ErrorFunction.java

  1. package org.drip.function.e2erf;

  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>ErrorFunction</i> implements the E<sub>2</sub> Error Function (erf). 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/e2erf/README.md">E<sub>2</sub> erf and erf<sup>-1</sup> Implementations</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

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

  120.     /**
  121.      * Construct the Euler-MacLaurin Instance of the E<sub>2</sub> erf
  122.      * 
  123.      * @param termCount The Count of Approximation Terms
  124.      * 
  125.      * @return The Euler-MacLaurin Instance of the E<sub>2</sub> erf
  126.      */

  128.     public static final ErrorFunction MacLaurin (
  129.         final int termCount)
  130.     {
  131.         final org.drip.function.e2erf.MacLaurinSeries e2MacLaurinSeriesGenerator =
  132.             org.drip.function.e2erf.MacLaurinSeries.ERF (termCount);

  134.         if (null == e2MacLaurinSeriesGenerator)
  135.         {
  136.             return null;
  137.         }

  139.         try
  140.         {
  141.             return new ErrorFunction (
  142.                 e2MacLaurinSeriesGenerator,
  143.                 null
  144.             )
  145.             {
  146.                 @Override public double evaluate (
  147.                     final double z)
  148.                     throws java.lang.Exception
  149.                 {
  150.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  151.                     {
  152.                         throw new java.lang.Exception
  153.                             ("ErrorFunction::MacLaurin::evaluate => Invalid Inputs");
  154.                     }

  156.                     double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
  157.                         e2MacLaurinSeriesGenerator.cumulative (
  158.                             0.,
  159.                             z
  160.                         );

  162.                     return erf > 1. ? 1. : erf;
  163.                 }
  164.             };
  165.         }
  166.         catch (java.lang.Exception e)
  167.         {
  168.             e.printStackTrace();
  169.         }

  171.         return null;
  172.     }

  174.     /**
  175.      * Construct the Convergent Hans Heinrich Burmann Version of the E<sub>2</sub> erf
  176.      * 
  177.      * @return The Convergent Hans Heinrich Burmann Version of the E<sub>2</sub> erf
  178.      */

  180.     public static final ErrorFunction HansHeinrichBurmannConvergent()
  181.     {
  182.         final org.drip.numerical.estimation.R1ToR1Series
  183.             hansHeinrichBurmannConvergentSeriesGenerator =
  184.                 org.drip.function.e2erf.HansHeinrichBurmannSeries.Convergent();

  186.         if (null == hansHeinrichBurmannConvergentSeriesGenerator)
  187.         {
  188.             return null;
  189.         }

  191.         try
  192.         {
  193.             return new ErrorFunction (
  194.                 hansHeinrichBurmannConvergentSeriesGenerator,
  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.                             ("ErrorFunction::HansHeinrichBurmannConvergent::evaluate => Invalid Inputs");
  206.                     }

  208.                     double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
  209.                         java.lang.Math.sqrt (1. - java.lang.Math.exp (-1. * z * z)) *
  210.                         hansHeinrichBurmannConvergentSeriesGenerator.cumulative (
  211.                             0.,
  212.                             z
  213.                         );

  215.                     return erf > 1. ? 1. : erf;
  216.                 }
  217.             };
  218.         }
  219.         catch (java.lang.Exception e)
  220.         {
  221.             e.printStackTrace();
  222.         }

  224.         return null;
  225.     }

  227.     /**
  228.      * Construct the Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E<sub>2</sub> erf
  229.      * 
  230.      * @return The Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E<sub>2</sub> erf
  231.      */

  233.     public static final ErrorFunction HansHeinrichBurmannSchopfSupancic2014()
  234.     {
  235.         final org.drip.numerical.estimation.R1ToR1Series hansHeinrichBurmannConvergentSeriesGenerator
  236.             = org.drip.function.e2erf.HansHeinrichBurmannSeries.SchopfSupancic2014();

  238.         if (null == hansHeinrichBurmannConvergentSeriesGenerator)
  239.         {
  240.             return null;
  241.         }

  243.         try
  244.         {
  245.             return new ErrorFunction (
  246.                 hansHeinrichBurmannConvergentSeriesGenerator,
  247.                 null
  248.             )
  249.             {
  250.                 @Override public double evaluate (
  251.                     final double z)
  252.                     throws java.lang.Exception
  253.                 {
  254.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z))
  255.                     {
  256.                         throw new java.lang.Exception
  257.                             ("ErrorFunction::HansHeinrichBurmannSchopfSupancic2014::evaluate => Invalid Inputs");
  258.                     }

  260.                     double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
  261.                         java.lang.Math.sqrt (1. - java.lang.Math.exp (-1. * z * z)) *
  262.                         hansHeinrichBurmannConvergentSeriesGenerator.cumulative (
  263.                             0.,
  264.                             z
  265.                         );

  267.                     return erf > 1. ? 1. : erf;
  268.                 }
  269.             };
  270.         }
  271.         catch (java.lang.Exception e)
  272.         {
  273.             e.printStackTrace();
  274.         }

