ErrorFunctionInverse.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>ErrorFunctionInverse</i> implements the E<sub>2</sub> erf Inverse erf<sup>-1</sup>. 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 abstract class ErrorFunctionInverse extends org.drip.numerical.estimation.R1ToR1Estimator
  117. {
  118.     private org.drip.numerical.estimation.R1ToR1Series _r1ToR1SeriesGenerator = null;

  120.     /**
  121.      * Construct Winitzki (2008) Version of the Analytical E<sub>2</sub> erf Inverse
  122.      * 
  123.      * @param a a
  124.      * 
  125.      * @return Winitzki (2008) Version of the Analytical E<sub>2</sub> erf Inverse
  126.      */

  128.     public static final org.drip.function.e2erf.ErrorFunctionInverse Winitzki2008 (
  129.         final double a)
  130.     {
  131.         try
  132.         {
  133.             return !org.drip.numerical.common.NumberUtil.IsValid (a) ? null :
  134.                 new org.drip.function.e2erf.ErrorFunctionInverse (
  135.                     null,
  136.                     null
  137.                 )
  138.             {
  139.                 @Override public double evaluate (
  140.                     final double z)
  141.                     throws java.lang.Exception
  142.                 {
  143.                     if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z <= -1. || z >= 1.)
  144.                     {
  145.                         throw new java.lang.Exception
  146.                             ("ErrorFunctionInverse::Winitzki2008::evaluate => Invalid Inputs");
  147.                     }

  149.                     if (0. == z)
  150.                     {
  151.                         return 0.;
  152.                     }

  154.                     if (0. > z)
  155.                     {
  156.                         return -1. * evaluate (-1. * z);
  157.                     }

  159.                     double twoOverPIA = 2. / (java.lang.Math.PI * a);

  161.                     double lnOneMinusZ2 = java.lang.Math.log (1. - z * z);

  163.                     double halfLnOneMinusZ2 = 0.5 * lnOneMinusZ2;
  164.                     double twoOverPIAPlusHalfLnOneMinusZ2 = twoOverPIA + halfLnOneMinusZ2;

  166.                     double erfi = java.lang.Math.sqrt (
  167.                         java.lang.Math.sqrt (
  168.                             twoOverPIAPlusHalfLnOneMinusZ2 * twoOverPIAPlusHalfLnOneMinusZ2 -
  169.                                 (lnOneMinusZ2 / a)
  170.                         ) - twoOverPIAPlusHalfLnOneMinusZ2
  171.                     );

  173.                     return erfi < 0. ? -1. * erfi : erfi;
  174.                 }
  175.             };
  176.         }
  177.         catch (java.lang.Exception e)
  178.         {
  179.             e.printStackTrace();
  180.         }

  182.         return null;
  183.     }

  185.     /**
  186.      * Construct Winitzki (2008a) Version of the Analytical E<sub>2</sub> erf Inverse
  187.      * 
  188.      * @return Winitzki (2008a) Version of the Analytical E<sub>2</sub> erf Inverse
  189.      */

  191.     public static final org.drip.function.e2erf.ErrorFunctionInverse Winitzki2008a()
  192.     {
  193.         return Winitzki2008 (
  194.             8. * (java.lang.Math.PI - 3.) / (3. * java.lang.Math.PI * (4. - java.lang.Math.PI))
  195.         );
  196.     }

  198.     /**
  199.      * Construct Winitzki (2008b) Version of the Analytical E<sub>2</sub> erf Inverse
  200.      * 
  201.      * @return Winitzki (2008b) Version of the Analytical E<sub>2</sub> erf Inverse
  202.      */

  204.     public static final org.drip.function.e2erf.ErrorFunctionInverse Winitzki2008b()
  205.     {
  206.         return Winitzki2008 (0.147);
  207.     }

  209.     /**
  210.      * Construct the Euler-MacLaurin Instance of the E<sub>2</sub> erf Inverse
  211.      * 
  212.      * @param termCount The Count of Approximation Terms
  213.      * 
  214.      * @return The Euler-MacLaurin Instance of the E<sub>2</sub> erf Inverse
  215.      */

  217.     public static final ErrorFunctionInverse MacLaurin (
  218.         final int termCount)
  219.     {
  220.         final org.drip.function.e2erf.MacLaurinSeries e2InverseMacLaurinSeriesGenerator =
  221.             org.drip.function.e2erf.MacLaurinSeries.ERFI (termCount);

  223.         if (null == e2InverseMacLaurinSeriesGenerator)
  224.         {
  225.             return null;
  226.         }

  228.         return new ErrorFunctionInverse (
  229.             e2InverseMacLaurinSeriesGenerator,
  230.             null
  231.         )
  232.         {
  233.             @Override public double evaluate (
  234.                 final double z)
  235.                 throws java.lang.Exception
  236.             {
  237.                 if (!org.drip.numerical.common.NumberUtil.IsValid (z) || -1. >= z || 1. <= z)
  238.                 {
  239.                     throw new java.lang.Exception
  240.                         ("ErrorFunctionInverse::MacLaurin::evaluate => Invalid Inputs");
  241.                 }

  243.                 double erfi = e2InverseMacLaurinSeriesGenerator.cumulative (
  244.                     0.,
  245.                     z
  246.                 );

  248.                 return erfi > 1. ? 1. : erfi;
  249.             }
  250.         };
  251.     }

  253.     protected ErrorFunctionInverse (
  254.         final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator,
  255.         final org.drip.numerical.differentiation.DerivativeControl dc)
  256.     {
  257.         super (dc);

  259.         _r1ToR1SeriesGenerator = r1ToR1SeriesGenerator;
  260.     }

  262.     @Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
  263.         final double x)
  264.     {
  265.         return null == _r1ToR1SeriesGenerator ? seriesEstimate (
  266.             x,
  267.             null,
  268.             null
  269.         ) : seriesEstimate (
  270.             x,
  271.             _r1ToR1SeriesGenerator.termWeightMap(),
  272.             _r1ToR1SeriesGenerator
  273.         );
  274.     }

  276.     /**
  277.      * Compute the Probit Value for the given p
  278.      * 
  279.      * @param p P
  280.      * 
  281.      * @return The Probit Value
  282.      * 
  283.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  284.      */

  286.     public double probit (
  287.         final double p)
  288.         throws java.lang.Exception
  289.     {
  290.         if (!org.drip.numerical.common.NumberUtil.IsValid (p))
  291.         {
  292.             throw new java.lang.Exception ("ErrorFunctionInverse::probit => Invalid Inputs");
  293.         }

  295.         return java.lang.Math.sqrt (2.) * evaluate (2. * p - 1.);
  296.     }

  298.     /**
  299.      * Compute the Inverse CDF Value for the given p
  300.      * 
  301.      * @param p P
  302.      * 
  303.      * @return The Inverse CDF Value
  304.      * 
  305.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  306.      */

  308.     public double inverseCDF (
  309.         final double p)
  310.         throws java.lang.Exception
  311.     {
  312.         if (!org.drip.numerical.common.NumberUtil.IsValid (p))
  313.         {
  314.             throw new java.lang.Exception ("ErrorFunctionInverse::inverseCDF => Invalid Inputs");
  315.         }

  317.         return java.lang.Math.sqrt (2.) * evaluate (2. * p - 1.);
  318.     }
  319. }
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