NormedR1ToL1R1Finite.java
package org.drip.spaces.functionclass;
/*
* -*- 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>NormedR1ToL1R1Finite</i> implements the Class f E F : Normed R<sup>1</sup> To L<sub>1</sub>
* R<sup>1</sup> Spaces of Finite Functions. 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/functionclass/README.md">Normed Finite Spaces Function Class</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class NormedR1ToL1R1Finite extends org.drip.spaces.functionclass.NormedR1ToNormedR1Finite {
/**
* Create Bounded R^1 To Bounded L1 R^1 Function Class for the specified Bounded Class of Finite
* Functions
*
* @param dblMaureyConstant Maurey Constant
* @param aR1ToR1 The Bounded R^1 To Bounded R^1 Function Set
* @param dblPredictorSupport The Set Predictor Support
* @param dblResponseBound The Set Response Bound
*
* @return The Bounded R^1 To Bounded R^1 Function Class for the specified Function Set
*/
public static final NormedR1ToL1R1Finite BoundedPredictorBoundedResponse (
final double dblMaureyConstant,
final org.drip.function.definition.R1ToR1[] aR1ToR1,
final double dblPredictorSupport,
final double dblResponseBound)
{
if (null == aR1ToR1) return null;
int iNumFunction = aR1ToR1.length;
org.drip.spaces.rxtor1.NormedR1ToNormedR1[] aR1ToR1FunctionSpace = new
org.drip.spaces.rxtor1.NormedR1ToNormedR1[iNumFunction];
if (0 == iNumFunction) return null;
try {
org.drip.spaces.metric.R1Continuous r1ContinuousInput = new org.drip.spaces.metric.R1Continuous
(-0.5 * dblPredictorSupport, 0.5 * dblPredictorSupport, null, 1);
org.drip.spaces.metric.R1Continuous r1ContinuousOutput = new org.drip.spaces.metric.R1Continuous
(-0.5 * dblResponseBound, 0.5 * dblResponseBound, null, 1);
for (int i = 0; i < iNumFunction; ++i)
aR1ToR1FunctionSpace[i] = new org.drip.spaces.rxtor1.NormedR1ContinuousToR1Continuous
(r1ContinuousInput, r1ContinuousOutput, aR1ToR1[i]);
return new NormedR1ToL1R1Finite (dblMaureyConstant, aR1ToR1FunctionSpace);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
protected NormedR1ToL1R1Finite (
final double dblMaureyConstant,
final org.drip.spaces.rxtor1.NormedR1ToNormedR1[] aR1ToR1FunctionSpace)
throws java.lang.Exception
{
super (dblMaureyConstant, aR1ToR1FunctionSpace);
}
@Override public org.drip.spaces.cover.FunctionClassCoveringBounds agnosticCoveringNumberBounds()
{
org.drip.spaces.rxtor1.NormedR1ToNormedR1[] aNormedR1ToNormedR1 =
(org.drip.spaces.rxtor1.NormedR1ToNormedR1[]) functionSpaces();
int iNumFunction = aNormedR1ToNormedR1.length;
double dblResponseLowerBound = java.lang.Double.NaN;
double dblResponseUpperBound = java.lang.Double.NaN;
double dblPredictorLowerBound = java.lang.Double.NaN;
double dblPredictorUpperBound = java.lang.Double.NaN;
for (int i = 0; i < iNumFunction; ++i) {
org.drip.spaces.rxtor1.NormedR1ToNormedR1 r1Tor1 = aNormedR1ToNormedR1[i];
org.drip.spaces.metric.R1Normed runsInput = r1Tor1.inputMetricVectorSpace();
org.drip.spaces.metric.R1Normed runsOutput = r1Tor1.outputMetricVectorSpace();
if (!runsInput.isPredictorBounded() || !runsOutput.isPredictorBounded()) return null;
double dblResponseLeftBound = runsOutput.leftEdge();
double dblPredictorLeftBound = runsInput.leftEdge();
double dblResponseRightBound = runsOutput.rightEdge();
double dblPredictorRightBound = runsInput.rightEdge();
if (!org.drip.numerical.common.NumberUtil.IsValid (dblPredictorLowerBound))
dblPredictorLowerBound = dblPredictorLeftBound;
else {
if (dblPredictorLowerBound > dblPredictorLeftBound)
dblPredictorLowerBound = dblPredictorLeftBound;
}
if (!org.drip.numerical.common.NumberUtil.IsValid (dblPredictorUpperBound))
dblPredictorUpperBound = dblPredictorRightBound;
else {
if (dblPredictorUpperBound < dblPredictorRightBound)
dblPredictorUpperBound = dblPredictorRightBound;
}
if (!org.drip.numerical.common.NumberUtil.IsValid (dblResponseLowerBound))
dblResponseLowerBound = dblResponseLeftBound;
else {
if (dblResponseLowerBound > dblResponseLeftBound)
dblResponseLowerBound = dblResponseLeftBound;
}
if (!org.drip.numerical.common.NumberUtil.IsValid (dblResponseUpperBound))
dblResponseUpperBound = dblResponseRightBound;
else {
if (dblResponseUpperBound < dblResponseRightBound)
dblResponseUpperBound = dblResponseRightBound;
}
}
double dblVariation = dblResponseUpperBound - dblResponseLowerBound;
try {
return new org.drip.spaces.cover.L1R1CoveringBounds (dblPredictorUpperBound -
dblPredictorLowerBound, dblVariation, dblVariation);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}