CumulativeSeriesEstimator.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>CumulativeSeriesEstimator</i> implements the Cumulative Series Based Digamma Estimation. 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 abstract class CumulativeSeriesEstimator extends org.drip.numerical.estimation.R1ToR1Estimator
{
private org.drip.numerical.estimation.R1ToR1Series _cumulativeSeries = null;
/**
* Compute the Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator
*
* @param termCount Number of Terms in the Estimation
*
* @return The Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator AbramowitzStegun2007 (
final int termCount)
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.AbramowitzStegun2007 (termCount),
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
("CumulativeSeriesEstimator::AbramowitzStegun2007::evaluate => Invalid Inputs");
}
return cumulativeSeries().evaluate (z - 1.) -
org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Harmonic Cumulative Series of Digamma Estimator
*
* @return The Harmonic Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator Harmonic()
{
try
{
return new CumulativeSeriesEstimator (
null,
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. >= z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::Harmonic::evaluate => Invalid Inputs");
}
double harmonicEstimate = 0.;
for (int i = 1; i < (int) z; ++i)
{
harmonicEstimate = harmonicEstimate + (1. / i);
}
return harmonicEstimate - org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Half-Integer Cumulative Series of Digamma Estimator
*
* @return The Half-Integer Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator HalfInteger()
{
try
{
return new CumulativeSeriesEstimator (
null,
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z || 0.5 != z - (int) z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::HalfInteger::evaluate => Invalid Inputs");
}
double halfIntegerEstimate = 0.;
for (int i = 1; i <= (int) z; ++i)
{
halfIntegerEstimate = halfIntegerEstimate + (1. / (-0.5 + i));
}
return halfIntegerEstimate - org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI
- java.lang.Math.log (4.);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Saddle-Point Cumulative Series of Digamma Estimator
*
* @param logGammaEstimator The Log Gamma Estimator
* @param saddlePointFunction The Saddle Point Generation Function
* @param saddlePointCount The Saddle Point Count
*
* @return The Saddle-Point Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator MezoHoffman2017 (
final org.drip.function.definition.R1ToR1 logGammaEstimator,
final org.drip.function.definition.R1ToR1 saddlePointFunction,
final int saddlePointCount)
{
if (null == logGammaEstimator)
{
return null;
}
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.MezoHoffman2017 (
saddlePointFunction,
saddlePointCount
),
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
("CumulativeSeriesEstimator::MezoHoffman2017::evaluate => Invalid Inputs");
}
return -1. * java.lang.Math.exp (
logGammaEstimator.evaluate (z) +
cumulativeSeries().evaluate (z) +
2. * org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI * z
);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Gauss Cumulative Series of Digamma Estimator
*
* @param termCount Term Count
*
* @return The Gauss Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator Gauss (
final int termCount)
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.Gauss (termCount),
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z || 1. < z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::Gauss::evaluate => Invalid Inputs");
}
return 2. * cumulativeSeries().evaluate (z) -
org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI -
java.lang.Math.log (2. * termCount) -
0.5 * java.lang.Math.PI / java.lang.Math.tan (java.lang.Math.PI * z);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Asymptotic Cumulative Series of Digamma Estimator
*
* @return The Asymptotic Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator Asymptotic()
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.Asymptotic(),
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::Asymptotic::evaluate => Invalid Inputs");
}
return java.lang.Math.log (z) - 0.5 / z + cumulativeSeries().evaluate (z);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Exponential Asymptotic Cumulative Series of Digamma Estimator
*
* @return The Exponential Asymptotic Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator ExponentialAsymptote()
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.ExponentialAsymptote(),
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::ExponentialAsymptote::evaluate => Invalid Inputs");
}
return cumulativeSeries().evaluate (z);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator
*
* @return The Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator
*/
public static final CumulativeSeriesEstimator ExponentialAsymptoteHalfShifted()
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.ExponentialAsymptoteHalfShifted(),
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
("CumulativeSeriesEstimator::ExponentialAsymptoteHalfShifted::evaluate => Invalid Inputs");
}
return z - 0.5 + cumulativeSeries().evaluate (z - 0.5);
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the Taylor-Riemann Zeta Cumulative Series of Digamma Estimator
*
* @param riemannZetaEstimator The Riemann-Zeta Estimator
* @param termCount Term Count
*
* @return The Taylor-Riemann Zeta Cumulative Series of Digamma Estimator
*/
public static final CumulativeSeriesEstimator TaylorRiemannZeta (
final org.drip.function.definition.R1ToR1 riemannZetaEstimator,
final int termCount)
{
try
{
return new CumulativeSeriesEstimator (
org.drip.specialfunction.digamma.CumulativeSeries.TaylorRiemannZeta (
riemannZetaEstimator,
termCount
),
null
)
{
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
{
throw new java.lang.Exception
("CumulativeSeriesEstimator::TaylorRiemannZeta::evaluate => Invalid Inputs");
}
return -1. * cumulativeSeries().evaluate (z - 1.) -
org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
protected CumulativeSeriesEstimator (
final org.drip.numerical.estimation.R1ToR1Series cumulativeSeries,
final org.drip.numerical.differentiation.DerivativeControl dc)
throws java.lang.Exception
{
super (dc);
_cumulativeSeries = cumulativeSeries;
}
/**
* Retrieve the Underlying Cumulative Series
*
* @return The Underlying Cumulative Series
*/
public org.drip.numerical.estimation.R1ToR1Series cumulativeSeries()
{
return _cumulativeSeries;
}
}