R2ToR1Series.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>R2ToR1Series</i> holds the R<sup>2</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.  *          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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  108.  *      <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>
  109.  *      <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>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class R2ToR1Series
  116. {
  117.     private boolean _proportional = false;
  118.     private org.drip.numerical.estimation.R2ToR1SeriesTerm _r2ToR1SeriesTerm = null;
  119.     private java.util.TreeMap<java.lang.Integer, java.lang.Double> _termWeightMap = null;

  121.     /**
  122.      * R2ToR1Series Constructor
  123.      * 
  124.      * @param r2ToR1SeriesTerm R<sup>2</sup> To R<sup>1</sup> Series Expansion Term
  125.      * @param proportional TRUE - The Expansion Term is Proportional
  126.      * @param termWeightMap Error Term Weight Map
  127.      * 
  128.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  129.      */

  131.     public R2ToR1Series (
  132.         final org.drip.numerical.estimation.R2ToR1SeriesTerm r2ToR1SeriesTerm,
  133.         final boolean proportional,
  134.         final java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap)
  135.         throws java.lang.Exception
  136.     {
  137.         _proportional = proportional;
  138.         _termWeightMap = termWeightMap;

  140.         if (null == (_r2ToR1SeriesTerm = r2ToR1SeriesTerm))
  141.         {
  142.             throw new java.lang.Exception ("R2ToR1Series Constructor => Invalid Inputs");
  143.         }
  144.     }

  146.     /**
  147.      * Retrieve the R<sup>2</sup> To R<sup>1</sup> Series Expansion Term
  148.      * 
  149.      * @return The R<sup>2</sup> To R<sup>1</sup> Series Expansion Term
  150.      */

  152.     public org.drip.numerical.estimation.R2ToR1SeriesTerm r1ToR1SeriesTerm()
  153.     {
  154.         return _r2ToR1SeriesTerm;
  155.     }

  157.     /**
  158.      * Indicate if the R<sup>x</sup> To R<sup>1</sup> Series Expansion Term is Proportional
  159.      * 
  160.      * @return TRUE - The R<sup>x</sup> To R<sup>1</sup> Series Expansion Term is Proportional
  161.      */

  163.     public boolean proportional()
  164.     {
  165.         return _proportional;
  166.     }

  168.     /**
  169.      * Retrieve the R<sup>x</sup> To R<sup>1</sup> Series Expansion Term Weight Map
  170.      * 
  171.      * @return The R<sup>x</sup> To R<sup>1</sup> Series Expansion Term Weight Map
  172.      */

  174.     public java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap()
  175.     {
  176.         return _termWeightMap;
  177.     }

  179.     /**
  180.      * Generate the R<sup>2</sup> To R<sup>1</sup> Series Expansion using the Term
  181.      * 
  182.      * @param zeroOrder The Zero Order Estimate
  183.      * @param x X
  184.      * @param y Y
  185.      * 
  186.      * @return The R<sup>2</sup> To R<sup>1</sup> Series Expansion
  187.      */

  189.     public java.util.TreeMap<java.lang.Integer, java.lang.Double> generate (
  190.         final double zeroOrder, 
  191.         final double x, 
  192.         final double y)
  193.     {
  194.         if (!org.drip.numerical.common.NumberUtil.IsValid (zeroOrder))
  195.         {
  196.             return null;
  197.         }

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

  202.         if (null == _termWeightMap || 0 == _termWeightMap.size())
  203.         {
  204.             return seriesExpansionMap;
  205.         }

  207.         double scale = _proportional ? zeroOrder : 1.;

  209.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> termWeightEntry :
  210.             _termWeightMap.entrySet())
  211.         {
  212.             int order = termWeightEntry.getKey();

  214.             try
  215.             {
  216.                 seriesExpansionMap.put (
  217.                     order,
  218.                     scale * termWeightEntry.getValue() * _r2ToR1SeriesTerm.value (
  219.                         order,
  220.                         x,
  221.                         y
  222.                     )
  223.                 );
  224.             }
  225.             catch (java.lang.Exception e)
  226.             {
  227.                 e.printStackTrace();

  229.                 return null;
  230.             }
  231.         }

  233.         return seriesExpansionMap;
  234.     }

  236.     /**
  237.      * Compute the Cumulative Series Value
  238.      * 
  239.      * @param zeroOrder The Zero Order Estimate
  240.      * @param x X
  241.      * @param y Y
  242.      * 
  243.      * @return The Cumulative Series Value
  244.      * 
  245.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  246.      */

  248.     public double cumulative (
  249.         final double zeroOrder, 
  250.         final double x,
  251.         final double y)
  252.         throws java.lang.Exception
  253.     {
  254.         java.util.TreeMap<java.lang.Integer, java.lang.Double> seriesMap = generate (
  255.             zeroOrder, 
  256.             x,
  257.             y
  258.         );

  260.         if (null == seriesMap)
  261.         {
  262.             throw new java.lang.Exception ("R2ToR1Series::cumulative => Invalid Inputs");
  263.         }

  265.         double cumulative = 0.;

  267.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> seriesEntry : seriesMap.entrySet())
  268.         {
  269.             cumulative = cumulative + seriesEntry.getValue();
  270.         }

  272.         return cumulative;
  273.     }

  275.     /**
  276.      * Evaluate for the given x, y
  277.      * 
  278.      * @param x X
  279.      * @param y Y
  280.      *  
  281.      * @return Returns the calculated value
  282.      * 
  283.      * @throws java.lang.Exception Thrown if evaluation cannot be done
  284.      */

  286.     public double evaluate (
  287.         final double x,
  288.         final double y)
  289.         throws java.lang.Exception
  290.     {
  291.         if (null == _termWeightMap || 0 == _termWeightMap.size())
  292.         {
  293.             return 0.;
  294.         }

  296.         double value = 0.;
  297.         double scale = _proportional ? 0. : 1.;

  299.         for (java.util.Map.Entry<java.lang.Integer, java.lang.Double> termWeightEntry :
  300.             _termWeightMap.entrySet())
  301.         {
  302.             value = value + scale * termWeightEntry.getValue() * _r2ToR1SeriesTerm.value (
  303.                 termWeightEntry.getKey(),
  304.                 x,
  305.                 y
  306.             );
  307.         }

  309.         return value;
  310.     }
  311. }
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