R1ToR1Series.java

  1. package org.drip.numerical.estimation;

  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>R1ToR1Series</i> holds the R<sup>1</sup> To R<sup>1</sup> Expansion Terms in the Ordered Series of the
  79.  * Numerical Estimate for a Function. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function <i>Computers and
  85.  *              Mathematics with Applications</i> <b>61 (11)</b> 3364-3369
  86.  *      </li>
  87.  *      <li>
  88.  *          National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical
  89.  *              Functions https://dlmf.nist.gov/5.11
  90.  *      </li>
  91.  *      <li>
  92.  *          Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n!
  93.  *              https://arxiv.org/abs/1003.2907 <b>arXiv</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Toth V. T. (2016): Programmable Calculators – The Gamma Function
  97.  *              http://www.rskey.org/CMS/index.php/the-library/11
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Stirling's Approximation
  101.  *              https://en.wikipedia.org/wiki/Stirling%27s_approximation
  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/numerical">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/estimation/README.md">Function Numerical Estimates/Corrections/Bounds</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class R1ToR1Series extends org.drip.numerical.estimation.RxToR1Series
  117. {
  118.     private org.drip.numerical.estimation.R1ToR1SeriesTerm _r1ToR1SeriesTerm = null;

  120.     /**
  121.      * R1ToR1Series Constructor
  122.      * 
  123.      * @param r1ToR1SeriesTerm R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
  124.      * @param proportional TRUE - The Expansion Term is Proportional
  125.      * @param termWeightMap Error Term Weight Map
  126.      * 
  127.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  128.      */

  130.     public R1ToR1Series (
  131.         final org.drip.numerical.estimation.R1ToR1SeriesTerm r1ToR1SeriesTerm,
  132.         final boolean proportional,
  133.         final java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap)
  134.         throws java.lang.Exception
  135.     {
  136.         super (
  137.             proportional,
  138.             termWeightMap
  139.         );

  141.         if (null == (_r1ToR1SeriesTerm = r1ToR1SeriesTerm))
  142.         {
  143.             throw new java.lang.Exception ("R1ToR1Series Constructor => Invalid Inputs");
  144.         }
  145.     }

  147.     /**
  148.      * Retrieve the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
  149.      * 
  150.      * @return The R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
  151.      */

  153.     public org.drip.numerical.estimation.R1ToR1SeriesTerm r1ToR1SeriesTerm()
  154.     {
  155.         return _r1ToR1SeriesTerm;
  156.     }

  158.     /**
  159.      * Generate the R<sup>1</sup> To R<sup>1</sup> Series Expansion using the Term
  160.      * 
  161.      * @param zeroOrder The Zero Order Estimate
  162.      * @param x X
  163.      * 
  164.      * @return The R<sup>1</sup> To R<sup>1</sup> Series Expansion
  165.      */

  167.     public java.util.TreeMap<java.lang.Integer, java.lang.Double> generate (
  168.         final double zeroOrder, 
  169.         final double x)
  170.     {
  171.         if (!org.drip.numerical.common.NumberUtil.IsValid (zeroOrder))
  172.         {
  173.             return null;
  174.         }

  176.         java.util.TreeMap<java.lang.Integer, java.lang.Double> seriesExpansionMap = new
  177.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  179.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = termWeightMap();

  181.         if (null == termWeightMap || 0 == termWeightMap.size())
  182.         {
  183.             return seriesExpansionMap;
  184.         }

  186.         double scale = proportional() ? zeroOrder : 1.;

  188.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> termWeightEntry :
  189.             termWeightMap.entrySet())
  190.         {
  191.             int order = termWeightEntry.getKey();

  193.             try
  194.             {
  195.                 seriesExpansionMap.put (
  196.                     order,
  197.                     scale * termWeightEntry.getValue() * _r1ToR1SeriesTerm.value (
  198.                         order,
  199.                         x
  200.                     )
  201.                 );
  202.             }
  203.             catch (java.lang.Exception e)
  204.             {
  205.                 e.printStackTrace();

  207.                 return null;
  208.             }
  209.         }

  211.         return seriesExpansionMap;
  212.     }

  214.     /**
  215.      * Compute the Cumulative Series Value
  216.      * 
  217.      * @param zeroOrder The Zero Order Estimate
  218.      * @param x X
  219.      * 
  220.      * @return The Cumulative Series Value
  221.      * 
  222.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  223.      */

  225.     public double cumulative (
  226.         final double zeroOrder, 
  227.         final double x)
  228.         throws java.lang.Exception
  229.     {
  230.         java.util.TreeMap<java.lang.Integer, java.lang.Double> seriesMap = generate (
  231.             zeroOrder, 
  232.             x
  233.         );

  235.         if (null == seriesMap)
  236.         {
  237.             throw new java.lang.Exception ("R1ToR1Series::cumulative => Invalid Inputs");
  238.         }

  240.         double cumulative = 0.;

  242.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> seriesEntry : seriesMap.entrySet())
  243.         {
  244.             cumulative = cumulative + seriesEntry.getValue();
  245.         }

  247.         return cumulative;
  248.     }

  250.     @Override public double evaluate (
  251.         final double x)
  252.         throws java.lang.Exception
  253.     {
  254.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = termWeightMap();

  256.         if (null == termWeightMap || 0 == termWeightMap.size())
  257.         {
  258.             return 0.;
  259.         }

  261.         double scale = proportional() ? 0. : 1.;

  263.         double value = 0.;

  265.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> termWeightEntry :
  266.             termWeightMap.entrySet())
  267.         {
  268.             value = value + scale * termWeightEntry.getValue() * _r1ToR1SeriesTerm.value (
  269.                 termWeightEntry.getKey(),
  270.                 x
  271.             );
  272.         }

  274.         return value;
  275.     }

  277.     @Override public double derivative (
  278.         final double x,
  279.         final int derivativeOrder)
  280.         throws java.lang.Exception
  281.     {
  282.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = termWeightMap();

  284.         if (null == termWeightMap || 0 == termWeightMap.size())
  285.         {
  286.             return 0.;
  287.         }

  289.         double scale = proportional() ? 0. : 1.;

  291.         double value = 0.;

  293.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> termWeightEntry :
  294.             termWeightMap.entrySet())
  295.         {
  296.             value = value + scale * termWeightEntry.getValue() * _r1ToR1SeriesTerm.derivative (
  297.                 termWeightEntry.getKey(),
  298.                 derivativeOrder,
  299.                 x
  300.             );
  301.         }

  303.         return value;
  304.     }
  305. }
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