IntegrandGenerator.java

  1. package org.drip.numerical.quadrature;

  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>IntegrandGenerator</i> contains the Settings that enable the Generation of Integrand Quadrature and
  79.  * Weights for the Specified Orthogonal Polynomial Scheme. 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/quadrature/README.md">R<sup>1</sup> Gaussian Integration Quadrature Schemes</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class IntegrandGenerator
  116. {
  117.     private double _lowerBound = java.lang.Double.NaN;
  118.     private double _upperBound = java.lang.Double.NaN;
  119.     private org.drip.function.definition.R1ToR1 _weightFunction = null;
  120.     private org.drip.numerical.quadrature.OrthogonalPolynomialSuite _orthogonalPolynomialSuite = null;

  122.     /**
  123.      * Construct the Gauss-Legendre Integrand Quadrature Generator
  124.      * 
  125.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  126.      * 
  127.      * @return The Gauss-Legendre Integrand Quadrature Generator
  128.      */

  130.     public static final IntegrandGenerator GaussLegendre (
  131.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite)
  132.     {
  133.         try
  134.         {
  135.             return new IntegrandGenerator (
  136.                 orthogonalPolynomialSuite,
  137.                 org.drip.numerical.quadrature.WeightFunctionBuilder.Legendre(),
  138.                 -1.,
  139.                 1.
  140.             );
  141.         }
  142.         catch (java.lang.Exception e)
  143.         {
  144.             e.printStackTrace();
  145.         }

  147.         return null;
  148.     }

  150.     /**
  151.      * Construct the Gauss-Jacobi Integrand Quadrature Generator
  152.      * 
  153.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  154.      * @param alpha Jacobi Alpha
  155.      * @param beta Jacobi Beta
  156.      * 
  157.      * @return The Gauss-Jacobi Integrand Quadrature Generator
  158.      */

  160.     public static final IntegrandGenerator GaussJacobi (
  161.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite,
  162.         final double alpha,
  163.         final double beta)
  164.     {
  165.         try
  166.         {
  167.             return new IntegrandGenerator (
  168.                 orthogonalPolynomialSuite,
  169.                 org.drip.numerical.quadrature.WeightFunctionBuilder.Jacobi (
  170.                     alpha,
  171.                     beta
  172.                 ),
  173.                 -1.,
  174.                 1.
  175.             );
  176.         }
  177.         catch (java.lang.Exception e)
  178.         {
  179.             e.printStackTrace();
  180.         }

  182.         return null;
  183.     }

  185.     /**
  186.      * Construct the Gauss-Chebyshev (Second-Kind) Integrand Quadrature Generator
  187.      * 
  188.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  189.      * 
  190.      * @return The Gauss-Chebyshev (Second-Kind) Integrand Quadrature Generator
  191.      */

  193.     public static final IntegrandGenerator GaussChebyshevSecondKind (
  194.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite)
  195.     {
  196.         try
  197.         {
  198.             return new IntegrandGenerator (
  199.                 orthogonalPolynomialSuite,
  200.                 org.drip.numerical.quadrature.WeightFunctionBuilder.ChebyshevSecondKind(),
  201.                 -1.,
  202.                 1.
  203.             );
  204.         }
  205.         catch (java.lang.Exception e)
  206.         {
  207.             e.printStackTrace();
  208.         }

  210.         return null;
  211.     }

  213.     /**
  214.      * Construct the Gauss-Chebyshev (First-Kind) Integrand Quadrature Generator
  215.      * 
  216.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  217.      * 
  218.      * @return The Gauss-Chebyshev (First-Kind) Integrand Quadrature Generator
  219.      */

  221.     public static final IntegrandGenerator GaussChebyshevFirstKind (
  222.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite)
  223.     {
  224.         try
  225.         {
  226.             return new IntegrandGenerator (
  227.                 orthogonalPolynomialSuite,
  228.                 org.drip.numerical.quadrature.WeightFunctionBuilder.ChebyshevFirstKind(),
  229.                 -1.,
  230.                 1.
  231.             );
  232.         }
  233.         catch (java.lang.Exception e)
  234.         {
  235.             e.printStackTrace();
  236.         }

  238.         return null;
  239.     }

  241.     /**
  242.      * Construct the Gauss-Laguerre Integrand Quadrature Generator
  243.      * 
  244.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  245.      * 
  246.      * @return The Gauss-Laguerre Integrand Quadrature Generator
  247.      */

  249.     public static final IntegrandGenerator GaussLaguerre (
  250.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite)
  251.     {
  252.         try
  253.         {
  254.             return new IntegrandGenerator (
  255.                 orthogonalPolynomialSuite,
  256.                 org.drip.numerical.quadrature.WeightFunctionBuilder.Laguerre(),
  257.                 -1.,
  258.                 1.
  259.             );
  260.         }
  261.         catch (java.lang.Exception e)
  262.         {
  263.             e.printStackTrace();
  264.         }

