EulerQuadratureEstimate.java
package org.drip.sample.hypergeometric;
import org.drip.function.definition.R2ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.beta.LogGammaEstimator;
import org.drip.specialfunction.definition.HypergeometricParameters;
import org.drip.specialfunction.hypergeometric.EulerQuadratureEstimator;
/*
* -*- 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>EulerQuadratureEstimate</i> estimates the Hyper-geometric Function using the Euler Integral
* Representation. The References are:
*
* <br><br>
* <ul>
* <li>
* Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
* on Mathematical Analysis</i> <b>13 (2)</b> 295-308
* </li>
* <li>
* Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
* Computation</i> <b>20 (4)</b> 399-417
* </li>
* <li>
* Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
* Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
* 293-300
* </li>
* <li>
* National Institute of Standards and Technology (2019): Hyper-geometric Function
* https://dlmf.nist.gov/15
* </li>
* <li>
* Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_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/hypergeometric/README.md">Estimates of Hyper-geometric Function</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class EulerQuadratureEstimate
{
private static final void Hypergeometric (
final double a,
final double b,
final double c,
final R2ToR1 logBetaEstimator,
final int quadratureCount,
final double[] zArray)
throws Exception
{
EulerQuadratureEstimator eulerQuadratureEstimator = new EulerQuadratureEstimator (
new HypergeometricParameters (
a,
b,
c
),
logBetaEstimator,
quadratureCount
);
for (double z : zArray)
{
System.out.println ("\t| {a=" +
FormatUtil.FormatDouble (a, 1, 2, 1., false) + ", b=" +
FormatUtil.FormatDouble (b, 1, 2, 1., false) + "; c=" +
FormatUtil.FormatDouble (c, 1, 2, 1., false) + "; z=" +
FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => " +
FormatUtil.FormatDouble (eulerQuadratureEstimator.evaluate (z), 2, 10, 1., false) + " ||"
);
}
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] aArray =
{
1.,
2.,
};
double[] bArray =
{
3.,
4.,
};
double[] cArray =
{
5.,
6.,
};
double[] zArray =
{
-1.00,
-0.75,
-0.50,
-0.25,
0.00,
0.25,
0.50,
0.75,
1.00
};
int logBetaTermCount = 1000;
int hypergeometricQuadratureCount = 10000;
R2ToR1 logBetaEstimator = LogGammaEstimator.Weierstrass (logBetaTermCount);
System.out.println ("\t|----------------------------------------------------||");
System.out.println ("\t| HYPER-GEOMETRIC FUNCTION EULER QUADRATURE ESTIMATE ||");
System.out.println ("\t|----------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - a ||");
System.out.println ("\t| - b ||");
System.out.println ("\t| - c ||");
System.out.println ("\t| - z ||");
System.out.println ("\t| - Estimate ||");
System.out.println ("\t|----------------------------------------------------||");
for (double a : aArray)
{
for (double b : bArray)
{
for (double c : cArray)
{
Hypergeometric (
a,
b,
c,
logBetaEstimator,
hypergeometricQuadratureCount,
zArray
);
}
}
}
System.out.println ("\t|----------------------------------------------------||");
EnvManager.TerminateEnv();
}
}