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

  114. public class CumulativeSeries
  115. {

  117.     /**
  118.      * Construct the R<sup>1</sup> To R<sup>1</sup> Infinite Abramowitz-Stegun (2007) Cumulative Series
  119.      * 
  120.      * @param termCount Count of the Number of Terms
  121.      * 
  122.      * @return The R<sup>1</sup> To R<sup>1</sup> Infinite Abramowitz-Stegun (2007) Cumulative Series
  123.      */

  125.     public static final org.drip.numerical.estimation.R1ToR1Series AbramowitzStegun2007 (
  126.         final int termCount)
  127.     {
  128.         try
  129.         {
  130.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  131.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  133.             for (int termIndex = 1; termIndex <= termCount; ++termIndex)
  134.             {
  135.                 termWeightMap.put (
  136.                     termIndex,
  137.                     1.
  138.                 );
  139.             }

  141.             return new org.drip.numerical.estimation.R1ToR1Series (
  142.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.AbramowitzStegun2007(),
  143.                 false,
  144.                 termWeightMap
  145.             );
  146.         }
  147.         catch (java.lang.Exception e)
  148.         {
  149.             e.printStackTrace();
  150.         }

  152.         return null;
  153.     }

  155.     /**
  156.      * Construct the R<sup>1</sup> To R<sup>1</sup> Infinite Saddle Point Cumulative Series
  157.      * 
  158.      * @param saddlePointFunction The Saddle Point Generation Function
  159.      * @param saddlePointCount The Saddle Point Count
  160.      * 
  161.      * @return The R<sup>1</sup> To R<sup>1</sup> Infinite Saddle Point Cumulative Series
  162.      */

  164.     public static final org.drip.numerical.estimation.R1ToR1Series MezoHoffman2017 (
  165.         final org.drip.function.definition.R1ToR1 saddlePointFunction,
  166.         final int saddlePointCount)
  167.     {
  168.         try
  169.         {
  170.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  171.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  173.             for (int termIndex = 0; termIndex <= saddlePointCount; ++termIndex)
  174.             {
  175.                 termWeightMap.put (
  176.                     termIndex,
  177.                     1.
  178.                 );
  179.             }

  181.             return new org.drip.numerical.estimation.R1ToR1Series (
  182.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.MezoHoffman2017 (
  183.                     org.drip.specialfunction.digamma.SaddlePoints.LeadingRoots (
  184.                         saddlePointFunction,
  185.                         saddlePointCount
  186.                     )
  187.                 ),
  188.                 false,
  189.                 termWeightMap
  190.             );
  191.         }
  192.         catch (java.lang.Exception e)
  193.         {
  194.             e.printStackTrace();
  195.         }

  197.         return null;
  198.     }

  200.     /**
  201.      * Construct the R<sup>1</sup> To R<sup>1</sup> Gauss Cumulative Series
  202.      * 
  203.      * @param termCount Count of the Number of Terms
  204.      * 
  205.      * @return The R<sup>1</sup> To R<sup>1</sup> Gauss Cumulative Series
  206.      */

  208.     public static final org.drip.numerical.estimation.R1ToR1Series Gauss (
  209.         final int termCount)
  210.     {
  211.         int seriesCount = (termCount - 1) / 2;

  213.         try
  214.         {
  215.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  216.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  218.             for (int termIndex = 1; termIndex <= seriesCount; ++termIndex)
  219.             {
  220.                 termWeightMap.put (
  221.                     termIndex,
  222.                     1.
  223.                 );
  224.             }

  226.             return new org.drip.numerical.estimation.R1ToR1Series (
  227.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.Gauss (termCount),
  228.                 false,
  229.                 termWeightMap
  230.             );
  231.         }
  232.         catch (java.lang.Exception e)
  233.         {
  234.             e.printStackTrace();
  235.         }

  237.         return null;
  238.     }

  240.     /**
  241.      * Construct the R<sup>1</sup> To R<sup>1</sup> Asymptotic Cumulative Series
  242.      * 
  243.      * @return The R<sup>1</sup> To R<sup>1</sup> Asymptotic Cumulative Series
  244.      */

  246.     public static final org.drip.numerical.estimation.R1ToR1Series Asymptotic()
  247.     {
  248.         try
  249.         {
  250.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  251.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  253.             termWeightMap.put (
  254.                 1,
  255.                 -1. / 12.
  256.             );

  258.             termWeightMap.put (
  259.                 2,
  260.                 1. / 120.
  261.             );

  263.             termWeightMap.put (
  264.                 3,
  265.                 -1. / 252.
  266.             );

  268.             termWeightMap.put (
  269.                 4,
  270.                 1. / 240.
  271.             );

  273.             termWeightMap.put (
  274.                 5,
  275.                 -1. / 132.
  276.             );

  278.             termWeightMap.put (
  279.                 6,
  280.                 691. / 32760.
  281.             );

  283.             termWeightMap.put (
  284.                 7,
  285.                 -1. / 12.
  286.             );