  266.         return null;
  267.     }

  269.     /**
  270.      * Construct the Generalized Gauss-Laguerre Integrand Quadrature Generator
  271.      * 
  272.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  273.      * @param alpha Generalized Laguerre Alpha
  274.      * 
  275.      * @return The Generalized Gauss-Laguerre Integrand Quadrature Generator
  276.      */

  278.     public static final IntegrandGenerator GeneralizedGaussLaguerre (
  279.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite,
  280.         final double alpha)
  281.     {
  282.         try
  283.         {
  284.             return new IntegrandGenerator (
  285.                 orthogonalPolynomialSuite,
  286.                 org.drip.numerical.quadrature.WeightFunctionBuilder.GeneralizedLaguerre (alpha),
  287.                 -1.,
  288.                 1.
  289.             );
  290.         }
  291.         catch (java.lang.Exception e)
  292.         {
  293.             e.printStackTrace();
  294.         }

  296.         return null;
  297.     }

  299.     /**
  300.      * Construct the Gauss-Hermite Integrand Quadrature Generator
  301.      * 
  302.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  303.      * 
  304.      * @return The Gauss-Hermite Integrand Quadrature Generator
  305.      */

  307.     public static final IntegrandGenerator GaussHermite (
  308.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite)
  309.     {
  310.         try
  311.         {
  312.             return new IntegrandGenerator (
  313.                 orthogonalPolynomialSuite,
  314.                 org.drip.numerical.quadrature.WeightFunctionBuilder.Hermite(),
  315.                 -1.,
  316.                 1.
  317.             );
  318.         }
  319.         catch (java.lang.Exception e)
  320.         {
  321.             e.printStackTrace();
  322.         }

  324.         return null;
  325.     }

  327.     /**
  328.      * IntegrandGenerator Constructor
  329.      * 
  330.      * @param orthogonalPolynomialSuite Orthogonal Polynomial Suite
  331.      * @param weightFunction Weight Function
  332.      * @param lowerBound Lower Bound
  333.      * @param upperBound Upper Bound
  334.      * 
  335.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  336.      */

  338.     public IntegrandGenerator (
  339.         final org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite,
  340.         final org.drip.function.definition.R1ToR1 weightFunction,
  341.         final double lowerBound,
  342.         final double upperBound)
  343.         throws java.lang.Exception
  344.     {
  345.         if (null == (_orthogonalPolynomialSuite = orthogonalPolynomialSuite) ||
  346.             null == (_weightFunction = weightFunction) ||
  347.             !org.drip.numerical.common.NumberUtil.IsValid (_lowerBound = lowerBound) ||
  348.             !org.drip.numerical.common.NumberUtil.IsValid (_upperBound = upperBound) ||
  349.                 _lowerBound >= _upperBound)
  350.         {
  351.             throw new java.lang.Exception ("IntegrandGenerator Constructor => Invalid Inputs");
  352.         }
  353.     }

  355.     /**
  356.      * Retrieve the Orthogonal Polynomial Suite
  357.      * 
  358.      * @return The Orthogonal Polynomial Suite
  359.      */

  361.     public org.drip.numerical.quadrature.OrthogonalPolynomialSuite orthogonalPolynomialSuite()
  362.     {
  363.         return _orthogonalPolynomialSuite;
  364.     }

  366.     /**
  367.      * Retrieve the Weight Function
  368.      * 
  369.      * @return The Weight Function
  370.      */

  372.     public org.drip.function.definition.R1ToR1 weightFunction()
  373.     {
  374.         return _weightFunction;
  375.     }

  377.     /**
  378.      * Retrieve the Lower Integration Bound
  379.      * 
  380.      * @return The Lower Integration Bound
  381.      */

  383.     public double lowerBound()
  384.     {
  385.         return _lowerBound;
  386.     }

  388.     /**
  389.      * Retrieve the Upper Integration Bound
  390.      * 
  391.      * @return The Upper Integration Bound
  392.      */

  394.     public double upperBound()
  395.     {
  396.         return _upperBound;
  397.     }

  399.     /**
  400.      * Generate the Integral of the Weight Function Over the Bounds
  401.      * 
  402.      * @return The Integral of the Weight Function Over the Bounds
  403.      * 
  404.      * @throws java.lang.Exception Thrown if it cannot be computed
  405.      */

  407.     public double weightFunctionIntegral()
  408.         throws java.lang.Exception
  409.     {
  410.         return _weightFunction.integrate (
  411.             _lowerBound,
  412.             _upperBound
  413.         );
  414.     }

