EulerQuadratureEstimator.java

  1. package org.drip.specialfunction.hypergeometric;

  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>EulerQuadratureEstimator</i> estimates the Hyper-geometric Function using the Euler Integral
  79.  * Representation. 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/hypergeometric/README.md">Hyper-geometric Function Estimation Schemes</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class EulerQuadratureEstimator extends
  117.     org.drip.specialfunction.definition.RegularHypergeometricEstimator
  118. {
  119.     private int _quadratureCount = -1;
  120.     private org.drip.function.definition.R2ToR1 _logBetaEstimator = null;

  122.     /**
  123.      * EulerQuadratureEstimator Constructor
  124.      * 
  125.      * @param hypergeometricParameters Hyper-geometric Parameters
  126.      * @param logBetaEstimator Log Beta Estimator
  127.      * @param quadratureCount Count of the Integrand Quadrature
  128.      * 
  129.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  130.      */

  132.     public EulerQuadratureEstimator (
  133.         final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters,
  134.         final org.drip.function.definition.R2ToR1 logBetaEstimator,
  135.         final int quadratureCount)
  136.         throws java.lang.Exception
  137.     {
  138.         super (hypergeometricParameters);

  140.         if (null == (_logBetaEstimator = logBetaEstimator) ||
  141.             0 >= (_quadratureCount = quadratureCount))
  142.         {
  143.             throw new java.lang.Exception ("EulerQuadratureEstimator Constructor => Invalid Inputs");
  144.         }
  145.     }

  147.     /**
  148.      * Retrieve the Quadrature Count
  149.      * 
  150.      * @return The Quadrature Count
  151.      */

  153.     public int quadratureCount()
  154.     {
  155.         return _quadratureCount;
  156.     }

  158.     /**
  159.      * Retrieve the Log Beta Estimator
  160.      * 
  161.      * @return The Log Beta Estimator
  162.      */

  164.     public org.drip.function.definition.R2ToR1 logBetaEstimator()
  165.     {
  166.         return _logBetaEstimator;
  167.     }

  169.     @Override public double regularHypergeometric (
  170.         final double z)
  171.         throws java.lang.Exception
  172.     {
  173.         if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z < -1. || z > 1.)
  174.         {
  175.             throw new java.lang.Exception ("EulerQuadratureEstimator::regularHypergeometric => Invalid Inputs");
  176.         }

  178.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  179.             hypergeometricParameters();

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

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

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

  187.         return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
  188.             0.,
  189.             1.,
  190.             _quadratureCount
  191.         ).integrate (
  192.             new org.drip.function.definition.R1ToR1 (null)
  193.             {
  194.                 @Override public double evaluate (
  195.                     final double t)
  196.                     throws java.lang.Exception
  197.                 {
  198.                     return 0. == t || 1. == t ? 0. :
  199.                         java.lang.Math.pow (
  200.                             t,
  201.                             b - 1.
  202.                         ) * java.lang.Math.pow (
  203.                             1. - t,
  204.                             c - b - 1.
  205.                         ) * java.lang.Math.pow (
  206.                             1. - z * t,
  207.                             -a
  208.                         );
  209.                 }
  210.             }
  211.         ) * java.lang.Math.exp (
  212.         -1. * _logBetaEstimator.evaluate (
  213.                 b,
  214.                 c - b
  215.             )
  216.         );
  217.     }

  219.     @Override public double derivative (
  220.         final double z,
  221.         final int order)
  222.         throws java.lang.Exception
  223.     {
  224.         org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
  225.             hypergeometricParameters();

  227.         double a = hypergeometricParameters.a();

  229.         double b = hypergeometricParameters.b();

  231.         double c = hypergeometricParameters.c();

  233.         return new EulerQuadratureEstimator (
  234.             new org.drip.specialfunction.definition.HypergeometricParameters (
  235.                 a + order,
  236.                 b + order,
  237.                 c + order
  238.             ),
  239.             _logBetaEstimator,
  240.             _quadratureCount
  241.         ).regularHypergeometric (z) * org.drip.numerical.common.NumberUtil.PochhammerSymbol (
  242.             a,
  243.             order
  244.         ) * org.drip.numerical.common.NumberUtil.PochhammerSymbol (
  245.             b,
  246.             order
  247.         ) / org.drip.numerical.common.NumberUtil.PochhammerSymbol (
  248.             c,
  249.             order
  250.         );
  251.     }

  253.     @Override public org.drip.specialfunction.definition.RegularHypergeometricEstimator albinate (
  254.         final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParametersAlbinate,
  255.         final org.drip.function.definition.R1ToR1 valueScaler,
  256.         final org.drip.function.definition.R1ToR1 zTransformer)
  257.     {
  258.         try
  259.         {
  260.             return new EulerQuadratureEstimator (
  261.                 hypergeometricParametersAlbinate,
  262.                 _logBetaEstimator,
  263.                 _quadratureCount
  264.             )
  265.             {
  266.                 @Override public double regularHypergeometric (
  267.                     final double z)
  268.                     throws java.lang.Exception
  269.                 {
  270.                     return (null == valueScaler ? 1. : valueScaler.evaluate (z)) *
  271.                         super.regularHypergeometric (null == zTransformer ? z : zTransformer.evaluate (z));
  272.                 }
  273.             };
  274.         }
  275.         catch (java.lang.Exception e)
  276.         {
  277.             e.printStackTrace();
  278.         }

  280.         return null;
  281.     }
  282. }
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