AkimaLocalC1Generator.java

  1. package org.drip.spline.pchip;

  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) 2013 Lakshmi Krishnamurthy
  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>AkimaLocalC1Generator</i> generates the local control C1 Slope using the Akima Cubic Algorithm.
  85.  *
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Akima (1970): A New Method of Interpolation and Smooth Curve Fitting based on Local Procedures
  90.  *              <i>Journal of the Association for the Computing Machinery</i> <b>17 (4)</b> 589-602
  91.  *      </li>
  92.  *  </ul>
  93.  *
  94.  * <br><br>
  95.  *  <ul>
  96.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  97.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/SplineBuilderLibrary.md">Spline Builder Library</a></li>
  98.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/README.md">Basis Splines and Linear Compounders across a Broad Family of Spline Basis Functions</a></li>
  99.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/pchip/README.md">Monotone Convex Themed PCHIP Splines</a></li>
  100.  *  </ul>
  101.  * <br><br>
  102.  *
  103.  * @author Lakshmi Krishnamurthy
  104.  */

  106. public class AkimaLocalC1Generator {
  107.     private double[] _adblResponseValue = null;
  108.     private double[] _adblPredictorOrdinate = null;
  109.     private double[] _adblExtendedResponseValue = null;
  110.     private double[] _adblExtendedPredictorOrdinate = null;

  112.     /**
  113.      * Construct an Instance of AkimaLocalC1Generator from the Array of the supplied Predictor Ordinates
  114.      *  and the Response Values
  115.      *  
  116.      * @param adblPredictorOrdinate Array of the Predictor Ordinates
  117.      * @param adblResponseValue Array of the Response Values
  118.      * 
  119.      * @return Instance of AkimaLocalC1Generator
  120.      */

  122.     public static final AkimaLocalC1Generator Create (
  123.         final double[] adblPredictorOrdinate,
  124.         final double[] adblResponseValue)
  125.     {
  126.         AkimaLocalC1Generator alcr = null;

  128.         try {
  129.             alcr = new AkimaLocalC1Generator (adblPredictorOrdinate, adblResponseValue);
  130.         } catch (java.lang.Exception e) {
  131.             e.printStackTrace();

  133.             return null;
  134.         }

  136.         return alcr.extendPredictorOrdinate() && alcr.extendResponseValue() ? alcr : null;
  137.     }

  139.     private AkimaLocalC1Generator (
  140.         final double[] adblPredictorOrdinate,
  141.         final double[] adblResponseValue)
  142.         throws java.lang.Exception
  143.     {
  144.         if (null == (_adblPredictorOrdinate = adblPredictorOrdinate) || null == (_adblResponseValue =
  145.             adblResponseValue))
  146.             throw new java.lang.Exception ("AkimaLocalC1Generator ctr: Invalid Inputs");

  148.         int iNumPredictorOrdinate = _adblPredictorOrdinate.length;

  150.         if (2 >= iNumPredictorOrdinate || iNumPredictorOrdinate != _adblResponseValue.length)
  151.             throw new java.lang.Exception ("AkimaLocalC1Generator ctr: Invalid Inputs");
  152.     }

  154.     private boolean extendPredictorOrdinate()
  155.     {
  156.         int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
  157.         int iNumExtendedPredictorOrdinate = iNumPredictorOrdinate + 4;
  158.         _adblExtendedPredictorOrdinate = new double[iNumExtendedPredictorOrdinate];

  160.         for (int i = 0; i < iNumExtendedPredictorOrdinate; ++i) {
  161.             if (2 <= i && iNumExtendedPredictorOrdinate - 3 >= i)
  162.                 _adblExtendedPredictorOrdinate[i] = _adblPredictorOrdinate[i - 2];
  163.         }

  165.         double dblSkippedLeftPredictorWidth = _adblPredictorOrdinate[2] - _adblPredictorOrdinate[0];
  166.         _adblExtendedPredictorOrdinate[0] = _adblPredictorOrdinate[0] - dblSkippedLeftPredictorWidth;
  167.         _adblExtendedPredictorOrdinate[1] = _adblPredictorOrdinate[1] - dblSkippedLeftPredictorWidth;
  168.         double dblSkippedRightPredictorWidth = _adblPredictorOrdinate[iNumPredictorOrdinate - 1] -
  169.             _adblPredictorOrdinate[iNumPredictorOrdinate - 3];
  170.         _adblExtendedPredictorOrdinate[iNumExtendedPredictorOrdinate - 2] =
  171.             _adblPredictorOrdinate[iNumPredictorOrdinate - 2] + dblSkippedRightPredictorWidth;
  172.         _adblExtendedPredictorOrdinate[iNumExtendedPredictorOrdinate - 1] =
  173.             _adblPredictorOrdinate[iNumPredictorOrdinate - 1] + dblSkippedRightPredictorWidth;
  174.         return true;
  175.     }

