CorrelatedPathVertexDimension.java
package org.drip.measure.discrete;
/*
* -*- 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
*
* 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>CorrelatedPathVertexDimension</i> generates Correlated R^d Random Numbers at the specified Vertexes,
* over the Specified Paths.
*
* <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/discrete/README.md">Antithetic, Quadratically Re-sampled, De-biased Distribution</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class CorrelatedPathVertexDimension {
private int _iNumPath = -1;
private int _iNumVertex = -1;
private double[][] _aadblCholesky = null;
private boolean _bApplyAntithetic = false;
private double[][] _aadblCorrelation = null;
private org.drip.measure.crng.RandomNumberGenerator _rng = null;
private org.drip.measure.discrete.QuadraticResampler _qr = null;
/**
* CorrelatedPathVertexDimension Constructor
*
* @param rng The Random Number Generator
* @param aadblCorrelation The Correlation Matrix
* @param iNumVertex Number of Vertexes
* @param iNumPath Number of Paths
* @param bApplyAntithetic TRUE - Apply Antithetic Variables Based Variance Reduction
* @param qr Quadratic Resampler Instance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public CorrelatedPathVertexDimension (
final org.drip.measure.crng.RandomNumberGenerator rng,
final double[][] aadblCorrelation,
final int iNumVertex,
final int iNumPath,
final boolean bApplyAntithetic,
final org.drip.measure.discrete.QuadraticResampler qr)
throws java.lang.Exception
{
if (null == (_rng = rng) || 0 >= (_iNumVertex = iNumVertex) || 0 >= (_iNumPath = iNumPath))
throw new java.lang.Exception ("CorrelatedPathVertexDimension Constructor => Invalid Inputs");
_qr = qr;
_bApplyAntithetic = bApplyAntithetic;
if (null == (_aadblCholesky = org.drip.numerical.linearalgebra.Matrix.CholeskyBanachiewiczFactorization
(_aadblCorrelation = aadblCorrelation)))
throw new java.lang.Exception ("CorrelatedPathVertexDimension Constructor => Invalid Inputs");
}
/**
* Retrieve the Random Number Generator
*
* @return The Random Number Generator Instance
*/
public org.drip.measure.crng.RandomNumberGenerator randomNumberGenerator()
{
return _rng;
}
/**
* Retrieve the Correlation Matrix
*
* @return The Correlation Matrix
*/
public double[][] correlation()
{
return _aadblCorrelation;
}
/**
* Retrieve the Cholesky Matrix
*
* @return The Cholesky Matrix
*/
public double[][] cholesky()
{
return _aadblCholesky;
}
/**
* Retrieve the Number of Vertexes
*
* @return The Number of Vertexes
*/
public int numVertex()
{
return _iNumVertex;
}
/**
* Retrieve the Number of Paths
*
* @return The Number of Paths
*/
public int numPath()
{
return _iNumPath;
}
/**
* Retrieve the Number of Dimensions
*
* @return The Number of Dimensions
*/
public int numDimension()
{
return _aadblCholesky.length;
}
/**
* Indicate if the Antithetic Variable Generation is to be applied
*
* @return TRUE - Apply Antithetic Variables Based Variance Reduction
*/
public boolean applyAntithetic()
{
return _bApplyAntithetic;
}
/**
* Retrieve the Quadratic Resampler Instance
*
* @return The Quadratic Resampler Instance
*/
public org.drip.measure.discrete.QuadraticResampler quadraticResampler()
{
return _qr;
}
/**
* Generate a Straight Single R^d Vertex Realization
*
* @return Straight Single R^d Vertex Realization
*/
public double[] straightVertexRealization()
{
int iDimension = _aadblCholesky.length;
double[] adblRdCorrelated = new double[iDimension];
double[] adblRdUncorrelated = new double[iDimension];
for (int i = 0; i < iDimension; ++i) {
try {
adblRdUncorrelated[i] = org.drip.measure.gaussian.NormalQuadrature.InverseCDF
(_rng.nextDouble01());
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
for (int i = 0; i < iDimension; ++i) {
adblRdCorrelated[i] = 0.;
