GeneralizedMidPointQuadrature.java

  1. package org.drip.numerical.integration;

  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>GeneralizedMidPointQuadrature</i> computes the R<sup>1</sup> Numerical Estimate of a Function
  79.  * Quadrature using the Generalized Mid-Point Scheme. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): <i>Frank-Wolfe Bayesian
  85.  *              Quadrature: Probabilistic Integration with Theoretical Guarantees</i> <b>arXiv</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): <i>Computer Methods for Mathematical
  89.  *              Computation</i> <b>Prentice Hall</b> Englewood Cliffs NJ
  90.  *      </li>
  91.  *      <li>
  92.  *          Leader, J. J. (2004): <i>Numerical Analysis and Scientific Computation</i> <b>Addison Wesley</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Stoer, J., and R. Bulirsch (1980): <i>Introduction to Numerical Analysis</i>
  96.  *              <b>Springer-Verlag</b> New York
  97.  *      </li>
  98.  *      <li>
  99.  *          Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration
  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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  107.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
  108.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/integration/README.md">R<sup>1</sup> R<sup>d</sup> Numerical Integration Schemes</a></li>
  109.  *  </ul>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public class GeneralizedMidPointQuadrature
  115. {
  116.     private int _nodeCount = -1;
  117.     private int _seriesTermCount = -1;
  118.     private org.drip.function.definition.R1ToR1 _r1ToR1 = null;

  120.     /**
  121.      * GeneralizedMidPointQuadrature Constructor
  122.      * 
  123.      * @param r1ToR1 R<sup>1</sup> To R<sup>1</sup> Integrand
  124.      * @param nodeCount Quadrature Node Count
  125.      * @param seriesTermCount Series Term Count
  126.      * 
  127.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  128.      */

  130.     public GeneralizedMidPointQuadrature (
  131.         final org.drip.function.definition.R1ToR1 r1ToR1,
  132.         final int nodeCount,
  133.         final int seriesTermCount)
  134.         throws java.lang.Exception
  135.     {
  136.         if (null == (_r1ToR1 = r1ToR1) ||
  137.             1 > (_nodeCount = nodeCount) ||
  138.             0 >= (_seriesTermCount = seriesTermCount))
  139.         {
  140.             throw new java.lang.Exception ("GeneralizedMidPointQuadrature Constructor => Invalid Inputs");
  141.         }
  142.     }

  144.     /**
  145.      * Retrieve the R<sup>1</sup> To R<sup>1</sup> Integrand
  146.      * 
  147.      * @return The R<sup>1</sup> To R<sup>1</sup> Integrand
  148.      */

  150.     public org.drip.function.definition.R1ToR1 r1ToR1()
  151.     {
  152.         return _r1ToR1;
  153.     }

  155.     /**
  156.      * Retrieve the Quadrature Node Count
  157.      * 
  158.      * @return The Quadrature Node Count
  159.      */

  161.     public int nodeCount()
  162.     {
  163.         return _nodeCount;
  164.     }

  166.     /**
  167.      * Retrieve the Series Term Count
  168.      * 
  169.      * @return The Series Term Count
  170.      */

  172.     public int seriesTermCount()
  173.     {
  174.         return _seriesTermCount;
  175.     }

  177.     /**
  178.      * Integrate the Integrand from Left Through Right
  179.      * 
  180.      * @param left Left Limit
  181.      * @param right Right Limit
  182.      * 
  183.      * @return The Integrand Quadrature
  184.      * 
  185.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  186.      */

  188.     public double integrate (
  189.         final double left,
  190.         final double right)
  191.         throws java.lang.Exception
  192.     {
  193.         if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
  194.             !org.drip.numerical.common.NumberUtil.IsValid (right))
  195.         {
  196.             throw new java.lang.Exception ("GeneralizedMidPointQuadrature::integrate => Invalid Inputs");
  197.         }

  199.         if (left == right)
  200.         {
  201.             return 0.;
  202.         }

  204.         boolean flip = false;
  205.         double quadrature = 0.;
  206.         double leftLimit = left;
  207.         double rightLimit = right;

  209.         if (leftLimit > rightLimit)
  210.         {
  211.             flip = true;
  212.             leftLimit = right;
  213.             rightLimit = left;
  214.         }

  216.         double m2 = 2. * _nodeCount;
  217.         double space = rightLimit - leftLimit;

  219.         for (int nodeIndex = 1; nodeIndex <= _nodeCount; ++nodeIndex)
  220.         {
  221.             for (int seriesTermIndex = 0; seriesTermIndex <= _seriesTermCount; ++seriesTermIndex)
  222.             {
  223.                 int seriesTermIndex2 = 2 * seriesTermIndex;
  224.                 int seriesTermIndex2Plus1 = seriesTermIndex2 + 1;

  226.                 quadrature = quadrature + _r1ToR1.derivative (
  227.                     space * (nodeIndex - 0.5) / _nodeCount + leftLimit,
  228.                     2 * seriesTermIndex
  229.                 ) / org.drip.numerical.common.NumberUtil.Factorial (seriesTermIndex2Plus1) /
  230.                 java.lang.Math.pow (
  231.                     m2,
  232.                     seriesTermIndex2Plus1
  233.                 );
  234.             }
  235.         }

  237.         return (flip ? -1. : 1.) * space * quadrature;
  238.     }
  239. }
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