# BLASFEO: basic linear algebra subroutines for embedded optimization

## TL;DR

BLASFEO is a specialized dense linear algebra library optimized for small to medium matrices, significantly outperforming existing BLAS and LAPACK routines in embedded optimization contexts.

## Contribution

It introduces three implementations of BLASFEO tailored for different matrix sizes, enhancing performance and portability for embedded optimization applications.

## Key findings

- 20-30% faster than level 3 BLAS for small matrices
- 2-3 times faster than LAPACK routines for small matrices
- Provides high-performance routines across a wide range of matrix sizes

## Abstract

BLASFEO is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization. A key difference with respect to existing high-performance implementations of BLAS is that the computational performance is optimized for small to medium scale matrices, i.e., for sizes up to a few hundred. BLASFEO comes with three different implementations: a high-performance implementation aiming at providing the highest performance for matrices fitting in cache, a reference implementation providing portability and embeddability and optimized for very small matrices, and a wrapper to standard BLAS and LAPACK providing high-performance on large matrices. The three implementations of BLASFEO together provide high-performance dense linear algebra routines for matrices ranging from very small to large. Compared to both open-source and proprietary highly-tuned BLAS libraries, for matrices of size up to about one hundred the high-performance implementation of BLASFEO is about 20-30% faster than the corresponding level 3 BLAS routines and 2-3 times faster than the corresponding LAPACK routines.