QuadratureEstimator.java

package org.drip.numerical.integration;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 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>QuadratureEstimator</i> estimates an Integrand Quadrature using the Array of Transformed Quadrature
 * Abscissa and their corresponding Weights. 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/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/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/integration/README.md">R<sup>1</sup> R<sup>d</sup> Numerical Integration Schemes</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class QuadratureEstimator
{
    private org.drip.numerical.common.Array2D _nodeWeightArray = null;
    private org.drip.numerical.integration.AbscissaTransform _abscissaTransform = null;

    /**
     * QuadratureEstimator Constructor
     * 
     * @param abscissaTransform The Abscissa Transform
     * @param nodeWeightArray Array of the Nodes and Weights
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public QuadratureEstimator (
        final org.drip.numerical.integration.AbscissaTransform abscissaTransform,
        final org.drip.numerical.common.Array2D nodeWeightArray)
        throws java.lang.Exception
    {
        if (null == (_abscissaTransform = abscissaTransform) ||
            null == (_nodeWeightArray = nodeWeightArray))
        {
            throw new java.lang.Exception ("QuadratureEstimator Constructor => Invalid Inputs");
        }
    }

    /**
     * Retrieve the Abscissa Transform
     * 
     * @return The Abscissa Transform
     */

    public org.drip.numerical.integration.AbscissaTransform abscissaTransform()
    {
        return _abscissaTransform;
    }

    /**
     * Retrieve the 2D Array of Nodes and Weights
     * 
     * @return 2D Array of Nodes and Weights
     */

    public org.drip.numerical.common.Array2D nodeWeightArray()
    {
        return _nodeWeightArray;
    }

    /**
     * Integrate the Specified Integrand over the Nodes
     * 
     * @param r1ToR1Integrand The R<sup>1</sup> To R<sup>1</sup> Integrand
     * 
     * @return The Integrand Quadrature
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public double integrate (
        final org.drip.function.definition.R1ToR1 r1ToR1Integrand)
        throws java.lang.Exception
    {
        if (null == r1ToR1Integrand)
        {
            throw new java.lang.Exception ("QuadratureEstimator::integrate => Invalid Inputs");
        }

        double[] weightArray = _nodeWeightArray.y();

        double[] abscissaArray = _nodeWeightArray.x();

        double quadrature = 0.;
        int nodeCount = abscissaArray.length;

        double quadratureScale = _abscissaTransform.quadratureScale();

        org.drip.function.definition.R1ToR1 r1PointValueScale = _abscissaTransform.pointValueScale();

        org.drip.function.definition.R1ToR1 r1ToR1VariateChange = _abscissaTransform.variateChange();

        for (int nodeIndex = 0; nodeIndex < nodeCount; ++nodeIndex)
        {
            quadrature = quadrature + quadratureScale * weightArray[nodeIndex] *
                r1PointValueScale.evaluate (abscissaArray[nodeIndex]) *
                r1ToR1Integrand.evaluate (r1ToR1VariateChange.evaluate (abscissaArray[nodeIndex]));
        }

        return quadrature;
    }
}