ERFIntegrand.java

package org.drip.sample.newtoncotes;

import java.util.Map;

import org.drip.function.definition.R1ToR1;
import org.drip.function.e2erf.BuiltInEntry;
import org.drip.function.e2erf.ErrorFunction;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.integration.NewtonCotesQuadratureGenerator;
import org.drip.service.env.EnvManager;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
 *      FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three main modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning Library
 *  - Numerical Optimizer Library
 *  - Machine Learning Library
 *  - Spline Builder Library
 * 
 *  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
 *  - 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>ERFIntegrand</i> computes the R<sup>1</sup> Numerical Estimate of the erf Integrand using Newton-Cotes
 * Grids. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): <i>Frank-Wolfe Bayesian
 *              Quadrature: Probabilistic Integration with Theoretical Guarantees</i> <b>arXiv</b>
 *      </li>
 *      <li>
 *          Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): <i>Computer Methods for Mathematical
 *              Computation</i> <b>Prentice Hall</b> Englewood Cliffs NJ
 *      </li>
 *      <li>
 *          Leader, J. J. (2004): <i>Numerical Analysis and Scientific Computation</i> <b>Addison Wesley</b>
 *      </li>
 *      <li>
 *          Stoer, J., and R. Bulirsch (1980): <i>Introduction to Numerical Analysis</i>
 *              <b>Springer-Verlag</b> New York
 *      </li>
 *      <li>
 *          Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/newtoncotes/README.md">R<sup>1</sup> Newton-Cotes Quadrature Schemes</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ERFIntegrand
{

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        R1ToR1 erfIntegrand = new ErrorFunction (
            null,
            null
        ).integrand();

        int nodeCount10 = 10;
        int nodeCount50 = 50;
        int nodeCount100 = 100;

        Map<Double, BuiltInEntry> builtInTable = BuiltInEntry.Table();

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

        System.out.println ("\t|                     Newton Cotes erf Estimate                      ||");

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

        System.out.println ("\t|        L -> R:                                                     ||");

        System.out.println ("\t|                - x                                                 ||");

        System.out.println ("\t|                - Built-in Estimate                                 ||");

        System.out.println ("\t|                - Newton Cotes Estimate (10 Nodes)                  ||");

        System.out.println ("\t|                - Newton Cotes Estimate (50 Nodes)                  ||");

        System.out.println ("\t|                - Newton Cotes Estimate (100 Nodes)                 ||");

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

        for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
        {
            double x = builtInTableEntry.getKey();

            double erfTable = builtInTableEntry.getValue().erf();

            double erfEstimate10 = NewtonCotesQuadratureGenerator.MinusOne_PlusOne (
                0.,
                x,
                nodeCount10
            ).integrate (erfIntegrand);

            double erfEstimate50 = NewtonCotesQuadratureGenerator.MinusOne_PlusOne (
                0.,
                x,
                nodeCount50
            ).integrate (erfIntegrand);

            double erfEstimate100 = NewtonCotesQuadratureGenerator.MinusOne_PlusOne (
                0.,
                x,
                nodeCount100
            ).integrate (erfIntegrand);

            System.out.println (
                "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
                FormatUtil.FormatDouble (erfTable, 1, 9, 1.) + " | " +
                FormatUtil.FormatDouble (erfEstimate10, 1, 9, 1.) + " | " +
                FormatUtil.FormatDouble (erfEstimate50, 1, 9, 1.) + " | " +
                FormatUtil.FormatDouble (erfEstimate100, 1, 9, 1.) + " ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}