R1PiecewiseLinear.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.  * 
  14.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  15.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  16.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  17.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  18.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  19.  *      and computational support.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three modules:
  24.  *  
  25.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  28.  * 
  29.  *  DROP Product Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Loan Analytics
  32.  *  - Transaction Cost Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Asset Liability Management Analytics
  37.  *  - Capital Estimation Analytics
  38.  *  - Exposure Analytics
  39.  *  - Margin Analytics
  40.  *  - XVA Analytics
  41.  * 
  42.  *  DROP Computational Core implements libraries for the following:
  43.  *  - Algorithm Support
  44.  *  - Computation Support
  45.  *  - Function Analysis
  46.  *  - Model Validation
  47.  *  - Numerical Analysis
  48.  *  - Numerical Optimizer
  49.  *  - Spline Builder
  50.  *  - Statistical Learning
  51.  * 
  52.  *  Documentation for DROP is Spread Over:
  53.  * 
  54.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  55.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  56.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  57.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  58.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  59.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  60.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  61.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  62.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  63.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  64.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  65.  * 
  66.  *  Licensed under the Apache License, Version 2.0 (the "License");
  67.  *      you may not use this file except in compliance with the License.
  68.  *   
  69.  *  You may obtain a copy of the License at
  70.  *      http://www.apache.org/licenses/LICENSE-2.0
  71.  *  
  72.  *  Unless required by applicable law or agreed to in writing, software
  73.  *      distributed under the License is distributed on an "AS IS" BASIS,
  74.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  75.  *  
  76.  *  See the License for the specific language governing permissions and
  77.  *      limitations under the License.
  78.  */

  80. /**
  81.  * <i>R1PiecewiseLinear</i> implements the Piecewise Linear R<sup>1</sup> Distributions. It exports the
  82.  * Methods corresponding to the R<sup>1</sup> Lebesgue Base Class.
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  87.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  88.  *      <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>
  89.  *      <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>
  90.  *  </ul>
  91.  *
  92.  * @author Lakshmi Krishnamurthy
  93.  */

  95. public class R1PiecewiseLinear extends org.drip.measure.lebesgue.R1Uniform {
  96.     private double[] _adblPiecewiseDensity = null;
  97.     private double[] _adblPredictorOrdinate = null;

  99.     /**
  100.      * Calibrate an R1PiecewiseLinear Lebesgue Instance
  101.      * 
  102.      * @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
  103.      * @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
  104.      * @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
  105.      * @param adblCumulativeProbability Array of corresponding Cumulative Probabilities
  106.      * 
  107.      * @return The R1PiecewiseLinearLebesgue Instance
  108.      */

  110.     public static final R1PiecewiseLinear Standard (
  111.         final double dblLeftPredictorOrdinateEdge,
  112.         final double dblRightPredictorOrdinateEdge,
  113.         final double[] adblPredictorOrdinate,
  114.         final double[] adblCumulativeProbability)
  115.     {
  116.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblLeftPredictorOrdinateEdge) ||
  117.             !org.drip.numerical.common.NumberUtil.IsValid (dblRightPredictorOrdinateEdge) ||
  118.                 dblLeftPredictorOrdinateEdge >= dblRightPredictorOrdinateEdge || null ==
  119.                     adblPredictorOrdinate || null == adblCumulativeProbability)
  120.             return null;

  122.         int iNumPredictorOrdinate = adblPredictorOrdinate.length;
  123.         double[] adblPiecewiseDensity = new double[iNumPredictorOrdinate + 1];

  125.         if (0 == iNumPredictorOrdinate || iNumPredictorOrdinate != adblCumulativeProbability.length)
  126.             return null;

  128.         for (int i = 0; i <= iNumPredictorOrdinate; ++i) {
  129.             double dblLeftPredictorOrdinate = 0 == i ? dblLeftPredictorOrdinateEdge :
  130.                 adblPredictorOrdinate[i - 1];

  132.             if (!org.drip.numerical.common.NumberUtil.IsValid (dblLeftPredictorOrdinate) ||
  133.                 dblLeftPredictorOrdinate < dblLeftPredictorOrdinateEdge)
  134.                 return null;

