LagrangianMultivariate.java

  1. package org.drip.function.rdtor1;

  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>LagrangianMultivariate</i> implements a R<sup>d</sup> To R<sup>1</sup> Multivariate Function along
  82.  * with the specified Set of Equality Constraints.
  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/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  89.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/rdtor1/README.md">Built-in R<sup>d</sup> To R<sup>1</sup> Functions</a></li>
  90.  *  </ul>
  91.  *
  92.  * @author Lakshmi Krishnamurthy
  93.  */

  95. public class LagrangianMultivariate extends org.drip.function.definition.RdToR1 {
  96.     private org.drip.function.definition.RdToR1 _RdToR1Objective = null;
  97.     private org.drip.function.definition.RdToR1[] _aRdToR1EqualityConstraint = null;

  99.     /**
  100.      * LagrangianMultivariate Constructor
  101.      * 
  102.      * @param RdToR1Objective The Objective Function
  103.      * @param aRdToR1EqualityConstraint Array of Equality Constraint Functions
  104.      * 
  105.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  106.      */

  108.     public LagrangianMultivariate (
  109.         final org.drip.function.definition.RdToR1 RdToR1Objective,
  110.         final org.drip.function.definition.RdToR1[] aRdToR1EqualityConstraint)
  111.         throws java.lang.Exception
  112.     {
  113.         super (null);

  115.         if (null == (_RdToR1Objective = RdToR1Objective))
  116.             throw new java.lang.Exception ("LagrangianMultivariate Constructor => Invalid Inputs");

  118.         _aRdToR1EqualityConstraint = aRdToR1EqualityConstraint;
  119.     }

  121.     /**
  122.      * Retrieve the Objective R^d To R^1 Function Instance
  123.      * 
  124.      * @return The Objective R^d To R^1 Function Instance
  125.      */

  127.     public org.drip.function.definition.RdToR1 objectiveFunction()
  128.     {
  129.         return _RdToR1Objective;
  130.     }

  132.     /**
  133.      * Retrieve the Array of the Constraint R^d To R^1 Function Instances
  134.      * 
  135.      * @return The Array of Constraint R^d To R^1 Function Instances
  136.      */

  138.     public org.drip.function.definition.RdToR1[] constraintFunctions()
  139.     {
  140.         return _aRdToR1EqualityConstraint;
  141.     }

  143.     /**
  144.      * Retrieve the Objective Function Dimension
  145.      * 
  146.      * @return The Objective Function Dimension
  147.      */

  149.     public int objectiveFunctionDimension()
  150.     {
  151.         return _RdToR1Objective.dimension();
  152.     }

  154.     /**
  155.      * Retrieve the Constraint Function Dimension
  156.      * 
  157.      * @return The Constraint Function Dimension
  158.      */

  160.     public int constraintFunctionDimension()
  161.     {
  162.         return null == _aRdToR1EqualityConstraint ? 0 : _aRdToR1EqualityConstraint.length;
  163.     }

  165.     @Override public int dimension()
  166.     {
  167.         return objectiveFunctionDimension() + constraintFunctionDimension();
  168.     }

  170.     @Override public double evaluate (
  171.         final double[] adblVariate)
  172.         throws java.lang.Exception
  173.     {
  174.         org.drip.function.rdtor1.ObjectiveConstraintVariateSet ocvs =
  175.             org.drip.function.rdtor1.ObjectiveConstraintVariateSet.Partition (adblVariate,
  176.                 objectiveFunctionDimension());

  178.         if (null == ocvs)
  179.             throw new java.lang.Exception ("LagrangianMultivariate::evaluate => Invalid Inputs");

  181.         double[] adblConstraintVariate = ocvs.constraintVariates();

  183.         double[] adblObjectiveVariate = ocvs.objectiveVariates();

  185.         int iNumConstraint = adblConstraintVariate.length;

  187.         double dblValue = _RdToR1Objective.evaluate (adblObjectiveVariate);

  189.         for (int i = 0; i < iNumConstraint; ++i)
  190.             dblValue += adblConstraintVariate[i] * _aRdToR1EqualityConstraint[i].evaluate
  191.                 (adblObjectiveVariate);

  193.         return dblValue;
  194.     }

  196.     @Override public double[] jacobian (
  197.         final double[] adblVariate)
  198.     {
  199.         int iObjectiveDimension = objectiveFunctionDimension();

  201.         int iConstraintDimension = constraintFunctionDimension();

  203.         double[] adblObjectiveVariate = null;
  204.         double[] adblConstraintVariate = null;
  205.         double[][] aadblConstraintJacobian = null;
  206.         double[] adblJacobian = new double[iObjectiveDimension + iConstraintDimension];

