AbscissaTransform.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>AbscissaTransform</i> transforms the Abscissa over into Corresponding Integrand Variable. The
  79.  * 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 AbscissaTransform
  115. {
  116.     private double _quadratureScale = java.lang.Double.NaN;
  117.     private org.drip.function.definition.R1ToR1 _r1PointValueScale = null;
  118.     private org.drip.function.definition.R1ToR1 _r1ToR1VariateChange = null;

  120.     /**
  121.      * Generate the Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)
  122.      * 
  123.      * @param left Span Left
  124.      * @param right Span Right
  125.      * 
  126.      * @return The Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)
  127.      */

  129.     public static final AbscissaTransform DisplaceAndScaleZero_PlusOne (
  130.         final double left,
  131.         final double right)
  132.     {
  133.         if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
  134.             !org.drip.numerical.common.NumberUtil.IsValid (right))
  135.         {
  136.             return null;
  137.         }

  139.         try
  140.         {
  141.             return new AbscissaTransform (
  142.                 new org.drip.function.definition.R1ToR1 (null)
  143.                 {
  144.                     @Override public double evaluate (
  145.                         final double x)
  146.                     {
  147.                         return (right - left) * x + left;
  148.                     }
  149.                 },
  150.                 new org.drip.function.definition.R1ToR1 (null)
  151.                 {
  152.                     @Override public double evaluate (
  153.                         final double x)
  154.                     {
  155.                         return 1.;
  156.                     }
  157.                 },
  158.                 right - left
  159.             );
  160.         }
  161.         catch (java.lang.Exception e)
  162.         {
  163.             e.printStackTrace();
  164.         }

  166.         return null;
  167.     }

  169.     /**
  170.      * Generate the Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)
  171.      * 
  172.      * @param left Span Left
  173.      * @param right Span Right
  174.      * 
  175.      * @return The Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)
  176.      */

  178.     public static final AbscissaTransform DisplaceAndScaleMinusOne_PlusOne (
  179.         final double left,
  180.         final double right)
  181.     {
  182.         if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
  183.             !org.drip.numerical.common.NumberUtil.IsValid (right))
  184.         {
  185.             return null;
  186.         }

  188.         final double scale = 0.5 * (right - left);
  189.         final double offset = 0.5 * (right + left);

  191.         try
  192.         {
  193.             return new AbscissaTransform (
  194.                 new org.drip.function.definition.R1ToR1 (null)
  195.                 {
  196.                     @Override public double evaluate (
  197.                         final double x)
  198.                     {
  199.                         return scale * x + offset;
  200.                     }
  201.                 },
  202.                 new org.drip.function.definition.R1ToR1 (null)
  203.                 {
  204.                     @Override public double evaluate (
  205.                         final double x)
  206.                     {
  207.                         return 1.;
  208.                     }
  209.                 },
  210.                 scale
  211.             );
  212.         }
  213.         catch (java.lang.Exception e)
  214.         {
  215.             e.printStackTrace();
  216.         }

  218.         return null;
  219.     }

  221.     /**
  222.      * Generate the Gauss-Hermite Abscissa Transform
  223.      * 
  224.      * @return The Gauss-Hermite Abscissa Transform
  225.      */

  227.     public static final AbscissaTransform GaussHermite()
  228.     {
  229.         try
  230.         {
  231.             return new AbscissaTransform (
  232.                 new org.drip.function.definition.R1ToR1 (null)
  233.                 {
  234.                     @Override public double evaluate (
  235.                         final double x)
  236.                     {
  237.                         return x / (1. - x * x);
  238.                     }
  239.                 },
  240.                 new org.drip.function.definition.R1ToR1 (null)
  241.                 {
  242.                     @Override public double evaluate (
  243.                         final double x)
  244.                     {
  245.                         double xSquared = x * x;

  247.                         return -1. == x || 1. == x ? 0. : (1. + xSquared) / (1. - xSquared) / (1. - xSquared);
  248.                     }
  249.                 },
  250.                 1.
  251.             );
  252.         }
  253.         catch (java.lang.Exception e)
  254.         {
  255.             e.printStackTrace();
  256.         }

  258.         return null;
  259.     }

  261.     /**
  262.      * Generate the Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]
  263.      * 
  264.      * @param left Span Left
  265.      * 
  266.      * @return The Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]
  267.      */