  288.             return new org.drip.numerical.estimation.R1ToR1Series (
  289.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.Asymptotic(),
  290.                 false,
  291.                 termWeightMap
  292.             );
  293.         }
  294.         catch (java.lang.Exception e)
  295.         {
  296.             e.printStackTrace();
  297.         }

  299.         return null;
  300.     }

  302.     /**
  303.      * Construct the R<sup>1</sup> To R<sup>1</sup> Exponential Asymptotic Cumulative Series
  304.      * 
  305.      * @return The R<sup>1</sup> To R<sup>1</sup> Exponential Asymptotic Cumulative Series
  306.      */

  308.     public static final org.drip.numerical.estimation.R1ToR1Series ExponentialAsymptote()
  309.     {
  310.         try
  311.         {
  312.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  313.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  315.             termWeightMap.put (
  316.                 1,
  317.                 1.
  318.             );

  320.             termWeightMap.put (
  321.                 2,
  322.                 1. / 2.
  323.             );

  325.             termWeightMap.put (
  326.                 3,
  327.                 5. / 24.
  328.             );

  330.             termWeightMap.put (
  331.                 4,
  332.                 1. / 16.
  333.             );

  335.             termWeightMap.put (
  336.                 5,
  337.                 47. / (48. * 120.)
  338.             );

  340.             termWeightMap.put (
  341.                 6,
  342.                 1. / (16. * 144.)
  343.             );

  345.             return new org.drip.numerical.estimation.R1ToR1Series (
  346.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.ExponentialAsymptote(),
  347.                 false,
  348.                 termWeightMap
  349.             );
  350.         }
  351.         catch (java.lang.Exception e)
  352.         {
  353.             e.printStackTrace();
  354.         }

  356.         return null;
  357.     }

  359.     /**
  360.      * Construct the R<sup>1</sup> To R<sup>1</sup> Exponential Half-Shifted Asymptotic Cumulative Series
  361.      * 
  362.      * @return The R<sup>1</sup> To R<sup>1</sup> Exponential Half-Shifted Asymptotic Cumulative Series
  363.      */

  365.     public static final org.drip.numerical.estimation.R1ToR1Series ExponentialAsymptoteHalfShifted()
  366.     {
  367.         try
  368.         {
  369.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  370.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  372.             termWeightMap.put (
  373.                 1,
  374.                 1. / org.drip.numerical.common.NumberUtil.Factorial (4)
  375.             );

  377.             termWeightMap.put (
  378.                 2,
  379.                 -37. / (8. * org.drip.numerical.common.NumberUtil.Factorial (6))
  380.             );

  382.             termWeightMap.put (
  383.                 3,
  384.                 10313. / (72. * org.drip.numerical.common.NumberUtil.Factorial (8))
  385.             );

  387.             termWeightMap.put (
  388.                 4,
  389.                 -5509121. / (384. * org.drip.numerical.common.NumberUtil.Factorial (10))
  390.             );

  392.             termWeightMap.put (
  393.                 5,
  394.                 47. / (48. * 120.)
  395.             );

  397.             termWeightMap.put (
  398.                 6,
  399.                 1. / (16. * 144.)
  400.             );

  402.             return new org.drip.numerical.estimation.R1ToR1Series (
  403.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.ExponentialAsymptoteHalfShifted(),
  404.                 false,
  405.                 termWeightMap
  406.             );
  407.         }
  408.         catch (java.lang.Exception e)
  409.         {
  410.             e.printStackTrace();
  411.         }

  413.         return null;
  414.     }

  416.     /**
  417.      * Construct the R<sup>1</sup> To R<sup>1</sup> Taylor Riemann-Zeta Cumulative Series
  418.      * 
  419.      * @param riemannZetaEstimator The Riemann-Zeta Estimator
  420.      * @param termCount Count of the Number of Terms
  421.      * 
  422.      * @return The R<sup>1</sup> To R<sup>1</sup> Taylor Riemann-Zeta Cumulative Series
  423.      */

  425.     public static final org.drip.numerical.estimation.R1ToR1Series TaylorRiemannZeta (
  426.         final org.drip.function.definition.R1ToR1 riemannZetaEstimator,
  427.         final int termCount)
  428.     {
  429.         try
  430.         {
  431.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  432.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  434.             for (int termIndex = 1; termIndex <= termCount; ++termIndex)
  435.             {
  436.                 termWeightMap.put (
  437.                     termIndex,
  438.                     1.
  439.                 );
  440.             }

  442.             return new org.drip.numerical.estimation.R1ToR1Series (
  443.                 org.drip.specialfunction.digamma.CumulativeSeriesTerm.TaylorRiemannZeta
  444.                     (riemannZetaEstimator),
  445.                 false,
  446.                 termWeightMap
  447.             );
  448.         }
  449.         catch (java.lang.Exception e)
  450.         {
  451.             e.printStackTrace();
  452.         }

  454.         return null;
  455.     }
  456. }
Created with JaCoCo 0.7.9.201702052155