R1PiecewiseDisplaced.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>R1PiecewiseDisplaced</i> implements the Displaced Piecewise Linear R<sup>1</sup> Distributions. It
  82.  * exports the 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 R1PiecewiseDisplaced extends org.drip.measure.lebesgue.R1Uniform {
  96.     private double[] _adblPredictorOrdinate = null;
  97.     private double[] _adblPiecewiseDensitySlope = null;
  98.     private double _dblDensityDisplacement = java.lang.Double.NaN;

  100.     /**
  101.      * Calibrate an R1PiecewiseDisplaced Lebesgue Instance
  102.      * 
  103.      * @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
  104.      * @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
  105.      * @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
  106.      * @param adblCumulativeProbability Array of corresponding Cumulative Probabilities
  107.      * @param dblMean The Distribution Mean
  108.      * 
  109.      * @return The R1PiecewiseDisplacedLebesgue Instance
  110.      */

  112.     public static final R1PiecewiseDisplaced Standard (
  113.         final double dblLeftPredictorOrdinateEdge,
  114.         final double dblRightPredictorOrdinateEdge,
  115.         final double[] adblPredictorOrdinate,
  116.         final double[] adblCumulativeProbability,
  117.         final double dblMean)
  118.     {
  119.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblLeftPredictorOrdinateEdge) ||
  120.             !org.drip.numerical.common.NumberUtil.IsValid (dblRightPredictorOrdinateEdge) ||
  121.                 dblLeftPredictorOrdinateEdge >= dblRightPredictorOrdinateEdge || null ==
  122.                     adblPredictorOrdinate || null == adblCumulativeProbability ||
  123.                         !org.drip.numerical.common.NumberUtil.IsValid (dblMean))
  124.             return null;

  126.         int iNumSegment = adblPredictorOrdinate.length + 1;
  127.         double[][] aadblM = new double[iNumSegment + 1][iNumSegment + 1];
  128.         double[] adblSecondDegreeIntegral = new double[iNumSegment];
  129.         double[] adblSlope = new double[iNumSegment];
  130.         double[] adblY = new double[iNumSegment + 1];
  131.         adblY[iNumSegment] = dblMean;
  132.         aadblM[iNumSegment][iNumSegment] = 0.5 * (dblRightPredictorOrdinateEdge *
  133.             dblRightPredictorOrdinateEdge - dblLeftPredictorOrdinateEdge * dblLeftPredictorOrdinateEdge);

  135.         if (1 == iNumSegment || iNumSegment - 1 != adblCumulativeProbability.length) return null;

  137.         for (int i = 0; i < iNumSegment; ++i) {
  138.             adblY[i] = i == iNumSegment - 1 ? 1. : adblCumulativeProbability[i];
  139.             double dblSegmentLeft = 0 == i ? dblLeftPredictorOrdinateEdge : adblPredictorOrdinate[i - 1];
  140.             double dblSegmentRight = iNumSegment - 1 == i ? dblRightPredictorOrdinateEdge :
  141.                 adblPredictorOrdinate[i];
  142.             adblSecondDegreeIntegral[i] = 0.5 * (dblSegmentRight * dblSegmentRight - dblSegmentLeft *
  143.                 dblSegmentLeft);
  144.             aadblM[i][iNumSegment] = dblSegmentRight - dblLeftPredictorOrdinateEdge;
  145.             aadblM[iNumSegment][i] = (dblSegmentRight * dblSegmentRight * dblSegmentRight - dblSegmentLeft *
  146.                 dblSegmentLeft * dblSegmentLeft) / 6.;

  148.             if (!org.drip.numerical.common.NumberUtil.IsValid (dblSegmentLeft) || dblSegmentLeft <
  149.                 dblLeftPredictorOrdinateEdge)
  150.                 return null;

  152.             if (!org.drip.numerical.common.NumberUtil.IsValid (dblSegmentRight) || dblSegmentRight <=
  153.                 dblSegmentLeft || dblSegmentRight > dblRightPredictorOrdinateEdge)
  154.                 return null;
  155.         }

  157.         for (int i = 0; i < iNumSegment; ++i) {
  158.             for (int k = 0; k < iNumSegment; ++k)
  159.                 aadblM[i][k] = k > i ? 0. : adblSecondDegreeIntegral[k];
  160.         }

