Package org.drip.specialfunction.lanczos

Class PSeriesGenerator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.RkToR1Series

org.drip.numerical.estimation.R0ToR1Series

org.drip.specialfunction.lanczos.PSeriesGenerator

public class PSeriesGenerator
extends R0ToR1Series

PSeriesGenerator generates the Terms of the Lanczos P Series. The References are:

• Godfrey, P. (2001): Lanczos Implementation of the Gamma Function http://www.numericana.com/answer/info/godfrey.htm
• Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): Numerical Recipes: The Art of Scientific Computing 3rd Edition Cambridge University Press New York
• Pugh, G. R. (2004): An Analysis of the Lanczos Gamma Approximation Ph. D. University of British Columbia
• Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
• Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation

It provides the following functionality:

• Construct a Standard Instance of the Lanczos P Series Generator
• PSeriesGenerator Constructor
• Retrieve the Chebyshev Coefficient Matrix
• Retrieve the Series Term Count

Module	Computational Core Module
Library	Function Analysis Library
Project	Special Function Implementation and Analysis
Package	Lanczos Scheme for Gamma Estimate

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
PSeriesGenerator(PSeriesTerm pSeriesTerm, java.util.TreeMap<java.lang.Integer,java.lang.Double> chebyshevCoefficientWeightMap, double[][] chebyshevCoefficientMatrix)	PSeriesGenerator Constructor

Method Summary

Modifier and Type	Method	Description
double[][]	_chebyshevCoefficientMatrix()	Retrieve the Chebyshev Coefficient Matrix
static PSeriesGenerator	Standard(int g, int termCount)	Construct a Standard Instance of the Lanczos P Series Generator
int	termCount()	Retrieve the Series Term Count

Methods inherited from class org.drip.numerical.estimation.R0ToR1Series

cumulative, derivative, evaluate, generate, r0Tor1SeriesTerm

Methods inherited from class org.drip.numerical.estimation.RkToR1Series

proportional, termWeightMap

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, conditionNumber, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

PSeriesGenerator

public PSeriesGenerator(PSeriesTerm pSeriesTerm,
java.util.TreeMap<java.lang.Integer,java.lang.Double> chebyshevCoefficientWeightMap,
double[][] chebyshevCoefficientMatrix)
                 throws java.lang.Exception

PSeriesGenerator Constructor

Parameters:

pSeriesTerm - Lanczos P Series Term

chebyshevCoefficientWeightMap - Chebyshev Coefficient Term Weight Map

chebyshevCoefficientMatrix - Chebyshev Coefficient Matrix

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Standard

public static final PSeriesGenerator Standard(int g,
int termCount)

Construct a Standard Instance of the Lanczos P Series Generator

Parameters:

g - Lanczos g Control

termCount - Lanczos Series Term Count

Returns:

Standard Instance of the Lanczos P Series Generator

_chebyshevCoefficientMatrix

public double[][] _chebyshevCoefficientMatrix()

Retrieve the Chebyshev Coefficient Matrix

Returns:

The Chebyshev Coefficient Matrix

termCount

public int termCount()

Retrieve the Series Term Count

Returns:

The Series Term Count