RdToRd.java

  1. package org.drip.function.definition;

  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>RdToRd</i> provides the evaluation of the R<sup>d</sup> To R<sup>d</sup> objective function and its
  83.  * derivatives for a specified set of R<sup>d</sup> variates. Default implementation of the derivatives are
  84.  * for non-analytical black box objective functions.
  85.  *
  86.  *  <br><br>
  87.  *  <ul>
  88.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  89.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  90.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  91.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/definition/README.md">Function Implementation Ancillary Support Objects</a></li>
  92.  *  </ul>
  93.  *
  94.  * @author Lakshmi Krishnamurthy
  95.  */

  97. public abstract class RdToRd {
  98.     private static final int QUADRATURE_SAMPLING = 10000;

  100.     protected org.drip.numerical.differentiation.DerivativeControl _dc = null;

  102.     protected RdToRd (
  103.         final org.drip.numerical.differentiation.DerivativeControl dc)
  104.     {
  105.         if (null == (_dc = dc)) _dc = new org.drip.numerical.differentiation.DerivativeControl();
  106.     }

  108.     /**
  109.      * Evaluate for the given Input R^d Variates
  110.      * 
  111.      * @param adblVariate Array of Input R^d Variates
  112.      *  
  113.      * @return The Output R^d Variates
  114.      */

  116.     public abstract double[] evaluate (
  117.         final double[] adblVariate);

  119.     /**
  120.      * Calculate the Array of Differentials
  121.      * 
  122.      * @param adblVariate Variate Array at which the derivative is to be calculated
  123.      * @param iVariateIndex Index of the Variate whose Derivative is to be computed
  124.      * @param iOrder Order of the derivative to be computed
  125.      * 
  126.      * @return The Array of Differentials
  127.      */

  129.     public org.drip.numerical.differentiation.Differential[] differential (
  130.         final double[] adblVariate,
  131.         final int iVariateIndex,
  132.         final int iOrder)
  133.     {
  134.         if (!org.drip.numerical.common.NumberUtil.IsValid (adblVariate) || 0 >= iOrder) return null;

  136.         int iOutputDimension = -1;
  137.         double[] adblDerivative = null;
  138.         int iNumVariate = adblVariate.length;
  139.         double dblOrderedVariateInfinitesimal = 1.;
  140.         double dblVariateInfinitesimal = java.lang.Double.NaN;

  142.         if (iNumVariate <= iVariateIndex) return null;

  144.         try {
  145.             dblVariateInfinitesimal = _dc.getVariateInfinitesimal (adblVariate[iVariateIndex]);
  146.         } catch (java.lang.Exception e) {
  147.             e.printStackTrace();

  149.             return null;
  150.         }

  152.         for (int i = 0; i <= iOrder; ++i) {
  153.             if (0 != i) dblOrderedVariateInfinitesimal *= (2. * dblVariateInfinitesimal);

  155.             double[] adblVariateIncremental = new double[iNumVariate];

  157.             for (int j = 0; i < iNumVariate; ++j)
  158.                 adblVariateIncremental[j] = j == iVariateIndex ? adblVariate[j] + dblVariateInfinitesimal *
  159.                     (iOrder - 2. * i) : adblVariate[j];

  161.             double[] adblValue = evaluate (adblVariateIncremental);

  163.             if (null == adblValue || 0 == (iOutputDimension = adblValue.length)) return null;

  165.             if (null == adblDerivative) {
  166.                 adblDerivative = new double[iOutputDimension];

  168.                 for (int j = 0; j < iOutputDimension; ++j)
  169.                     adblDerivative[j] = 0.;
  170.             }

  172.             try {
  173.                 for (int j = 0; j < iOutputDimension; ++j)
  174.                     adblDerivative[j] += (i % 2 == 0 ? 1 : -1) * org.drip.numerical.common.NumberUtil.NCK
  175.                         (iOrder, i) * adblValue[j];
  176.             } catch (java.lang.Exception e) {
  177.                 e.printStackTrace();

