PSeriesGenerator.java
package org.drip.specialfunction.lanczos;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 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>PSeriesGenerator</i> generates the Terms of the Lanczos P Series. The References are:
*
* <br><br>
* <ul>
* <li>
* Godfrey, P. (2001): Lanczos Implementation of the Gamma Function
* http://www.numericana.com/answer/info/godfrey.htm
* </li>
* <li>
* Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
* The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
* </li>
* <li>
* Pugh, G. R. (2004): <i>An Analysis of the Lanczos Gamma Approximation</i> Ph. D. <b>University of
* British Columbia</b>
* </li>
* <li>
* Toth V. T. (2016): Programmable Calculators – The Gamma Function
* http://www.rskey.org/CMS/index.php/the-library/11
* </li>
* <li>
* Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation
* </li>
* </ul>
*
* <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/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/lanczos/README.md">Lanczos Scheme for Gamma Estimate</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class PSeriesGenerator extends org.drip.numerical.estimation.R0ToR1Series
{
private double[][] _chebyshevCoefficientMatrix = null;
/**
* Construct a Standard Instance of the Lanczos P Series Generator
*
* @param g Lanczos g Control
* @param termCount Lanczos Series Term Count
*
* @return Standard Instance of the Lanczos P Series Generator
*/
public static final PSeriesGenerator Standard (
final int g,
final int termCount)
{
double[][] chebyshevCoefficientMatrix = org.drip.specialfunction.lanczos.ChebyshevCoefficientMatrix.Rollout
(2 * termCount);
if (null == chebyshevCoefficientMatrix)
{
return null;
}
java.util.TreeMap<java.lang.Integer, java.lang.Double> chebyshevCoefficientWeightMap = new
java.util.TreeMap<java.lang.Integer, java.lang.Double>();
double sqrt2OverPI = java.lang.Math.sqrt (2.) / java.lang.Math.PI;
for (int termIndex = 0; termIndex <= termCount; ++termIndex)
{
chebyshevCoefficientWeightMap.put (
termIndex,
sqrt2OverPI * chebyshevCoefficientMatrix[2 * termCount][2 * termIndex]
);
}
try
{
return new PSeriesGenerator (
new org.drip.specialfunction.lanczos.PSeriesTerm (g),
chebyshevCoefficientWeightMap,
chebyshevCoefficientMatrix
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* PSeriesGenerator Constructor
*
* @param pSeriesTerm Lanczos P Series Term
* @param chebyshevCoefficientWeightMap Chebyshev Coefficient Term Weight Map
* @param chebyshevCoefficientMatrix Chebyshev Coefficient Matrix
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public PSeriesGenerator (
final org.drip.specialfunction.lanczos.PSeriesTerm pSeriesTerm,
final java.util.TreeMap<java.lang.Integer, java.lang.Double> chebyshevCoefficientWeightMap,
final double[][] chebyshevCoefficientMatrix)
throws java.lang.Exception
{
super (
pSeriesTerm,
false,
chebyshevCoefficientWeightMap,
true
);
_chebyshevCoefficientMatrix = chebyshevCoefficientMatrix;
}
/**
* Retrieve the Chebyshev Coefficient Matrix
*
* @return The Chebyshev Coefficient Matrix
*/
public double[][] _chebyshevCoefficientMatrix()
{
return _chebyshevCoefficientMatrix;
}
/**
* Retrieve the Series Term Count
*
* @return The Series Term Count
*/
public int termCount()
{
return _chebyshevCoefficientMatrix.length;
}
}