R1ToR1.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.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2013 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2012 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  19.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  20.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  21.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  22.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  23.  *      and computational support.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  32.  * 
  33.  *  DROP Product Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Loan Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Portfolio Core implements libraries for the following:
  39.  *  - Asset Allocation Analytics
  40.  *  - Asset Liability Management Analytics
  41.  *  - Capital Estimation Analytics
  42.  *  - Exposure Analytics
  43.  *  - Margin Analytics
  44.  *  - XVA Analytics
  45.  * 
  46.  *  DROP Computational Core implements libraries for the following:
  47.  *  - Algorithm Support
  48.  *  - Computation Support
  49.  *  - Function Analysis
  50.  *  - Model Validation
  51.  *  - Numerical Analysis
  52.  *  - Numerical Optimizer
  53.  *  - Spline Builder
  54.  *  - Statistical Learning
  55.  * 
  56.  *  Documentation for DROP is Spread Over:
  57.  * 
  58.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  59.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  60.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  61.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  62.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  63.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  64.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  65.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  66.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  67.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  68.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  69.  * 
  70.  *  Licensed under the Apache License, Version 2.0 (the "License");
  71.  *      you may not use this file except in compliance with the License.
  72.  *   
  73.  *  You may obtain a copy of the License at
  74.  *      http://www.apache.org/licenses/LICENSE-2.0
  75.  *  
  76.  *  Unless required by applicable law or agreed to in writing, software
  77.  *      distributed under the License is distributed on an "AS IS" BASIS,
  78.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  79.  *  
  80.  *  See the License for the specific language governing permissions and
  81.  *      limitations under the License.
  82.  */

  84. /**
  85.  * <i>R1ToR1</i> provides the evaluation of the objective function and its derivatives for a specified
  86.  * variate. Default implementation of the derivatives are for non-analytical black box objective functions.
  87.  *
  88.  *  <br><br>
  89.  *  <ul>
  90.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  91.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  92.  *      <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>
  93.  *      <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>
  94.  *  </ul>
  95.  *
  96.  * @author Lakshmi Krishnamurthy
  97.  */

  99. public abstract class R1ToR1 {
  100.     protected org.drip.numerical.differentiation.DerivativeControl _dc = null;

  102.     protected R1ToR1 (
  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 variate
  110.      * 
  111.      * @param dblVariate Variate
  112.      *  
  113.      * @return Returns the calculated value
  114.      * 
  115.      * @throws java.lang.Exception Thrown if evaluation cannot be done
  116.      */

  118.     public abstract double evaluate (
  119.         final double dblVariate)
  120.         throws java.lang.Exception;

  122.     /**
  123.      * Calculate the Differential
  124.      * 
  125.      * @param dblVariate Variate at which the derivative is to be calculated
  126.      * @param dblOFBase Base Value for the Objective Function
  127.      * @param iOrder Order of the derivative to be computed
  128.      * 
  129.      * @return The Derivative
  130.      */

  132.     public org.drip.numerical.differentiation.Differential differential (
  133.         final double dblVariate,
  134.         final double dblOFBase,
  135.         final int iOrder)
  136.     {
  137.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariate) || 0 >= iOrder) return null;

  139.         double dblDerivative = 0.;
  140.         double dblOrderedVariateInfinitesimal = 1.;
  141.         double dblVariateInfinitesimal = java.lang.Double.NaN;

  143.         try {
  144.             dblVariateInfinitesimal = _dc.getVariateInfinitesimal (dblVariate);
  145.         } catch (java.lang.Exception e) {
  146.             e.printStackTrace();

  148.             return null;
  149.         }

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

  154.             try {
  155.                 dblDerivative += (i % 2 == 0 ? 1 : -1) * org.drip.numerical.common.NumberUtil.NCK (iOrder, i) *
  156.                     evaluate (dblVariate + dblVariateInfinitesimal * (iOrder - 2. * i));
  157.             } catch (java.lang.Exception e) {
  158.                 e.printStackTrace();

  160.                 return null;
  161.             }
  162.         }

  164.         try {
  165.             return new org.drip.numerical.differentiation.Differential (dblOrderedVariateInfinitesimal, dblDerivative);
  166.         } catch (java.lang.Exception e) {
  167.             e.printStackTrace();
  168.         }

