ACTS is a free and open-source software project for track reconstruction in particle physics experiments. As a modernized version of the particle tracking code used by the ATLAS experiment at the CERN Large Hadron Collider, the project is focused on adoption of modern C++ standards, usability in multi-threaded workflows, and increased use of vectorization.

The fitting step of track reconstruction, in which particle track hypotheses are confronted to experimental data, uses the Kalman Filter algorithm in the 5-dimensional space of possible track parameters. This entails performing linear algebra operations on a large amount of 5x5 matrices, a problem which has only received a limited amount of scrutinity from the linear algebra community in the past. We are thus evaluating the relative performance of multiple linear algebra toolkits on this problem, using realistic input data from typical ACTS use cases.

The linear algebra operations of ACTS are currently implemented using Eigen. In this project, we want to investigate especially the use of xtensor, another C++ library for linear algebra, which has the advantage of being designed for interface and implementation compatibility with the NumPy library that is popular in the Python scientific ecosystem.

We already have a benchmarking infrastructure in place for comparing Eigen with custom SIMD instructions written on top of the Boost.SIMD library, in the Kalman Filter use case. In this project, we want to write an xtensor version to this benchmark, and compare the performance of this library with its alternatives.

If the performance is satisfactory, or can be made so through reasonable contributions to the xtensor project, the next step will be to investigate to which extent xtensor and Eigen can coexist in the ACTS codebase, as a way to avoid an impractical replacement of all uses of Eigen in ACTS in one go.

In the context of a key step of particle hunting, this project gives the opportunity to compare several C++ linear algebra libraries (especially a NumPy inspired one), experience their mixed use, and eventually invent some new optimizations for the 5x5 operations.

- Reimplement our benchmark with xtensor, and compare performance with other existing implementations (eigen, and custom Boost.SIMD code).
- Study interoperability with eigen.
- Prototype use of xtensor within ACTS.

- Performance comparison between xtensor & eigen for our 5x5 algebra.
- ACTS demonstrator mixing eigen and xtensor.
- Eventually, suggestions of implementation improvements for 5x5 vectorized algebra ?

C++, SIMD Vectorisation, Linear Algebra.