AbramowitzStegunSeriesGenerator.java

  1. package org.drip.function.e2erf;

  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>AbramowitzStegunSeriesGenerator</i> implements the E<sub>2</sub> erf Abramowitz-Stegun Variant of
  79.  * Series Term Generator. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  85.  *              on Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
  89.  *              Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
  90.  *      </li>
  91.  *      <li>
  92.  *          Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
  93.  *              Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
  94.  *              22-32
  95.  *      </li>
  96.  *      <li>
  97.  *          Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
  98.  *              Linear and Non-linear Heat Transfer and Diffusion
  99.  *              https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
  100.  *      </li>
  101.  *      <li>
  102.  *          Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  110.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  111.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/e2erf/README.md">E<sub>2</sub> erf and erf<sup>-1</sup> Implementations</a></li>
  112.  *  </ul>
  113.  *
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public class AbramowitzStegunSeriesGenerator extends org.drip.numerical.estimation.R1ToR1Series
  118. {

  120.     /**
  121.      * Construct a Inverse Polynomial Degree 4 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  122.      * 
  123.      * @return Inverse Polynomial Degree 4 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  124.      */

  126.     public static final AbramowitzStegunSeriesGenerator InversePolynomial4()
  127.     {
  128.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  129.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  131.         termWeightMap.put (
  132.             0,
  133.             1.000000
  134.         );

  136.         termWeightMap.put (
  137.             1,
  138.             0.278393
  139.         );

  141.         termWeightMap.put (
  142.             2,
  143.             0.230289
  144.         );

  146.         termWeightMap.put (
  147.             3,
  148.             0.000972
  149.         );

  151.         termWeightMap.put (
  152.             4,
  153.             0.078108
  154.         );

  156.         try
  157.         {
  158.             return new AbramowitzStegunSeriesGenerator (
  159.                 org.drip.numerical.estimation.R1ToR1SeriesTerm.Taylor(),
  160.                 termWeightMap
  161.             );
  162.         }
  163.         catch (java.lang.Exception e)
  164.         {
  165.             e.printStackTrace();
  166.         }

  168.         return null;
  169.     }

  171.     /**
  172.      * Construct a Mixed Polynomial Degree 3 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  173.      * 
  174.      * @return Mixed Polynomial Degree 3 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  175.      */

  177.     public static final AbramowitzStegunSeriesGenerator MixedPolynomial3()
  178.     {
  179.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  180.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  182.         termWeightMap.put (
  183.             1,
  184.             0.3480242
  185.         );

  187.         termWeightMap.put (
  188.             2,
  189.             -0.0958798
  190.         );

  192.         termWeightMap.put (
  193.             3,
  194.             0.7478556
  195.         );

  197.         try
  198.         {
  199.             return new AbramowitzStegunSeriesGenerator (
  200.                 org.drip.numerical.estimation.R1ToR1SeriesTerm.Taylor(),
  201.                 termWeightMap
  202.             );
  203.         }
  204.         catch (java.lang.Exception e)
  205.         {
  206.             e.printStackTrace();
  207.         }

  209.         return null;
  210.     }

  212.     /**
  213.      * Construct a Inverse Polynomial Degree 6 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  214.      * 
  215.      * @return Inverse Polynomial Degree 6 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  216.      */

  218.     public static final AbramowitzStegunSeriesGenerator InversePolynomial6()
  219.     {
  220.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  221.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  223.         termWeightMap.put (
  224.             0,
  225.             1.0000000000
  226.         );

  228.         termWeightMap.put (
  229.             1,
  230.             0.0705230784
  231.         );

  233.         termWeightMap.put (
  234.             2,
  235.             0.0422820123
  236.         );

  238.         termWeightMap.put (
  239.             3,
  240.             0.0092705272
  241.         );

  243.         termWeightMap.put (
  244.             4,
  245.             0.0001520143
  246.         );

  248.         termWeightMap.put (
  249.             5,
  250.             0.0002765672
  251.         );

