GaussLobattoQuadratureGenerator.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>GaussLobattoQuadratureGenerator</i> generates the Array of Orthogonal Lobatto Polynomial Gaussian
  79.  * Quadrature Based Abscissa and their corresponding Weights. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  85.  *              on Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Gil, A., J. Segura, and N. M. Temme (2007): <i>Numerical Methods for Special Functions</i>
  89.  *              <b>Society for Industrial and Applied Mathematics</b> Philadelphia
  90.  *      </li>
  91.  *      <li>
  92.  *          Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
  93.  *              The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
  94.  *      </li>
  95.  *      <li>
  96.  *          Stoer, J., and R. Bulirsch (2002): <i>Introduction to Numerical Analysis 3rd Edition</i>
  97.  *              <b>Springer</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature
  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/README.md">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/integration/README.md">R<sup>1</sup> R<sup>d</sup> Numerical Integration Schemes</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class GaussLobattoQuadratureGenerator
  116. {

  118.     /**
  119.      * Generate the Three Point Gauss Lobatto Quadrature over [-1, +1]
  120.      * 
  121.      * @param abscissaTransformer The Abscissa Transformer
  122.      * 
  123.      * @return The Three Point Gauss Lobatto Quadrature over [-1, +1]
  124.      */

  126.     public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
  127.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  128.     {
  129.         try
  130.         {
  131.             return new org.drip.numerical.integration.QuadratureEstimator (
  132.                 abscissaTransformer,
  133.                 org.drip.numerical.common.Array2D.FromArray (
  134.                     new double[]
  135.                     {
  136.                         -1.000000000000000,
  137.                          0.000000000000000,
  138.                          1.000000000000000,
  139.                     },
  140.                     new double[]
  141.                     {
  142.                         1. / 3.,
  143.                         4. / 3.,
  144.                         1. / 3.,
  145.                     }
  146.                 )
  147.             );
  148.         }
  149.         catch (java.lang.Exception e)
  150.         {
  151.             e.printStackTrace();
  152.         }

  154.         return null;
  155.     }

  157.     /**
  158.      * Generate the Four Point Gauss Lobatto Quadrature over [-1, +1]
  159.      * 
  160.      * @param abscissaTransformer The Abscissa Transformer
  161.      * 
  162.      * @return The Four Point Gauss Lobatto Quadrature over [-1, +1]
  163.      */

  165.     public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
  166.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  167.     {
  168.         double sqrt_1Over5_ = java.lang.Math.sqrt (0.2);

  170.         try
  171.         {
  172.             return new org.drip.numerical.integration.QuadratureEstimator (
  173.                 abscissaTransformer,
  174.                 org.drip.numerical.common.Array2D.FromArray (
  175.                     new double[]
  176.                     {
  177.                         -1.000000000000000,
  178.                         -sqrt_1Over5_,
  179.                          sqrt_1Over5_,
  180.                          1.000000000000000,
  181.                     },
  182.                     new double[]
  183.                     {
  184.                         1. / 6.,
  185.                         5. / 6.,
  186.                         5. / 6.,
  187.                         1. / 6.,
  188.                     }
  189.                 )
  190.             );
  191.         }
  192.         catch (java.lang.Exception e)
  193.         {
  194.             e.printStackTrace();
  195.         }

  197.         return null;
  198.     }

  200.     /**
  201.      * Generate the Five Point Gauss Lobatto Quadrature over [-1, +1]
  202.      * 
  203.      * @param abscissaTransformer The Abscissa Transformer
  204.      * 
  205.      * @return The Five Point Gauss Lobatto Quadrature over [-1, +1]
  206.      */

  208.     public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
  209.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  210.     {
  211.         double sqrt_3Over7_ = java.lang.Math.sqrt (3. / 7.);

  213.         try
  214.         {
  215.             return new org.drip.numerical.integration.QuadratureEstimator (
  216.                 abscissaTransformer,
  217.                 org.drip.numerical.common.Array2D.FromArray (
  218.                     new double[]
  219.                     {
  220.                         -1.000000000000000,
  221.                         -sqrt_3Over7_,
  222.                          0.000000000000000,
  223.                          sqrt_3Over7_,
  224.                          1.000000000000000,
  225.                     },
  226.                     new double[]
  227.                     {
  228.                          1. / 10.,
  229.                         49. / 90.,
  230.                         32. / 45.,
  231.                         49. / 90.,
  232.                          1. / 10.,
  233.                     }
  234.                 )
  235.             );
  236.         }
  237.         catch (java.lang.Exception e)
  238.         {
  239.             e.printStackTrace();
  240.         }

  242.         return null;
  243.     }

  245.     /**
  246.      * Generate the Six Point Gauss Lobatto Quadrature over [-1, +1]
  247.      * 
  248.      * @param abscissaTransformer The Abscissa Transformer
  249.      * 
  250.      * @return The Six Point Gauss Lobatto Quadrature over [-1, +1]
  251.      */

  253.     public static final org.drip.numerical.integration.QuadratureEstimator SixPoint (
  254.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  255.     {
  256.         double sqrt7 = java.lang.Math.sqrt (7.);

  258.         double twoSqrt_7_Over21 = 2. / 21. * sqrt7;
  259.         double nearWeight = (14. + sqrt7) / 30.;
  260.         double farWeight = (14. - sqrt7) / 30.;

  262.         double farNode = java.lang.Math.sqrt ((1. / 3.) + twoSqrt_7_Over21);

  264.         double nearNode = java.lang.Math.sqrt ((1. / 3.) - twoSqrt_7_Over21);

  266.         try
  267.         {
  268.             return new org.drip.numerical.integration.QuadratureEstimator (
  269.                 abscissaTransformer,
  270.                 org.drip.numerical.common.Array2D.FromArray (
  271.                     new double[]
  272.                     {
  273.                         -1.000000000000000,
  274.                         -farNode,
  275.                         -nearNode,
  276.                          nearNode,
  277.                          farNode,
  278.                          1.000000000000000,
  279.                     },
  280.                     new double[]
  281.                     {
  282.                         1. / 15.,
  283.                         farWeight,
  284.                         nearWeight,
  285.                         nearWeight,
  286.                         farWeight,
  287.                         1. / 15.,
  288.                     }
  289.                 )
  290.             );
  291.         }
  292.         catch (java.lang.Exception e)
  293.         {
  294.             e.printStackTrace();
  295.         }

  297.         return null;
  298.     }

  300.     /**
  301.      * Generate the Seven Point Gauss Lobatto Quadrature over [-1, +1]
  302.      * 
  303.      * @param abscissaTransformer The Abscissa Transformer
  304.      * 
  305.      * @return The Seven Point Gauss Lobatto Quadrature over [-1, +1]
  306.      */

  308.     public static final org.drip.numerical.integration.QuadratureEstimator SevenPoint (
  309.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  310.     {
  311.         double twoOver11Sqrt_5Over3_ = 2. / 11. * java.lang.Math.sqrt (5. / 3.);

  313.         double farNode = java.lang.Math.sqrt ((5. / 11.) + twoOver11Sqrt_5Over3_);

  315.         double nearNode = java.lang.Math.sqrt ((5. / 11.) - twoOver11Sqrt_5Over3_);

  317.         double sevenSqrt15 = 7. * java.lang.Math.sqrt (15.);

  319.         double nearWeight = (124. + sevenSqrt15) / 350.;
  320.         double farWeight = (124. - sevenSqrt15) / 350.;

  322.         try
  323.         {
  324.             return new org.drip.numerical.integration.QuadratureEstimator (
  325.                 abscissaTransformer,
  326.                 org.drip.numerical.common.Array2D.FromArray (
  327.                     new double[]
  328.                     {
  329.                         -1.000000000000000,
  330.                         -farNode,
  331.                         -nearNode,
  332.                          0.000000000000000,
  333.                          nearNode,
  334.                          farNode,
  335.                          1.000000000000000,
  336.                     },
  337.                     new double[]
  338.                     {
  339.                         1. / 21.,
  340.                         farWeight,
  341.                         nearWeight,
  342.                         256. / 525.,
  343.                         nearWeight,
  344.                         farWeight,
  345.                         1. / 21.,
  346.                     }
  347.                 )
  348.             );
  349.         }
  350.         catch (java.lang.Exception e)
  351.         {
  352.             e.printStackTrace();
  353.         }

  355.         return null;
  356.     }

  358.     /**
  359.      * Generate the Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  360.      * 
  361.      * @param left Left Integrand Quadrature Limit
  362.      * @param right Right Integrand Quadrature Limit
  363.      * 
  364.      * @return The Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  365.      */

  367.     public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
  368.         final double left,
  369.         final double right)
  370.     {
  371.         return ThreePoint (
  372.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  373.                 left,
  374.                 right
  375.             )
  376.         );
  377.     }

  379.     /**
  380.      * Generate the Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  381.      * 
  382.      * @param left Left Integrand Quadrature Limit
  383.      * @param right Right Integrand Quadrature Limit
  384.      * 
  385.      * @return The Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  386.      */

  388.     public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
  389.         final double left,
  390.         final double right)
  391.     {
  392.         return FourPoint (
  393.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  394.                 left,
  395.                 right
  396.             )
  397.         );
  398.     }

  400.     /**
  401.      * Generate the Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  402.      * 
  403.      * @param left Left Integrand Quadrature Limit
  404.      * @param right Right Integrand Quadrature Limit
  405.      * 
  406.      * @return The Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  407.      */

  409.     public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
  410.         final double left,
  411.         final double right)
  412.     {
  413.         return FivePoint (
  414.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  415.                 left,
  416.                 right
  417.             )
  418.         );
  419.     }

  421.     /**
  422.      * Generate the Six Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  423.      * 
  424.      * @param left Left Integrand Quadrature Limit
  425.      * @param right Right Integrand Quadrature Limit
  426.      * 
  427.      * @return The Six Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  428.      */

  430.     public static final org.drip.numerical.integration.QuadratureEstimator SixPoint (
  431.         final double left,
  432.         final double right)
  433.     {
  434.         return SixPoint (
  435.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  436.                 left,
  437.                 right
  438.             )
  439.         );
  440.     }

  442.     /**
  443.      * Generate the Seven Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  444.      * 
  445.      * @param left Left Integrand Quadrature Limit
  446.      * @param right Right Integrand Quadrature Limit
  447.      * 
  448.      * @return The Seven Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  449.      */

  451.     public static final org.drip.numerical.integration.QuadratureEstimator SevenPoint (
  452.         final double left,
  453.         final double right)
  454.     {
  455.         return SevenPoint (
  456.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  457.                 left,
  458.                 right
  459.             )
  460.         );
  461.     }
  462. }
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