R1MultivariateNormal.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>R1MultivariateNormal</i> contains the Generalized Joint Multivariate R<sup>1</sup> Normal
* 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/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1MultivariateNormal extends org.drip.measure.continuous.R1Multivariate {
private double[] _adblMean = null;
private org.drip.measure.gaussian.Covariance _covariance = null;
/**
* Construct a Standard R1MultivariateNormal Instance
*
* @param meta The R^1 Multivariate Meta Headers
* @param adblMean Array of the Univariate Means
* @param aadblCovariance The Covariance Matrix
*
* @return The Standard Normal Univariate Distribution
*/
public static final R1MultivariateNormal Standard (
final org.drip.measure.continuous.MultivariateMeta meta,
final double[] adblMean,
final double[][] aadblCovariance)
{
try {
return new R1MultivariateNormal (meta, adblMean, new org.drip.measure.gaussian.Covariance
(aadblCovariance));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard R1MultivariateNormal Instance
*
* @param astrVariateID Array of Variate IDs
* @param adblMean Array of the Univariate Means
* @param aadblCovariance The Covariance Matrix
*
* @return The Standard Normal Univariate Distribution
*/
public static final R1MultivariateNormal Standard (
final java.lang.String[] astrVariateID,
final double[] adblMean,
final double[][] aadblCovariance)
{
try {
return new R1MultivariateNormal (new org.drip.measure.continuous.MultivariateMeta
(astrVariateID), adblMean, new org.drip.measure.gaussian.Covariance (aadblCovariance));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* R1MultivariateNormal Constructor
*
* @param meta The R^1 Multivariate Meta Headers
* @param adblMean Array of the Univariate Means
* @param covariance The Multivariate Covariance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1MultivariateNormal (
final org.drip.measure.continuous.MultivariateMeta meta,
final double[] adblMean,
final org.drip.measure.gaussian.Covariance covariance)
throws java.lang.Exception
{
super (meta);
if (null == (_adblMean = adblMean) || null == (_covariance = covariance))
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
int iNumVariate = meta.numVariable();
if (iNumVariate != _adblMean.length || iNumVariate != _covariance.numVariate() ||
!org.drip.numerical.common.NumberUtil.IsValid (_adblMean)) {
System.out.println ("iNumVariate = " + iNumVariate);
System.out.println ("_adblMean = " + _adblMean.length);
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
}
}
/**
* Compute the Co-variance of the Distribution
*
* @return The Co-variance of the Distribution
*/
public org.drip.measure.gaussian.Covariance covariance()
{
return _covariance;
}
@Override public double density (
final double[] adblVariate)
throws java.lang.Exception
{
if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate))
throw new java.lang.Exception ("R1MultivariateNormal::density => Invalid Inputs");
double dblDensity = 0.;
int iNumVariate = _adblMean.length;
double[] adblVariateOffset = new double[iNumVariate];
if (iNumVariate != adblVariate.length)
throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
for (int i = 0; i < iNumVariate; ++i)
adblVariateOffset[i] = adblVariate[i] - _adblMean[i];
double[][] aadblPrecision = _covariance.precisionMatrix();
for (int i = 0; i < iNumVariate; ++i) {
for (int j = 0; j < iNumVariate; ++j)
dblDensity = dblDensity + adblVariateOffset[i] * aadblPrecision[i][j] *
adblVariateOffset[j];
}
return java.lang.Math.exp (dblDensity) * java.lang.Math.pow (2. * java.lang.Math.PI, -0.5 *
iNumVariate);
}
@Override public double[] mean()
{
return _adblMean;
}
@Override public double[] variance()
{
return _covariance.variance();
}
}