GaussContiguousProperty4.java
package org.drip.sample.hypergeometric;
import org.drip.function.definition.R1PropertyVerification;
import org.drip.function.definition.R1ToR1Property;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.property.GaussContiguousEqualityLemma;
/*
* -*- 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>GaussContiguousProperty4</i> verifies the Gauss Contiguous Identity #4 Lemma for Hyper-geometric
* Functions. 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 GaussContiguousProperty4
{
private static final void Verifier (
final double a,
final double b,
final double c,
final double[] zArray,
final R1ToR1Property gaussContiguousProperty4)
throws Exception
{
System.out.println ("\t|----------------------------------------------||");
System.out.println ("\t| GAUSS CONTIGUOUS PROPERTY #4 ||");
System.out.println ("\t| a = " + FormatUtil.FormatDouble (a, 1, 1, 1.));
System.out.println ("\t| b = " + FormatUtil.FormatDouble (b, 1, 1, 1.));
System.out.println ("\t| c = " + FormatUtil.FormatDouble (c, 1, 1, 1.));
System.out.println ("\t|----------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - z ||");
System.out.println ("\t| - LHS Value ||");
System.out.println ("\t| - RHS Value ||");
System.out.println ("\t| - Verification Success? ||");
System.out.println ("\t|----------------------------------------------||");
for (double z : zArray)
{
R1PropertyVerification propertyVerification = gaussContiguousProperty4.verify (z);
System.out.println (
"\t|" + FormatUtil.FormatDouble (z, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (propertyVerification.lValue(), 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (propertyVerification.rValue(), 1, 10, 1.) + " | " +
propertyVerification.verified() + " ||"
);
}
System.out.println ("\t|----------------------------------------------||");
System.out.println();
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] aArray =
{
1.,
2.,
3.,
4.,
5.,
};
double[] bArray =
{
3.,
4.,
};
double[] cArray =
{
5.,
6.,
};
double[] zArray =
{
-0.80,
-0.60,
-0.40,
-0.20,
0.00,
0.20,
0.40,
0.60,
0.80
};
for (double a : aArray)
{
for (double b : bArray)
{
for (double c : cArray)
{
Verifier (
a,
b,
c,
zArray,
GaussContiguousEqualityLemma.RelationIdentity4 (
a,
b,
c
)
);
}
}
}
EnvManager.TerminateEnv();
}
}