UpperLimitPowerEstimate.java
package org.drip.sample.gammaincomplete;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.integration.NewtonCotesQuadratureGenerator;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.incompletegamma.UpperLimitPowerIntegrand;
/*
* -*- 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>UpperLimitPowerEstimate</i> illustrates the Estimation of the Integral of the Product of the Limit
* Raised to an Exponent and the corresponding Upper Incomplete Gamma Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
* Definite Integrals involving Elementary Functions via Differentiation of Special Functions
* <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
* </li>
* <li>
* Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
* <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
* </li>
* <li>
* Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
* e<sup>iπx</sup> x<sup>(1/x)</sup> between 1 and ∞
* https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
* </li>
* <li>
* National Institute of Standards and Technology (2019a): Incomplete Gamma and Related Functions
* https://dlmf.nist.gov/8
* </li>
* <li>
* Wikipedia (2019): Incomplete Gamma Function
* https://en.wikipedia.org/wiki/Incomplete_gamma_function
* </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">Function</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gammaincomplete/README.md">Estimates of Incomplete Gamma Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class UpperLimitPowerEstimate
{
private static final void QuadratureComparison (
final UpperLimitPowerIntegrand upperLimitPowerIntegrand,
final double s,
final double limitExponent,
final double[] leftArray,
final double[] rightArray,
final int intermediatePointCount)
throws Exception
{
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| QUADRATURE COMPARISON - s => " + FormatUtil.FormatDouble (s, 1, 1, 1.) + " | Exponent => " + FormatUtil.FormatDouble (limitExponent, 1, 1, 1.));
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - s ||");
System.out.println ("\t| - [Comparison Pair] ||");
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
for (double left : leftArray)
{
String display = "\t|" + FormatUtil.FormatDouble (left, 1, 1, 1.) + " => ";
for (double right : rightArray)
{
display = display + "[" + FormatUtil.FormatDouble (
NewtonCotesQuadratureGenerator.Zero_PlusOne (
left,
right,
intermediatePointCount
).integrate (upperLimitPowerIntegrand), 4, 2, 1.
) + " - " + FormatUtil.FormatDouble (
upperLimitPowerIntegrand.integrate (
left,
right
), 4, 2, 1.
) + "] |";
}
System.out.println (display + "|");
}
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int intermediatePointCount = 100;
double[] leftArray =
{
1.,
2.,
3.,
4.,
5.,
};
double[] rightArray =
{
10.,
15.,
20.,
25.,
30.,
};
double[] sArray =
{
3.,
4.,
5.,
6.,
7.,
};
double[] limitExponentArray =
{
3.,
4.,
5.,
6.,
7.,
};
for (double s : sArray)
{
for (double limitExponent : limitExponentArray)
{
UpperLimitPowerIntegrand upperLimitPowerIntegrand = new UpperLimitPowerIntegrand (
null,
s,
limitExponent
);
QuadratureComparison (
upperLimitPowerIntegrand,
s,
limitExponent,
leftArray,
rightArray,
intermediatePointCount
);
}
}
EnvManager.TerminateEnv();
}
}