FixedPointSearch.java

package org.drip.sample.numerical;

import org.drip.function.definition.R1ToR1;
import org.drip.function.r1tor1solver.*;
import org.drip.numerical.common.*;
import org.drip.numerical.differentiation.*;
import org.drip.numerical.integration.R1ToR1Integrator;

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

/*!
 * 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 DRIP, a free-software/open-source library for buy/side financial/trading model
 *  	libraries targeting analysts and developers
 *  	https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *  	Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *  	Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *  	Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *  	Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *  	Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * FixedPointSearch contains a sample illustration of usage of the Root Finder Library. It demonstrates the
 * 	fixed point extraction using the following techniques:
 * 	- Newton-Raphson method
 * 	- Bisection Method
 * 	- False Position
 * 	- Quadratic Interpolation
 * 	- Inverse Quadratic Interpolation
 * 	- Ridder's method
 * 	- Brent's method
 * 	- Zheng's method
 *
 * @author Lakshmi Krishnamurthy
 */

public class FixedPointSearch {

	/*
	 * Sample illustrating the Invocation of the Newton-Raphson Open Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeNewton (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderNewton (
				0.,
				func,
				true
			).findRoot();

			System.out.println ("--------\nNEWTON START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nNEWTON FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Bisection Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeBisection (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBracketing (
				0.,
				func,
				null,
				VariateIteratorPrimitive.BISECTION,
				true
			).findRoot();

			System.out.println ("--------\nBISECTION START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nBISECTION FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the False Position Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeFalsePosition (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBracketing (
				0.,
				func,
				null,
				VariateIteratorPrimitive.FALSE_POSITION,
				true
			).findRoot();

			System.out.println ("--------\nFALSE POSITION START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nFALSE POSITION FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Quadratic Interpolation Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeQuadraticInterpolation (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBracketing (
				0.,
				func,
				null,
				VariateIteratorPrimitive.QUADRATIC_INTERPOLATION,
				true
			).findRoot();

			System.out.println ("--------\nQUADRATIC INTERPOLATION START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nQUADRATIC INTERPOLATION FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Inverse Quadratic Interpolation Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeInverseQuadraticInterpolation (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBracketing (
				0.,
				func,
				null,
				VariateIteratorPrimitive.INVERSE_QUADRATIC_INTERPOLATION,
				true
			).findRoot();

			System.out.println ("--------\nINVERSE QUADRATIC INTERPOLATION START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nINVERSE QUADRATIC INTERPOLATION FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Ridder Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeRidder (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBracketing (
				0.,
				func,
				null,
				VariateIteratorPrimitive.RIDDER,
				true
			).findRoot();

			System.out.println ("--------\nRIDDER START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nRIDDER FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Brent's Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeBrent (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderBrent (
				0.,
				func,
				true
			).findRoot();

			System.out.println ("--------\nBRENT START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nBRENT FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	/*
	 * Sample illustrating the Invocation of the Zheng's Bracketing Method
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static final void InvokeZheng (
		final R1ToR1 func)
	{
		try {
			FixedPointFinderOutput fpop = new FixedPointFinderZheng (
				0.,
				func,
				true
			).findRoot();

			System.out.println ("--------\nZHENG START\n-------");

			if (null != fpop && fpop.containsRoot()) {
				System.out.println ("Root: " + FormatUtil.FormatDouble (fpop.getRoot(), 1, 4, 1.));

				System.out.println (fpop.displayString());
			} else
				System.out.println ("Root searched failed!");

			System.out.println ("--------\nZHENG FINISH\n-------\n");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	public static final void main (
		final String[] astrArgs)
	{
		/*
		 * Define and implement the objective function
		 */

		R1ToR1 func = new R1ToR1 (null) {
			@Override public double evaluate (
				final double dblVariate)
				throws Exception
			{
				return Math.cos (dblVariate) - dblVariate * dblVariate * dblVariate;

				/* return dblVariate * dblVariate * dblVariate - 3. * dblVariate * dblVariate + 2. *
					dblVariate;

				return dblVariate * dblVariate * dblVariate + 4. * dblVariate + 4.;

				return 32. * dblVariate * dblVariate * dblVariate * dblVariate * dblVariate * dblVariate
					- 48. * dblVariate * dblVariate * dblVariate * dblVariate + 18. * dblVariate *
						dblVariate - 1.;

				return 1. + 3. * dblVariate - 2. * java.lang.Math.sin (dblVariate); */
			}

			@Override public Differential differential (
				final double dblVariate,
				final double dblOFBase,
				final int iOrder)
			{
				if (0 >= iOrder || 2 < iOrder) return null;

				double dblVariateInfinitesimal = Double.NaN;

				try {
					dblVariateInfinitesimal = _dc.getVariateInfinitesimal (dblVariate);
				} catch (Exception e) {
					e.printStackTrace();

					return null;
				}

				if (1 != iOrder) {
					try {
						return new Differential (dblVariateInfinitesimal, (-1. * Math.cos (dblVariate) - 6. * dblVariate)
							* dblVariateInfinitesimal);

						/* return new Differential (dblVariateInfinitesimal, (6. * dblVariate - 6.) * dblVariateInfinitesimal);

						return new Differential (dblVariateInfinitesimal, (6. * dblVariate) * dblVariateInfinitesimal);

						return new Differential (dblVariateInfinitesimal, (960. * dblVariate * dblVariate * dblVariate *
						 	dblVariate - 576. * dblVariate * dblVariate + 36.) * dblVariateInfinitesimal);

						return new Differential (dblVariateInfinitesimal, (2. * Math.sin (dblVariate)) * dblVariateInfinitesimal); */
					} catch (Exception e) {
						e.printStackTrace();
					}

					return null;
				}

				try {
					return new Differential (dblVariateInfinitesimal, (-1. * Math.sin (dblVariate) - 3. * dblVariate * dblVariate) *
				 		dblVariateInfinitesimal);

					/* return new Differential (dblVariateInfinitesimal, (3. * dblVariate * dblVariate - 6. * dblVariate + 2.) *
					 	dblVariateInfinitesimal);

					return new Differential (dblVariateInfinitesimal, (3. * dblVariate * dblVariate + 4.) * dblVariateInfinitesimal);

					return new Differential (dblVariateInfinitesimal, (192. * dblVariate * dblVariate * dblVariate * dblVariate *
						dblVariate - 192. * dblVariate * dblVariate * dblVariate + 36. * dblVariate) * dblVariateInfinitesimal);

					return new Differential (dblVariateInfinitesimal, (3. - 2. * Math.cos (dblVariate)) * dblVariateInfinitesimal); */
				} catch (Exception e) {
					e.printStackTrace();
				}

				return null;
			}

			@Override public double integrate (
				final double dblBegin,
				final double dblEnd)
				throws Exception
			{
				return R1ToR1Integrator.Boole (this, dblBegin, dblEnd);
			}
		};

		InvokeNewton (func);

		InvokeBisection (func);

		InvokeFalsePosition (func);

		InvokeQuadraticInterpolation (func);

		InvokeInverseQuadraticInterpolation (func);

		InvokeRidder (func);

		InvokeBrent (func);

		InvokeZheng (func);
	}
}