Covariance.java
package org.drip.measure.gaussian;
/*
* -*- 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>Covariance</i> holds the Standard Covariance Matrix, and provides functions to manipulate it.
*
* <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/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class Covariance {
private double[][] _aadblPrecision = null;
private double[][] _aadblCovariance = null;
/**
* Covariance Constructor
*
* @param aadblCovariance Double Array of the Covariance Matrix
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public Covariance (
final double[][] aadblCovariance)
throws java.lang.Exception
{
if (null == (_aadblCovariance = aadblCovariance))
throw new java.lang.Exception ("Covariance Constructor => Invalid Inputs!");
int iNumVariate = _aadblCovariance.length;
if (0 == iNumVariate)
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
for (int i = 0; i < iNumVariate; ++i) {
if (null == _aadblCovariance[i] || iNumVariate != _aadblCovariance[i].length ||
!org.drip.numerical.common.NumberUtil.IsValid (_aadblCovariance[i]))
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
}
if (null == (_aadblPrecision = org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination
(_aadblCovariance)))
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
}
/**
* Retrieve the Number of Variates
*
* @return The Number of Variates
*/
public int numVariate()
{
return _aadblCovariance.length;
}
/**
* Retrieve the Covariance Matrix
*
* @return The Covariance Matrix
*/
public double[][] covarianceMatrix()
{
return _aadblCovariance;
}
/**
* Retrieve the Precision Matrix
*
* @return The Precision Matrix
*/
public double[][] precisionMatrix()
{
return _aadblPrecision;
}
/**
* Retrieve the Variance Array
*
* @return The Variance Array
*/
public double[] variance()
{
int iNumVariate = _aadblCovariance.length;
double[] adblVariance = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i)
adblVariance[i] = _aadblCovariance[i][i];
return adblVariance;
}
/**
* Retrieve the Volatility Array
*
* @return The Volatility Array
*/
public double[] volatility()
{
int iNumVariate = _aadblCovariance.length;
double[] adblVolatility = new double[iNumVariate];
for (int i = 0; i < iNumVariate; ++i)
adblVolatility[i] = java.lang.Math.sqrt (_aadblCovariance[i][i]);
return adblVolatility;
}
/**
* Retrieve the Correlation Matrix
*
* @return The Correlation Matrix
*/
public double[][] correlationMatrix()
{
int iNumVariate = _aadblCovariance.length;
double[][] aadblCorrelation = new double[iNumVariate][iNumVariate];
double[] adblVolatility = volatility();
for (int i = 0; i < iNumVariate; ++i) {
for (int j = 0; j < iNumVariate; ++j)
aadblCorrelation[i][j] = _aadblCovariance[i][j] / (adblVolatility[i] * adblVolatility[j]);
}
return aadblCorrelation;
}
}