  136.             double dblRightPredictorOrdinate = iNumPredictorOrdinate == i ? dblRightPredictorOrdinateEdge :
  137.                 adblPredictorOrdinate[i];

  139.             if (!org.drip.numerical.common.NumberUtil.IsValid (dblRightPredictorOrdinate) ||
  140.                 dblRightPredictorOrdinate <= dblLeftPredictorOrdinate || dblRightPredictorOrdinate >
  141.                     dblRightPredictorOrdinateEdge)
  142.                 return null;

  144.             double dblLeftCumulativeProbability = 0 == i ? 0. : adblCumulativeProbability[i - 1];
  145.             double dblRightCumulativeProbability = iNumPredictorOrdinate == i ? 1. :
  146.                 adblCumulativeProbability[i];
  147.             adblPiecewiseDensity[i] = 2. * (dblRightCumulativeProbability - dblLeftCumulativeProbability) /
  148.                 (dblRightPredictorOrdinate * dblRightPredictorOrdinate - dblLeftPredictorOrdinate *
  149.                     dblLeftPredictorOrdinate);
  150.         }

  152.         try {
  153.             return new R1PiecewiseLinear (dblLeftPredictorOrdinateEdge,
  154.                 dblRightPredictorOrdinateEdge, adblPredictorOrdinate,  adblPiecewiseDensity);
  155.         } catch (java.lang.Exception e) {
  156.             e.printStackTrace();
  157.         }

  159.         return null;
  160.     }

  162.     /**
  163.      * R1PiecewiseLinear Constructor
  164.      * 
  165.      * @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
  166.      * @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
  167.      * @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
  168.      * @param adblPiecewiseDensity Array of corresponding Piece-wise Densities
  169.      * 
  170.      * @throws java.lang.Exception Thrown if the Inputs are invalid
  171.      */

  173.     public R1PiecewiseLinear (
  174.         final double dblLeftPredictorOrdinateEdge,
  175.         final double dblRightPredictorOrdinateEdge,
  176.         final double[] adblPredictorOrdinate,
  177.         final double[] adblPiecewiseDensity)
  178.         throws java.lang.Exception
  179.     {
  180.         super (dblLeftPredictorOrdinateEdge, dblRightPredictorOrdinateEdge);

  182.         if (null == (_adblPredictorOrdinate = adblPredictorOrdinate) || null == (_adblPiecewiseDensity =
  183.             adblPiecewiseDensity))
  184.             throw new java.lang.Exception ("R1PiecewiseLinear Constructor: Invalid Inputs");

  186.         int iNumPredictorOrdinate = _adblPredictorOrdinate.length;

  188.         if (0 == iNumPredictorOrdinate || iNumPredictorOrdinate + 1 != _adblPiecewiseDensity.length)
  189.             throw new java.lang.Exception ("R1PiecewiseLinear Constructor: Invalid Inputs");
  190.     }

  192.     /**
  193.      * Retrieve the Array of Predictor Ordinates
  194.      * 
  195.      * @return The Array of Predictor Ordinates
  196.      */

  198.     public double[] predictorOrdinates()
  199.     {
  200.         return _adblPredictorOrdinate;
  201.     }

  203.     /**
  204.      * Retrieve the Array of Piecewise Densities
  205.      * 
  206.      * @return The Array of Piecewise Densities
  207.      */

  209.     public double[] piecewiseDensities()
  210.     {
  211.         return _adblPiecewiseDensity;
  212.     }

  214.     @Override public double cumulative (
  215.         final double dblX)
  216.         throws java.lang.Exception
  217.     {
  218.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  219.             throw new java.lang.Exception ("R1PiecewiseLinear::cumulative => Invalid Inputs");

  221.         double dblLeftEdge = leftEdge();

  223.         double dblRightEdge = rightEdge();

  225.         if (dblX <= dblLeftEdge) return 0.;

  227.         if (dblX >= dblRightEdge) return 1.;

  229.         int iSegmentIndex = 0;
  230.         double dblSegmentLeft = dblLeftEdge;
  231.         double dblCumulativeProbability = 0.;
  232.         int iMaxSegmentIndex = _adblPiecewiseDensity.length - 1;

