ErrorFunctionComplement.java

  1. package org.drip.function.e2erfc;

  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>ErrorFunctionComplement</i> implements the Error Function Complement (erfc). The References are:
  79.  * 
  80.  * <br><br>
  81.  *  <ul>
  82.  *      <li>
  83.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  84.  *              on Mathematics</b>
  85.  *      </li>
  86.  *      <li>
  87.  *          Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
  88.  *              Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
  89.  *      </li>
  90.  *      <li>
  91.  *          Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
  92.  *              Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
  93.  *              22-32
  94.  *      </li>
  95.  *      <li>
  96.  *          Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
  97.  *              Linear and Non-linear Heat Transfer and Diffusion
  98.  *              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/
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  109.  *      <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>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/e2erfc/README.md">E<sub>2</sub> erfc Estimation Function Implementation</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class ErrorFunctionComplement extends org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator
  117. {
  118.     private org.drip.numerical.estimation.R1ToR1Series _r1ToR1SeriesGenerator = null;

  120.     /**
  121.      * Construct the Asymptotic Expansion Version of ErrorFunctionComplement
  122.      * 
  123.      * @param termCount Count of the Number of Terms
  124.      * 
  125.      * @return The Asymptotic Expansion Version of ErrorFunctionComplement
  126.      */

  128.     public static final ErrorFunctionComplement AsymptoticExpansion (
  129.         final int termCount)
  130.     {
  131.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator =
  132.             org.drip.function.e2erfc.AsymptoticExpansion.SeriesGenerator (termCount);

  134.         try
  135.         {
  136.             return new ErrorFunctionComplement (
  137.                 r1ToR1SeriesGenerator,
  138.                 null
  139.             )
  140.             {
  141.                 @Override public double evaluate (
  142.                     final double z)
  143.                     throws java.lang.Exception
  144.                 {
  145.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  146.                     {
  147.                         throw new java.lang.Exception
  148.                             ("ErrorFunctionComplement::AsymptoticExpansion::evaluate => Invalid Inputs");
  149.                     }

  151.                     if (0. == z)
  152.                     {
  153.                         return 1.;
  154.                     }

  156.                     if (z < 0)
  157.                     {
  158.                         return 2. - evaluate (-1. * z);
  159.                     }

  161.                     return java.lang.Math.exp (-1. * z * z) / (z * java.lang.Math.sqrt (java.lang.Math.PI)) *
  162.                         r1ToR1SeriesGenerator.cumulative (
  163.                             0.,
  164.                             z
  165.                         );
  166.                 }
  167.             };
  168.         }
  169.         catch (java.lang.Exception e)
  170.         {
  171.             e.printStackTrace();
  172.         }

  174.         return null;
  175.     }

  177.     /**
  178.      * Construct the Inverse Factorial Expansion Version of ErrorFunctionComplement
  179.      * 
  180.      * @param termCount Count of the Number of Terms
  181.      * 
  182.      * @return The Inverse Factorial Expansion Version of ErrorFunctionComplement
  183.      */

  185.     public static final ErrorFunctionComplement InverseFactorialExpansion (
  186.         final int termCount)
  187.     {
  188.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator =
  189.             org.drip.function.e2erfc.InverseFactorialExpansion.SeriesGenerator (termCount);

  191.         try
  192.         {
  193.             return new ErrorFunctionComplement (
  194.                 r1ToR1SeriesGenerator,
  195.                 null
  196.             )
  197.             {
  198.                 @Override public double evaluate (
  199.                     final double z)
  200.                     throws java.lang.Exception
  201.                 {
  202.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  203.                     {
  204.                         throw new java.lang.Exception
  205.                             ("ErrorFunctionComplement::InverseFactorialExpansion::evaluate => Invalid Inputs");
  206.                     }

  208.                     if (0. == z)
  209.                     {
  210.                         return 1.;
  211.                     }

  213.                     if (z < 0)
  214.                     {
  215.                         return 2. - evaluate (-1. * z);
  216.                     }

