EulerQuadratureEstimator.java
package org.drip.specialfunction.hypergeometric;
/*
* -*- 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>EulerQuadratureEstimator</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/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/hypergeometric/README.md">Hyper-geometric Function Estimation Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class EulerQuadratureEstimator extends
org.drip.specialfunction.definition.RegularHypergeometricEstimator
{
private int _quadratureCount = -1;
private org.drip.function.definition.R2ToR1 _logBetaEstimator = null;
/**
* EulerQuadratureEstimator Constructor
*
* @param hypergeometricParameters Hyper-geometric Parameters
* @param logBetaEstimator Log Beta Estimator
* @param quadratureCount Count of the Integrand Quadrature
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public EulerQuadratureEstimator (
final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters,
final org.drip.function.definition.R2ToR1 logBetaEstimator,
final int quadratureCount)
throws java.lang.Exception
{
super (hypergeometricParameters);
if (null == (_logBetaEstimator = logBetaEstimator) ||
0 >= (_quadratureCount = quadratureCount))
{
throw new java.lang.Exception ("EulerQuadratureEstimator Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Quadrature Count
*
* @return The Quadrature Count
*/
public int quadratureCount()
{
return _quadratureCount;
}
/**
* Retrieve the Log Beta Estimator
*
* @return The Log Beta Estimator
*/
public org.drip.function.definition.R2ToR1 logBetaEstimator()
{
return _logBetaEstimator;
}
@Override public double regularHypergeometric (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z < -1. || z > 1.)
{
throw new java.lang.Exception ("EulerQuadratureEstimator::regularHypergeometric => Invalid Inputs");
}
org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
hypergeometricParameters();
final double a = hypergeometricParameters.a();
final double b = hypergeometricParameters.b();
final double c = hypergeometricParameters.c();
return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
0.,
1.,
_quadratureCount
).integrate (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return 0. == t || 1. == t ? 0. :
java.lang.Math.pow (
t,
b - 1.
) * java.lang.Math.pow (
1. - t,
c - b - 1.
) * java.lang.Math.pow (
1. - z * t,
-a
);
}
}
) * java.lang.Math.exp (
-1. * _logBetaEstimator.evaluate (
b,
c - b
)
);
}
@Override public double derivative (
final double z,
final int order)
throws java.lang.Exception
{
org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters =
hypergeometricParameters();
double a = hypergeometricParameters.a();
double b = hypergeometricParameters.b();
double c = hypergeometricParameters.c();
return new EulerQuadratureEstimator (
new org.drip.specialfunction.definition.HypergeometricParameters (
a + order,
b + order,
c + order
),
_logBetaEstimator,
_quadratureCount
).regularHypergeometric (z) * org.drip.numerical.common.NumberUtil.PochhammerSymbol (
a,
order
) * org.drip.numerical.common.NumberUtil.PochhammerSymbol (
b,
order
) / org.drip.numerical.common.NumberUtil.PochhammerSymbol (
c,
order
);
}
@Override public org.drip.specialfunction.definition.RegularHypergeometricEstimator albinate (
final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParametersAlbinate,
final org.drip.function.definition.R1ToR1 valueScaler,
final org.drip.function.definition.R1ToR1 zTransformer)
{
try
{
return new EulerQuadratureEstimator (
hypergeometricParametersAlbinate,
_logBetaEstimator,
_quadratureCount
)
{
@Override public double regularHypergeometric (
final double z)
throws java.lang.Exception
{
return (null == valueScaler ? 1. : valueScaler.evaluate (z)) *
super.regularHypergeometric (null == zTransformer ? z : zTransformer.evaluate (z));
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}