PSeriesGenerator.java

  1. package org.drip.specialfunction.lanczos;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>PSeriesGenerator</i> generates the Terms of the Lanczos P Series. The References are:
  79.  * 
  80.  * <br><br>
  81.  *  <ul>
  82.  *      <li>
  83.  *          Godfrey, P. (2001): Lanczos Implementation of the Gamma Function
  84.  *              http://www.numericana.com/answer/info/godfrey.htm
  85.  *      </li>
  86.  *      <li>
  87.  *          Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
  88.  *              The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
  89.  *      </li>
  90.  *      <li>
  91.  *          Pugh, G. R. (2004): <i>An Analysis of the Lanczos Gamma Approximation</i> Ph. D. <b>University of
  92.  *              British Columbia</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Toth V. T. (2016): Programmable Calculators – The Gamma Function
  96.  *              http://www.rskey.org/CMS/index.php/the-library/11
  97.  *      </li>
  98.  *      <li>
  99.  *          Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation
  100.  *      </li>
  101.  *  </ul>
  102.  *
  103.  *  <br><br>
  104.  *  <ul>
  105.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  106.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  107.  *      <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>
  108.  *      <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>
  109.  *  </ul>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public class PSeriesGenerator extends org.drip.numerical.estimation.R0ToR1Series
  115. {
  116.     private double[][] _chebyshevCoefficientMatrix = null;

  118.     /**
  119.      * Construct a Standard Instance of the Lanczos P Series Generator
  120.      * 
  121.      * @param g Lanczos g Control
  122.      * @param termCount Lanczos Series Term Count
  123.      * 
  124.      * @return Standard Instance of the Lanczos P Series Generator
  125.      */

  127.     public static final PSeriesGenerator Standard (
  128.         final int g,
  129.         final int termCount)
  130.     {
  131.         double[][] chebyshevCoefficientMatrix = org.drip.specialfunction.lanczos.ChebyshevCoefficientMatrix.Rollout
  132.             (2 * termCount);

  134.         if (null == chebyshevCoefficientMatrix)
  135.         {
  136.             return null;
  137.         }

  139.         java.util.TreeMap<java.lang.Integer, java.lang.Double> chebyshevCoefficientWeightMap = new
  140.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  142.         double sqrt2OverPI = java.lang.Math.sqrt (2.) / java.lang.Math.PI;

  144.         for (int termIndex = 0; termIndex <= termCount; ++termIndex)
  145.         {
  146.             chebyshevCoefficientWeightMap.put (
  147.                 termIndex,
  148.                 sqrt2OverPI * chebyshevCoefficientMatrix[2 * termCount][2 * termIndex]
  149.             );
  150.         }

  152.         try
  153.         {
  154.             return new PSeriesGenerator (
  155.                 new org.drip.specialfunction.lanczos.PSeriesTerm (g),
  156.                 chebyshevCoefficientWeightMap,
  157.                 chebyshevCoefficientMatrix
  158.             );
  159.         }
  160.         catch (java.lang.Exception e)
  161.         {
  162.             e.printStackTrace();
  163.         }

  165.         return null;
  166.     }

  168.     /**
  169.      * PSeriesGenerator Constructor
  170.      * 
  171.      * @param pSeriesTerm Lanczos P Series Term
  172.      * @param chebyshevCoefficientWeightMap Chebyshev Coefficient Term Weight Map
  173.      * @param chebyshevCoefficientMatrix Chebyshev Coefficient Matrix
  174.      * 
  175.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  176.      */

  178.     public PSeriesGenerator (
  179.         final org.drip.specialfunction.lanczos.PSeriesTerm pSeriesTerm,
  180.         final java.util.TreeMap<java.lang.Integer, java.lang.Double> chebyshevCoefficientWeightMap,
  181.         final double[][] chebyshevCoefficientMatrix)
  182.         throws java.lang.Exception
  183.     {
  184.         super (
  185.             pSeriesTerm,
  186.             false,
  187.             chebyshevCoefficientWeightMap,
  188.             true
  189.         );

  191.         _chebyshevCoefficientMatrix = chebyshevCoefficientMatrix;
  192.     }

  194.     /**
  195.      * Retrieve the Chebyshev Coefficient Matrix
  196.      * 
  197.      * @return The Chebyshev Coefficient Matrix
  198.      */

  200.     public double[][] _chebyshevCoefficientMatrix()
  201.     {
  202.         return _chebyshevCoefficientMatrix;
  203.     }

  205.     /**
  206.      * Retrieve the Series Term Count
  207.      * 
  208.      * @return The Series Term Count
  209.      */

  211.     public int termCount()
  212.     {
  213.         return _chebyshevCoefficientMatrix.length;
  214.     }
  215. }
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