  253.         termWeightMap.put (
  254.             6,
  255.             0.0000430638
  256.         );

  258.         try
  259.         {
  260.             return new AbramowitzStegunSeriesGenerator (
  261.                 org.drip.numerical.estimation.R1ToR1SeriesTerm.Taylor(),
  262.                 termWeightMap
  263.             );
  264.         }
  265.         catch (java.lang.Exception e)
  266.         {
  267.             e.printStackTrace();
  268.         }

  270.         return null;
  271.     }

  273.     /**
  274.      * Construct a Mixed Polynomial Degree 5 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  275.      * 
  276.      * @return Mixed Polynomial Degree 5 Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  277.      */

  279.     public static final AbramowitzStegunSeriesGenerator MixedPolynomial5()
  280.     {
  281.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  282.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  284.         termWeightMap.put (
  285.             1,
  286.             0.254829592
  287.         );

  289.         termWeightMap.put (
  290.             2,
  291.             -0.284496736
  292.         );

  294.         termWeightMap.put (
  295.             3,
  296.             1.421413741
  297.         );

  299.         termWeightMap.put (
  300.             4,
  301.             -1.453152027
  302.         );

  304.         termWeightMap.put (
  305.             5,
  306.             1.061405429
  307.         );

  309.         try
  310.         {
  311.             return new AbramowitzStegunSeriesGenerator (
  312.                 org.drip.numerical.estimation.R1ToR1SeriesTerm.Taylor(),
  313.                 termWeightMap
  314.             );
  315.         }
  316.         catch (java.lang.Exception e)
  317.         {
  318.             e.printStackTrace();
  319.         }

  321.         return null;
  322.     }

  324.     /**
  325.      * Construct the Numerical Recipes Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  326.      * 
  327.      * @return Numerical Recipes Version of E<sub>2</sub> erf AbramowitzStegunSeriesGenerator
  328.      */

  330.     public static final AbramowitzStegunSeriesGenerator NumericalRecipe2007()
  331.     {
  332.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  333.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  335.         termWeightMap.put (
  336.             0,
  337.             -1.26551223
  338.         );

  340.         termWeightMap.put (
  341.             1,
  342.             1.00002368
  343.         );

  345.         termWeightMap.put (
  346.             2,
  347.             0.37409196
  348.         );

  350.         termWeightMap.put (
  351.             3,
  352.             0.09678418
  353.         );

  355.         termWeightMap.put (
  356.             4,
  357.             -0.18628806
  358.         );

  360.         termWeightMap.put (
  361.             5,
  362.             0.27886807
  363.         );

  365.         termWeightMap.put (
  366.             6,
  367.             -1.13520398
  368.         );

  370.         termWeightMap.put (
  371.             7,
  372.             1.48851587
  373.         );

  375.         termWeightMap.put (
  376.             8,
  377.             -0.82215223
  378.         );

  380.         termWeightMap.put (
  381.             9,
  382.             0.17087277
  383.         );

  385.         try
  386.         {
  387.             return new AbramowitzStegunSeriesGenerator (
  388.                 org.drip.numerical.estimation.R1ToR1SeriesTerm.Taylor(),
  389.                 termWeightMap
  390.             );
  391.         }
  392.         catch (java.lang.Exception e)
  393.         {
  394.             e.printStackTrace();
  395.         }

  397.         return null;
  398.     }

  400.     /**
  401.      * AbramowitzStegunSeriesGenerator Constructor
  402.      * 
  403.      * @param r1ToR1SeriesTerm R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
  404.      * @param termWeightMap Error Term Weight Map
  405.      * 
  406.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  407.      */

  409.     public AbramowitzStegunSeriesGenerator (
  410.         final org.drip.numerical.estimation.R1ToR1SeriesTerm r1ToR1SeriesTerm,
  411.         final java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap)
  412.         throws java.lang.Exception
  413.     {
  414.         super (
  415.             r1ToR1SeriesTerm,
  416.             false,
  417.             termWeightMap
  418.         );
  419.     }
  420. }
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