GaussKronrodQuadratureGenerator.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>GaussKronrodQuadratureGenerator</i> generates the Array of Gaussian Quadrature Based Abscissa and their
  79.  * corresponding Weights, with the Kronrod Extensions applied. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Holoborodko, P. (2011): Gauss-Kronrod Quadrature Nodes and Weights
  85.  *              https://www.advanpix.com/2011/11/07/gauss-kronrod-quadrature-nodes-weights/
  86.  *      </li>
  87.  *      <li>
  88.  *          Kahaner, D., C. Moler, and S. Nash (1989): <i>Numerical Methods and Software</i> <b>Prentice
  89.  *              Hall</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Laurie, D. (1997): Calculation of Gauss-Kronrod Quadrature Rules <i>Mathematics of
  93.  *              Computation</i> <b>66 (219)</b> 1133-1145
  94.  *      </li>
  95.  *      <li>
  96.  *          Piessens, R., E. de Doncker-Kapenga, C. W. Uberhuber, and D. K. Kahaner (1983): <i>QUADPACK – A
  97.  *              Subroutine Package for Automatic Integration</i> <b>Springer-Verlag</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Gauss-Kronrod Quadrature Formula
  101.  *              https://en.wikipedia.org/wiki/Gauss%E2%80%93Kronrod_quadrature_formula
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  109.  *      <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>
  110.  *      <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>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class GaussKronrodQuadratureGenerator
  117. {

  119.     /**
  120.      * Generate the Nested/Embedded G7 Gaussian Quadrature over (0, +1)
  121.      * 
  122.      * @param abscissaTransformer The Abscissa Transformer
  123.      * 
  124.      * @return The Nested/Embedded G7 Gaussian Quadrature over (0, +1)
  125.      */

  127.     public static final org.drip.numerical.integration.QuadratureEstimator G7 (
  128.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  129.     {
  130.         try
  131.         {
  132.             return new org.drip.numerical.integration.QuadratureEstimator (
  133.                 abscissaTransformer,
  134.                 org.drip.numerical.common.Array2D.FromArray (
  135.                     new double[]
  136.                     {
  137.                         -0.949107912342759,
  138.                         -0.741531185599394,
  139.                         -0.405845151377397,
  140.                          0.000000000000000,
  141.                          0.405845151377397,
  142.                          0.741531185599394,
  143.                          0.949107912342759,
  144.                     },
  145.                     new double[]
  146.                     {
  147.                         0.129484966168870,
  148.                         0.279705391489277,
  149.                         0.381830050505119,
  150.                         0.417959183673469,
  151.                         0.381830050505119,
  152.                         0.279705391489277,
  153.                         0.129484966168870,
  154.                     }
  155.                 )
  156.             );
  157.         }
  158.         catch (java.lang.Exception e)
  159.         {
  160.             e.printStackTrace();
  161.         }

  163.         return null;
  164.     }

  166.     /**
  167.      * Generate the K15 Gaussian Quadrature over (0, +1)
  168.      * 
  169.      * @param abscissaTransformer The Abscissa Transformer
  170.      * 
  171.      * @return The K15 Gaussian Quadrature over (0, +1)
  172.      */

  174.     public static final org.drip.numerical.integration.QuadratureEstimator K15 (
  175.         final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
  176.     {
  177.         try
  178.         {
  179.             return new org.drip.numerical.integration.QuadratureEstimator (
  180.                 abscissaTransformer,
  181.                 org.drip.numerical.common.Array2D.FromArray (
  182.                     new double[]
  183.                     {
  184.                         -0.991455371120813,
  185.                         -0.949107912342759,
  186.                         -0.864864423359769,
  187.                         -0.741531185599394,
  188.                         -0.586087235467691,
  189.                         -0.405845151377397,
  190.                         -0.207784955007898,
  191.                          0.000000000000000,
  192.                          0.207784955007898,
  193.                          0.405845151377397,
  194.                          0.586087235467691,
  195.                          0.741531185599394,
  196.                          0.864864423359769,
  197.                          0.949107912342759,
  198.                          0.991455371120813,
  199.                     },
  200.                     new double[]
  201.                     {
  202.                         0.022935322010529,
  203.                         0.063092092629979,
  204.                         0.104790010322250,
  205.                         0.140653259715525,
  206.                         0.169004726639267,
  207.                         0.190350578064785,
  208.                         0.204432940075298,
  209.                         0.209482141084728,
  210.                         0.204432940075298,
  211.                         0.190350578064785,
  212.                         0.169004726639267,
  213.                         0.140653259715525,
  214.                         0.104790010322250,
  215.                         0.063092092629979,
  216.                         0.022935322010529,
  217.                     }
  218.                 )
  219.             );
  220.         }
  221.         catch (java.lang.Exception e)
  222.         {
  223.             e.printStackTrace();
  224.         }

