MultivariateMoments.java
package org.drip.measure.statistics;
/*
* -*- 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>MultivariateMoments</i> generates and holds the Specified Multivariate Series Mean, Co-variance, and
* other selected Moments.
*
* <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/statistics/README.md">R<sup>1</sup> R<sup>d</sup> Thin Thick Moments</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class MultivariateMoments {
private org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double> _mapMean = new
org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double>();
private org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double> _mapCovariance = new
org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double>();
/**
* Generate the MultivariateMetrics Instance from the Series Realizations provided
*
* @param astrVariateName Array of Variate Name Headers
* @param aadblVariate Array of Variate Realization Arrays
*
* @return The MultivariateMetrics Instance
*/
public static final MultivariateMoments Standard (
final java.lang.String[] astrVariateName,
final double[][] aadblVariate)
{
if (null == astrVariateName || null == aadblVariate) return null;
int iNumVariate = astrVariateName.length;
double[] adblMean = new double[iNumVariate];
if (0 == iNumVariate || iNumVariate != aadblVariate.length) return null;
int iNumSample = aadblVariate[0].length;
if (0 == iNumSample) return null;
MultivariateMoments mvm = new MultivariateMoments();
for (int i = 0; i < iNumVariate; ++i) {
adblMean[i] = 0.;
double[] adblVariateSample = aadblVariate[i];
if (null == adblVariateSample || adblVariateSample.length != iNumSample) return null;
for (int k = 0; k < iNumSample; ++k) {
if (!org.drip.numerical.common.NumberUtil.IsValid (adblVariateSample[k])) return null;
adblMean[i] += adblVariateSample[k];
}
if (!mvm.addMean (astrVariateName[i], adblMean[i] /= iNumSample)) return null;
}
for (int i = 0; i < iNumVariate; ++i) {
for (int j = 0; j < iNumVariate; ++j) {
double dblCovariance = 0.;
for (int k = 0; k < iNumSample; ++k)
dblCovariance += (aadblVariate[i][k] - adblMean[i]) * (aadblVariate[j][k] - adblMean[j]);
if (!mvm.addCovariance (astrVariateName[i], astrVariateName[j], dblCovariance / iNumSample))
return null;
}
}
return mvm;
}
/**
* Generate the MultivariateMetrics Instance from the Specified Mean and Co-variance Inputs
*
* @param astrVariateName Array of Variate Name Headers
* @param adblMean Array of Variate Means
* @param aadblCovariance Double Array of the Variate Co-variance
*
* @return The MultivariateMetrics Instance
*/
public static final MultivariateMoments Standard (
final java.lang.String[] astrVariateName,
final double[] adblMean,
final double[][] aadblCovariance)
{
if (null == astrVariateName || null == adblMean || null == aadblCovariance) return null;
int iNumVariate = astrVariateName.length;
if (0 == iNumVariate || iNumVariate != adblMean.length || iNumVariate != aadblCovariance.length ||
null == aadblCovariance[0] || iNumVariate != aadblCovariance[0].length)
return null;
MultivariateMoments mvm = new MultivariateMoments();
for (int i = 0; i < iNumVariate; ++i) {
if (!mvm.addMean (astrVariateName[i], adblMean[i])) return null;
}
for (int i = 0; i < iNumVariate; ++i) {
for (int j = 0; j < iNumVariate; ++j) {
if (!mvm.addCovariance (astrVariateName[i], astrVariateName[j], aadblCovariance[i][j]))
return null;
}
}
return mvm;
}
protected MultivariateMoments()
{
}
/**
* Retrieve the Number of Variates in the Distribution
*
* @return The Number of Variates in the Distribution
*/
public int numVariate()
{
return _mapMean.size();
}
/**
* Retrieve the Variates for which the Metrics are available
*
* @return The Set of Variates
*/
public java.util.Set<java.lang.String> variateList()
{
return _mapMean.keySet();
}
/**
* Add the Mean for the Named Variate
*