  177.     private boolean setExtendedResponseValue (
  178.         final int i,
  179.         final boolean bRight)
  180.     {
  181.         if (bRight) {
  182.             _adblExtendedResponseValue[i] = 2. * (_adblExtendedResponseValue[i - 1] -
  183.                 _adblExtendedResponseValue[i - 2]) / (_adblExtendedPredictorOrdinate[i - 1] -
  184.                     _adblExtendedPredictorOrdinate[i - 2]) - ((_adblExtendedResponseValue[i - 2] -
  185.                         _adblExtendedResponseValue[i - 3]) / (_adblExtendedPredictorOrdinate[i - 2] -
  186.                             _adblExtendedPredictorOrdinate[i - 3]));
  187.             _adblExtendedResponseValue[i] = _adblExtendedResponseValue[i] * (_adblExtendedResponseValue[i] -
  188.                 _adblExtendedResponseValue[i - 1]) + _adblExtendedResponseValue[i - 1];
  189.         } else {
  190.             _adblExtendedResponseValue[i] = 2. * (_adblExtendedResponseValue[i + 2] -
  191.                 _adblExtendedResponseValue[i + 1]) / (_adblExtendedPredictorOrdinate[i + 2] -
  192.                     _adblExtendedPredictorOrdinate[i + 1]) - ((_adblExtendedResponseValue[i + 3] -
  193.                         _adblExtendedResponseValue[i + 2]) / (_adblExtendedPredictorOrdinate[i + 3] -
  194.                             _adblExtendedPredictorOrdinate[i + 2]));
  195.             _adblExtendedResponseValue[i] = _adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]
  196.                 * (_adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]);
  197.         }

  199.         return true;
  200.     }

  202.     private boolean extendResponseValue()
  203.     {
  204.         int iNumResponseValue = _adblResponseValue.length;
  205.         int iNumExtendedResponseValue = iNumResponseValue + 4;
  206.         _adblExtendedResponseValue = new double[iNumExtendedResponseValue];

  208.         for (int i = 0; i < iNumExtendedResponseValue; ++i) {
  209.             if (2 <= i && iNumExtendedResponseValue - 3 >= i)
  210.                 _adblExtendedResponseValue[i] = _adblResponseValue[i - 2];
  211.         }

  213.         return setExtendedResponseValue (1, false) && setExtendedResponseValue (0, false) &&
  214.             setExtendedResponseValue (iNumExtendedResponseValue - 2, true) && setExtendedResponseValue
  215.                 (iNumExtendedResponseValue - 1, true) ? true : false;
  216.     }

  218.     public double[] C1()
  219.     {
  220.         int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
  221.         double[] adblC1 = new double[iNumPredictorOrdinate];
  222.         double[] adblExtendedSlope = new double[iNumPredictorOrdinate + 3];

  224.         for (int i = 0; i < iNumPredictorOrdinate + 3; ++i)
  225.             adblExtendedSlope[i] = (_adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]) /
  226.                 (_adblExtendedPredictorOrdinate[i + 1] - _adblExtendedPredictorOrdinate[i]);

  228.         for (int i = 0; i < iNumPredictorOrdinate; ++i) {
  229.             double dblSlope10 = java.lang.Math.abs (adblExtendedSlope[i + 1] - adblExtendedSlope[i]);

  231.             double dblSlope32 = java.lang.Math.abs (adblExtendedSlope[i + 3] - adblExtendedSlope[i + 2]);

  233.             if (0. == dblSlope10 && 0. == dblSlope32)
  234.                 adblC1[i] = 0.5 * (adblExtendedSlope[i + 1] + adblExtendedSlope[i + 2]);
  235.             else
  236.                 adblC1[i] = (dblSlope32 * adblExtendedSlope[i + 1] + dblSlope10 * adblExtendedSlope[i + 2]) /
  237.                     (dblSlope10 + dblSlope32);
  238.         }

  240.         return adblC1;
  241.     }
  242. }
Created with JaCoCo 0.7.9.201702052155