NewtonFixedPointFinder.java

package org.drip.function.rdtor1solver;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * <i>NewtonFixedPointFinder</i> generates the Iterators for solving R<sup>d</sup> To R<sup>1</sup>
 * Convex/Non-Convex Functions Using the Multivariate Newton Method.
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/README.md">Function</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/rdtor1solver/README.md">R<sup>d</sup> To R<sup>1</sup> Solver</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class NewtonFixedPointFinder
    extends org.drip.function.rdtor1solver.FixedRdFinder
{

    /**
     * NewtonFixedPointFinder Constructor
     * 
     * @param objectiveFunction The Objective Function
     * @param lineStepEvolutionControl The Line Step Evolution Control
     * @param convergenceControl Convergence Control Parameters
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public NewtonFixedPointFinder (
        final org.drip.function.definition.RdToR1 objectiveFunction,
        final org.drip.function.rdtor1descent.LineStepEvolutionControl lineStepEvolutionControl,
        final org.drip.function.rdtor1solver.ConvergenceControl convergenceControl)
        throws java.lang.Exception
    {
        super (
            objectiveFunction,
            lineStepEvolutionControl,
            convergenceControl
        );
    }

    @Override public org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier increment (
        final org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier curentVariateConstraint)
    {
        if (null == curentVariateConstraint)
        {
            return null;
        }

        double[] variateArray = curentVariateConstraint.variateArray();

        org.drip.function.definition.RdToR1 objectiveFunction = objectiveFunction();

        double[] variateIncrementArray = org.drip.numerical.linearalgebra.Matrix.Product (
            org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination (
                objectiveFunction.hessian (
                    variateArray
                )
            ),
            objectiveFunction.jacobian (
                variateArray
            )
        );

        if (null == variateIncrementArray)
        {
            return null;
        }

        int variateDimension = variateIncrementArray.length;

        for (int variateDimensionIndex = 0;
            variateDimensionIndex < variateDimension;
            ++variateDimensionIndex)
        {
            variateIncrementArray[variateDimensionIndex] =
                -1. * variateIncrementArray[variateDimensionIndex];
        }

        try
        {
            return new org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier (
                true,
                variateIncrementArray,
                null
            );
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();
        }

        return null;
    }

    @Override public org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier next (
        final org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier curentVariateConstraint,
        final org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier
            incrementalVariateConstraint,
        final double incrementFraction)
    {
        return org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier.Add (
            curentVariateConstraint,
            incrementalVariateConstraint,
            incrementFraction,
            null
        );
    }
}