https://doi.org/10.1051/epjconf/202024502015
Automatic Differentiation in ROOT
1
Princeton University, Princeton, New Jersey 08544, United States
2
University of Nebraska Lincoln, 1400 R St, Lincoln, NE 68588, United States
* e-mail: vvasilev@cern.ch
** e-mail: xefremale@gmail.com
*** e-mail: oksana.shadura@cern.ch
Published online: 16 November 2020
In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc.) and control flow statements. AD takes source code of a function as input and produces source code of the derived function. By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. This paper presents AD techniques available in ROOT, supported by Cling, to produce derivatives of arbitrary C/C++ functions through implementing source code transformation and employing the chain rule of differential calculus in both forward mode and reverse mode. We explain its current integration for gradient computation in TFormula. We demonstrate the correctness and performance improvements in ROOT’s fitting algorithms.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
