HilleQForm2F1.java
package org.drip.specialfunction.ode;
/*
* -*- 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>HilleQForm2F1</i> exposes the Coefficient Terms on the Q-form 2F1 Hyper-geometric ODE. 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/ode/README.md">Special Function Ordinary Differential Equations</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class HilleQForm2F1 extends org.drip.specialfunction.ode.SecondOrder
{
private org.drip.function.definition.R1ToR1 _q = null;
private org.drip.function.definition.R1ToR1 _v = null;
/**
* Construct the Hille Q-Form of 2F1 ODE
*
* @param a A
* @param b B
* @param c C
*
* @return Hille Q-Form of 2F1 ODE
*/
public static final HilleQForm2F1 Standard (
final double a,
final double b,
final double c)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (a) ||
!org.drip.numerical.common.NumberUtil.IsValid (b) ||
!org.drip.numerical.common.NumberUtil.IsValid (c))
{
return null;
}
final org.drip.function.definition.R1ToR1 q = new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z))
{
throw new java.lang.Exception
("HilleQForm2F1::Standard::q::evaluate => Invalid Inputs");
}
double aMinusB = a - b;
double zMinus1 = z - 1.;
return (z * z * (1. - aMinusB * aMinusB) + z * (2. * c * (a + b - 1.) - 4. * a * b) + c *
(2. - c)) / (4. * z * z * zMinus1 * zMinus1);
}
};
try
{
return new HilleQForm2F1 (
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double u)
throws java.lang.Exception
{
return 1.;
}
},
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double w)
throws java.lang.Exception
{
return 0.;
}
},
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double u)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (u))
{
throw new java.lang.Exception
("HilleQForm2F1::Standard::ZeroOrder::evaluate => Invalid Inputs");
}
return q.evaluate (z) * u;
}
},
q,
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z))
{
throw new java.lang.Exception
("HilleQForm2F1::Standard::v::evaluate => Invalid Inputs");
}
return java.lang.Math.pow (
z,
-0.5 * c
) * java.lang.Math.pow (
1. - z,
0.5 * (c - a - b - 1.)
);
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
private HilleQForm2F1 (
final org.drip.function.definition.R2ToR1 secondDerivativeCoefficient,
final org.drip.function.definition.R2ToR1 firstDerivativeCoefficient,
final org.drip.function.definition.R2ToR1 zeroDerivativeCoefficient,
final org.drip.function.definition.R1ToR1 q,
final org.drip.function.definition.R1ToR1 v)
throws java.lang.Exception
{
super (
secondDerivativeCoefficient,
firstDerivativeCoefficient,
zeroDerivativeCoefficient
);
if (null == (_q = q) ||
null == (_v = v))
{
throw new java.lang.Exception ("HilleQForm2F1 Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Q Form Function
*
* @return The Q Form Function
*/
public org.drip.function.definition.R1ToR1 q()
{
return _q;
}
/**
* Retrieve the v Function
*
* @return The v Function
*/
public org.drip.function.definition.R1ToR1 v()
{
return _v;
}
}