GeneralizedErrorFunction.java

  1. package org.drip.function.enerf;

  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>GeneralizedErrorFunction</i> implements the Generalized E<sub>n</sub> Error Function (erf). The
  79.  * References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  85.  *              on Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
  89.  *              Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
  90.  *      </li>
  91.  *      <li>
  92.  *          Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
  93.  *              Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
  94.  *              22-32
  95.  *      </li>
  96.  *      <li>
  97.  *          Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
  98.  *              Linear and Non-linear Heat Transfer and Diffusion
  99.  *              https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
  100.  *      </li>
  101.  *      <li>
  102.  *          Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  110.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  111.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/enerf/README.md">E<sub>n</sub> erf Series and Generators</a></li>
  112.  *  </ul>
  113.  *
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public abstract class GeneralizedErrorFunction extends org.drip.numerical.estimation.R1ToR1Estimator
  118. {
  119.     private int _degree = -1;
  120.     private org.drip.numerical.estimation.R1ToR1Series _r1ToR1SeriesGenerator = null;

  122.     /**
  123.      * Construct the Euler-MacLaurin Instance of the E<sub>n</sub> erf
  124.      * 
  125.      * @param degree Degree Generalized E<sub>n</sub> Degree
  126.      * @param termCount The Count of Approximation Terms
  127.      * 
  128.      * @return The Euler-MacLaurin Instance of the E<sub>n</sub> erf
  129.      */

  131.     public static final GeneralizedErrorFunction MacLaurin (
  132.         final int degree,
  133.         final int termCount)
  134.     {
  135.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator =
  136.             org.drip.function.enerf.GeneralizedMacLaurinSeriesGenerator.ERF (
  137.                 degree,
  138.                 termCount
  139.             );

  141.         if (null == r1ToR1SeriesGenerator)
  142.         {
  143.             return null;
  144.         }

  146.         try
  147.         {
  148.             return new GeneralizedErrorFunction (
  149.                 r1ToR1SeriesGenerator,
  150.                 null,
  151.                 degree
  152.             )
  153.             {
  154.                 @Override public double evaluate (
  155.                     final double z)
  156.                     throws java.lang.Exception
  157.                 {
  158.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  159.                     {
  160.                         throw new java.lang.Exception
  161.                             ("GeneralizedErrorFunction::MacLaurin::evaluate => Invalid Inputs");
  162.                     }

  164.                     double erf = org.drip.numerical.common.NumberUtil.Factorial (degree) /
  165.                         java.lang.Math.sqrt (java.lang.Math.PI) *
  166.                         r1ToR1SeriesGenerator.cumulative (
  167.                             0.,
  168.                             z
  169.                         );

  171.                     return erf > 1. ? 1. : erf;
  172.                 }
  173.             };
  174.         }
  175.         catch (java.lang.Exception e)
  176.         {
  177.             e.printStackTrace();
  178.         }

  180.         return null;
  181.     }

  183.     protected GeneralizedErrorFunction (
  184.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator,
  185.         final org.drip.numerical.differentiation.DerivativeControl dc,
  186.         final int degree)
  187.         throws java.lang.Exception
  188.     {
  189.         super (dc);

  191.         _r1ToR1SeriesGenerator = r1ToR1SeriesGenerator;

  193.         if (0 > (_degree = degree))
  194.         {
  195.             throw new java.lang.Exception ("GeneralizedErrorFunction Constructor => Invalid Inputs");
  196.         }
  197.     }

  199.     /**
  200.      * Retrieve the Degree of the E<sub>n</sub> erf
  201.      * 
  202.      * @return Degree of the E<sub>n</sub> erf
  203.      */

  205.     public int degree()
  206.     {
  207.         return _degree;
  208.     }

  210.     @Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
  211.         final double x)
  212.     {
  213.         return null == _r1ToR1SeriesGenerator ? seriesEstimate (
  214.             x,
  215.             null,
  216.             null
  217.         ) : seriesEstimate (
  218.             x,
  219.             _r1ToR1SeriesGenerator.termWeightMap(),
  220.             _r1ToR1SeriesGenerator
  221.         );
  222.     }
  223. }
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