* @param strVariateName The Named Variate
* @param dblMean The Variate Mean
*
* @return TRUE - The Variate Mean successfully added
*/
public boolean addMean (
final java.lang.String strVariateName,
final double dblMean)
{
if (null == strVariateName || strVariateName.isEmpty() || !org.drip.numerical.common.NumberUtil.IsValid
(dblMean))
return false;
_mapMean.put (strVariateName, dblMean);
return true;
}
/**
* Retrieve the Mean of the Named Variate
*
* @param strVariateName The Named Variate
*
* @return Mean of the Named Variate
*
* @throws java.lang.Exception Thrown if the Named Variate Mean cannot be retrieved
*/
public double mean (
final java.lang.String strVariateName)
throws java.lang.Exception
{
if (null == strVariateName || strVariateName.isEmpty() || !_mapMean.containsKey (strVariateName))
throw new java.lang.Exception ("MultivariateMetrics::mean => Invalid Inputs");
return _mapMean.get (strVariateName);
}
/**
* Add the Co-variance for the Named Variate Pair
*
* @param strVariate1Name The Named Variate #1
* @param strVariate2Name The Named Variate #2
* @param dblCovariance The Variate Mean
*
* @return TRUE - The Variate Pair Co-variance successfully added
*/
public boolean addCovariance (
final java.lang.String strVariate1Name,
final java.lang.String strVariate2Name,
final double dblCovariance)
{
if (null == strVariate1Name || strVariate1Name.isEmpty() || null == strVariate2Name ||
strVariate2Name.isEmpty() || !org.drip.numerical.common.NumberUtil.IsValid (dblCovariance))
return false;
_mapCovariance.put (strVariate1Name + "@#" + strVariate2Name, dblCovariance);
_mapCovariance.put (strVariate2Name + "@#" + strVariate1Name, dblCovariance);
return true;
}
/**
* Retrieve the Variance of the Named Variate
*
* @param strVariateName The Named Variate
*
* @return Variance of the Named Variate
*
* @throws java.lang.Exception Thrown if the Named Variate Variance cannot be retrieved
*/
public double variance (
final java.lang.String strVariateName)
throws java.lang.Exception
{
if (null == strVariateName || strVariateName.isEmpty())
throw new java.lang.Exception ("MultivariateMetrics::variance => Invalid Inputs");
java.lang.String strVarianceEntry = strVariateName + "@#" + strVariateName;
if (!_mapCovariance.containsKey (strVarianceEntry))
throw new java.lang.Exception ("MultivariateMetrics::variance => Invalid Inputs");
return _mapCovariance.get (strVarianceEntry);
}
/**
* Retrieve the Co-variance of the Named Variate Pair
*
* @param strVariate1Name The Named Variate #1
* @param strVariate2Name The Named Variate #2
*
* @return Co-variance of the Named Variate Pair
*
* @throws java.lang.Exception Thrown if the Named Variate Co-variance cannot be retrieved
*/
public double covariance (
final java.lang.String strVariate1Name,
final java.lang.String strVariate2Name)
throws java.lang.Exception
{
if (null == strVariate1Name || strVariate1Name.isEmpty() || null == strVariate2Name ||
strVariate2Name.isEmpty())
throw new java.lang.Exception ("MultivariateMetrics::covariance => Invalid Inputs");
java.lang.String strCovarianceEntry = strVariate1Name + "@#" + strVariate2Name;
if (!_mapCovariance.containsKey (strCovarianceEntry))
throw new java.lang.Exception ("MultivariateMetrics::coariance => Invalid Inputs");
return _mapCovariance.get (strCovarianceEntry);
}
/**
* Retrieve the Correlation between the Named Variate Pair
*
* @param strVariate1Name The Named Variate #1
* @param strVariate2Name The Named Variate #2
*
* @return Correlation between the Named Variate Pair
*
* @throws java.lang.Exception Thrown if the Named Variate Correlation cannot be retrieved
*/
public double correlation (
final java.lang.String strVariate1Name,
final java.lang.String strVariate2Name)
throws java.lang.Exception
{
return covariance (strVariate1Name, strVariate2Name) / java.lang.Math.sqrt (variance
(strVariate1Name) * variance (strVariate2Name));
}
}