  276.         return null;
  277.     }

  279.     /**
  280.      * ErrorFunction Constructor
  281.      * 
  282.      * @param r1ToR1SeriesGenerator R<sup>1</sup> To R<sup>1</sup> Series Generator
  283.      * @param dc Differential Control
  284.      * 
  285.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  286.      */

  288.     public ErrorFunction (
  289.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator,
  290.         final org.drip.numerical.differentiation.DerivativeControl dc)
  291.         throws java.lang.Exception
  292.     {
  293.         super (
  294.             dc,
  295.             0.
  296.         );

  298.         _r1ToR1SeriesGenerator = r1ToR1SeriesGenerator;
  299.     }

  301.     @Override public double derivative (
  302.         final double z,
  303.         final int order)
  304.         throws java.lang.Exception
  305.     {
  306.         if (!org.drip.numerical.common.NumberUtil.IsValid (z) ||
  307.             1 > order)
  308.         {
  309.             throw new java.lang.Exception ("ErrorFunction::derivative => Invalid Inputs");
  310.         }

  312.         return 1 == order ? 2. * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI) :
  313.             super.derivative (
  314.                 z,
  315.                 order
  316.             );
  317.     }

  319.     @Override public org.drip.function.definition.R1ToR1 antiDerivative()
  320.     {
  321.         return new org.drip.function.definition.R1ToR1 (null)
  322.         {
  323.             @Override public double evaluate (
  324.                 final double x)
  325.                 throws java.lang.Exception
  326.             {
  327.                 if (!org.drip.numerical.common.NumberUtil.IsValid (x))
  328.                 {
  329.                     throw new java.lang.Exception
  330.                         ("ErrorFunction::antiDerivative::evaluate => Invalid Inputs");
  331.                 }

  333.                 return x * this.evaluate (x) + java.lang.Math.exp (-1. * x * x) / java.lang.Math.sqrt
  334.                     (java.lang.Math.PI);
  335.             }
  336.         };
  337.     }

  339.     @Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
  340.         final double x)
  341.     {
  342.         return null == _r1ToR1SeriesGenerator ? seriesEstimate (
  343.             x,
  344.             null,
  345.             null
  346.         ) : seriesEstimate (
  347.             x,
  348.             _r1ToR1SeriesGenerator.termWeightMap(),
  349.             _r1ToR1SeriesGenerator
  350.         );
  351.     }

  353.     @Override public org.drip.function.definition.R1ToR1 integrand()
  354.     {
  355.         return new org.drip.function.definition.R1ToR1 (null)
  356.         {
  357.             @Override public double evaluate (
  358.                 final double z)
  359.             {
  360.                 return 2. * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI);
  361.             }
  362.         };
  363.     }

  365.     /**
  366.      * Compute the Q Value for the given X
  367.      * 
  368.      * @param x X
  369.      * 
  370.      * @return The Q Value
  371.      * 
  372.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  373.      */

  375.     public double q (
  376.         final double x)
  377.         throws java.lang.Exception
  378.     {
  379.         return 0.5 * (1. - evaluate (x / java.lang.Math.sqrt (2.)));
  380.     }

  382.     /**
  383.      * Compute the CDF Value for the given X
  384.      * 
  385.      * @param x X
  386.      * 
  387.      * @return The CDF Value
  388.      * 
  389.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  390.      */

  392.     public double cdf (
  393.         final double x)
  394.         throws java.lang.Exception
  395.     {
  396.         return 0.5 * (1. + evaluate (x / java.lang.Math.sqrt (2.)));
  397.     }

  399.     /**
  400.      * Compute the erfc Value for the given X
  401.      * 
  402.      * @param x X
  403.      * 
  404.      * @return The erfc Value
  405.      * 
  406.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  407.      */

  409.     public double erfc (
  410.         final double x)
  411.         throws java.lang.Exception
  412.     {
  413.         return 1. - evaluate (x);
  414.     }

  416.     /**
  417.      * Compute the E<sub>2</sub> erf Gaussian Density Integral over -inf to +inf
  418.      * 
  419.      * @param a The Scale Parameter
  420.      * @param b The Displacement Parameter
  421.      * @param r1UnivariateNormal The R<sup>1</sup> Gaussian Distribution Parameters
  422.      * 
  423.      * @return The E<sub>2</sub> erf Gaussian Density Integral over -inf to +inf
  424.      * 
  425.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  426.      */

  428.     public double gaussianDensityIntegral (
  429.         final double a,
  430.         final double b,
  431.         final org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal)
  432.         throws java.lang.Exception
  433.     {
  434.         if (!org.drip.numerical.common.NumberUtil.IsValid (a) ||
  435.             !org.drip.numerical.common.NumberUtil.IsValid (b) ||
  436.             null == r1UnivariateNormal)
  437.         {
  438.             throw new java.lang.Exception ("ErrorFunction::gaussianDensityIntegral => Invalid Inputs");
  439.         }

  441.         double sigma = r1UnivariateNormal.variance();

  443.         return evaluate (
  444.             (a * r1UnivariateNormal.mean() + b) / java.lang.Math.sqrt (1. + 2 * sigma * sigma * a * a)
  445.         );
  446.     }
  447. }
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