GeneralizedMidPointQuadrature.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>GeneralizedMidPointQuadrature</i> computes the R<sup>1</sup> Numerical Estimate of a Function
* Quadrature using the Generalized Mid-Point Scheme. 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 GeneralizedMidPointQuadrature
{
private int _nodeCount = -1;
private int _seriesTermCount = -1;
private org.drip.function.definition.R1ToR1 _r1ToR1 = null;
/**
* GeneralizedMidPointQuadrature Constructor
*
* @param r1ToR1 R<sup>1</sup> To R<sup>1</sup> Integrand
* @param nodeCount Quadrature Node Count
* @param seriesTermCount Series Term Count
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public GeneralizedMidPointQuadrature (
final org.drip.function.definition.R1ToR1 r1ToR1,
final int nodeCount,
final int seriesTermCount)
throws java.lang.Exception
{
if (null == (_r1ToR1 = r1ToR1) ||
1 > (_nodeCount = nodeCount) ||
0 >= (_seriesTermCount = seriesTermCount))
{
throw new java.lang.Exception ("GeneralizedMidPointQuadrature Constructor => Invalid Inputs");
}
}
/**
* Retrieve the R<sup>1</sup> To R<sup>1</sup> Integrand
*
* @return The R<sup>1</sup> To R<sup>1</sup> Integrand
*/
public org.drip.function.definition.R1ToR1 r1ToR1()
{
return _r1ToR1;
}
/**
* Retrieve the Quadrature Node Count
*
* @return The Quadrature Node Count
*/
public int nodeCount()
{
return _nodeCount;
}
/**
* Retrieve the Series Term Count
*
* @return The Series Term Count
*/
public int seriesTermCount()
{
return _seriesTermCount;
}
/**
* Integrate the Integrand from Left Through Right
*
* @param left Left Limit
* @param right Right Limit
*
* @return The Integrand Quadrature
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double integrate (
final double left,
final double right)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
!org.drip.numerical.common.NumberUtil.IsValid (right))
{
throw new java.lang.Exception ("GeneralizedMidPointQuadrature::integrate => Invalid Inputs");
}
if (left == right)
{
return 0.;
}
boolean flip = false;
double quadrature = 0.;
double leftLimit = left;
double rightLimit = right;
if (leftLimit > rightLimit)
{
flip = true;
leftLimit = right;
rightLimit = left;
}
double m2 = 2. * _nodeCount;
double space = rightLimit - leftLimit;
for (int nodeIndex = 1; nodeIndex <= _nodeCount; ++nodeIndex)
{
for (int seriesTermIndex = 0; seriesTermIndex <= _seriesTermCount; ++seriesTermIndex)
{
int seriesTermIndex2 = 2 * seriesTermIndex;
int seriesTermIndex2Plus1 = seriesTermIndex2 + 1;
quadrature = quadrature + _r1ToR1.derivative (
space * (nodeIndex - 0.5) / _nodeCount + leftLimit,
2 * seriesTermIndex
) / org.drip.numerical.common.NumberUtil.Factorial (seriesTermIndex2Plus1) /
java.lang.Math.pow (
m2,
seriesTermIndex2Plus1
);
}
}
return (flip ? -1. : 1.) * space * quadrature;
}
}