HilleQForm2F1.java

  1. package org.drip.specialfunction.ode;

  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>HilleQForm2F1</i> exposes the Coefficient Terms on the Q-form 2F1 Hyper-geometric ODE. The References
  79.  * 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/ode/README.md">Special Function Ordinary Differential Equations</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class HilleQForm2F1 extends org.drip.specialfunction.ode.SecondOrder
  117. {
  118.     private org.drip.function.definition.R1ToR1 _q = null;
  119.     private org.drip.function.definition.R1ToR1 _v = null;

  121.     /**
  122.      * Construct the Hille Q-Form of 2F1 ODE
  123.      * 
  124.      * @param a A
  125.      * @param b B
  126.      * @param c C
  127.      * 
  128.      * @return Hille Q-Form of 2F1 ODE
  129.      */

  131.     public static final HilleQForm2F1 Standard (
  132.         final double a,
  133.         final double b,
  134.         final double c)
  135.     {
  136.         if (!org.drip.numerical.common.NumberUtil.IsValid (a) ||
  137.             !org.drip.numerical.common.NumberUtil.IsValid (b) ||
  138.             !org.drip.numerical.common.NumberUtil.IsValid (c))
  139.         {
  140.             return null;
  141.         }

  143.         final org.drip.function.definition.R1ToR1 q = new org.drip.function.definition.R1ToR1 (null)
  144.         {
  145.             @Override public double evaluate (
  146.                 final double z)
  147.                 throws java.lang.Exception
  148.             {
  149.                 if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  150.                 {
  151.                     throw new java.lang.Exception
  152.                         ("HilleQForm2F1::Standard::q::evaluate => Invalid Inputs");
  153.                 }

  155.                 double aMinusB = a - b;
  156.                 double zMinus1 = z - 1.;

  158.                 return (z * z * (1. - aMinusB * aMinusB) + z * (2. * c * (a + b - 1.) - 4. * a * b) + c *
  159.                     (2. - c)) / (4. * z * z * zMinus1 * zMinus1);
  160.             }
  161.         };

  163.         try
  164.         {
  165.             return new HilleQForm2F1 (
  166.                 new org.drip.function.definition.R2ToR1()
  167.                 {
  168.                     @Override public double evaluate (
  169.                         final double z,
  170.                         final double u)
  171.                         throws java.lang.Exception
  172.                     {
  173.                         return 1.;
  174.                     }
  175.                 },
  176.                 new org.drip.function.definition.R2ToR1()
  177.                 {
  178.                     @Override public double evaluate (
  179.                         final double z,
  180.                         final double w)
  181.                         throws java.lang.Exception
  182.                     {
  183.                         return 0.;
  184.                     }
  185.                 },
  186.                 new org.drip.function.definition.R2ToR1()
  187.                 {
  188.                     @Override public double evaluate (
  189.                         final double z,
  190.                         final double u)
  191.                         throws java.lang.Exception
  192.                     {
  193.                         if (!org.drip.numerical.common.NumberUtil.IsValid (u))
  194.                         {
  195.                             throw new java.lang.Exception
  196.                                 ("HilleQForm2F1::Standard::ZeroOrder::evaluate => Invalid Inputs");
  197.                         }

  199.                         return q.evaluate (z) * u;
  200.                     }
  201.                 },
  202.                 q,
  203.                 new org.drip.function.definition.R1ToR1 (null)
  204.                 {
  205.                     @Override public double evaluate (
  206.                         final double z)
  207.                         throws java.lang.Exception
  208.                     {
  209.                         if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  210.                         {
  211.                             throw new java.lang.Exception
  212.                                 ("HilleQForm2F1::Standard::v::evaluate => Invalid Inputs");
  213.                         }

  215.                         return java.lang.Math.pow (
  216.                             z,
  217.                             -0.5 * c
  218.                         ) * java.lang.Math.pow (
  219.                             1. - z,
  220.                             0.5 * (c - a - b - 1.)
  221.                         );
  222.                     }
  223.                 }
  224.             );
  225.         }
  226.         catch (java.lang.Exception e)
  227.         {
  228.             e.printStackTrace();
  229.         }

  231.         return null;
  232.     }

  234.     private HilleQForm2F1 (
  235.         final org.drip.function.definition.R2ToR1 secondDerivativeCoefficient,
  236.         final org.drip.function.definition.R2ToR1 firstDerivativeCoefficient,
  237.         final org.drip.function.definition.R2ToR1 zeroDerivativeCoefficient,
  238.         final org.drip.function.definition.R1ToR1 q,
  239.         final org.drip.function.definition.R1ToR1 v)
  240.         throws java.lang.Exception
  241.     {
  242.         super (
  243.             secondDerivativeCoefficient,
  244.             firstDerivativeCoefficient,
  245.             zeroDerivativeCoefficient
  246.         );

  248.         if (null == (_q = q) ||
  249.             null == (_v = v))
  250.         {
  251.             throw new java.lang.Exception ("HilleQForm2F1 Constructor => Invalid Inputs");
  252.         }
  253.     }

  255.     /**
  256.      * Retrieve the Q Form Function
  257.      * 
  258.      * @return The Q Form Function
  259.      */

  261.     public org.drip.function.definition.R1ToR1 q()
  262.     {
  263.         return _q;
  264.     }

  266.     /**
  267.      * Retrieve the v Function
  268.      * 
  269.      * @return The v Function
  270.      */

  272.     public org.drip.function.definition.R1ToR1 v()
  273.     {
  274.         return _v;
  275.     }
  276. }
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