NewtonCotesQuadratureGenerator.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>NewtonCotesQuadratureGenerator</i> generates the Array of Newton-Cotes Based Quadrature Abscissa and
  79.  * their corresponding Weights. 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 NewtonCotesQuadratureGenerator
  115. {

  117.     /**
  118.      * Generate the Newton-Cotes of Equally Spaced Quadrature over (0, +1)
  119.      * 
  120.      * @param abscissaTransformer The Abscissa Transformer
  121.      * @param intermediatePointCount Number of Intermediate Points
  122.      * 
  123.      * @return The Newton-Cotes of Equally Spaced Quadrature over (0, +1)
  124.      */

  126.     public static final org.drip.numerical.integration.QuadratureEstimator Zero_PlusOne (
  127.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer,
  128.         final int intermediatePointCount)
  129.     {
  130.         if (0 >= intermediatePointCount)
  131.         {
  132.             return null;
  133.         }

  135.         int nodeCount = intermediatePointCount + 2;
  136.         double width = 1. / (intermediatePointCount + 1);
  137.         double[] abscissaArray = new double[nodeCount];
  138.         double[] weightArray = new double[nodeCount];
  139.         weightArray[intermediatePointCount + 1] = 0.5 * width;
  140.         abscissaArray[intermediatePointCount + 1] = 1.;
  141.         weightArray[0] = 0.5 * width;
  142.         abscissaArray[0] = 0.;

  144.         for (int intermediatePointIndex = 0; intermediatePointIndex < intermediatePointCount;
  145.             ++intermediatePointIndex)
  146.         {
  147.             weightArray[intermediatePointIndex + 1] = width;
  148.             abscissaArray[intermediatePointIndex + 1] = width * (intermediatePointIndex + 1);
  149.         }

  151.         try
  152.         {
  153.             return new org.drip.numerical.integration.QuadratureEstimator (
  154.                 abscissaTransformer,
  155.                 org.drip.numerical.common.Array2D.FromArray (
  156.                     abscissaArray,
  157.                     weightArray
  158.                 )
  159.             );
  160.         }
  161.         catch (java.lang.Exception e)
  162.         {
  163.             e.printStackTrace();
  164.         }

  166.         return null;
  167.     }


  170.     /**
  171.      * Generate the Newton-Cotes of Equally Spaced Quadrature over (-1, +1)
  172.      * 
  173.      * @param abscissaTransformer The Abscissa Transformer
  174.      * @param intermediatePointCount Number of Intermediate Points
  175.      * 
  176.      * @return The Newton-Cotes of Equally Spaced Quadrature over (1, +1)
  177.      */

  179.     public static final org.drip.numerical.integration.QuadratureEstimator MinusOne_PlusOne (
  180.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer,
  181.         final int intermediatePointCount)
  182.     {
  183.         if (0 >= intermediatePointCount)
  184.         {
  185.             return null;
  186.         }

  188.         int nodeCount = intermediatePointCount + 2;
  189.         double[] weightArray = new double[nodeCount];
  190.         double[] abscissaArray = new double[nodeCount];
  191.         double width = 2. / (intermediatePointCount + 1);
  192.         weightArray[intermediatePointCount + 1] = 0.5 * width;
  193.         abscissaArray[intermediatePointCount + 1] = 1.;
  194.         weightArray[0] = 0.5 * width;
  195.         abscissaArray[0] = -1.;

  197.         for (int intermediatePointIndex = 0; intermediatePointIndex < intermediatePointCount;
  198.             ++intermediatePointIndex)
  199.         {
  200.             weightArray[intermediatePointIndex + 1] = width;
  201.             abscissaArray[intermediatePointIndex + 1] = width * (intermediatePointIndex + 1) - 1.;
  202.         }

  204.         try
  205.         {
  206.             return new org.drip.numerical.integration.QuadratureEstimator (
  207.                 abscissaTransformer,
  208.                 org.drip.numerical.common.Array2D.FromArray (
  209.                     abscissaArray,
  210.                     weightArray
  211.                 )
  212.             );
  213.         }
  214.         catch (java.lang.Exception e)
  215.         {
  216.             e.printStackTrace();
  217.         }

  219.         return null;
  220.     }

  222.     /**
  223.      * Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
  224.      * 
  225.      * @param left Left Integrand Quadrature Limit
  226.      * @param right Right Integrand Quadrature Limit
  227.      * @param intermediatePointCount Number of Intermediate Points
  228.      * 
  229.      * @return The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
  230.      */

  232.     public static final org.drip.numerical.integration.QuadratureEstimator Zero_PlusOne (
  233.         final double left,
  234.         final double right,
  235.         final int intermediatePointCount)
  236.     {
  237.         return Zero_PlusOne (
  238.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleZero_PlusOne (
  239.                 left,
  240.                 right
  241.             ),
  242.             intermediatePointCount
  243.         );
  244.     }

  246.     /**
  247.      * Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
  248.      * 
  249.      * @param left Left Integrand Quadrature Limit
  250.      * @param right Right Integrand Quadrature Limit
  251.      * @param intermediatePointCount Number of Intermediate Points
  252.      * 
  253.      * @return The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
  254.      */

  256.     public static final org.drip.numerical.integration.QuadratureEstimator MinusOne_PlusOne (
  257.         final double left,
  258.         final double right,
  259.         final int intermediatePointCount)
  260.     {
  261.         return MinusOne_PlusOne (
  262.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  263.                 left,
  264.                 right
  265.             ),
  266.             intermediatePointCount
  267.         );
  268.     }

  270.     /**
  271.      * Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
  272.      * 
  273.      * @param left Left Integrand Quadrature Limit
  274.      * @param intermediatePointCount Number of Intermediate Points
  275.      * 
  276.      * @return The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
  277.      */

  279.     public static final org.drip.numerical.integration.QuadratureEstimator GaussLaguerreLeftDefinite (
  280.         final double left,
  281.         final int intermediatePointCount)
  282.     {
  283.         return Zero_PlusOne (
  284.             org.drip.numerical.integration.AbscissaTransform.GaussLaguerreLeftDefinite (left),
  285.             intermediatePointCount
  286.         );
  287.     }

  289.     /**
  290.      * Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
  291.      * 
  292.      * @param right Right Integrand Quadrature Limit
  293.      * @param intermediatePointCount Number of Intermediate Points
  294.      * 
  295.      * @return The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
  296.      */

  298.     public static final org.drip.numerical.integration.QuadratureEstimator GaussLaguerreRightDefinite (
  299.         final double right,
  300.         final int intermediatePointCount)
  301.     {
  302.         return Zero_PlusOne (
  303.             org.drip.numerical.integration.AbscissaTransform.GaussLaguerreRightDefinite (right),
  304.             intermediatePointCount
  305.         );
  306.     }

  308.     /**
  309.      * Generate the Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over
  310.      *      (-Infinity, +Infinity)
  311.      * 
  312.      * @param intermediatePointCount Number of Intermediate Points
  313.      * 
  314.      * @return The Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over
  315.      *      (-Infinity, +Infinity)
  316.      */

  318.     public static final org.drip.numerical.integration.QuadratureEstimator GaussHermite (
  319.         final int intermediatePointCount)
  320.     {
  321.         return MinusOne_PlusOne (
  322.             org.drip.numerical.integration.AbscissaTransform.GaussHermite(),
  323.             intermediatePointCount
  324.         );
  325.     }
  326. }
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