ErrorFunction.java
package org.drip.function.e2erf;
/*
* -*- 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>ErrorFunction</i> implements the E<sub>2</sub> Error Function (erf). 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/e2erf/README.md">E<sub>2</sub> erf and erf<sup>-1</sup> Implementations</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ErrorFunction extends org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator
{
private org.drip.numerical.estimation.R1ToR1Series _r1ToR1SeriesGenerator = null;
/**
* Construct the Euler-MacLaurin Instance of the E<sub>2</sub> erf
*
* @param termCount The Count of Approximation Terms
*
* @return The Euler-MacLaurin Instance of the E<sub>2</sub> erf
*/
public static final ErrorFunction MacLaurin (
final int termCount)
{
final org.drip.function.e2erf.MacLaurinSeries e2MacLaurinSeriesGenerator =
org.drip.function.e2erf.MacLaurinSeries.ERF (termCount);
if (null == e2MacLaurinSeriesGenerator)
{
return null;
}
try
{
return new ErrorFunction (
e2MacLaurinSeriesGenerator,
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
("ErrorFunction::MacLaurin::evaluate => Invalid Inputs");
}
double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
e2MacLaurinSeriesGenerator.cumulative (
0.,
z
);
return erf > 1. ? 1. : erf;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Convergent Hans Heinrich Burmann Version of the E<sub>2</sub> erf
*
* @return The Convergent Hans Heinrich Burmann Version of the E<sub>2</sub> erf
*/
public static final ErrorFunction HansHeinrichBurmannConvergent()
{
final org.drip.numerical.estimation.R1ToR1Series
hansHeinrichBurmannConvergentSeriesGenerator =
org.drip.function.e2erf.HansHeinrichBurmannSeries.Convergent();
if (null == hansHeinrichBurmannConvergentSeriesGenerator)
{
return null;
}
try
{
return new ErrorFunction (
hansHeinrichBurmannConvergentSeriesGenerator,
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
("ErrorFunction::HansHeinrichBurmannConvergent::evaluate => Invalid Inputs");
}
double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
java.lang.Math.sqrt (1. - java.lang.Math.exp (-1. * z * z)) *
hansHeinrichBurmannConvergentSeriesGenerator.cumulative (
0.,
z
);
return erf > 1. ? 1. : erf;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E<sub>2</sub> erf
*
* @return The Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E<sub>2</sub> erf
*/
public static final ErrorFunction HansHeinrichBurmannSchopfSupancic2014()
{
final org.drip.numerical.estimation.R1ToR1Series hansHeinrichBurmannConvergentSeriesGenerator
= org.drip.function.e2erf.HansHeinrichBurmannSeries.SchopfSupancic2014();
if (null == hansHeinrichBurmannConvergentSeriesGenerator)
{
return null;
}
try
{
return new ErrorFunction (
hansHeinrichBurmannConvergentSeriesGenerator,
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
("ErrorFunction::HansHeinrichBurmannSchopfSupancic2014::evaluate => Invalid Inputs");
}
double erf = 2. / java.lang.Math.sqrt (java.lang.Math.PI) *
java.lang.Math.sqrt (1. - java.lang.Math.exp (-1. * z * z)) *
hansHeinrichBurmannConvergentSeriesGenerator.cumulative (
0.,
z
);
return erf > 1. ? 1. : erf;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* ErrorFunction Constructor
*
* @param r1ToR1SeriesGenerator R<sup>1</sup> To R<sup>1</sup> Series Generator
* @param dc Differential Control
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ErrorFunction (
final org.drip.numerical.estimation.R1ToR1Series r1ToR1SeriesGenerator,
final org.drip.numerical.differentiation.DerivativeControl dc)
throws java.lang.Exception
{
super (
dc,
0.
);
_r1ToR1SeriesGenerator = r1ToR1SeriesGenerator;
}
@Override public double derivative (
final double z,
final int order)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) ||
1 > order)
{
throw new java.lang.Exception ("ErrorFunction::derivative => Invalid Inputs");
}
return 1 == order ? 2. * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI) :
super.derivative (
z,
order
);
}
@Override public org.drip.function.definition.R1ToR1 antiDerivative()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("ErrorFunction::antiDerivative::evaluate => Invalid Inputs");
}
return x * this.evaluate (x) + java.lang.Math.exp (-1. * x * x) / java.lang.Math.sqrt
(java.lang.Math.PI);
}
};
}
@Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
final double x)
{
return null == _r1ToR1SeriesGenerator ? seriesEstimate (
x,
null,
null
) : seriesEstimate (
x,
_r1ToR1SeriesGenerator.termWeightMap(),
_r1ToR1SeriesGenerator
);
}
@Override public org.drip.function.definition.R1ToR1 integrand()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double z)
{
return 2. * java.lang.Math.exp (-1. * z * z) / java.lang.Math.sqrt (java.lang.Math.PI);
}
};
}
/**
* Compute the Q Value for the given X
*
* @param x X
*
* @return The Q Value
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double q (
final double x)
throws java.lang.Exception
{
return 0.5 * (1. - evaluate (x / java.lang.Math.sqrt (2.)));
}
/**
* Compute the CDF Value for the given X
*
* @param x X
*
* @return The CDF Value
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double cdf (
final double x)
throws java.lang.Exception
{
return 0.5 * (1. + evaluate (x / java.lang.Math.sqrt (2.)));
}
/**
* Compute the erfc Value for the given X
*
* @param x X
*
* @return The erfc Value
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double erfc (
final double x)
throws java.lang.Exception
{
return 1. - evaluate (x);
}
/**
* Compute the E<sub>2</sub> erf Gaussian Density Integral over -inf to +inf
*
* @param a The Scale Parameter
* @param b The Displacement Parameter
* @param r1UnivariateNormal The R<sup>1</sup> Gaussian Distribution Parameters
*
* @return The E<sub>2</sub> erf Gaussian Density Integral over -inf to +inf
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double gaussianDensityIntegral (
final double a,
final double b,
final org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (a) ||
!org.drip.numerical.common.NumberUtil.IsValid (b) ||
null == r1UnivariateNormal)
{
throw new java.lang.Exception ("ErrorFunction::gaussianDensityIntegral => Invalid Inputs");
}
double sigma = r1UnivariateNormal.variance();
return evaluate (
(a * r1UnivariateNormal.mean() + b) / java.lang.Math.sqrt (1. + 2 * sigma * sigma * a * a)
);
}
}