RegularHypergeometricEstimator.java

  1. package org.drip.specialfunction.definition;

  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>RegularHypergeometricEstimator</i> exposes the Stubs for estimating the 2F1 Hyper-geometric Function
  79.  * and its Jacobian using the 2F1 Hyper-geometric 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/definition/README.md">Definition of Special Function Estimators</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public abstract class RegularHypergeometricEstimator extends
  117.     org.drip.specialfunction.definition.HypergeometricEstimator
  118. {

  120.     protected RegularHypergeometricEstimator (
  121.         final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters)
  122.         throws java.lang.Exception
  123.     {
  124.         super (hypergeometricParameters);
  125.     }

  127.     @Override public double evaluate (
  128.         final double z)
  129.         throws java.lang.Exception
  130.     {
  131.         return regularHypergeometric (z);
  132.     }

  134.     /**
  135.      * Evaluate Regular Hyper-geometric Function
  136.      * 
  137.      * @param z Z
  138.      *  
  139.      * @return Regular Hyper-geometric Value
  140.      * 
  141.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  142.      */

  144.     public abstract double regularHypergeometric (
  145.         final double z)
  146.         throws java.lang.Exception;

  148.     /**
  149.      * Albinate (i.e., Clone + Mutate) an Instance of Regular Hyper-geometric Estimator
  150.      * 
  151.      * @param hypergeometricParametersAlbinate The Albination Hyper-geometric Parameters
  152.      * @param valueScaler The Estimator Value Scaler
  153.      * @param zTransformer The Z Transformation Function
  154.      * 
  155.      * @return Albinated Instance of Regular Hyper-geometric Estimator
  156.      */

  158.     public abstract org.drip.specialfunction.definition.RegularHypergeometricEstimator albinate (
  159.         final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParametersAlbinate,
  160.         final org.drip.function.definition.R1ToR1 valueScaler,
  161.         final org.drip.function.definition.R1ToR1 zTransformer);

  163.     /**
  164.      * Construct the Kummer24 Euler Transformation on 2F1
  165.      * 
  166.      * @return The Kummer24 Euler Transformation on 2F1
  167.      */

  169.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator albinateEuler()
  170.     {
  171.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  172.             hypergeometricParameters();

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

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

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

  180.         try
  181.         {
  182.             return albinate (
  183.                 new org.drip.specialfunction.definition.HypergeometricParameters (
  184.                     c - a,
  185.                     c - b,
  186.                     c
  187.                 ),
  188.                 new org.drip.function.definition.R1ToR1 (null)
  189.                 {
  190.                     @Override public double evaluate (
  191.                         final double z)
  192.                         throws java.lang.Exception
  193.                     {
  194.                         return java.lang.Math.pow (
  195.                             1. - z,
  196.                             c - a - b
  197.                         );
  198.                     }
  199.                 },
  200.                 null
  201.             );
  202.         }
  203.         catch (java.lang.Exception e)
  204.         {
  205.             e.printStackTrace();
  206.         }

  208.         return null;
  209.     }

  211.     /**
  212.      * Construct the Kummer24 Pfaff First Transformation on 2F1
  213.      * 
  214.      * @return The Kummer24 Pfaff First Transformation on 2F1
  215.      */

  217.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator albinatePfaffFirst()
  218.     {
  219.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  220.             hypergeometricParameters();

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

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

  226.         try
  227.         {
  228.             return albinate (
  229.                 new org.drip.specialfunction.definition.HypergeometricParameters (
  230.                     a,
  231.                     c - hypergeometricParameters.b(),
  232.                     c
  233.                 ),
  234.                 new org.drip.function.definition.R1ToR1 (null)
  235.                 {
  236.                     @Override public double evaluate (
  237.                         final double z)
  238.                         throws java.lang.Exception
  239.                     {
  240.                         return java.lang.Math.pow (
  241.                             1. - z,
  242.                             -a
  243.                         );
  244.                     }
  245.                 },
  246.                 new org.drip.function.definition.R1ToR1 (null)
  247.                 {
  248.                     @Override public double evaluate (
  249.                         final double z)
  250.                         throws java.lang.Exception
  251.                     {
  252.                         return z / (z - 1.);
  253.                     }
  254.                 }
  255.             );
  256.         }
  257.         catch (java.lang.Exception e)
  258.         {
  259.             e.printStackTrace();
  260.         }

  262.         return null;
  263.     }

  265.     /**
  266.      * Construct the Kummer24 Pfaff Second Transformation on 2F1
  267.      * 
  268.      * @return The Kummer24 Pfaff Second Transformation on 2F1
  269.      */

  271.     public org.drip.specialfunction.definition.RegularHypergeometricEstimator albinatePfaffSecond()
  272.     {
  273.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  274.             hypergeometricParameters();

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

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

  280.         try {
  281.             return albinate (
  282.                 new org.drip.specialfunction.definition.HypergeometricParameters (
  283.                     c - hypergeometricParameters.a(),
  284.                     b,
  285.                     c
  286.                 ),
  287.                 new org.drip.function.definition.R1ToR1 (null)
  288.                 {
  289.                     @Override public double evaluate (
  290.                         final double z)
  291.                         throws java.lang.Exception
  292.                     {
  293.                         return java.lang.Math.pow (
  294.                             1. - z,
  295.                             -b
  296.                         );
  297.                     }
  298.                 },
  299.                 new org.drip.function.definition.R1ToR1 (null)
  300.                 {
  301.                     @Override public double evaluate (
  302.                         final double z)
  303.                         throws java.lang.Exception
  304.                     {
  305.                         return z / (z - 1.);
  306.                     }
  307.                 }
  308.             );
  309.         }
  310.         catch (java.lang.Exception e)
  311.         {
  312.             e.printStackTrace();
  313.         }

  315.         return null;
  316.     }
  317. }
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