FixedPointFinder.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>FixedPointFinder</i> is the base abstract class that is implemented by customized invocations, e.g.,
 * Newton's method, or any of the bracketing methodologies.
 * <br><br>
 * FixedPointFinder invokes the core routine for determining the fixed point from the goal. The
 *  ExecutionControl determines the execution termination. The initialization heuristics implements
 *  targeted customization of the search.
 * <br><br>
 * FixedPointFinder main flow comprises of the following steps:
 * <br>
 * <ul>
 *  <li>
 *      Initialize the fixed point search zone by determining either a) the brackets, or b) the starting
 *          variate.
 *  </li>
 *  <li>
 *      Compute the absolute OF tolerance that establishes the attainment of the fixed point.
 *  </li>
 *  <li>
 *      Launch the variate iterator that iterates the variate.
 *  </li>
 *  <li>
 *      Iterate until the desired tolerance has been attained
 *  </li>
 *  <li>
 *      Return the fixed point output.
 *  </li>
 * </ul>
 * <br><br>
 * Fixed point finders that derive from this provide implementations for the following:
 * <br>
 * <ul>
 *  <li>
 *  - Variate initialization: They may choose either bracketing initializer, or the convergence initializer -
 *      functionality is provided for both in this module.
 *  </li>
 *  <li>
 *  - Variate Iteration: Variates are iterated using a) any of the standard primitive built-in variate
 *      iterators (or custom ones), or b) a variate selector scheme for each iteration.
 *  </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 abstract class FixedPointFinder {
    protected boolean _bWhine = false;
    protected double _dblOFGoal = java.lang.Double.NaN;
    protected org.drip.function.r1tor1solver.ExecutionControl _ec = null;
    protected org.drip.function.definition.R1ToR1 _of = null;

    protected FixedPointFinder (
        final double dblOFGoal,
        final org.drip.function.definition.R1ToR1 of,
        final org.drip.function.r1tor1solver.ExecutionControl ec,
        final boolean bWhine)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (_dblOFGoal = dblOFGoal) || null == (_of = of))
            throw new java.lang.Exception ("FixedPointFinder constructor: Invalid inputs");

        _ec = new org.drip.function.r1tor1solver.ExecutionControl (of, null);

        _bWhine = bWhine;
    }

    protected abstract boolean iterateVariate (
        final org.drip.function.r1tor1solver.IteratedVariate vi,
        final org.drip.function.r1tor1solver.FixedPointFinderOutput rfop);

    protected abstract org.drip.function.r1tor1solver.ExecutionInitializationOutput initializeVariateZone (
        final org.drip.function.r1tor1solver.InitializationHeuristics ih);

    /**
     * Invoke the solution 1D root finding sequence
     * 
     * @param ih Optional Initialization Heuristics
     * 
     * @return Root finder Solution Object for the variate
     */

    public org.drip.function.r1tor1solver.FixedPointFinderOutput findRoot (
        final org.drip.function.r1tor1solver.InitializationHeuristics ih)
    {
        org.drip.function.r1tor1solver.FixedPointFinderOutput rfop = null;

        org.drip.function.r1tor1solver.ExecutionInitializationOutput eiop = initializeVariateZone (ih);

        if (null == eiop || !eiop.isDone()) return null;

        try {
            rfop = new org.drip.function.r1tor1solver.FixedPointFinderOutput (eiop);

            if (!rfop.incrOFCalcs()) return rfop;

            double dblOF = _of.evaluate (eiop.getStartingVariate());

            double dblAbsoluteTolerance = _ec.calcAbsoluteOFTolerance (dblOF);

            double dblAbsoluteConvergence = _ec.calcAbsoluteVariateConvergence (eiop.getStartingVariate());

            org.drip.function.r1tor1solver.IteratedVariate iv = new
                org.drip.function.r1tor1solver.IteratedVariate (eiop, dblOF);

            int iNumIterationsPending = _ec.getNumIterations();

            while (!_ec.hasOFReachedGoal (dblAbsoluteTolerance, iv.getOF(), _dblOFGoal)) {
                double dblPrevVariate = iv.getVariate();

                if (!rfop.incrIterations() || 0 == --iNumIterationsPending || !iterateVariate (iv, rfop))
                    return rfop;

                if (_ec.isVariateConvergenceCheckEnabled() && (java.lang.Math.abs (dblPrevVariate -
                    iv.getVariate()) < dblAbsoluteConvergence))
                    break;
            }

            rfop.setRoot (iv.getVariate());
        } catch (java.lang.Exception e) {
            if (_bWhine) e.printStackTrace();
        }

        return rfop;
    }

    /**
     * Invoke the solution 1D root finding sequence
     * 
     * @return Root finder Solution Object for the variate
     */

    public org.drip.function.r1tor1solver.FixedPointFinderOutput findRoot()
    {
        return findRoot (null);
    }
}