IntegralEstimator.java
package org.drip.specialfunction.digamma;
/*
* -*- 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>IntegralEstimator</i> demonstrates the Estimation of the Digamma Function using the Integral
* Representations. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
* Mathematics</b>
* </li>
* <li>
* Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
* Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
* </li>
* <li>
* Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
* Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
* </li>
* <li>
* Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
* University Press</b> New York
* </li>
* <li>
* Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_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/digamma/README.md">Estimation Techniques for Digamma Function</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class IntegralEstimator
{
/**
* Generate the Gaussian Integral Digamma Estimator
*
* @return The Gaussian Integral Digamma Estimator
*/
public static final org.drip.numerical.estimation.R1ToR1IntegrandEstimator Gauss()
{
try
{
return new org.drip.numerical.estimation.R1ToR1IntegrandEstimator (
null,
new org.drip.numerical.estimation.R1ToR1IntegrandGenerator()
{
@Override public org.drip.numerical.estimation.R1ToR1Estimator integrand (
final double z)
{
try
{
return new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
double ePowerMinusT = java.lang.Math.exp (-t);
return 0. == t || java.lang.Double.isInfinite (t) ? 0. :
(ePowerMinusT / t) - (java.lang.Math.exp (-z * t) /
(1. - ePowerMinusT));
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
},
org.drip.numerical.estimation.R1ToR1IntegrandEstimator.INTEGRAND_LIMITS_SETTING_ZERO_INFINITY,
1.,
new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
return 0.;
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Gauss-Euler-Mascheroni Integral Digamma Estimator
*
* @return The Gauss-Euler-Mascheroni Integral Digamma Estimator
*/
public static final org.drip.numerical.estimation.R1ToR1IntegrandEstimator GaussEulerMascheroni()
{
try
{
return new org.drip.numerical.estimation.R1ToR1IntegrandEstimator (
null,
new org.drip.numerical.estimation.R1ToR1IntegrandGenerator()
{
@Override public org.drip.numerical.estimation.R1ToR1Estimator integrand (
final double z)
{
try
{
return new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return 0. == t ? 1. -
org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI : 1. == t
? -org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI : (
1. - java.lang.Math.pow (
t,
z - 1.
)
) / (1. - t);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
},
org.drip.numerical.estimation.R1ToR1IntegrandEstimator.INTEGRAND_LIMITS_SETTING_ZERO_ONE,
1.,
new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
return -org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI;
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Dirichlet Integral Digamma Estimator
*
* @return The Dirichlet Integral Digamma Estimator
*/
public static final org.drip.numerical.estimation.R1ToR1IntegrandEstimator Dirichlet()
{
try
{
return new org.drip.numerical.estimation.R1ToR1IntegrandEstimator (
null,
new org.drip.numerical.estimation.R1ToR1IntegrandGenerator()
{
@Override public org.drip.numerical.estimation.R1ToR1Estimator integrand (
final double z)
{
try
{
return new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return 0. == t || java.lang.Double.isInfinite (t) ? 0. : (
java.lang.Math.exp (-t) - java.lang.Math.pow (
1. + t,
-z
)
) / t;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
},
org.drip.numerical.estimation.R1ToR1IntegrandEstimator.INTEGRAND_LIMITS_SETTING_ZERO_INFINITY,
1.,
new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
return 0.;
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Binet Second Integral Digamma Estimator
*
* @return The Binet Second Integral Digamma Estimator
*/
public static final org.drip.numerical.estimation.R1ToR1IntegrandEstimator BinetSecond()
{
try
{
return new org.drip.numerical.estimation.R1ToR1IntegrandEstimator (
null,
new org.drip.numerical.estimation.R1ToR1IntegrandGenerator()
{
@Override public org.drip.numerical.estimation.R1ToR1Estimator integrand (
final double z)
{
try
{
return new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return 0. == t || java.lang.Double.isInfinite (t) ? 0. : t / (
(t * t + z * z) *
(java.lang.Math.exp (2. * java.lang.Math.PI * t) - 1.)
);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
},
org.drip.numerical.estimation.R1ToR1IntegrandEstimator.INTEGRAND_LIMITS_SETTING_ZERO_INFINITY,
-2.,
new org.drip.numerical.estimation.R1ToR1Estimator (null)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
return 0. == z ? 0. : java.lang.Math.log (z) - 0.5 / z;
}
}
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}