NormedRxToNormedRd.java
package org.drip.spaces.rxtord;
/*
* -*- 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>NormedRxToNormedRd</i> is the Abstract Class that exposes f : Normed R<sup>x</sup> (x .gte. 1) To
* Normed R<sup>d</sup> Function Space. The Reference we've used is:
*
* <br><br>
* <ul>
* <li>
* Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
* <b>Cambridge University Press</b> Cambridge UK
* </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/rxtord/README.md">R<sup>x</sup> To R<sup>d</sup> Normed Function Spaces</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class NormedRxToNormedRd {
/**
* Retrieve the Input Metric Vector Space
*
* @return The Input Metric Vector Space
*/
public abstract org.drip.spaces.metric.GeneralizedMetricVectorSpace inputMetricVectorSpace();
/**
* Retrieve the Output Metric Vector Space
*
* @return The Output Metric Vector Space
*/
public abstract org.drip.spaces.metric.RdNormed outputMetricVectorSpace();
/**
* Retrieve the Sample Supremum Norm Array
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Sample Supremum Norm Array
*/
public abstract double[] sampleSupremumNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi);
/**
* Retrieve the Sample Metric Norm Array
*
* @param gvvi The Validated Vector Space Instance
*
* @return The Sample Metric Norm Array
*/
public abstract double[] sampleMetricNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi);
/**
* Retrieve the Sample Covering Number Array
*
* @param gvvi The Validated Vector Space Instance
* @param dblCover The Cover
*
* @return The Sample Covering Number Array
*/
public double[] sampleCoveringNumber (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
final double dblCover)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;
double[] adblSampleMetricNorm = sampleMetricNorm (gvvi);
if (null == adblSampleMetricNorm) return null;
int iOutputDimensionality = adblSampleMetricNorm.length;
double[] adblSampleCoveringNumber = new double[iOutputDimensionality];
if (0 == iOutputDimensionality) return null;
double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());
for (int i = 0; i < iOutputDimensionality; ++i)
adblSampleCoveringNumber[i] = adblSampleMetricNorm[i] / dblCoverBallVolume;
return adblSampleCoveringNumber;
}
/**
* Retrieve the Sample Supremum Covering Number Array
*
* @param gvvi The Validated Vector Space Instance
* @param dblCover The Cover
*
* @return The Sample Supremum Covering Number Array
*/
public double[] sampleSupremumCoveringNumber (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
final double dblCover)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;
double[] adblSampleSupremumNorm = sampleSupremumNorm (gvvi);
if (null == adblSampleSupremumNorm) return null;
int iOutputDimensionality = adblSampleSupremumNorm.length;
double[] adblSampleSupremumCoveringNumber = new double[iOutputDimensionality];
if (0 == iOutputDimensionality) return null;
double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());
for (int i = 0; i < iOutputDimensionality; ++i)
adblSampleSupremumCoveringNumber[i] = adblSampleSupremumNorm[i] / dblCoverBallVolume;
return adblSampleSupremumCoveringNumber;
}
/**
* Retrieve the Population ESS (Essential Spectrum) Array
*
* @return The Population ESS (Essential Spectrum) Array
*/
public abstract double[] populationESS();
/**
* Retrieve the Population Metric Norm Array
*
* @return The Population Metric Norm Array
*/
public abstract double[] populationMetricNorm();
/**
* Retrieve the Population Supremum Norm Array
*
* @return The Population Supremum Norm Array
*/
public double[] populationSupremumNorm()
{
return populationMetricNorm();
}
/**
* Retrieve the Population Covering Number Array
*
* @param dblCover The Cover
*
* @return The Population Covering Number Array
*/
public double[] populationCoveringNumber (
final double dblCover)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;
double[] adblPopulationMetricNorm = populationMetricNorm();
if (null == adblPopulationMetricNorm) return null;
int iOutputDimensionality = adblPopulationMetricNorm.length;
double[] adblPopulationCoveringNumber = new double[iOutputDimensionality];
if (0 == iOutputDimensionality) return null;
double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());
for (int i = 0; i < iOutputDimensionality; ++i)
adblPopulationCoveringNumber[i] = adblPopulationMetricNorm[i] / dblCoverBallVolume;
return adblPopulationCoveringNumber;
}
/**
* Retrieve the Population Supremum Covering Number Array
*
* @param dblCover The Cover
*
* @return The Population Supremum Covering Number Array
*/
public double[] populationSupremumCoveringNumber (
final double dblCover)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;
double[] adblPopulationSupremumNorm = populationSupremumNorm();
if (null == adblPopulationSupremumNorm) return null;
int iOutputDimensionality = adblPopulationSupremumNorm.length;
double[] adblPopulationSupremumCoveringNumber = new double[iOutputDimensionality];
if (0 == iOutputDimensionality) return null;
double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());
for (int i = 0; i < iOutputDimensionality; ++i)
adblPopulationSupremumCoveringNumber[i] = adblPopulationSupremumNorm[i] / dblCoverBallVolume;
return adblPopulationSupremumCoveringNumber;
}
}