R1Uniform.java

  1. package org.drip.measure.lebesgue;

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

  81. /**
  82.  * <i>R1Uniform</i> implements the R<sup>1</sup> Lebesgue (i.e., Bounded Uniform) Distribution, with a
  83.  * Uniform Distribution between a Lower and an Upper Bound.
  84.  *
  85.  *  <br><br>
  86.  *  <ul>
  87.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  88.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  89.  *      <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>
  90.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/lebesgue/README.md">Uniform Piece-wise Lebesgue Measure</a></li>
  91.  *  </ul>
  92.  *
  93.  * @author Lakshmi Krishnamurthy
  94.  */

  96. public class R1Uniform extends org.drip.measure.continuous.R1Univariate {
  97.     protected static final int GRID_WIDTH = 100;

  99.     private double _dblLeftPredictorOrdinateEdge = java.lang.Double.NaN;
  100.     private double _dblRightPredictorOrdinateEdge = java.lang.Double.NaN;

  102.     /**
  103.      * Construct a R^1 Bounded Uniform Distribution
  104.      * 
  105.      * @param dblLeftPredictorOrdinateEdge The Left Predictor Ordinate Edge
  106.      * @param dblRightPredictorOrdinateEdge The Right Predictor Ordinate Edge
  107.      * 
  108.      * @throws java.lang.Exception Thrown if the inputs are invalid
  109.      */

  111.     public R1Uniform (
  112.         final double dblLeftPredictorOrdinateEdge,
  113.         final double dblRightPredictorOrdinateEdge)
  114.         throws java.lang.Exception
  115.     {
  116.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLeftPredictorOrdinateEdge =
  117.             dblLeftPredictorOrdinateEdge) || !org.drip.numerical.common.NumberUtil.IsValid
  118.                 (_dblRightPredictorOrdinateEdge = dblRightPredictorOrdinateEdge) ||
  119.                     _dblRightPredictorOrdinateEdge <= _dblLeftPredictorOrdinateEdge)
  120.             throw new java.lang.Exception ("R1Uniform Constructor: Invalid Inputs");
  121.     }

  123.     /**
  124.      * Retrieve the Left Predictor Ordinate Edge
  125.      * 
  126.      * @return The Left Predictor Ordinate Edge
  127.      */

  129.     public double leftEdge()
  130.     {
  131.         return _dblLeftPredictorOrdinateEdge;
  132.     }

  134.     /**
  135.      * Retrieve the Right Predictor Ordinate Edge
  136.      * 
  137.      * @return The Right Predictor Ordinat Edge
  138.      */

  140.     public double rightEdge()
  141.     {
  142.         return _dblRightPredictorOrdinateEdge;
  143.     }

  145.     @Override public double[] support()
  146.     {
  147.         return new double[]
  148.         {
  149.             _dblLeftPredictorOrdinateEdge,
  150.             _dblRightPredictorOrdinateEdge
  151.         };
  152.     }

  154.     @Override public double cumulative (
  155.         final double dblX)
  156.         throws java.lang.Exception
  157.     {
  158.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  159.             throw new java.lang.Exception ("R1Uniform::cumulative => Invalid Inputs");

  161.         if (dblX <= _dblLeftPredictorOrdinateEdge) return 0.;

  163.         if (dblX >= _dblRightPredictorOrdinateEdge) return 1.;

  165.         return (dblX - _dblLeftPredictorOrdinateEdge) / (_dblRightPredictorOrdinateEdge -
  166.             _dblLeftPredictorOrdinateEdge);
  167.     }

  169.     @Override public double incremental (
  170.         final double dblXLeft,
  171.         final double dblXRight)
  172.         throws java.lang.Exception
  173.     {
  174.         return cumulative (dblXRight) - cumulative (dblXLeft);
  175.     }

  177.     @Override public double invCumulative (
  178.         final double dblY)
  179.         throws java.lang.Exception
  180.     {
  181.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || dblY < 0. || dblY > 1.)
  182.             throw new java.lang.Exception ("R1Uniform::invCumulative => Invalid inputs");

  184.         return dblY * (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) +
  185.             _dblLeftPredictorOrdinateEdge;
  186.     }

  188.     @Override public double density (
  189.         final double dblX)
  190.         throws java.lang.Exception
  191.     {
  192.         return dblX <= _dblLeftPredictorOrdinateEdge || dblX >= _dblRightPredictorOrdinateEdge ? 0. : 1. /
  193.             (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge);
  194.     }

  196.     @Override public double mean()
  197.     {
  198.         return 0.5 * (_dblRightPredictorOrdinateEdge + _dblLeftPredictorOrdinateEdge);
  199.     }

  201.     @Override public double variance()
  202.     {
  203.         return (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) *
  204.             (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) / 12.;
  205.     }

  207.     @Override public org.drip.numerical.common.Array2D histogram()
  208.     {
  209.         double[] adblX = new double[GRID_WIDTH];
  210.         double[] adblY = new double[GRID_WIDTH];
  211.         double dblWidth = (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) / GRID_WIDTH;

  213.         for (int i = 0; i < GRID_WIDTH; ++i) {
  214.             adblY[i] = 1. / GRID_WIDTH;
  215.             adblX[i] = _dblLeftPredictorOrdinateEdge + (i + 1) * dblWidth;
  216.         }

  218.         return org.drip.numerical.common.Array2D.FromArray (adblX, adblY);
  219.     }
  220. }
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