SpecialValues.java

  1. package org.drip.specialfunction.digamma;

  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>SpecialValues</i> holds a specific Collection of Special Values of the Digamma Function. The References
  79.  * are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
  85.  *              Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
  89.  *              Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
  93.  *              Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
  94.  *      </li>
  95.  *      <li>
  96.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  97.  *              University Press</b> New York
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function
  101.  *      </li>
  102.  *  </ul>
  103.  *
  104.  *  <br><br>
  105.  *  <ul>
  106.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  107.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  108.  *      <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>
  109.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/digamma/README.md">Estimation Techniques for Digamma Function</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class SpecialValues
  116. {

  118.     /**
  119.      * Construct the Fractionals Map for Leading Digamma Fractions
  120.      * 
  121.      * @return Fractionals Map for Leading Digamma Fractions
  122.      */

  124.     public static final java.util.Map<java.lang.Double, java.lang.Double> Fractionals()
  125.     {
  126.         java.util.Map<java.lang.Double, java.lang.Double> fractionalsMap = new
  127.             java.util.TreeMap<java.lang.Double, java.lang.Double>();

  129.         double log2 = java.lang.Math.log (2.);

  131.         double log3 = java.lang.Math.log (3.);

  133.         double sqrt2 = java.lang.Math.sqrt (2.);

  135.         double sqrt3 = java.lang.Math.sqrt (3.);

  137.         fractionalsMap.put (
  138.             1.,
  139.             -org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  140.         );

  142.         fractionalsMap.put (
  143.             1. / 2.,
  144.             -2. * log2 - org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  145.         );

  147.         fractionalsMap.put (
  148.             1. / 3.,
  149.             -0.5 * java.lang.Math.PI / sqrt3 - 1.5 * log3 -
  150.                 org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  151.         );

  153.         fractionalsMap.put (
  154.             1. / 4.,
  155.             -0.5 * java.lang.Math.PI - 3. * log2 -
  156.                 org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  157.         );

  159.         fractionalsMap.put (
  160.             1. / 6.,
  161.             -0.5 * java.lang.Math.PI * log3 - 2. * log2 - 1.5 * log3 -
  162.                 org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  163.         );

  165.         fractionalsMap.put (
  166.             1. / 8.,
  167.             -0.5 * java.lang.Math.PI - 4. * log2 -
  168.                 (java.lang.Math.PI + java.lang.Math.log (2. + sqrt2) - java.lang.Math.log (2. - sqrt2)) /
  169.                     sqrt2 -
  170.                 org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
  171.         );

  173.         return fractionalsMap;
  174.     }

  176.     /**
  177.      * Construct the Unit Imaginary Digamma Complex Number
  178.      *  
  179.      * @param termCount The Term Count
  180.      * 
  181.      * @return Unit Imaginary Digamma Complex Number
  182.      */

  184.     public static final org.drip.function.definition.CartesianComplexNumber UnitImaginary (
  185.         final int termCount)
  186.     {
  187.         if (0 >= termCount)
  188.         {
  189.             return null;
  190.         }

  192.         double realPart = -1. * org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI;

  194.         for (int n = 1; n <= termCount; ++n)
  195.         {
  196.             realPart = realPart + (1. - n) / (n * n * n + n * n + n + 1);
  197.         }

  199.         try
  200.         {
  201.             return new org.drip.function.definition.CartesianComplexNumber (
  202.                 realPart,
  203.                 0.5 + 0.5 * java.lang.Math.PI / java.lang.Math.tanh (java.lang.Math.PI)
  204.             );
  205.         }
  206.         catch (java.lang.Exception e)
  207.         {
  208.             e.printStackTrace();
  209.         }

  211.         return null;
  212.     }
  213. }
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