  226.         return null;
  227.     }

  229.     /**
  230.      * Generate the Nested/Embedded G7 Gaussian Quadrature over (a, b) onto (-1, +1)
  231.      * 
  232.      * @param left Left Integrand Quadrature Limit
  233.      * @param right Right Integrand Quadrature Limit
  234.      * 
  235.      * @return The Nested/Embedded G7 Gaussian Quadrature over (a, b) onto (-1, +1)
  236.      */

  238.     public static final org.drip.numerical.integration.QuadratureEstimator G7 (
  239.         final double left,
  240.         final double right)
  241.     {
  242.         return G7 (
  243.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  244.                 left,
  245.                 right
  246.             )
  247.         );
  248.     }

  250.     /**
  251.      * Generate the K15 Gaussian Quadrature over (a, b) onto (-1, +1)
  252.      * 
  253.      * @param left Left Integrand Quadrature Limit
  254.      * @param right Right Integrand Quadrature Limit
  255.      * 
  256.      * @return The K15 Gaussian Quadrature over (a, b) onto (-1, +1)
  257.      */

  259.     public static final org.drip.numerical.integration.QuadratureEstimator K15 (
  260.         final double left,
  261.         final double right)
  262.     {
  263.         return K15 (
  264.             org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  265.                 left,
  266.                 right
  267.             )
  268.         );
  269.     }

  271.     /**
  272.      * Generate the G7-K15 Nested Quadrature Estimator over (a, b) onto (-1, +1)
  273.      * 
  274.      * @param left Left Integrand Quadrature Limit
  275.      * @param right Right Integrand Quadrature Limit
  276.      * 
  277.      * @return The G7-K15 Nested Quadrature Estimator over (a, b) onto (-1, +1)
  278.      */

  280.     public static final org.drip.numerical.integration.NestedQuadratureEstimator G7K15 (
  281.         final double left,
  282.         final double right)
  283.     {
  284.         try
  285.         {
  286.             return new org.drip.numerical.integration.NestedQuadratureEstimator (
  287.                 org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
  288.                     left,
  289.                     right
  290.                 ),
  291.                 org.drip.numerical.common.Array2D.FromArray (
  292.                     new double[]
  293.                     {
  294.                         -0.991455371120813,
  295.                         -0.949107912342759,
  296.                         -0.864864423359769,
  297.                         -0.741531185599394,
  298.                         -0.586087235467691,
  299.                         -0.405845151377397,
  300.                         -0.207784955007898,
  301.                          0.000000000000000,
  302.                          0.207784955007898,
  303.                          0.405845151377397,
  304.                          0.586087235467691,
  305.                          0.741531185599394,
  306.                          0.864864423359769,
  307.                          0.949107912342759,
  308.                          0.991455371120813,
  309.                     },
  310.                     new double[]
  311.                     {
  312.                         0.022935322010529,
  313.                         0.063092092629979,
  314.                         0.104790010322250,
  315.                         0.140653259715525,
  316.                         0.169004726639267,
  317.                         0.190350578064785,
  318.                         0.204432940075298,
  319.                         0.209482141084728,
  320.                         0.204432940075298,
  321.                         0.190350578064785,
  322.                         0.169004726639267,
  323.                         0.140653259715525,
  324.                         0.104790010322250,
  325.                         0.063092092629979,
  326.                         0.022935322010529,
  327.                     }
  328.                 ),
  329.                 G7 (
  330.                     left,
  331.                     right
  332.                 )
  333.             );
  334.         }
  335.         catch (java.lang.Exception e)
  336.         {
  337.             e.printStackTrace();
  338.         }

  340.         return null;
  341.     }
  342. }
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