  170.         return null;
  171.     }

  173.     /**
  174.      * Calculate the Differential
  175.      * 
  176.      * @param dblVariate Variate at which the derivative is to be calculated
  177.      * @param iOrder Order of the derivative to be computed
  178.      * 
  179.      * @return The Derivative
  180.      */

  182.     public org.drip.numerical.differentiation.Differential differential (
  183.         final double dblVariate,
  184.         final int iOrder)
  185.     {
  186.         try {
  187.             return differential (dblVariate, evaluate (dblVariate), iOrder);
  188.         } catch (java.lang.Exception e) {
  189.             e.printStackTrace();
  190.         }

  192.         return null;
  193.     }

  195.     /**
  196.      * Calculate the derivative as a double
  197.      * 
  198.      * @param dblVariate Variate at which the derivative is to be calculated
  199.      * @param iOrder Order of the derivative to be computed
  200.      * 
  201.      * @return The Derivative
  202.      * 
  203.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  204.      */

  206.     public double derivative (
  207.         final double dblVariate,
  208.         final int iOrder)
  209.         throws java.lang.Exception
  210.     {
  211.         return differential (dblVariate, evaluate (dblVariate), iOrder).calcSlope (true);
  212.     }

  214.     /**
  215.      * Integrate over the given range
  216.      * 
  217.      * @param dblBegin Range Begin 
  218.      * @param dblEnd Range End 
  219.      *  
  220.      * @return The Integrated Value
  221.      * 
  222.      * @throws java.lang.Exception Thrown if evaluation cannot be done
  223.      */

  225.     public double integrate (
  226.         final double dblBegin,
  227.         final double dblEnd)
  228.         throws java.lang.Exception
  229.     {
  230.         return org.drip.numerical.integration.R1ToR1Integrator.Boole (this, dblBegin, dblEnd);
  231.     }

  233.     /**
  234.      * Compute the Maximal Variate and the Corresponding Function Value
  235.      * 
  236.      * @return The Maximal Variate and the Corresponding Function Value
  237.      */

  239.     public org.drip.function.definition.VariateOutputPair maxima()
  240.     {
  241.         R1ToR1 auDerivative = new R1ToR1 (null) {
  242.             @Override public double evaluate (
  243.                 final double dblX)
  244.                 throws java.lang.Exception
  245.             {
  246.                 return derivative (dblX, 1);
  247.             }
  248.         };

  250.         try {
  251.             org.drip.function.r1tor1solver.FixedPointFinder fpf = new
  252.                 org.drip.function.r1tor1solver.FixedPointFinderZheng (0., auDerivative, false);

  254.             org.drip.function.r1tor1solver.FixedPointFinderOutput fpfo = fpf.findRoot();

  256.             if (null == fpfo) return null;

  258.             double dblExtrema = fpfo.getRoot();

  260.             if (0. <= derivative (dblExtrema, 2)) return null;

  262.             return new org.drip.function.definition.VariateOutputPair (new double[] {dblExtrema}, new
  263.                 double[] {evaluate (dblExtrema)});
  264.         } catch (java.lang.Exception e) {
  265.             e.printStackTrace();
  266.         }

  268.         return null;
  269.     }

  271.     /**
  272.      * Compute the Maximum VOP within the Variate Range
  273.      * 
  274.      * @param dblVariateLeft The Range Left End
  275.      * @param dblVariateRight The Range Right End
  276.      * 
  277.      * @return The Maximum VOP
  278.      */

  280.     public org.drip.function.definition.VariateOutputPair maxima (
  281.         final double dblVariateLeft,
  282.         final double dblVariateRight)
  283.     {
  284.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariateLeft) ||
  285.             !org.drip.numerical.common.NumberUtil.IsValid (dblVariateRight) || dblVariateLeft >= dblVariateRight)
  286.             return null;

  288.         org.drip.function.definition.VariateOutputPair vop = maxima();

  290.         if (null != vop) {
  291.             double dblRoot = vop.variates()[0];

  293.             if (dblVariateLeft <= dblRoot && dblVariateRight >= dblRoot) return vop;
  294.         }

  296.         try {
  297.             double dblLeftOutput = evaluate (dblVariateLeft);

  299.             double dblRightOutput = evaluate (dblVariateRight);

  301.             return dblLeftOutput > dblRightOutput ? new org.drip.function.definition.VariateOutputPair
  302.                 (new double[] {dblVariateLeft}, new double[] {dblLeftOutput}) : new
  303.                     org.drip.function.definition.VariateOutputPair (new double[] {dblVariateRight}, new
  304.                         double[] {dblRightOutput});
  305.         } catch (java.lang.Exception e) {
  306.             e.printStackTrace();
  307.         }

  309.         return null;
  310.     }

  312.     /**
  313.      * Compute the Minimal Variate and the Corresponding Function Value
  314.      * 
  315.      * @return The Minimal Variate and the Corresponding Function Value
  316.      */

  318.     public org.drip.function.definition.VariateOutputPair minima()
  319.     {
  320.         R1ToR1 auDerivative = new R1ToR1 (null) {
  321.             @Override public double evaluate (
  322.                 final double dblX)
  323.                 throws java.lang.Exception
  324.             {
  325.                 return derivative (dblX, 1);
  326.             }
  327.         };

  329.         try {
  330.             org.drip.function.r1tor1solver.FixedPointFinder fpf = new
  331.                 org.drip.function.r1tor1solver.FixedPointFinderZheng (0., auDerivative, false);

  333.             org.drip.function.r1tor1solver.FixedPointFinderOutput fpfo = fpf.findRoot();

  335.             if (null == fpfo) return null;

  337.             double dblExtrema = fpfo.getRoot();

  339.             if (0. >= derivative (dblExtrema, 2)) return null;

  341.             return new org.drip.function.definition.VariateOutputPair (new double[] {dblExtrema}, new
  342.                 double[] {evaluate (dblExtrema)});
  343.         } catch (java.lang.Exception e) {
  344.             e.printStackTrace();
  345.         }

  347.         return null;
  348.     }

  350.     /**
  351.      * Compute the Minimum VOP within the Variate Range
  352.      * 
  353.      * @param dblVariateLeft The Range Left End
  354.      * @param dblVariateRight The Range Right End
  355.      * 
  356.      * @return The Minimum VOP
  357.      */

  359.     public org.drip.function.definition.VariateOutputPair minima (
  360.         final double dblVariateLeft,
  361.         final double dblVariateRight)
  362.     {
  363.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariateLeft) ||
  364.             !org.drip.numerical.common.NumberUtil.IsValid (dblVariateRight) || dblVariateLeft >= dblVariateRight)
  365.             return null;

  367.         org.drip.function.definition.VariateOutputPair vop = minima();

  369.         if (null != vop) {
  370.             double dblRoot = vop.variates()[0];

  372.             if (dblVariateLeft <= dblRoot && dblVariateRight >= dblRoot) return vop;
  373.         }

  375.         try {
  376.             double dblLeftOutput = evaluate (dblVariateLeft);

  378.             double dblRightOutput = evaluate (dblVariateRight);

  380.             return dblLeftOutput < dblRightOutput ? new org.drip.function.definition.VariateOutputPair
  381.                 (new double[] {dblVariateLeft}, new double[] {dblLeftOutput}) : new
  382.                     org.drip.function.definition.VariateOutputPair (new double[] {dblVariateRight}, new
  383.                         double[] {dblRightOutput});
  384.         } catch (java.lang.Exception e) {
  385.             e.printStackTrace();
  386.         }

  388.         return null;
  389.     }

  391.     /**
  392.      * Compute the Anti-Derivative Function
  393.      * 
  394.      * @return The Anti-Derivative Function
  395.      */

  397.     public R1ToR1 antiDerivative()
  398.     {
  399.         return null;
  400.     }

  402.     /**
  403.      * Compute the Residue if the Variate is a Pole
  404.      * 
  405.      * @param x Variate
  406.      * 
  407.      * @return The Residue if the Variate is a Pole
  408.      */

  410.     public org.drip.function.definition.PoleResidue poleResidue (
  411.         final double x)
  412.     {
  413.         return null;
  414.     }
  415. }
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