Vincia Tools

Here will be documented the numerical integrators, spliners, root finders, clustering maps etc, that Vincia uses, along with how small utility functions, such as num2str, work. The idea is to help people who look in the code themselves and/or who wish to modify it themselves.

The VinClu clustering map

AB->arb The VinClu clustering map is a 3->2 clustering map rather similar to that of the Arclus jet clustering algorithm. Its principal advantage is that it contains the exact inverses of the Vincia kinematics mappings, and hence it can be used to "undo" branchings and/or reconstruct the exact intermediate shower states from a given momentum configuration. The clustering is invoked using:

Rambo Generator

Text Output Utilities

Mathematical Functions and Constants

Binomial and Factorial

The binomial coefficients, (n,m), and the factorial, n!, are available inside namespace Vincia as:

Dilogarithms

The dilogarithm, Li2(x), is available inside namespace Vincia as:

The Gamma Function

The Gamma function, Gamma(x) is implemented for x > 0, and is based on the approximation by Lanczos (see Numerical Recipes). Two function calls are availabe inside namespace Vincia: The former is often more useful in calculations involving ratios of the Gamma function with large numbers, which would be cast as differences of logs.

Numerical Integration and Root Finding

One-dimensional Splines

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