R1Multivariate.java
package org.drip.measure.continuous;
/*
* -*- 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
*
* 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>R1Multivariate</i> contains the Generalized R<sup>1</sup> Multivariate Distributions.
*
* <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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/continuous/README.md">R<sup>1</sup> and R<sup>d</sup> Continuous Random Measure</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class R1Multivariate {
private org.drip.measure.continuous.MultivariateMeta _meta = null;
protected R1Multivariate (
final org.drip.measure.continuous.MultivariateMeta meta)
throws java.lang.Exception
{
if (null == (_meta = meta))
throw new java.lang.Exception ("R1Multivariate Constructor => Invalid Inputs");
}
/**
* Retrieve the Multivariate Meta Instance
*
* @return The Multivariate Meta Instance
*/
public org.drip.measure.continuous.MultivariateMeta meta()
{
return _meta;
}
/**
* Retrieve the Left Edge Bounding Multivariate
*
* @return The Left Edge Bounding Multivariate
*/
public double[] leftEdge()
{
int iNumVariate = _meta.numVariable();
double[] adblLeftEdge = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i)
adblLeftEdge[i] = java.lang.Double.MIN_NORMAL;
return adblLeftEdge;
}
/**
* Retrieve the Right Edge Bounding Multivariate
*
* @return The Right Edge Bounding Multivariate
*/
public double[] rightEdge()
{
int iNumVariate = _meta.numVariable();
double[] adblRightEdge = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i)
adblRightEdge[i] = java.lang.Double.MAX_VALUE;
return adblRightEdge;
}
/**
* Compute the Density under the Distribution at the given Multivariate
*
* @param adblVariate The Multivariate at which the Density needs to be computed
*
* @return The Density
*
* @throws java.lang.Exception Thrown if the Density cannot be computed
*/
public abstract double density (
final double[] adblVariate)
throws java.lang.Exception;
/**
* Convert the Multivariate Density into an RdToR1 Functions Instance
*
* @return The Multivariate Density converted into an RdToR1 Functions Instance
*/
public org.drip.function.definition.RdToR1 densityRdToR1()
{
return new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return _meta.numVariable();
}
@Override public double evaluate (
final double[] adblVariate)
throws java.lang.Exception
{
return density (adblVariate);
}
};
}
/**
* Compute the Cumulative under the Distribution to the given Variate Values
*
* @param adblVariate Array of Variate Values to which the Cumulative is to be computed
*
* @return The Cumulative
*
* @throws java.lang.Exception Thrown if the Cumulative cannot be computed
*/
public double cumulative (
final double[] adblVariate)
throws java.lang.Exception
{
return densityRdToR1().integrate (leftEdge(), adblVariate);
}
/**
* Compute the Incremental under the Distribution between the 2 Multivariate Instances
*
* @param adblVariateLeft Left Multivariate Instance to which the Cumulative is to be computed
* @param adblVariateRight Right Multivariate Instance to which the Cumulative is to be computed
*
* @return The Incremental
*
* @throws java.lang.Exception Thrown if the Incremental cannot be computed
*/
public double incremental (
final double[] adblVariateLeft,
final double[] adblVariateRight)
throws java.lang.Exception
{
return densityRdToR1().integrate (adblVariateLeft, adblVariateRight);
}
/**
* Compute the Expectation of the Specified R^d To R^1 Function Instance
*
* @param funcRdToR1 The R^d To R^1 Function Instance
*
* @return The Expectation of the Specified R^d To R^1 Function Instance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double expectation (
final org.drip.function.definition.RdToR1 funcRdToR1)
throws java.lang.Exception
{
if (null == funcRdToR1)
throw new java.lang.Exception ("R1Multivariate::expectation => Invalid Inputs");
return new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return _meta.numVariable();
}
@Override public double evaluate (
final double[] adblVariate)
throws java.lang.Exception
{
return density (adblVariate) * funcRdToR1.evaluate (adblVariate);
}
}.integrate (leftEdge(), rightEdge());
}
/**
* Compute the Mean of the Distribution
*
* @return The Mean of the Distribution
*/
public double[] mean()
{
int iNumVariate = _meta.numVariable();
double[] adblMean = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i) {
final int iVariate = i;
try {
adblMean[i] = expectation (new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return _meta.numVariable();
}
@Override public double evaluate (
final double[] adblVariate)
throws java.lang.Exception
{
return density (adblVariate) * adblVariate[iVariate];
}
});
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
return adblMean;
}
/**
* Compute the Variance of the Distribution
*
* @return The Variance of the Distribution
*/
public double[] variance()
{
final double[] adblMean = mean();
if (null == adblMean) return null;
final int iNumVariate = adblMean.length;
double[] adblVariance = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i) {
final int iVariate = i;
try {
adblVariance[i] = expectation (new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return _meta.numVariable();
}
@Override public double evaluate (
final double[] adblVariate)
throws java.lang.Exception
{
double dblSecondMoment = 0.;
for (int i = 0; i < iNumVariate; ++i) {
double dblOffset = adblVariate[iVariate] - adblMean[iVariate];
dblSecondMoment = dblSecondMoment + dblOffset * dblOffset;
}
return density (adblVariate) * dblSecondMoment;
}
});
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
return adblVariance;
}
}