  416.     /**
  417.      * Generate the Weight at the specified Node for the specified Orthogonal Polynomial
  418.      * 
  419.      * @param x X Node
  420.      * @param degree Orthogonal Polynomial Degree
  421.      * 
  422.      * @return The Weight at the specified Node for the specified Orthogonal Polynomial
  423.      * 
  424.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  425.      */

  427.     public double nodeWeight (
  428.         final double x,
  429.         final int degree)
  430.         throws java.lang.Exception
  431.     {
  432.         if (!org.drip.numerical.common.NumberUtil.IsValid (x))
  433.         {
  434.             throw new java.lang.Exception ("IntegrandGenerator::nodeWeight => Invalid Inputs");
  435.         }

  437.         if (0 > degree)
  438.         {
  439.             return 0.;
  440.         }

  442.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomialN =
  443.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree);

  445.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomialNMinusOne =
  446.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree - 1);

  448.         if (null == orthogonalPolynomialN || null == orthogonalPolynomialNMinusOne)
  449.         {
  450.             throw new java.lang.Exception ("IntegrandGenerator::nodeWeight => Invalid Inputs");
  451.         }

  453.         double weightIntegrand = new org.drip.function.definition.R1ToR1 (null)
  454.         {
  455.             @Override public double evaluate (
  456.                 final double z)
  457.                 throws java.lang.Exception
  458.             {
  459.                 double pNMinusOne = orthogonalPolynomialNMinusOne.evaluate (z);

  461.                 return _weightFunction.evaluate (z) * pNMinusOne * pNMinusOne;
  462.             }
  463.         }.integrate (
  464.             _lowerBound,
  465.             _upperBound
  466.         );

  468.         return orthogonalPolynomialN.degreeCoefficient() * weightIntegrand / (
  469.             orthogonalPolynomialNMinusOne.degreeCoefficient() *
  470.             orthogonalPolynomialNMinusOne.evaluate (x) *
  471.             orthogonalPolynomialN.derivative (
  472.                 x,
  473.                 1
  474.             )
  475.         );
  476.     }

  478.     /**
  479.      * Compute the Loaded Inner Product between the Polynomial identified by their Degrees
  480.      * 
  481.      * @param degree1 Polynomial Degree #1
  482.      * @param degree2 Polynomial Degree #2
  483.      * 
  484.      * @return The Loaded Inner Product
  485.      * 
  486.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  487.      */

  489.     public double loadedInnerProduct (
  490.         final int degree1,
  491.         final int degree2)
  492.         throws java.lang.Exception
  493.     {
  494.         if (0 > degree1 || 0 > degree2)
  495.         {
  496.             return 0.;
  497.         }

  499.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomial1 =
  500.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree1);

  502.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomial2 =
  503.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree2);

  505.         if (null == orthogonalPolynomial1 || null == orthogonalPolynomial2)
  506.         {
  507.             throw new java.lang.Exception ("IntegrandGenerator::loadedInnerProduct => Invalid Inputs");
  508.         }

  510.         return new org.drip.function.definition.R1ToR1 (null)
  511.         {
  512.             @Override public double evaluate (
  513.                 final double z)
  514.                 throws java.lang.Exception
  515.             {
  516.                 return z * _weightFunction.evaluate (z) * orthogonalPolynomial1.evaluate (z) *
  517.                     orthogonalPolynomial2.evaluate (z);
  518.             }
  519.         }.integrate (
  520.             _lowerBound,
  521.             _upperBound
  522.         );
  523.     }

  525.     /**
  526.      * Compute the Unloaded Inner Product between the Polynomial identified by their Degrees
  527.      * 
  528.      * @param degree1 Polynomial Degree #1
  529.      * @param degree2 Polynomial Degree #2
  530.      * 
  531.      * @return The Unloaded Inner Product
  532.      * 
  533.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  534.      */

  536.     public double unloadedInnerProduct (
  537.         final int degree1,
  538.         final int degree2)
  539.         throws java.lang.Exception
  540.     {
  541.         if (0 > degree1 || 0 > degree2)
  542.         {
  543.             return 0.;
  544.         }

  546.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomial1 =
  547.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree1);

  549.         final org.drip.numerical.quadrature.OrthogonalPolynomial orthogonalPolynomial2 =
  550.             _orthogonalPolynomialSuite.orthogonalPolynomial (degree2);

  552.         if (null == orthogonalPolynomial1 || null == orthogonalPolynomial2)
  553.         {
  554.             throw new java.lang.Exception ("IntegrandGenerator::unloadedInnerProduct => Invalid Inputs");
  555.         }

  557.         return new org.drip.function.definition.R1ToR1 (null)
  558.         {
  559.             @Override public double evaluate (
  560.                 final double z)
  561.                 throws java.lang.Exception
  562.             {
  563.                 return _weightFunction.evaluate (z) * orthogonalPolynomial1.evaluate (z) *
  564.                     orthogonalPolynomial2.evaluate (z);
  565.             }
  566.         }.integrate (
  567.             _lowerBound,
  568.             _upperBound
  569.         );
  570.     }