for (int j = 0; j < iDimension; ++j)
adblRdCorrelated[i] += _aadblCholesky[i][j] * adblRdUncorrelated[j];
}
return adblRdCorrelated;
}
/**
* Generate an Antithetic R^d Vertex Pair Realization
*
* @return Antithetic R^d Vertex Pair Realization
*/
public double[][] antitheticVertexPairRealization()
{
double[] adblStraightVertexRealization = straightVertexRealization();
int iDimension = _aadblCholesky.length;
double[] adblAntitheticVertexRealization = new double[iDimension];
for (int i = 0; i < iDimension; ++i)
adblAntitheticVertexRealization[i] = -1. * adblStraightVertexRealization[i];
return new double[][] {adblStraightVertexRealization, adblAntitheticVertexRealization};
}
/**
* Generate a Single Straight Path R^d Vertex Realization
*
* @return Single Straight Path R^d Vertex Realization
*/
public org.drip.measure.discrete.VertexRd straightPathVertexRd()
{
org.drip.measure.discrete.VertexRd vertexRealization = new
org.drip.measure.discrete.VertexRd();
for (int i = 0; i < _iNumVertex; ++i) {
if (!vertexRealization.add (i, straightVertexRealization())) return null;
}
return null != _qr ? org.drip.measure.discrete.VertexRd.FromFlatForm (_qr.transform
(vertexRealization.flatform())) : vertexRealization;
}
/**
* Generate an Antithetic Pair Path R^d Vertex Realizations
*
* @return Antithetic Pair Path R^d Vertex Realizations
*/
public org.drip.measure.discrete.VertexRd[] antitheticPairPathVertexRd()
{
org.drip.measure.discrete.VertexRd straightVertexRealization = new
org.drip.measure.discrete.VertexRd();
org.drip.measure.discrete.VertexRd antitheticVertexRealization = new
org.drip.measure.discrete.VertexRd();
for (int i = 0; i < _iNumVertex; ++i) {
double[][] aadblStraightAntitheticRealization = antitheticVertexPairRealization();
if (!straightVertexRealization.add (i, aadblStraightAntitheticRealization[0]) ||
!antitheticVertexRealization.add (i, aadblStraightAntitheticRealization[1]))
return null;
}
if (null == _qr)
return new org.drip.measure.discrete.VertexRd[] {straightVertexRealization,
antitheticVertexRealization};
return new org.drip.measure.discrete.VertexRd[] {org.drip.measure.discrete.VertexRd.FromFlatForm
(_qr.transform (straightVertexRealization.flatform())),
org.drip.measure.discrete.VertexRd.FromFlatForm (_qr.transform
(antitheticVertexRealization.flatform()))};
}
/**
* Generate Straight Multi-Path R^d Vertex Realizations Array
*
* @return Straight Multi-Path R^d Vertex Realizations Array
*/
public org.drip.measure.discrete.VertexRd[] straightMultiPathVertexRd()
{
org.drip.measure.discrete.VertexRd[] aVertexRd = new
org.drip.measure.discrete.VertexRd[_iNumPath];
for (int i = 0; i < _iNumPath; ++i) {
if (null == (aVertexRd[i] = straightPathVertexRd())) return null;
}
return aVertexRd;
}
/**
* Generate Antithetic Multi-Path R^d Vertex Realizations Array
*
* @return Antithetic Multi-Path R^d Vertex Realizations Array
*/
public org.drip.measure.discrete.VertexRd[] antitheticMultiPathVertexRd()
{
org.drip.measure.discrete.VertexRd[] aVertexRd = new
org.drip.measure.discrete.VertexRd[_iNumPath];
int iNumGeneration = _iNumPath / 2;
for (int i = 0; i < iNumGeneration; ++i) {
org.drip.measure.discrete.VertexRd[] aAntitheticVertexRd = antitheticPairPathVertexRd();
if (null == aAntitheticVertexRd || 2 != aAntitheticVertexRd.length) return null;
if (null == (aVertexRd[i] = aAntitheticVertexRd[0]) || null == (aVertexRd[i + iNumGeneration] =
aAntitheticVertexRd[1]))
return null;
}
if (1 == (_iNumPath % 2)) aVertexRd[_iNumPath - 1] = straightPathVertexRd();
return aVertexRd;
}
/**
* Generate Multi-Path R^d Vertex Realizations Array
*
* @return Multi-Path R^d Vertex Realizations Array
*/
public org.drip.measure.discrete.VertexRd[] multiPathVertexRd()
{
return _bApplyAntithetic ? antitheticMultiPathVertexRd() : straightMultiPathVertexRd();
}
}