
};
return occb;
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}