SecondOrderHelmholtz.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>SecondOrderHelmholtz</i> exposes the Coefficient Terms in the Helmholtz ODE. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
* on Mathematics</b>
* </li>
* <li>
* Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
* Edition</i> <b>Harcourt</b> San Diego
* </li>
* <li>
* Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
* Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
* </li>
* <li>
* Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
* Press</b>
* </li>
* <li>
* Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_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 SecondOrderHelmholtz extends org.drip.specialfunction.ode.SecondOrder
{
private double _alpha = java.lang.Double.NaN;
/**
* Construct the Standard Second Order Helmholtz ODE
*
* @param alpha Alpha
*
* @return The Standard Second Order Helmholtz ODE
*/
public static final SecondOrderHelmholtz Standard (
final double alpha)
{
try
{
return new SecondOrderHelmholtz (
alpha,
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double w)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z))
{
throw new java.lang.Exception
("SecondOrderHelmholtz::SecondOrder::evaluate => Invalid Inputs");
}
return z * z;
}
},
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double w)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z))
{
throw new java.lang.Exception
("SecondOrderHelmholtz::SecondOrder::evaluate => Invalid Inputs");
}
return 2. * z;
}
},
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double z,
final double w)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) ||
!org.drip.numerical.common.NumberUtil.IsValid (w))
{
throw new java.lang.Exception
("SecondOrderHelmholtz::SecondOrder::evaluate => Invalid Inputs");
}
return (z * z - alpha * (alpha + 1.)) * w;
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
private SecondOrderHelmholtz (
final double alpha,
final org.drip.function.definition.R2ToR1 secondDerivativeCoefficient,
final org.drip.function.definition.R2ToR1 firstDerivativeCoefficient,
final org.drip.function.definition.R2ToR1 zeroDerivativeCoefficient)
throws java.lang.Exception
{
super (
secondDerivativeCoefficient,
firstDerivativeCoefficient,
zeroDerivativeCoefficient
);
if (!org.drip.numerical.common.NumberUtil.IsValid(_alpha = alpha))
{
throw new java.lang.Exception ("SecondOrderHelmholtz Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Alpha
*
* @return Alpha
*/
public double alpha()
{
return _alpha;
}
@Override public java.util.TreeSet<java.lang.Double> orderedRegularSingularPoints()
{
return null;
}
}