  162.         org.drip.numerical.linearalgebra.LinearizationOutput lo =
  163.             org.drip.numerical.linearalgebra.LinearSystemSolver.SolveUsingMatrixInversion (aadblM, adblY);

  165.         if (null == lo) return null;

  167.         double[] adblSlopeDisplacement = lo.getTransformedRHS();

  169.         if (null == adblSlopeDisplacement || adblSlopeDisplacement.length != iNumSegment + 1) return null;

  171.         for (int i = 0; i < iNumSegment; ++i)
  172.             adblSlope[i] = adblSlopeDisplacement[i];

  174.         try {
  175.             return new R1PiecewiseDisplaced (dblLeftPredictorOrdinateEdge,
  176.                 dblRightPredictorOrdinateEdge, adblPredictorOrdinate, adblSlope,
  177.                     adblSlopeDisplacement[iNumSegment]);
  178.         } catch (java.lang.Exception e) {
  179.             e.printStackTrace();
  180.         }

  182.         return null;
  183.     }

  185.     /**
  186.      * R1PiecewiseDisplaced Constructor
  187.      * 
  188.      * @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
  189.      * @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
  190.      * @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
  191.      * @param adblPiecewiseDensitySlope Array of corresponding Piece-wise Density Slopes
  192.      * @param dblDensityDisplacement Uniform Density Displacement
  193.      * 
  194.      * @throws java.lang.Exception Thrown if the Inputs are invalid
  195.      */

  197.     public R1PiecewiseDisplaced (
  198.         final double dblLeftPredictorOrdinateEdge,
  199.         final double dblRightPredictorOrdinateEdge,
  200.         final double[] adblPredictorOrdinate,
  201.         final double[] adblPiecewiseDensitySlope,
  202.         final double dblDensityDisplacement)
  203.         throws java.lang.Exception
  204.     {
  205.         super (dblLeftPredictorOrdinateEdge, dblRightPredictorOrdinateEdge);

  207.         if (null == (_adblPredictorOrdinate = adblPredictorOrdinate) || null == (_adblPiecewiseDensitySlope =
  208.             adblPiecewiseDensitySlope) || !org.drip.numerical.common.NumberUtil.IsValid (_dblDensityDisplacement
  209.                 = dblDensityDisplacement))
  210.             throw new java.lang.Exception ("R1PiecewiseDisplaced Constructor: Invalid Inputs");

  212.         int iNumPredictorOrdinate = _adblPredictorOrdinate.length;

  214.         if (0 == iNumPredictorOrdinate || iNumPredictorOrdinate + 1 != _adblPiecewiseDensitySlope.length)
  215.             throw new java.lang.Exception ("R1PiecewiseDisplaced Constructor: Invalid Inputs");
  216.     }

  218.     /**
  219.      * Retrieve the Array of Predictor Ordinates
  220.      * 
  221.      * @return The Array of Predictor Ordinates
  222.      */

  224.     public double[] predictorOrdinates()
  225.     {
  226.         return _adblPredictorOrdinate;
  227.     }

  229.     /**
  230.      * Retrieve the Array of Piecewise Density Slopes
  231.      * 
  232.      * @return The Array of Piecewise Density Slopes
  233.      */

  235.     public double[] piecewiseDensitySlopes()
  236.     {
  237.         return _adblPiecewiseDensitySlope;
  238.     }

  240.     /**
  241.      * Retrieve the Density Displacement
  242.      * 
  243.      * @return The Density Displacement
  244.      */

  246.     public double densityDisplacement()
  247.     {
  248.         return _dblDensityDisplacement;
  249.     }

  251.     @Override public double cumulative (
  252.         final double dblX)
  253.         throws java.lang.Exception
  254.     {
  255.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  256.             throw new java.lang.Exception ("R1PiecewiseDisplaced::cumulative => Invalid Inputs");

  258.         double dblLeftEdge = leftEdge();

  260.         double dblRightEdge = rightEdge();

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

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

  266.         int iSegmentIndex = 0;
  267.         double dblSegmentLeft = dblLeftEdge;
  268.         double dblCumulativeProbability = 0.;
  269.         int iMaxSegmentIndex = _adblPiecewiseDensitySlope.length - 1;

