NormedR1ToNormedR1.java
package org.drip.spaces.rxtor1;
/*
* -*- 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>NormedR1ToNormedR1</i> is the Abstract Class underlying the f : Validated Normed R<sup>1</sup> To
* Validated Normed R<sup>1</sup> Function Spaces. 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/rxtor1/README.md">R<sup>x</sup> To R<sup>1</sup> Normed Function Spaces</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class NormedR1ToNormedR1 extends org.drip.spaces.rxtor1.NormedRxToNormedR1 {
private org.drip.spaces.metric.R1Normed _r1Input = null;
private org.drip.spaces.metric.R1Normed _r1Output = null;
private org.drip.function.definition.R1ToR1 _funcR1ToR1 = null;
protected NormedR1ToNormedR1 (
final org.drip.spaces.metric.R1Normed r1Input,
final org.drip.spaces.metric.R1Normed r1Output,
final org.drip.function.definition.R1ToR1 funcR1ToR1)
throws java.lang.Exception
{
if (null == (_r1Input = r1Input) || null == (_r1Output = r1Output))
throw new java.lang.Exception ("NormedR1ToNormedR1 ctr: Invalid Inputs");
_funcR1ToR1 = funcR1ToR1;
}
/**
* Retrieve the Underlying R1ToR1 Function
*
* @return The Underlying R1ToR1 Function
*/
public org.drip.function.definition.R1ToR1 function()
{
return _funcR1ToR1;
}
@Override public double sampleSupremumNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
throws java.lang.Exception
{
if (null == _funcR1ToR1 || null == gvvi || !gvvi.tensorSpaceType().match (_r1Input))
throw new java.lang.Exception ("NormedR1ToNormedR1::sampleSupremumNorm => Invalid Input");
double[] adblInstance = ((org.drip.spaces.instance.ValidatedR1) gvvi).instance();
int iNumSample = adblInstance.length;
double dblSupremumNorm = java.lang.Math.abs (_funcR1ToR1.evaluate (adblInstance[0]));
for (int i = 1; i < iNumSample; ++i) {
double dblResponse = java.lang.Math.abs (_funcR1ToR1.evaluate (adblInstance[i]));
if (dblResponse > dblSupremumNorm) dblSupremumNorm = dblResponse;
}
return dblSupremumNorm;
}
@Override public double sampleMetricNorm (
final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
throws java.lang.Exception
{
int iPNorm = _r1Output.pNorm();
if (java.lang.Integer.MAX_VALUE == iPNorm) return sampleSupremumNorm (gvvi);
if (null == _funcR1ToR1 || null == gvvi || !gvvi.tensorSpaceType().match (_r1Input))
throw new java.lang.Exception ("NormedR1ToNormedR1::sampleMetricNorm => Invalid Input");
double[] adblInstance = ((org.drip.spaces.instance.ValidatedR1) gvvi).instance();
double dblNorm = 0.;
int iNumSample = adblInstance.length;
for (int i = 0; i < iNumSample; ++i)
dblNorm += java.lang.Math.pow (java.lang.Math.abs (_funcR1ToR1.evaluate (adblInstance[i])),
iPNorm);
return java.lang.Math.pow (dblNorm, 1. / iPNorm);
}
@Override public double populationESS()
throws java.lang.Exception
{
if (null == _funcR1ToR1)
throw new java.lang.Exception ("NormedR1ToNormedR1::populationESS => Invalid Input");
return _funcR1ToR1.evaluate (_r1Input.populationMode());
}
@Override public org.drip.spaces.metric.R1Normed outputMetricVectorSpace()
{
return _r1Output;
}
@Override public org.drip.spaces.metric.R1Normed inputMetricVectorSpace()
{
return _r1Input;
}
}