FixedPointFinderNewton.java

package org.drip.function.r1tor1solver;

/*
 * -*- 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
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * Copyright (C) 2014 Lakshmi Krishnamurthy
 * Copyright (C) 2013 Lakshmi Krishnamurthy
 * Copyright (C) 2012 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>FixedPointFinderNewton</i> customizes the FixedPointFinder for Open (Newton's) fixed point finder
 *  functionality.
 * <br><br>
 * FixedPointFinderNewton applies the following customization:
 * <br>
 * <ul>
 *  <li>
 *      Initializes the fixed point finder by computing a starting variate in the convergence zone
 *  </li>
 *  <li>
 *      Iterating the next search variate using the Newton's method.
 *  </li>
 * </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
 *      <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>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/r1tor1solver/README.md">Built-in R<sup>1</sup> To R<sup>1</sup> Solvers</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class FixedPointFinderNewton extends org.drip.function.r1tor1solver.FixedPointFinder {
    private org.drip.function.r1tor1solver.ExecutionInitializer _ei = null;

    private double calcVariateOFSlope (
        final double dblVariate)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariate))
            throw new java.lang.Exception ("FixedPointFinderNewton::calcVariateOFSlope => Invalid input!");

        org.drip.numerical.differentiation.Differential diff = _of.differential (dblVariate, 1);

        if (null == diff)
            throw new java.lang.Exception
                ("FixedPointFinderNewton::calcVariateTargetSlope => Cannot evaluate Derivative for variate "
                    + dblVariate);

        return diff.calcSlope (false);
    }

    @Override protected boolean iterateVariate (
        final org.drip.function.r1tor1solver.IteratedVariate vi,
        final org.drip.function.r1tor1solver.FixedPointFinderOutput rfop)
    {
        if (null == vi || null == rfop) return false;

        double dblVariate = vi.getVariate();

        try {
            double dblVariateNext = dblVariate - calcVariateOFSlope (dblVariate) * vi.getOF();

            return vi.setVariate (dblVariateNext) && vi.setOF (_of.evaluate (dblVariateNext)) &&
                rfop.incrOFDerivCalcs() && rfop.incrOFCalcs();
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return false;
    }

    @Override protected org.drip.function.r1tor1solver.ExecutionInitializationOutput initializeVariateZone (
        final org.drip.function.r1tor1solver.InitializationHeuristics ih)
    {
        return _ei.initializeBracket (ih, _dblOFGoal);
    }

    /**
     * FixedPointFinderNewton constructor
     * 
     * @param dblOFGoal OF Goal
     * @param of Objective Function
     * @param bWhine TRUE - Balk on Encountering Exception
     * 
     * @throws java.lang.Exception Propogated from underneath
     */

    public FixedPointFinderNewton (
        final double dblOFGoal,
        final org.drip.function.definition.R1ToR1 of,
        final boolean bWhine)
        throws java.lang.Exception
    {
        super (dblOFGoal, of, null, bWhine);

        _ei = new org.drip.function.r1tor1solver.ExecutionInitializer (_of, null, true);
    }
}