Package org.drip.numerical.estimation

Class R1ToR1Series

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.RkToR1Series
org.drip.numerical.estimation.R1ToR1Series
Direct Known Subclasses:
AbramowitzStegunSeriesGenerator, ASeriesGenerator, LowerSFixedSeries, MacLaurinSeries, OrthogonalPolynomial
public class R1ToR1Series
extends RkToR1Series
R1ToR1Series holds the R1 To R1 Expansion Terms in the Ordered Series of the Numerical Estimate for a Function. The References are:

  • Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function Computers and Mathematics with Applications 61 (11) 3364-3369
  • National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.11
  • Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n! https://arxiv.org/abs/1003.2907 arXiv
  • Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
  • Wikipedia (2019): Stirling's Approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    R1ToR1Series​(R1ToR1SeriesTerm r1ToR1SeriesTerm, boolean proportional, java.util.TreeMap<java.lang.Integer,​java.lang.Double> termWeightMap)
    R1ToR1Series Constructor

  • Method Summary

    Modifier and Type Method Description
    double cumulative​(double zeroOrder, double x)
    Compute the Cumulative Series Value
    double derivative​(double x, int derivativeOrder)
    Calculate the derivative as a double
    double evaluate​(double x)
    Evaluate for the given variate
    java.util.TreeMap<java.lang.Integer,​java.lang.Double> generate​(double zeroOrder, double x)
    Generate the R1 To R1 Series Expansion using the Term
    R1ToR1SeriesTerm r1ToR1SeriesTerm()
    Retrieve the R1 To R1 Series Expansion Term

    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

    • R1ToR1Series

      public R1ToR1Series​(R1ToR1SeriesTerm r1ToR1SeriesTerm, boolean proportional, java.util.TreeMap<java.lang.Integer,​java.lang.Double> termWeightMap) throws java.lang.Exception
      R1ToR1Series Constructor
      Parameters:
      r1ToR1SeriesTerm - R1 To R1 Series Expansion Term
      proportional - TRUE - The Expansion Term is Proportional
      termWeightMap - Error Term Weight Map
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • r1ToR1SeriesTerm

      public R1ToR1SeriesTerm r1ToR1SeriesTerm()
      Retrieve the R1 To R1 Series Expansion Term
      Returns:
      The R1 To R1 Series Expansion Term

    • generate

      public java.util.TreeMap<java.lang.Integer,​java.lang.Double> generate​(double zeroOrder, double x)
      Generate the R1 To R1 Series Expansion using the Term
      Parameters:
      zeroOrder - The Zero Order Estimate
      x - X
      Returns:
      The R1 To R1 Series Expansion

    • cumulative

      public double cumulative​(double zeroOrder, double x) throws java.lang.Exception
      Compute the Cumulative Series Value
      Parameters:
      zeroOrder - The Zero Order Estimate
      x - X
      Returns:
      The Cumulative Series Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • evaluate

      public double evaluate​(double x) throws java.lang.Exception
      Description copied from class: R1ToR1
      Evaluate for the given variate
      Specified by:
      evaluate in class R1ToR1
      Parameters:
      x - Variate
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done

    • derivative

      public double derivative​(double x, int derivativeOrder) throws java.lang.Exception
      Description copied from class: R1ToR1
      Calculate the derivative as a double
      Overrides:
      derivative in class R1ToR1
      Parameters:
      x - Variate at which the derivative is to be calculated
      derivativeOrder - Order of the derivative to be computed
      Returns:
      The Derivative
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid