GaussLegendreQuadratureGenerator.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>GaussLegendreQuadratureGenerator</i> generates the Array of Orthogonal Legendre 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 GaussLegendreQuadratureGenerator
  116. {

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

  126.     public static final org.drip.numerical.integration.QuadratureEstimator OnePoint (
  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.                         0.000000000000000,
  137.                     },
  138.                     new double[]
  139.                     {
  140.                         2.000000000000000,
  141.                     }
  142.                 )
  143.             );
  144.         }
  145.         catch (java.lang.Exception e)
  146.         {
  147.             e.printStackTrace();
  148.         }

  150.         return null;
  151.     }

  153.     /**
  154.      * Generate the Two Point Gauss Legendre Quadrature over [-1, +1]
  155.      * 
  156.      * @param abscissaTransformer The Abscissa Transformer
  157.      * 
  158.      * @return The Two Point Gauss Legendre Quadrature over [-1, +1]
  159.      */

  161.     public static final org.drip.numerical.integration.QuadratureEstimator TwoPoint (
  162.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  163.     {
  164.         double sqrt_1Over3_ = java.lang.Math.sqrt (1. / 3.);

  166.         try
  167.         {
  168.             return new org.drip.numerical.integration.QuadratureEstimator (
  169.                 abscissaTransformer,
  170.                 org.drip.numerical.common.Array2D.FromArray (
  171.                     new double[]
  172.                     {
  173.                         -sqrt_1Over3_,
  174.                          sqrt_1Over3_,
  175.                     },
  176.                     new double[]
  177.                     {
  178.                         1.000000000000000,
  179.                         1.000000000000000,
  180.                     }
  181.                 )
  182.             );
  183.         }
  184.         catch (java.lang.Exception e)
  185.         {
  186.             e.printStackTrace();
  187.         }

  189.         return null;
  190.     }

  192.     /**
  193.      * Generate the Three Point Gauss Legendre Quadrature over [-1, +1]
  194.      * 
  195.      * @param abscissaTransformer The Abscissa Transformer
  196.      * 
  197.      * @return The Three Point Gauss Legendre Quadrature over [-1, +1]
  198.      */

  200.     public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
  201.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  202.     {
  203.         double sqrt_3Over5_ = java.lang.Math.sqrt (3. / 5.);

  205.         try
  206.         {
  207.             return new org.drip.numerical.integration.QuadratureEstimator (
  208.                 abscissaTransformer,
  209.                 org.drip.numerical.common.Array2D.FromArray (
  210.                     new double[]
  211.                     {
  212.                         -sqrt_3Over5_,
  213.                          0.000000000000000,
  214.                          sqrt_3Over5_,
  215.                     },
  216.                     new double[]
  217.                     {
  218.                         5. / 9.,
  219.                         8. / 9.,
  220.                         5. / 9.,
  221.                     }
  222.                 )
  223.             );
  224.         }
  225.         catch (java.lang.Exception e)
  226.         {
  227.             e.printStackTrace();
  228.         }

  230.         return null;
  231.     }

  233.     /**
  234.      * Generate the Four Point Gauss Legendre Quadrature over [-1, +1]
  235.      * 
  236.      * @param abscissaTransformer The Abscissa Transformer
  237.      * 
  238.      * @return The Four Point Gauss Legendre Quadrature over [-1, +1]
  239.      */

  241.     public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
  242.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  243.     {
  244.         double sqrt_30_Over36 = java.lang.Math.sqrt (30.) / 36.;

  246.         double nearWeight = 0.5 + sqrt_30_Over36;
  247.         double farWeight = 0.5 - sqrt_30_Over36;
  248.         double threeOver7 = 3. / 7.;

  250.         double twoOver7Sqrt_6Over5_ = 2. / 7. * java.lang.Math.sqrt (6. / 5.);

  252.         double farNode = java.lang.Math.sqrt (threeOver7 + twoOver7Sqrt_6Over5_);

  254.         double nearNode = java.lang.Math.sqrt (threeOver7 - twoOver7Sqrt_6Over5_);

  256.         try
  257.         {
  258.             return new org.drip.numerical.integration.QuadratureEstimator (
  259.                 abscissaTransformer,
  260.                 org.drip.numerical.common.Array2D.FromArray (
  261.                     new double[]
  262.                     {
  263.                         -farNode,
  264.                         -nearNode,
  265.                          nearNode,
  266.                          farNode,
  267.                     },
  268.                     new double[]
  269.                     {
  270.                         farWeight,
  271.                         nearWeight,
  272.                         nearWeight,
  273.                         farWeight,
  274.                     }
  275.                 )
  276.             );
  277.         }
  278.         catch (java.lang.Exception e)
  279.         {
  280.             e.printStackTrace();
  281.         }

