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);
    }
}