SchwarzTriangleMap.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>SchwarzTriangleMap</i> contains the Ratio of the Linearly Independent Solution pair corresponding to a
  79.  * given Singularity 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 SchwarzTriangleMap
  117. {
  118.     private double _singularity = java.lang.Double.NaN;
  119.     private double _connectionCoefficient = java.lang.Double.NaN;
  120.     private org.drip.function.definition.R1ToR1 _singularitySolution0 = null;
  121.     private org.drip.function.definition.R1ToR1 _singularitySolution1 = null;
  122.     private org.drip.function.definition.R1ToR1 _singularityAsymptoteOrderTerm = null;

  124.     /**
  125.      * SchwarzTriangleMap Constructor
  126.      * 
  127.      * @param singularity The Singularity
  128.      * @param singularitySolution0 The Singularity Solution 0
  129.      * @param singularitySolution1 The Singularity Solution 1
  130.      * @param singularityAsymptoteOrderTerm The Singularity Asymptote Order Term
  131.      * @param connectionCoefficient The Connection Coefficient
  132.      * 
  133.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  134.      */

  136.     public SchwarzTriangleMap (
  137.         final double singularity,
  138.         final org.drip.function.definition.R1ToR1 singularitySolution0,
  139.         final org.drip.function.definition.R1ToR1 singularitySolution1,
  140.         final org.drip.function.definition.R1ToR1 singularityAsymptoteOrderTerm,
  141.         final double connectionCoefficient)
  142.         throws java.lang.Exception
  143.     {
  144.         if (java.lang.Double.isNaN (_singularity = singularity) ||
  145.             null == (_singularitySolution0 = singularitySolution0) ||
  146.             null == (_singularitySolution1 = singularitySolution1) ||
  147.             null == (_singularityAsymptoteOrderTerm = singularityAsymptoteOrderTerm) ||
  148.             !org.drip.numerical.common.NumberUtil.IsValid (_connectionCoefficient = connectionCoefficient))
  149.         {
  150.             throw new java.lang.Exception ("SchwarzTriangleMap Constructor => Invalid Inputs");
  151.         }
  152.     }

  154.     /**
  155.      * Retrieve the Singularity
  156.      * 
  157.      * @return The Singularity
  158.      */

  160.     public double singularity()
  161.     {
  162.         return _singularity;
  163.     }

  165.     /**
  166.      * Retrieve the Singularity Solution 0
  167.      * 
  168.      * @return The Singularity Solution 0
  169.      */

  171.     public org.drip.function.definition.R1ToR1 singularitySolution0()
  172.     {
  173.         return _singularitySolution0;
  174.     }

  176.     /**
  177.      * Retrieve the Singularity Solution 1
  178.      * 
  179.      * @return The Singularity Solution 1
  180.      */

  182.     public org.drip.function.definition.R1ToR1 singularitySolution1()
  183.     {
  184.         return _singularitySolution1;
  185.     }

  187.     /**
  188.      * Retrieve the Singularity Asymptote Order Term
  189.      * 
  190.      * @return The Singularity Asymptote Order Term
  191.      */

  193.     public org.drip.function.definition.R1ToR1 singularityAsymptoteOrderTerm()
  194.     {
  195.         return _singularityAsymptoteOrderTerm;
  196.     }

  198.     /**
  199.      * Retrieve the Connection Coefficient
  200.      * 
  201.      * @return The Connection Coefficient
  202.      */

  204.     public double connectionCoefficient()
  205.     {
  206.         return _connectionCoefficient;
  207.     }

  209.     /**
  210.      * Indicate if the Triangle Map is Conformal
  211.      * 
  212.      * @return TRUE - The Triangle Map is Conformal
  213.      */

  215.     public boolean isConformal()
  216.     {
  217.         return 0. <= _connectionCoefficient && 1. > _connectionCoefficient;
  218.     }

  220.     /**
  221.      * Generate the s-Function corresponding to the Singularity Solution Pair
  222.      * 
  223.      * @return The s-Function corresponding to the Singularity Solution Pair
  224.      */

  226.     public org.drip.function.definition.R1ToR1 sFunction()
  227.     {
  228.         return new org.drip.function.definition.R1ToR1 (null)
  229.         {
  230.             @Override public double evaluate (
  231.                 final double z)
  232.                 throws java.lang.Exception
  233.             {
  234.                 return _singularitySolution1.evaluate (z) / _singularitySolution0.evaluate (z);
  235.             }
  236.         };
  237.     }

  239.     /**
  240.      * Generate the Schwarz-Christoffel Triangle Vertex
  241.      * 
  242.      * @return The Schwarz-Christoffel Triangle Vertex
  243.      */

  245.     public org.drip.specialfunction.group.SchwarzChristoffelVertex schwarzChristoffelVertex()
  246.     {
  247.         try
  248.         {
  249.             return new org.drip.specialfunction.group.SchwarzChristoffelVertex (
  250.                 new org.drip.function.definition.R1ToR1 (null)
  251.                 {
  252.                     @Override public double evaluate (
  253.                         final double z)
  254.                         throws java.lang.Exception
  255.                     {
  256.                         return java.lang.Math.pow (
  257.                             _singularityAsymptoteOrderTerm.evaluate (z),
  258.                             _connectionCoefficient
  259.                         );
  260.                     }
  261.                 },
  262.                 _singularityAsymptoteOrderTerm,
  263.                 java.lang.Math.PI * _connectionCoefficient
  264.             );
  265.         }
  266.         catch (java.lang.Exception e)
  267.         {
  268.             e.printStackTrace();
  269.         }

  271.         return null;
  272.     }
  273. }
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