  179.                 return null;
  180.             }
  181.         }

  183.         org.drip.numerical.differentiation.Differential[] aDiff = new
  184.             org.drip.numerical.differentiation.Differential[iOutputDimension];

  186.         try {
  187.             for (int j = 0; j < iOutputDimension; ++j)
  188.                 aDiff[j] = new org.drip.numerical.differentiation.Differential (dblOrderedVariateInfinitesimal,
  189.                     adblDerivative[j]);
  190.         } catch (java.lang.Exception e) {
  191.             e.printStackTrace();

  193.             return null;
  194.         }

  196.         return aDiff;
  197.     }

  199.     /**
  200.      * Calculate the Derivative Array as a double
  201.      * 
  202.      * @param adblVariate Variate Array at which the derivative is to be calculated
  203.      * @param iVariateIndex Index of the Variate whose Derivative is to be computed
  204.      * @param iOrder Order of the derivative to be computed
  205.      * 
  206.      * @return The Derivative Array
  207.      */

  209.     public double[] derivative (
  210.         final double[] adblVariate,
  211.         final int iVariateIndex,
  212.         final int iOrder)
  213.     {
  214.         org.drip.numerical.differentiation.Differential[] aDiff = differential (adblVariate, iVariateIndex, iOrder);

  216.         if (null == aDiff) return null;

  218.         int iOutputDimension = aDiff.length;
  219.         double[] adblDerivative = new double[iOutputDimension];

  221.         if (0 == iOutputDimension) return null;

  223.         for (int i = 0; i < iOutputDimension; ++i)
  224.             adblDerivative[i] = aDiff[i].calcSlope (true);

  226.         return adblDerivative;
  227.     }

  229.     /**
  230.      * Integrate over the given Input Range Using Uniform Monte-Carlo
  231.      * 
  232.      * @param adblLeftEdge Array of Input Left Edge
  233.      * @param adblRightEdge Array of Input Right Edge
  234.      *  
  235.      * @return The Array Containing the Result of the Integration over the specified Range
  236.      */

  238.     public double[] integrate (
  239.         final double[] adblLeftEdge,
  240.         final double[] adblRightEdge)
  241.     {
  242.         if (!org.drip.numerical.common.NumberUtil.IsValid (adblLeftEdge) ||
  243.             !org.drip.numerical.common.NumberUtil.IsValid (adblRightEdge))
  244.             return null;

  246.         int iOutputDimension = -1;
  247.         double[] adblIntegrand = null;
  248.         int iNumVariate = adblLeftEdge.length;
  249.         double[] adblVariate = new double[iNumVariate];
  250.         double[] adblVariateWidth = new double[iNumVariate];

  252.         if (adblRightEdge.length != iNumVariate) return null;

  254.         for (int j = 0; j < iNumVariate; ++j)
  255.             adblVariateWidth[j] = adblRightEdge[j] - adblLeftEdge[j];

  257.         for (int i = 0; i < QUADRATURE_SAMPLING; ++i) {
  258.             for (int j = 0; j < iNumVariate; ++j)
  259.                 adblVariate[j] = adblLeftEdge[j] + java.lang.Math.random() * adblVariateWidth[j];

  261.             double[] adblValue = evaluate (adblVariate);

  263.             if (null == adblValue || 0 == (iOutputDimension = adblValue.length)) return null;

  265.             if (null == adblIntegrand) adblIntegrand = new double[iOutputDimension];

  267.             for (int j = 0; j < iOutputDimension; ++j)
  268.                 adblIntegrand[j] += adblValue[j];
  269.         }

  271.         for (int i = 0; i < iOutputDimension; ++i) {
  272.             for (int j = 0; j < iNumVariate; ++j)
  273.                 adblIntegrand[i] = adblIntegrand[i] * adblVariateWidth[j];

  275.             adblIntegrand[i] /= QUADRATURE_SAMPLING;
  276.         }

  278.         return adblIntegrand;
  279.     }
  280. }
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