  283.         return null;
  284.     }

  286.     /**
  287.      * Generate the Five Point Gauss Legendre Quadrature over [-1, +1]
  288.      * 
  289.      * @param abscissaTransformer The Abscissa Transformer
  290.      * 
  291.      * @return The Five Point Gauss Legendre Quadrature over [-1, +1]
  292.      */

  294.     public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
  295.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  296.     {
  297.         double thirteenSqrt_70_ = 13. * java.lang.Math.sqrt (70.);

  299.         double nearWeight = (322. + thirteenSqrt_70_) / 900.;
  300.         double farWeight = (322. - thirteenSqrt_70_) / 900.;

  302.         double twoSqrt_10Over7_ = 2. * java.lang.Math.sqrt (10. / 7.);

  304.         double farNode = java.lang.Math.sqrt (5. + twoSqrt_10Over7_) / 3.;

  306.         double nearNode = java.lang.Math.sqrt (5. - twoSqrt_10Over7_) / 3.;

  308.         try
  309.         {
  310.             return new org.drip.numerical.integration.QuadratureEstimator (
  311.                 abscissaTransformer,
  312.                 org.drip.numerical.common.Array2D.FromArray (
  313.                     new double[]
  314.                     {
  315.                         -farNode,
  316.                         -nearNode,
  317.                          0.000000000000000,
  318.                          nearNode,
  319.                          farNode,
  320.                     },
  321.                     new double[]
  322.                     {
  323.                         farWeight,
  324.                         nearWeight,
  325.                         128. / 225.,
  326.                         nearWeight,
  327.                         farWeight,
  328.                     }
  329.                 )
  330.             );
  331.         }
  332.         catch (java.lang.Exception e)
  333.         {
  334.             e.printStackTrace();
  335.         }

  337.         return null;
  338.     }

  340.     /**
  341.      * Generate the One Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  342.      * 
  343.      * @param left Left Integrand Quadrature Limit
  344.      * @param right Right Integrand Quadrature Limit
  345.      * 
  346.      * @return The One Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  347.      */

  349.     public static final org.drip.numerical.integration.QuadratureEstimator OnePoint (
  350.         final double left,
  351.         final double right)
  352.     {
  353.         return OnePoint (
  354.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  355.                 left,
  356.                 right
  357.             )
  358.         );
  359.     }

  361.     /**
  362.      * Generate the Two Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  363.      * 
  364.      * @param left Left Integrand Quadrature Limit
  365.      * @param right Right Integrand Quadrature Limit
  366.      * 
  367.      * @return The Two Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  368.      */

  370.     public static final org.drip.numerical.integration.QuadratureEstimator TwoPoint (
  371.         final double left,
  372.         final double right)
  373.     {
  374.         return TwoPoint (
  375.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  376.                 left,
  377.                 right
  378.             )
  379.         );
  380.     }

  382.     /**
  383.      * Generate the Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  384.      * 
  385.      * @param left Left Integrand Quadrature Limit
  386.      * @param right Right Integrand Quadrature Limit
  387.      * 
  388.      * @return The Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  389.      */

  391.     public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
  392.         final double left,
  393.         final double right)
  394.     {
  395.         return ThreePoint (
  396.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  397.                 left,
  398.                 right
  399.             )
  400.         );
  401.     }

  403.     /**
  404.      * Generate the Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  405.      * 
  406.      * @param left Left Integrand Quadrature Limit
  407.      * @param right Right Integrand Quadrature Limit
  408.      * 
  409.      * @return The Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  410.      */

  412.     public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
  413.         final double left,
  414.         final double right)
  415.     {
  416.         return FourPoint (
  417.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  418.                 left,
  419.                 right
  420.             )
  421.         );
  422.     }

  424.     /**
  425.      * Generate the Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  426.      * 
  427.      * @param left Left Integrand Quadrature Limit
  428.      * @param right Right Integrand Quadrature Limit
  429.      * 
  430.      * @return The Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
  431.      */

  433.     public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
  434.         final double left,
  435.         final double right)
  436.     {
  437.         return FivePoint (
  438.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  439.                 left,
  440.                 right
  441.             )
  442.         );
  443.     }
  444. }
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