RiemannSphereSpanner2F1.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>RiemannSphereSpanner</i> determines the Conformality and Tile Scheme of the Schwarz Singular Triangle
  79.  * Maps over the Riemann Sphere composed of the 2F1 Solutions. 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 RiemannSphereSpanner2F1
  117. {

  119.     /**
  120.      * Generate the 2F1 Instance of the RiemannSphereSpanner
  121.      * 
  122.      * @param regularHypergeometricEstimator Regular Hyper-geometric Estimator
  123.      * @param connectionCoefficientArray Array of the Singularity Point Connection Coefficients
  124.      * 
  125.      * @return The 2F1 Instance of the RiemannSphereSpanner
  126.      */

  128.     public static final org.drip.specialfunction.group.RiemannSphereSpanner Generate (
  129.         final org.drip.specialfunction.definition.RegularHypergeometricEstimator
  130.             regularHypergeometricEstimator,
  131.         final double[] connectionCoefficientArray)
  132.     {
  133.         if (null == connectionCoefficientArray || 3 != connectionCoefficientArray.length)
  134.         {
  135.             return null;
  136.         }

  138.         org.drip.specialfunction.ode.RegularSingularityIndependentSolution
  139.             regularSingularityIndependentSolution2F1 =
  140.                 org.drip.specialfunction.ode.RegularSingularityIndependentSolution2F1.Create
  141.                     (regularHypergeometricEstimator);

  143.         if (null == regularSingularityIndependentSolution2F1)
  144.         {
  145.             return null;
  146.         }

  148.         java.util.Map<java.lang.Double, org.drip.specialfunction.ode.IndependentLinearSolutionList>
  149.             linearSolutionFunctionMap = regularSingularityIndependentSolution2F1.linearSolutionFunctionMap();

  151.         if (null == linearSolutionFunctionMap ||
  152.             !linearSolutionFunctionMap.containsKey (0.) ||
  153.             !linearSolutionFunctionMap.containsKey (1.) ||
  154.             !linearSolutionFunctionMap.containsKey (java.lang.Double.POSITIVE_INFINITY))
  155.         {
  156.             return null;
  157.         }

  159.         org.drip.specialfunction.group.SchwarzTriangleMap[] schwarzTriangleMapArray = new
  160.             org.drip.specialfunction.group.SchwarzTriangleMap[3];

  162.         try
  163.         {
  164.             java.util.List<org.drip.function.definition.R1ToR1> solutionFunctionList0 =
  165.                 linearSolutionFunctionMap.get (0.).solutionFunctionList();

  167.             schwarzTriangleMapArray[0] = new org.drip.specialfunction.group.SchwarzTriangleMap (
  168.                 0.,
  169.                 solutionFunctionList0.get (0),
  170.                 solutionFunctionList0.get (1),
  171.                 new org.drip.function.definition.R1ToR1 (null)
  172.                 {
  173.                     @Override public double evaluate (
  174.                         final double z)
  175.                     {
  176.                         return z;
  177.                     }
  178.                 },
  179.                 connectionCoefficientArray[0]
  180.             );

  182.             java.util.List<org.drip.function.definition.R1ToR1> solutionFunctionList1 =
  183.                 linearSolutionFunctionMap.get (1.).solutionFunctionList();

  185.             schwarzTriangleMapArray[1] = new org.drip.specialfunction.group.SchwarzTriangleMap (
  186.                 1.,
  187.                 solutionFunctionList1.get (0),
  188.                 solutionFunctionList1.get (1),
  189.                 new org.drip.function.definition.R1ToR1 (null)
  190.                 {
  191.                     @Override public double evaluate (
  192.                         final double z)
  193.                     {
  194.                         return 1. - z;
  195.                     }
  196.                 },
  197.                 connectionCoefficientArray[1]
  198.             );

  200.             java.util.List<org.drip.function.definition.R1ToR1> solutionFunctionList2 =
  201.                 linearSolutionFunctionMap.get (java.lang.Double.POSITIVE_INFINITY).solutionFunctionList();

  203.             schwarzTriangleMapArray[2] = new org.drip.specialfunction.group.SchwarzTriangleMap (
  204.                 java.lang.Double.POSITIVE_INFINITY,
  205.                 solutionFunctionList2.get (0),
  206.                 solutionFunctionList2.get (1),
  207.                 new org.drip.function.definition.R1ToR1 (null)
  208.                 {
  209.                     @Override public double evaluate (
  210.                         final double z)
  211.                     {
  212.                         return 1. / z;
  213.                     }
  214.                 },
  215.                 connectionCoefficientArray[2]
  216.             );

  218.             return new org.drip.specialfunction.group.RiemannSphereSpanner (schwarzTriangleMapArray);
  219.         }
  220.         catch (java.lang.Exception e)
  221.         {
  222.             e.printStackTrace();
  223.         }

  225.         return null;
  226.     }
  227. }
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