  572.     /**
  573.      * Generate the Golub-Welsch Matrix A Entry
  574.      * 
  575.      * @param degree The Orthogonal Polynomial Degree
  576.      * 
  577.      * @return The Golub-Welsch Matrix A Entry
  578.      * 
  579.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  580.      */

  582.     public double golubWelschA (
  583.         final int degree)
  584.         throws java.lang.Exception
  585.     {
  586.         return loadedInnerProduct (
  587.             degree,
  588.             degree
  589.         ) / unloadedInnerProduct (
  590.             degree,
  591.             degree
  592.         );
  593.     }

  595.     /**
  596.      * Generate the Golub-Welsch Matrix B Entry
  597.      * 
  598.      * @param degree The Orthogonal Polynomial Degree
  599.      * 
  600.      * @return The Golub-Welsch Matrix B Entry
  601.      * 
  602.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  603.      */

  605.     public double golubWelschB (
  606.         final int degree)
  607.         throws java.lang.Exception
  608.     {
  609.         return unloadedInnerProduct (
  610.             degree,
  611.             degree
  612.         ) / unloadedInnerProduct (
  613.             degree - 1,
  614.             degree - 1
  615.         );
  616.     }

  618.     /**
  619.      * Generate the Cross Polynomial Recurrence Matrix to be used in the Golub-Welsch Algorithm
  620.      * 
  621.      * @return The Cross Polynomial Recurrence Matrix to be used in the Golub-Welsch Algorithm
  622.      */

  624.     public org.drip.numerical.quadrature.GolubWelsch generateRecurrenceMatrix()
  625.     {
  626.         int size = _orthogonalPolynomialSuite.size();

  628.         double[][] golubWelschMatrix = new double[size][size];

  630.         for (int row = 0; row < size; ++row)
  631.         {
  632.             for (int column = 0; column < size; ++column)
  633.             {
  634.                 golubWelschMatrix[row][column] = column == row + 1 ? 1. : 0.;
  635.             }
  636.         }

  638.         try
  639.         {
  640.             for (int row = 0; row < size; ++row)
  641.             {
  642.                 golubWelschMatrix[row][row] = loadedInnerProduct (
  643.                     row,
  644.                     row
  645.                 ) / unloadedInnerProduct (
  646.                     row,
  647.                     row
  648.                 );

  650.                 if (0 < row)
  651.                 {
  652.                     golubWelschMatrix[row][row - 1] = unloadedInnerProduct (
  653.                         row,
  654.                         row
  655.                     ) / unloadedInnerProduct (
  656.                         row - 1,
  657.                         row - 1
  658.                     );
  659.                 }
  660.             }

  662.             return new org.drip.numerical.quadrature.GolubWelsch (golubWelschMatrix);
  663.         }
  664.         catch (java.lang.Exception e)
  665.         {
  666.             e.printStackTrace();
  667.         }

  669.         return null;
  670.     }

  672.     /**
  673.      * Generate the Quadrature Nodes and Scaled Weights Using the Gil, Segura, and Temme (2007) Scheme
  674.      * 
  675.      * @return The Quadrature Nodes and Scaled Weights
  676.      */

  678.     public org.drip.numerical.common.Array2D gilSeguraTemme2007()
  679.     {
  680.         org.drip.numerical.quadrature.GolubWelsch golubWelsch = generateRecurrenceMatrix();

  682.         if (null == golubWelsch)
  683.         {
  684.             return null;
  685.         }

  687.         org.drip.numerical.common.Array2D nodesAndUnscaledWeights = golubWelsch.nodesAndUnscaledWeights();

  689.         if (null == nodesAndUnscaledWeights)
  690.         {
  691.             return null;
  692.         }

  694.         double[] unscaledWeightArray = nodesAndUnscaledWeights.y();

  696.         double[] nodeArray = nodesAndUnscaledWeights.x();

  698.         int size = nodeArray.length;
  699.         double[] scaledWeightArray = new double[size];

  701.         try
  702.         {
  703.             double weightFunctionIntegral = weightFunctionIntegral();

  705.             for (int nodeIndex = 0; nodeIndex < size; ++nodeIndex)
  706.             {
  707.                 scaledWeightArray[nodeIndex] = unscaledWeightArray[nodeIndex] * weightFunctionIntegral;
  708.             }
  709.         }
  710.         catch (java.lang.Exception e)
  711.         {
  712.             e.printStackTrace();

  714.             return null;
  715.         }

  717.         return org.drip.numerical.common.Array2D.FromArray (
  718.             nodeArray,
  719.             scaledWeightArray
  720.         );
  721.     }
  722. }
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