  269.     public static final AbscissaTransform GaussLaguerreLeftDefinite (
  270.         final double left)
  271.     {
  272.         if (!org.drip.numerical.common.NumberUtil.IsValid (left))
  273.         {
  274.             return null;
  275.         }

  277.         try
  278.         {
  279.             return new AbscissaTransform (
  280.                 new org.drip.function.definition.R1ToR1 (null)
  281.                 {
  282.                     @Override public double evaluate (
  283.                         final double x)
  284.                     {
  285.                         return left + (x / (1. - x));
  286.                     }
  287.                 },
  288.                 new org.drip.function.definition.R1ToR1 (null)
  289.                 {
  290.                     @Override public double evaluate (
  291.                         final double x)
  292.                     {
  293.                         return -1. == x || 1. == x ? 0. : 1. / (1. - x) / (1. - x);
  294.                     }
  295.                 },
  296.                 1.
  297.             );
  298.         }
  299.         catch (java.lang.Exception e)
  300.         {
  301.             e.printStackTrace();
  302.         }

  304.         return null;
  305.     }

  307.     /**
  308.      * Generate the Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]
  309.      * 
  310.      * @param right Span Right
  311.      * 
  312.      * @return The Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]
  313.      */

  315.     public static final AbscissaTransform GaussLaguerreRightDefinite (
  316.         final double right)
  317.     {
  318.         if (!org.drip.numerical.common.NumberUtil.IsValid (right))
  319.         {
  320.             return null;
  321.         }

  323.         try
  324.         {
  325.             return new AbscissaTransform (
  326.                 new org.drip.function.definition.R1ToR1 (null)
  327.                 {
  328.                     @Override public double evaluate (
  329.                         final double x)
  330.                     {
  331.                         return right - ((1. - x) / x);
  332.                     }
  333.                 },
  334.                 new org.drip.function.definition.R1ToR1 (null)
  335.                 {
  336.                     @Override public double evaluate (
  337.                         final double x)
  338.                     {
  339.                         return 0. == x ? 0. : 1. / (x * x);
  340.                     }
  341.                 },
  342.                 1.
  343.             );
  344.         }
  345.         catch (java.lang.Exception e)
  346.         {
  347.             e.printStackTrace();
  348.         }

  350.         return null;
  351.     }

  353.     /**
  354.      * AbscissaTransform Constructor
  355.      * 
  356.      * @param r1ToR1VariateChange R<sup>1</sup> to R<sup>1</sup> Variate Change Function
  357.      * @param r1PointValueScale R<sup>1</sup> Point Value Scale Function
  358.      * @param quadratureScale Quadrature Scale
  359.      * 
  360.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  361.      */

  363.     public AbscissaTransform (
  364.         final org.drip.function.definition.R1ToR1 r1ToR1VariateChange,
  365.         final org.drip.function.definition.R1ToR1 r1PointValueScale,
  366.         final double quadratureScale)
  367.         throws java.lang.Exception
  368.     {
  369.         if (null == (_r1ToR1VariateChange = r1ToR1VariateChange) ||
  370.             null == (_r1PointValueScale = r1PointValueScale) ||
  371.             !org.drip.numerical.common.NumberUtil.IsValid (_quadratureScale = quadratureScale))
  372.         {
  373.             throw new java.lang.Exception ("AbscissaTransform Constructor => Invalid Inputs");
  374.         }
  375.     }

  377.     /**
  378.      * Retrieve the R<sup>1</sup> to R<sup>1</sup> Variate Change Function
  379.      * 
  380.      * @return The R<sup>1</sup> to R<sup>1</sup> Variate Change Function
  381.      */

  383.     public org.drip.function.definition.R1ToR1 variateChange()
  384.     {
  385.         return _r1ToR1VariateChange;
  386.     }

  388.     /**
  389.      * Retrieve the R<sup>1</sup> Point Value Scale Function
  390.      * 
  391.      * @return The R<sup>1</sup> Point Value Scale Function
  392.      */

  394.     public org.drip.function.definition.R1ToR1 pointValueScale()
  395.     {
  396.         return _r1PointValueScale;
  397.     }

  399.     /**
  400.      * Retrieve the Quadrature Scale
  401.      * 
  402.      * @return The Quadrature Scale
  403.      */

  405.     public double quadratureScale()
  406.     {
  407.         return _quadratureScale;
  408.     }
  409. }
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