  271.         while (iSegmentIndex < iMaxSegmentIndex) {
  272.             double dblSegmentRight = _adblPredictorOrdinate[iSegmentIndex];

  274.             if (dblX >= dblSegmentLeft && dblX <= dblSegmentRight)
  275.                 return dblCumulativeProbability + 0.5 * _adblPiecewiseDensitySlope[iSegmentIndex] * (dblX *
  276.                     dblX - dblSegmentLeft * dblSegmentLeft) + _dblDensityDisplacement * (dblX -
  277.                         dblSegmentLeft);

  279.             dblCumulativeProbability += (0.5 * _adblPiecewiseDensitySlope[iSegmentIndex] * (dblSegmentRight *
  280.                 dblSegmentRight - dblSegmentLeft * dblSegmentLeft) + _dblDensityDisplacement *
  281.                     (dblSegmentRight - dblSegmentLeft));
  282.             dblSegmentLeft = dblSegmentRight;
  283.             ++iSegmentIndex;
  284.         }

  286.         return dblCumulativeProbability + 0.5 * _adblPiecewiseDensitySlope[iMaxSegmentIndex] * (dblX * dblX -
  287.             _adblPredictorOrdinate[iMaxSegmentIndex - 1] * _adblPredictorOrdinate[iMaxSegmentIndex - 1]) +
  288.                 _dblDensityDisplacement * (dblX - _adblPredictorOrdinate[iMaxSegmentIndex - 1]);
  289.     }

  291.     @Override public double invCumulative (
  292.         final double dblY)
  293.         throws java.lang.Exception
  294.     {
  295.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || dblY < 0. || dblY > 1.)
  296.             throw new java.lang.Exception ("R1PiecewiseDisplaced::invCumulative => Invalid inputs");

  298.         org.drip.function.definition.R1ToR1 r1ToR1CumulativeProbability = new
  299.             org.drip.function.definition.R1ToR1 (null) {
  300.             @Override public double evaluate (
  301.                 final double dblX)
  302.                 throws java.lang.Exception
  303.             {
  304.                 return cumulative (dblX);
  305.             }
  306.         };

  308.         org.drip.function.r1tor1solver.FixedPointFinderOutput fpfo = new
  309.             org.drip.function.r1tor1solver.FixedPointFinderBracketing (dblY, r1ToR1CumulativeProbability,
  310.                 null, org.drip.function.r1tor1solver.VariateIteratorPrimitive.BISECTION, true).findRoot
  311.                     (org.drip.function.r1tor1solver.InitializationHeuristics.FromHardSearchEdges (leftEdge(),
  312.                         rightEdge()));

  314.         if (null == fpfo || !fpfo.containsRoot())
  315.             throw new java.lang.Exception ("R1PiecewiseDisplaced::invCumulative => No roots");

  317.         return fpfo.getRoot();
  318.     }

  320.     @Override public double density (
  321.         final double dblX)
  322.         throws java.lang.Exception
  323.     {
  324.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  325.             throw new java.lang.Exception ("R1PiecewiseDisplaced::density => Invalid Inputs");

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

  329.         int iSegmentIndex = 0;
  330.         int iMaxSegmentIndex = _adblPiecewiseDensitySlope.length - 1;

  332.         while (iSegmentIndex < iMaxSegmentIndex) {
  333.             if (dblX >= _adblPredictorOrdinate[iSegmentIndex] && dblX <=
  334.                 _adblPredictorOrdinate[iSegmentIndex + 1])
  335.                 break;

  337.             ++iSegmentIndex;
  338.         }

  340.         return _adblPiecewiseDensitySlope[iSegmentIndex] * dblX + _dblDensityDisplacement;
  341.     }

  343.     @Override public org.drip.numerical.common.Array2D histogram()
  344.     {
  345.         double dblLeftEdge = leftEdge();

  347.         double[] adblX = new double[GRID_WIDTH];
  348.         double[] adblY = new double[GRID_WIDTH];

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

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

  355.             try {
  356.                 adblY[i] = incremental (adblX[i] - dblWidth, adblX[i]);
  357.             } catch (java.lang.Exception e) {
  358.                 e.printStackTrace();

  360.                 return null;
  361.             }
  362.         }

  364.         return org.drip.numerical.common.Array2D.FromArray (adblX, adblY);
  365.     }
  366. }
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