  218.                     return java.lang.Math.exp (-1. * z * z) / (z * java.lang.Math.sqrt (java.lang.Math.PI)) *
  219.                         r1ToR1SeriesGenerator.cumulative (
  220.                             0.,
  221.                             z
  222.                         );
  223.                 }
  224.             };
  225.         }
  226.         catch (java.lang.Exception e)
  227.         {
  228.             e.printStackTrace();
  229.         }

  231.         return null;
  232.     }

  234.     /**
  235.      * ErrorFunctionComplement Constructor
  236.      * 
  237.      * @param r1ToR1SeriesGenerator R<sup>1</sup> To R<sup>1</sup> Series Generator
  238.      * @param dc Differential Control
  239.      * 
  240.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  241.      */

  243.     public ErrorFunctionComplement (
  244.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator,
  245.         final org.drip.numerical.differentiation.DerivativeControl dc)
  246.         throws java.lang.Exception
  247.     {
  248.         super (
  249.             dc,
  250.             0.
  251.         );

  253.         _r1ToR1SeriesGenerator = r1ToR1SeriesGenerator;
  254.     }

  256.     @Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
  257.         final double x)
  258.     {
  259.         return null == _r1ToR1SeriesGenerator ? seriesEstimate (
  260.             x,
  261.             null,
  262.             null
  263.         ) : seriesEstimate (
  264.             x,
  265.             _r1ToR1SeriesGenerator.termWeightMap(),
  266.             _r1ToR1SeriesGenerator
  267.         );
  268.     }

  270.     @Override public org.drip.function.definition.R1ToR1 integrand()
  271.     {
  272.         return new org.drip.function.definition.R1ToR1 (null)
  273.         {
  274.             @Override public double evaluate (
  275.                 final double z)
  276.             {
  277.                 return 1. - 2. * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI);
  278.             }
  279.         };
  280.     }

  282.     /**
  283.      * Compute the Q Value for the given X
  284.      * 
  285.      * @param x X
  286.      * 
  287.      * @return The Q Value
  288.      * 
  289.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  290.      */

  292.     public double q (
  293.         final double x)
  294.         throws java.lang.Exception
  295.     {
  296.         if (!org.drip.numerical.common.NumberUtil.IsValid (x))
  297.         {
  298.             throw new java.lang.Exception ("ErrorFunctionComplement::q => Invalid Inputs");
  299.         }

  301.         return 0.5 * evaluate (x / java.lang.Math.sqrt (2.));
  302.     }

  304.     /**
  305.      * Compute the CDF Value for the given X
  306.      * 
  307.      * @param x X
  308.      * 
  309.      * @return The CDF Value
  310.      * 
  311.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  312.      */

  314.     public double cdf (
  315.         final double x)
  316.         throws java.lang.Exception
  317.     {
  318.         if (!org.drip.numerical.common.NumberUtil.IsValid (x))
  319.         {
  320.             throw new java.lang.Exception ("ErrorFunctionComplement::cdf => Invalid Inputs");
  321.         }

  323.         return 0.5 * evaluate (-1. * x / java.lang.Math.sqrt (2.));
  324.     }

  326.     /**
  327.      * Compute the erf Value for the given X
  328.      * 
  329.      * @param x X
  330.      * 
  331.      * @return The erf Value
  332.      * 
  333.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  334.      */

  336.     public double erf (
  337.         final double x)
  338.         throws java.lang.Exception
  339.     {
  340.         return 1. - evaluate (x);
  341.     }

  343.     /**
  344.      * Compute the erfcx Value for the given X
  345.      * 
  346.      * @param x X
  347.      * 
  348.      * @return The erfcx Value
  349.      * 
  350.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  351.      */

  353.     public double erfcx (
  354.         final double x)
  355.         throws java.lang.Exception
  356.     {
  357.         return java.lang.Math.exp (x * x) * evaluate (x);
  358.     }
  359. }
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