ErrorFunctionComplementAnalytical.java
package org.drip.function.e2erfc;
/*
* -*- 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>ErrorFunctionComplementAnalytical</i> implements Analytical Versions of the Error Function Complement
* (erfc) Estimate. 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>
* Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
* Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
* </li>
* <li>
* Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
* Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
* 22-32
* </li>
* <li>
* Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
* Linear and Non-linear Heat Transfer and Diffusion
* https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
* </li>
* <li>
* Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/e2erfc/README.md">E<sub>2</sub> erfc Estimation Function Implementation</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ErrorFunctionComplementAnalytical
{
private static final double ContinuedFractionRecursor (
final double z,
final int termIndex,
final int termCount)
{
if (termIndex == termCount)
{
return 0.;
}
return ((1 == termIndex % 2) ? z * z : 1.) + 0.5 * termIndex / (
1. + ContinuedFractionRecursor (
z,
termIndex + 1,
termCount
)
);
}
/**
* Construct Karagiannidis-Lioumpas (2007) Version of the Analytical Error Function Complement
*
* @param A A
* @param B B
*
* @return Karagiannidis-Lioumpas (2007) Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement KaragiannidisLioumpas2007 (
final double A,
final double B)
{
try
{
return !org.drip.numerical.common.NumberUtil.IsValid (A) ||
!org.drip.numerical.common.NumberUtil.IsValid (B) ? null :
new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::KaragiannidisLioumpas2007::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return (1. - java.lang.Math.exp (-1. * A * z)) * java.lang.Math.exp (-1. * z * z) /
(B * z * java.lang.Math.sqrt (java.lang.Math.PI));
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct Karagiannidis-Lioumpas (2007) Version of the Analytical Error Function Complement
*
* @return Karagiannidis-Lioumpas (2007) Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement KaragiannidisLioumpas2007()
{
return KaragiannidisLioumpas2007 (
1.980,
1.135
);
}
/**
* Construct the Chiani-Dardari-Simon (2012a) Version of the Analytical Error Function Complement
*
* @return The Chiani-Dardari-Simon (2012a) Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement ChianiDardariSimon2012a()
{
try
{
return new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::ChianiDardariSimon2012a::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return 0.5 * java.lang.Math.exp (-2. * z * z) + 0.5 * java.lang.Math.exp (-1. * z * z);
}
@Override public org.drip.numerical.estimation.R1Estimate boundedEstimate (
final double z)
{
try
{
double baseline = evaluate (z);
return new org.drip.numerical.estimation.R1Estimate (
baseline,
baseline,
java.lang.Math.exp (-1. * z * z)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Chiani-Dardari-Simon (2012b) Version of the Analytical Error Function Complement
*
* @return The Chiani-Dardari-Simon (2012b) Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement ChianiDardariSimon2012b()
{
try
{
return new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::ChianiDardariSimon2012b::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return java.lang.Math.exp (-1. * z * z) / 6. + 0.5 * java.lang.Math.exp (-4. * z * z / 3.);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Chang-Cosman-Milstein (2011) Version of the Analytical Error Function Complement
*
* @param beta Beta
*
* @return The Chang-Cosman-Milstein (2011) Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement ChangCosmanMilstein2011 (
final double beta)
{
try
{
return !org.drip.numerical.common.NumberUtil.IsValid (beta) || 1. >= beta ? null :
new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::ChangCosmanMilstein2011::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return java.lang.Math.sqrt (2. * java.lang.Math.E * (beta - 1.) / java.lang.Math.PI) *
java.lang.Math.exp (-1. * beta * z * z) / beta;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Continued Fraction Expansion Version of the Analytical Error Function Complement
*
* @param termCount Term Count
*
* @return The Continued Fraction Expansion Version of the Analytical Error Function Complement
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement ContinuedFractionExpansion (
final int termCount)
{
try
{
return 0 >= termCount ? null : new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::ContinuedFractionExpansion::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return z * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI) /
ContinuedFractionRecursor (
z,
1,
termCount
);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Craig 1991 Version of the ErrorFunctionComplement Quadrature
*
* @return The Craig 1991 Version of the ErrorFunctionComplement Quadrature
*/
public static final org.drip.function.e2erfc.ErrorFunctionComplement Craig1991()
{
try
{
return new org.drip.function.e2erfc.ErrorFunctionComplement (
null,
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
("ErrorFunctionComplementAnalytical::Craig1991::evaluate => Invalid Inputs");
}
if (0. == z)
{
return 1.;
}
if (z < 0)
{
return 2. - evaluate (-1. * z);
}
return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
0.,
z,
100
).integrate (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double theta)
throws java.lang.Exception
{
if (0. == theta)
{
return 0.;
}
double sinTheta = java.lang.Math.sin (theta);
return 2. * java.lang.Math.exp (-1. * z * z / (sinTheta * sinTheta)) /
java.lang.Math.PI;
}
}
);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}