SymmetricRdToNormedR1Kernel.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>SymmetricRdToNormedR1Kernel</i> exposes the Functionality behind the Kernel that is Normed
* R<sup>d</sup> X Normed R<sup>d</sup> To Supremum R<sup>1</sup>, that is, a Kernel that symmetric in the
* Input Metric Vector Space in terms of both the Metric and the Dimensionality.
*
* <br><br>
* The References are:
* <br><br>
* <ul>
* <li>
* Ash, R. (1965): <i>Information Theory</i> <b>Inter-science</b> New York
* </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 SymmetricRdToNormedR1Kernel {
private org.drip.spaces.metric.RdNormed _rdContinuousInput = null;
private org.drip.spaces.metric.R1Normed _r1ContinuousOutput = null;
/**
* SymmetricRdToNormedR1Kernel Constructor
*
* @param rdContinuousInput The Symmetric Input R^d Metric Vector Space
* @param r1ContinuousOutput The Output R^1 Metric Vector Space
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public SymmetricRdToNormedR1Kernel (
final org.drip.spaces.metric.RdNormed rdContinuousInput,
final org.drip.spaces.metric.R1Normed r1ContinuousOutput)
throws java.lang.Exception
{
if (null == (_rdContinuousInput = rdContinuousInput) || null == (_r1ContinuousOutput =
r1ContinuousOutput))
throw new java.lang.Exception ("SymmetricRdToNormedR1Kernel ctr: Invalid Inputs");
}
/**
* Retrieve the Symmetric Input Metric R^d Vector Space
*
* @return The Symmetric Input Metric R^d Vector Space
*/
public org.drip.spaces.metric.RdNormed inputMetricVectorSpace()
{
return _rdContinuousInput;
}
/**
* Retrieve the Output R^1 Metric Vector Space
*
* @return The Output R^1 Metric Vector Space
*/
public org.drip.spaces.metric.R1Normed outputMetricVectorSpace()
{
return _r1ContinuousOutput;
}
/**
* Compute the Feature Space Input Dimension
*
* @return The Feature Space Input Dimension
*/
public int featureSpaceDimension()
{
return _rdContinuousInput.dimension();
}
/**
* Compute the Kernel's R^d X R^d To R^1 Value
*
* @param adblX Validated Vector Instance X
* @param adblY Validated Vector Instance Y
*
* @return The Kernel's R^d X R^d To R^1 Value
*
* @throws java.lang.Exception Thrown if the Inputs are invalid
*/
public abstract double evaluate (
final double[] adblX,
final double[] adblY)
throws java.lang.Exception;
}