IntegrandQuadrature.java

package org.drip.sample.numerical;

import org.drip.function.definition.R1ToR1;
import org.drip.function.r1tor1.*;
import org.drip.numerical.common.*;
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
 * 
 *  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.
 */

/**
 * IntegrandQuadrature shows samples for the following routines for integrating the objective function:
 * 	- Mid-Point Scheme
 * 	- Trapezoidal Scheme
 * 	- Simpson/Simpson38 schemes
 * 	- Boole Scheme
 * 
 * @author Lakshmi Krishnamurthy
 */

public class IntegrandQuadrature {

	/*
	 * Compute the Integrand Quadrature for the specified Univariate Function using the various methods.
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static void ComputeQuadrature (
		final R1ToR1 au,
		final double dblActual,
		final double dblStart,
		final double dblEnd)
		throws Exception
	{
		int iRightDecimal = 8;

		System.out.println ("\t\tActual      : " +
			FormatUtil.FormatDouble (dblActual, 1, iRightDecimal, 1.)
		);

		System.out.println ("\t\tLinear      : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.LinearQuadrature (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);

		System.out.println ("\t\tMidPoint     : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.MidPoint (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);

		System.out.println ("\t\tTrapezoidal  : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.Trapezoidal (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);

		System.out.println ("\t\tSimpson      : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.Simpson (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);

		System.out.println ("\t\tSimpson 38   : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.Simpson38 (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);

		System.out.println ("\t\tBoole        : " +
			FormatUtil.FormatDouble (
				R1ToR1Integrator.Boole (
					au,
					dblStart,
					dblEnd
				),
				1,
				iRightDecimal,
				1.
			)
		);
	}

	/*
	 * Compute the Integrand Quadrature for the various Univariate Functions using the different methods.
	 * 
	 * 	WARNING: Insufficient Error Checking, so use caution
	 */

	private static void IntegrandQuadratureSample()
		throws Exception
	{
		double dblStart = 0.;
		double dblEnd = 1.;

		R1ToR1 auExp = new ExponentialTension (
			Math.E,
			1.
		);

		System.out.println ("\n\t-------------------------------------\n");

		ComputeQuadrature (
			auExp,
			auExp.evaluate (dblEnd) - auExp.evaluate (dblStart),
			dblStart,
			dblEnd
		);

		System.out.println ("\n\t-------------------------------------\n");

		R1ToR1 au1 = new R1ToR1 (null) {
			@Override public double evaluate (
				final double dblVariate)
				throws Exception
			{
				return Math.cos (dblVariate) - dblVariate * dblVariate * dblVariate;
			}
		};

		ComputeQuadrature (
			au1,
			Math.sin (dblEnd) - Math.sin (dblStart) - 0.25 * (dblEnd * dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart * dblStart),
			dblStart,
			dblEnd
		);

		System.out.println ("\n\t-------------------------------------\n");

		R1ToR1 au2 = new R1ToR1 (null) {
			@Override public double evaluate (
				final double dblVariate)
				throws Exception
			{
				return dblVariate * dblVariate * dblVariate - 3. * dblVariate * dblVariate + 2. * dblVariate;
			}
		};

		ComputeQuadrature (
			au2,
			0.25 * (dblEnd * dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart * dblStart) -
				(dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart) +
				(dblEnd * dblEnd - dblStart * dblStart),
			dblStart,
			dblEnd
		);

		System.out.println ("\n\t-------------------------------------\n");
	}

	public static void main (
		final String astrArgs[])
		throws Exception
	{
		IntegrandQuadratureSample();
	}
}