NormalQuadrature.java

  1. package org.drip.measure.gaussian;

  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.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2011 Robert Sedgewick
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  18.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  19.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  20.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  21.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  22.  *      and computational support.
  23.  *  
  24.  *      https://lakshmidrip.github.io/DROP/
  25.  *  
  26.  *  DROP is composed of three modules:
  27.  *  
  28.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  29.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  30.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  31.  * 
  32.  *  DROP Product Core implements libraries for the following:
  33.  *  - Fixed Income Analytics
  34.  *  - Loan Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Asset Liability Management Analytics
  40.  *  - Capital Estimation Analytics
  41.  *  - Exposure Analytics
  42.  *  - Margin Analytics
  43.  *  - XVA Analytics
  44.  * 
  45.  *  DROP Computational Core implements libraries for the following:
  46.  *  - Algorithm Support
  47.  *  - Computation Support
  48.  *  - Function Analysis
  49.  *  - Model Validation
  50.  *  - Numerical Analysis
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Statistical Learning
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>NormalQuadrature</i> implements the Quadrature Metrics behind the Univariate Normal Distribution. It
  85.  * implements the Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities.
  86.  *
  87.  *  <br><br>
  88.  *  <ul>
  89.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  90.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  91.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
  92.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
  93.  *  </ul>
  94.  *
  95.  * @author Robert Sedgewick
  96.  * @author Lakshmi Krishnamurthy
  97.  */

  99. public class NormalQuadrature {
  100.     private static final double InverseCDF (
  101.         final double dblY,
  102.         final double dblTolerance,
  103.         final double dblLowCutoff,
  104.         final double dblHighCutoff)
  105.         throws java.lang.Exception
  106.     {
  107.         double dblMid = 0.5 * (dblHighCutoff + dblLowCutoff);

  109.         if (dblHighCutoff - dblLowCutoff < dblTolerance) return dblMid;

  111.         return CDF (dblMid) > dblY ? InverseCDF (dblY, dblTolerance, dblLowCutoff, dblMid) : InverseCDF
  112.             (dblY, dblTolerance, dblMid, dblHighCutoff);
  113.     }

  115.     /**
  116.      * Retrieve the Density at the specified Point using Zero Mean and Unit Variance
  117.      * 
  118.      * @param dblX The Ordinate
  119.      * 
  120.      * @return The Density at the specified Point Zero Mean and Unit Variance
  121.      * 
  122.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  123.      */

  125.     public static final double Density (
  126.         final double dblX)
  127.         throws java.lang.Exception
  128.     {
  129.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  130.             throw new java.lang.Exception ("NormalQuadrature::Density => Invalid Inputs");

  132.         return java.lang.Math.exp (-0.5 * dblX * dblX) / java.lang.Math.sqrt (2 * java.lang.Math.PI);
  133.     }

  135.     /**
  136.      * Compute the Cumulative Distribution Function up to the specified Variate
  137.      * 
  138.      * @param dblX The Variate
  139.      * 
  140.      * @return The Cumulative Distribution Function up to the specified Variate
  141.      * 
  142.      * @throws java.lang.Exception thrown if the Inputs are Invalid
  143.      */

  145.     public static final double CDF (
  146.         final double dblX)
  147.         throws java.lang.Exception
  148.     {
  149.         if (java.lang.Double.isNaN (dblX))
  150.             throw new java.lang.Exception ("NormalQuadrature::CDF => Invalid Inputs");

  152.         if (dblX < -8.) return 0.;

  154.         if (dblX > 8.) return 1.;

  156.         double dblSum = 0.;
  157.         double dblTerm = dblX;

  159.         for (int i = 3; dblSum + dblTerm != dblSum; i += 2) {
  160.             dblSum  = dblSum + dblTerm;
  161.             dblTerm = dblTerm * dblX * dblX / i;
  162.         }

  164.         return 0.5 + dblSum * Density (dblX);
  165.     }

  167.     /**
  168.      * Compute the Inverse CDF of the Distribution up to the specified Y
  169.      * 
  170.      * @param dblY Y
  171.      * 
  172.      * @return The Inverse CDF of the Distribution up to the specified Y
  173.      * 
  174.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  175.      */

  177.     public static final double InverseCDF (
  178.         final double dblY)
  179.         throws java.lang.Exception
  180.     {
  181.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY))
  182.             throw new java.lang.Exception ("NormalQuadrature::InverseCDF => Invalid Inputs");

  184.         return InverseCDF (dblY, .00000001, -8., 8.);
  185.     } 

  187.     /**
  188.      * Compute the Probit of the Distribution up to the specified p
  189.      * 
  190.      * @param p p
  191.      * 
  192.      * @return The Probit of the Distribution up to the specified p
  193.      * 
  194.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  195.      */

  197.     public static final double Probit (
  198.         final double p)
  199.         throws java.lang.Exception
  200.     {
  201.         return InverseCDF (p);
  202.     } 

  204.     /**
  205.      * Generate a Random Univariate Number following a Gaussian Distribution
  206.      * 
  207.      * @return The Random Univariate Number
  208.      * 
  209.      * @throws java.lang.Exception Thrown the Random Number cannot be generated
  210.      */

  212.     public static final double Random()
  213.         throws java.lang.Exception
  214.     {
  215.         return InverseCDF (java.lang.Math.random());
  216.     }

  218.     /**
  219.      * Compute the Error Function of x
  220.      * 
  221.      * @param x x
  222.      * 
  223.      * @return The Error Function of x
  224.      * 
  225.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  226.      */

  228.     public static final double ERF (
  229.         final double x)
  230.         throws java.lang.Exception
  231.     {
  232.         return 2. * CDF (x * java.lang.Math.sqrt (2.)) - 1.;
  233.     }

  235.     /**
  236.      * Compute the Error Function Complement of x
  237.      * 
  238.      * @param x x
  239.      * 
  240.      * @return The Error Function Complement of x
  241.      * 
  242.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  243.      */

  245.     public static final double ERFC (
  246.         final double x)
  247.         throws java.lang.Exception
  248.     {
  249.         return 2. * CDF (1. - x * java.lang.Math.sqrt (2.));
  250.     }
  251. }
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