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);
}
}