Kummer24.java

  1. package org.drip.specialfunction.group;

  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>Kummer24</i> contains the Isomorphic Klein-4 Group of the Transformations built out of the Solutions
  79.  * emanating from the Singularities of the Hyper-geometric 2F1 Function. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
  85.  *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
  86.  *      </li>
  87.  *      <li>
  88.  *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
  89.  *              Computation</i> <b>20 (4)</b> 399-417
  90.  *      </li>
  91.  *      <li>
  92.  *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
  93.  *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
  94.  *              293-300
  95.  *      </li>
  96.  *      <li>
  97.  *          National Institute of Standards and Technology (2019): Hyper-geometric Function
  98.  *              https://dlmf.nist.gov/15
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  109.  *      <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>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/group/README.md">Special Function Singularity Solution Group</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class Kummer24 extends org.drip.specialfunction.group.FuchsianEquation
  117. {

  119.     /**
  120.      * Construct the Kummer24 Isomorphic Array Version of the Fuchsian Equation
  121.      * 
  122.      * @param regularHypergeometricEstimator The Regular Hyper-geometric Estimator
  123.      * 
  124.      * @return The Kummer24 Isomorphic Array Version of the Fuchsian Equation
  125.      */

  127.     public static final Kummer24 Standard (
  128.         final org.drip.specialfunction.definition.RegularHypergeometricEstimator
  129.             regularHypergeometricEstimator)
  130.     {
  131.         if (null == regularHypergeometricEstimator)
  132.         {
  133.             return null;
  134.         }

  136.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  137.             regularHypergeometricEstimator.hypergeometricParameters();

  139.         final double a = hypergeometricParameters.a();

  141.         final double b = hypergeometricParameters.b();

  143.         final double c = hypergeometricParameters.c();

  145.         try
  146.         {
  147.             return new Kummer24 (
  148.                 new org.drip.function.definition.R1ToR1[]
  149.                 {
  150.                     regularHypergeometricEstimator.albinate (
  151.                         new org.drip.specialfunction.definition.HypergeometricParameters (
  152.                             a,
  153.                             c - b,
  154.                             c
  155.                         ),
  156.                         new org.drip.function.definition.R1ToR1 (null)
  157.                         {
  158.                             @Override public double evaluate (
  159.                                 final double z)
  160.                                 throws java.lang.Exception
  161.                             {
  162.                                 return java.lang.Math.pow (
  163.                                     1. - z,
  164.                                     -a
  165.                                 );
  166.                             }
  167.                         },
  168.                         new org.drip.function.definition.R1ToR1 (null)
  169.                         {
  170.                             @Override public double evaluate (
  171.                                 final double z)
  172.                                 throws java.lang.Exception
  173.                             {
  174.                                 return z / (z - 1.);
  175.                             }
  176.                         }
  177.                     ),
  178.                     regularHypergeometricEstimator.albinate (
  179.                         new org.drip.specialfunction.definition.HypergeometricParameters (
  180.                             a,
  181.                             b,
  182.                             1. + a + b - c
  183.                         ),
  184.                         null,
  185.                         new org.drip.function.definition.R1ToR1 (null)
  186.                         {
  187.                             @Override public double evaluate (
  188.                                 final double z)
  189.                                 throws java.lang.Exception
  190.                             {
  191.                                 return 1. - z;
  192.                             }
  193.                         }
  194.                     ),
  195.                     regularHypergeometricEstimator.albinate (
  196.                         new org.drip.specialfunction.definition.HypergeometricParameters (
  197.                             c - a,
  198.                             b,
  199.                             c
  200.                         ),
  201.                         new org.drip.function.definition.R1ToR1 (null)
  202.                         {
  203.                             @Override public double evaluate (
  204.                                 final double z)
  205.                                 throws java.lang.Exception
  206.                             {
  207.                                 return java.lang.Math.pow (
  208.                                     1. - z,
  209.                                     -b
  210.                                 );
  211.                             }
  212.                         },
  213.                         new org.drip.function.definition.R1ToR1 (null)
  214.                         {
  215.                             @Override public double evaluate (
  216.                                 final double z)
  217.                                 throws java.lang.Exception
  218.                             {
  219.                                 return z / (z - 1.);
  220.                             }
  221.                         }
  222.                     ),
  223.                 }
  224.             );
  225.         }
  226.         catch (java.lang.Exception e)
  227.         {
  228.             e.printStackTrace();
  229.         }

  231.         return null;
  232.     }

  234.     protected Kummer24 (
  235.         final org.drip.function.definition.R1ToR1[] kleinGroupFunctionArray)
  236.         throws java.lang.Exception
  237.     {
  238.         super (kleinGroupFunctionArray);
  239.     }

  241.     /**
  242.      * Generate the Transposition (12) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  243.      * 
  244.      * @return The Transposition (12) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  245.      */

  247.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator transposition12()
  248.     {
  249.         return (org.drip.specialfunction.definition.RegularHypergeometricEstimator)
  250.             kleinGroupFunctionArray()[0];
  251.     }

  253.     /**
  254.      * Generate the Transposition (23) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  255.      * 
  256.      * @return The Transposition (23) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  257.      */

  259.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator transposition23()
  260.     {
  261.         return (org.drip.specialfunction.definition.RegularHypergeometricEstimator)
  262.             kleinGroupFunctionArray()[1];
  263.     }

  265.     /**
  266.      * Generate the Transposition (34) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  267.      * 
  268.      * @return The Transposition (34) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  269.      */

  271.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator transposition34()
  272.     {
  273.         return (org.drip.specialfunction.definition.RegularHypergeometricEstimator)
  274.             kleinGroupFunctionArray()[2];
  275.     }
  276. }
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