R1Continuous.java
package org.drip.spaces.metric;
/*
* -*- 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>R1Continuous</i> implements the Normed, Bounded/Unbounded Continuous l<sub>p</sub> R<sup>1</sup>
* 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/metric/README.md">Hilbert/Banach Normed Metric Spaces</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class R1Continuous extends org.drip.spaces.tensor.R1ContinuousVector implements
org.drip.spaces.metric.R1Normed {
private int _iPNorm = -1;
private org.drip.measure.continuous.R1Univariate _distR1 = null;
/**
* Construct the Standard l^p R^1 Continuous Space Instance
*
* @param dblLeftEdge The Left Edge
* @param dblRightEdge The Right Edge
* @param distR1 The R^1 Borel Sigma Measure
* @param iPNorm The p-norm of the Space
*
* @return The Standard l^p R^1 Continuous Space Instance
*/
public static final R1Continuous Standard (
final double dblLeftEdge,
final double dblRightEdge,
final org.drip.measure.continuous.R1Univariate distR1,
final int iPNorm)
{
try {
return new R1Continuous (dblLeftEdge, dblRightEdge, distR1, iPNorm);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Construct the Supremum (i.e., l^Infinity) R^1 Continuous Space Instance
*
* @param dblLeftEdge The Left Edge
* @param dblRightEdge The Right Edge
* @param distR1 The R^1 Borel Sigma Measure
*
* @return The Supremum (i.e., l^Infinity) R^1 Continuous Space Instance
*/
public static final R1Continuous Supremum (
final double dblLeftEdge,
final double dblRightEdge,
final org.drip.measure.continuous.R1Univariate distR1)
{
try {
return new R1Continuous (dblLeftEdge, dblRightEdge, distR1, java.lang.Integer.MAX_VALUE);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* R1Continuous Space Constructor
*
* @param dblLeftEdge The Left Edge
* @param dblRightEdge The Right Edge
* @param distR1 The R^1 Borel Sigma Measure
* @param iPNorm The p-norm of the Space
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1Continuous (
final double dblLeftEdge,
final double dblRightEdge,
final org.drip.measure.continuous.R1Univariate distR1,
final int iPNorm)
throws java.lang.Exception
{
super (dblLeftEdge, dblRightEdge);
if (0 > (_iPNorm = iPNorm))
throw new java.lang.Exception ("R1Continuous Constructor: Invalid p-norm");
_distR1 = distR1;
}
@Override public int pNorm()
{
return _iPNorm;
}
@Override public org.drip.measure.continuous.R1Univariate borelSigmaMeasure()
{
return _distR1;
}
@Override public double sampleMetricNorm (
final double dblX)
throws java.lang.Exception
{
if (!validateInstance (dblX))
throw new java.lang.Exception ("R1Continuous::sampleMetricNorm => Invalid Inputs");
return java.lang.Math.abs (dblX);
}
@Override public double populationMode()
throws java.lang.Exception
{
if (null == _distR1)
throw new java.lang.Exception ("R1Continuous::populationMode => Invalid Inputs");
org.drip.function.definition.R1ToR1 funcR1ToR1 = new org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblX)
throws java.lang.Exception
{
return _distR1.density (dblX);
}
};
org.drip.function.definition.VariateOutputPair vopMode = funcR1ToR1.maxima (leftEdge(), rightEdge());
if (null == vopMode)
throw new java.lang.Exception ("R1Continuous::populationMode => Cannot compute VOP Mode");
return vopMode.variates()[0];
}
@Override public double populationMetricNorm()
throws java.lang.Exception
{
if (null == _distR1)
throw new java.lang.Exception ("R1Continuous::populationMetricNorm => Invalid Inputs");
org.drip.function.definition.R1ToR1 funcR1ToR1 = new org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblX)
throws java.lang.Exception
{
return sampleMetricNorm (dblX) * _distR1.density (dblX);
}
};
return funcR1ToR1.integrate (leftEdge(), rightEdge());
}
@Override public double borelMeasureSpaceExpectation (
final org.drip.function.definition.R1ToR1 funcR1ToR1)
throws java.lang.Exception
{
if (null == funcR1ToR1 || null == _distR1)
throw new java.lang.Exception ("R1Continuous::borelMeasureSpaceExpectation => Invalid Inputs");
org.drip.function.definition.R1ToR1 funcDensityR1ToR1 = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblX)
throws java.lang.Exception
{
return funcR1ToR1.evaluate (dblX) * _distR1.density (dblX);
}
};
return funcDensityR1ToR1.integrate (leftEdge(), rightEdge());
}
}