Abstract
The ROOT Mathematical and Statistical libraries have been recently improved both to increase their performance and to facilitate the modelling of parametric functions that can be used for performing maximum likelihood fits to data sets to estimate parameters and their uncertainties. First, we report on the new functionalities introduced in ROOT’s TFormula and TF1 classes to build these models in a convenient way for the users. We show how function objects, represented in ROOT by TF1 classes, can be used as probability density functions and how they can be combined together—via an addition operator—to perform extended likelihood fit of several normalized components. We also describe the new operators introduced to perform the convolution of two functions. Finally, we report on the improvements in the performance of the ROOT fitting algorithm, by using SIMD vectorization when evaluating the model function on large data sets and by exploiting multi-thread parallelization when computing the likelihood function.
Highlights
Fitting and modeling in ROOTFitting of data distributions, a fundamental operation in High Energy Physics (HEP) analysis, is one of the most demanding and computing-intensive activities when performing data analysis on the results of the LHC.ROOT [1] offers several techniques for fitting and modeling data distributions, from integration of the most popular minimizers, to objective function classes, to function classes for the user’s provided model function to interface with the minimizer
We introduce the recent improvements implemented in the mathematical libraries that make fitting directly in ROOT easier and faster
We extend the functionality of the TFormula class in ROOT, adding argument parsing and allowing to freely pass variables and parameters into pre-defined and user-defined functions
Summary
A fundamental operation in High Energy Physics (HEP) analysis, is one of the most demanding and computing-intensive activities when performing data analysis on the results of the LHC. We introduce the recent improvements implemented in the mathematical libraries that make fitting directly in ROOT easier and faster. We define a new syntax to use certain function compositions techniques, namely normalized sums and convolutions, directly in the TF1 function class. We introduce parallelization at data-level in the mathematical libraries and parallelization both at task-level and at data-level in the objective functions of the fitting, testing the potential to speed up parallelizable computations. We introduce new developments in both classes, such as improved support and argument expression of TFormula function definitions and the introduction of new operators in TF1 to express two methods of function composition: the normalized sum of functions and the convolution
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