  208.         if (0 == iConstraintDimension)
  209.             adblObjectiveVariate = adblVariate;
  210.         else {
  211.             org.drip.function.rdtor1.ObjectiveConstraintVariateSet ocvs =
  212.                 org.drip.function.rdtor1.ObjectiveConstraintVariateSet.Partition (adblVariate,
  213.                     iObjectiveDimension);

  215.             if (null == ocvs) return null;

  217.             adblObjectiveVariate = ocvs.objectiveVariates();

  219.             adblConstraintVariate = ocvs.constraintVariates();
  220.         }

  222.         double[] adblObjectiveJacobian = _RdToR1Objective.jacobian (adblObjectiveVariate);

  224.         if (null == adblObjectiveJacobian) return null;

  226.         if (0 != iConstraintDimension) aadblConstraintJacobian = new double[iConstraintDimension][];

  228.         for (int i = 0; i < iConstraintDimension; ++i) {
  229.             if (null == (aadblConstraintJacobian[i] = _aRdToR1EqualityConstraint[i].jacobian
  230.                 (adblObjectiveVariate)))
  231.                 return null;

  233.             try {
  234.                 adblJacobian[iObjectiveDimension + i] = _aRdToR1EqualityConstraint[i].evaluate
  235.                     (adblObjectiveVariate);
  236.             } catch (java.lang.Exception e) {
  237.                 e.printStackTrace();

  239.                 return null;
  240.             }
  241.         }

  243.         for (int i = 0; i < iObjectiveDimension; ++i) {
  244.             adblJacobian[i] = adblObjectiveJacobian[i];

  246.             for (int j = 0; j < iConstraintDimension; ++j)
  247.                 adblJacobian[i] += adblConstraintVariate[j] * aadblConstraintJacobian[j][i];
  248.         }

  250.         return adblJacobian;
  251.     }

  253.     @Override public double[][] hessian (
  254.         final double[] adblVariate)
  255.     {
  256.         int iObjectiveDimension = objectiveFunctionDimension();

  258.         int iConstraintDimension = constraintFunctionDimension();

  260.         double[] adblObjectiveVariate = null;
  261.         double[] adblConstraintVariate = null;

  263.         if (0 == iConstraintDimension)
  264.             adblObjectiveVariate = adblVariate;
  265.         else {
  266.             org.drip.function.rdtor1.ObjectiveConstraintVariateSet ocvs =
  267.                 org.drip.function.rdtor1.ObjectiveConstraintVariateSet.Partition (adblVariate,
  268.                     iObjectiveDimension);

  270.             if (null == ocvs) return null;

  272.             adblObjectiveVariate = ocvs.objectiveVariates();

  274.             adblConstraintVariate = ocvs.constraintVariates();
  275.         }

  277.         double[][] aadblObjectiveHessian = _RdToR1Objective.hessian (adblObjectiveVariate);

  279.         double[][] aadblConstraintJacobian = null;
  280.         double[][][] aaadblConstraintHessian = null;
  281.         int iDimension = iObjectiveDimension + iConstraintDimension;
  282.         double[][] aadblHessian = new double[iDimension][iDimension];

  284.         if (0 != iConstraintDimension) {
  285.             aadblConstraintJacobian = new double[iConstraintDimension][];
  286.             aaadblConstraintHessian = new double[iConstraintDimension][][];
  287.         }

  289.         for (int i = 0; i < iConstraintDimension; ++i) {
  290.             if (null == (aaadblConstraintHessian[i] = _aRdToR1EqualityConstraint[i].hessian
  291.                 (adblObjectiveVariate)))
  292.                 return null;
  293.         }

  295.         for (int i = 0; i < iObjectiveDimension; ++i) {
  296.             for (int j = 0; j < iObjectiveDimension; ++j) {
  297.                 aadblHessian[i][j] = aadblObjectiveHessian[i][j];

  299.                 for (int k = 0; k < iConstraintDimension; ++k)
  300.                     aadblHessian[i][j] += adblConstraintVariate[k] * aaadblConstraintHessian[k][i][j];
  301.             }
  302.         }

  304.         for (int i = 0; i < iConstraintDimension; ++i) {
  305.             for (int j = 0; j < iConstraintDimension; ++j)
  306.                 aadblHessian[i + iObjectiveDimension][j + iObjectiveDimension] = 0.;

  308.             if (null == (aadblConstraintJacobian[i] = _aRdToR1EqualityConstraint[i].jacobian
  309.                 (adblObjectiveVariate)))
  310.                 return null;
  311.         }

  313.         for (int i = 0; i < iConstraintDimension; ++i) {
  314.             for (int j = 0; j < iObjectiveDimension; ++j) {
  315.                 aadblHessian[iObjectiveDimension + i][j] = aadblConstraintJacobian[i][j];
  316.                 aadblHessian[j][iObjectiveDimension + i] = aadblConstraintJacobian[i][j];
  317.             }
  318.         }

  320.         return aadblHessian;
  321.     }
  322. }
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