  234.         while (iSegmentIndex < iMaxSegmentIndex) {
  235.             double dblSegmentRight = _adblPredictorOrdinate[iSegmentIndex];

  237.             if (dblX >= dblSegmentLeft && dblX <= dblSegmentRight)
  238.                 return dblCumulativeProbability + 0.5 * _adblPiecewiseDensity[iSegmentIndex] * (dblX * dblX -
  239.                     dblSegmentLeft * dblSegmentLeft);

  241.             dblCumulativeProbability += 0.5 * _adblPiecewiseDensity[iSegmentIndex] * (dblSegmentRight *
  242.                 dblSegmentRight - dblSegmentLeft * dblSegmentLeft);
  243.             dblSegmentLeft = dblSegmentRight;
  244.             ++iSegmentIndex;
  245.         }

  247.         return dblCumulativeProbability + 0.5 * _adblPiecewiseDensity[iMaxSegmentIndex] * (dblX * dblX -
  248.             dblRightEdge * dblRightEdge);
  249.     }

  251.     @Override public double invCumulative (
  252.         final double dblY)
  253.         throws java.lang.Exception
  254.     {
  255.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || dblY < 0. || dblY > 1.)
  256.             throw new java.lang.Exception ("R1PiecewiseLinear::invCumulative => Invalid inputs");

  258.         org.drip.function.definition.R1ToR1 r1ToR1CumulativeProbability = new
  259.             org.drip.function.definition.R1ToR1 (null) {
  260.             @Override public double evaluate (
  261.                 final double dblX)
  262.                 throws java.lang.Exception
  263.             {
  264.                 return cumulative (dblX);
  265.             }
  266.         };

  268.         org.drip.function.r1tor1solver.FixedPointFinderOutput fpfo = new
  269.             org.drip.function.r1tor1solver.FixedPointFinderBracketing (dblY, r1ToR1CumulativeProbability,
  270.                 null, org.drip.function.r1tor1solver.VariateIteratorPrimitive.BISECTION, true).findRoot();

  272.         if (null == fpfo || !fpfo.containsRoot())
  273.             throw new java.lang.Exception ("R1PiecewiseLinear::invCumulative => No roots");

  275.         return fpfo.getRoot();
  276.     }

  278.     @Override public double density (
  279.         final double dblX)
  280.         throws java.lang.Exception
  281.     {
  282.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  283.             throw new java.lang.Exception ("R1PiecewiseLinear::density => Invalid Inputs");

  285.         if (dblX <= leftEdge() || dblX >= rightEdge()) return 0.;

  287.         int iSegmentIndex = 0;
  288.         int iMaxSegmentIndex = _adblPiecewiseDensity.length - 1;

  290.         while (iSegmentIndex < iMaxSegmentIndex) {
  291.             if (dblX >= _adblPredictorOrdinate[iSegmentIndex] && dblX <=
  292.                 _adblPredictorOrdinate[iSegmentIndex + 1])
  293.                 break;

  295.             ++iSegmentIndex;
  296.         }

  298.         return _adblPiecewiseDensity[iSegmentIndex] * dblX;
  299.     }

  301.     @Override public org.drip.numerical.common.Array2D histogram()
  302.     {
  303.         double dblLeftEdge = leftEdge();

  305.         double[] adblX = new double[GRID_WIDTH];
  306.         double[] adblY = new double[GRID_WIDTH];

  308.         double dblWidth = (rightEdge() - dblLeftEdge) / GRID_WIDTH;

  310.         for (int i = 0; i < GRID_WIDTH; ++i) {
  311.             adblX[i] = dblLeftEdge + (i + 1) * dblWidth;

  313.             try {
  314.                 adblY[i] = incremental (adblX[i] - dblWidth, adblX[i]);
  315.             } catch (java.lang.Exception e) {
  316.                 e.printStackTrace();

  318.                 return null;
  319.             }
  320.         }

  322.         return org.drip.numerical.common.Array2D.FromArray (adblX, adblY);
  323.     }
  324. }
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