> iirc they all link against something that has a BLAS/LAPACK API Eigen can consume these I think, but they are optional. It has it’s own implementation of the

> iirc they all link against something that has a BLAS/LAPACK API Eigen can consume these I think, but they are optional. It has it’s own implementation of these, written in manually vectorized C++, with intrinsics, up to and including AVX512 (controlled with macros). For parallelization it uses OpenMP provided by the compiler (also controlled with a macro). > Has that changed? It’s hard to directly compare Eigen to the rest of them. They don’t do the same thing. One feature of Eigen is lazy evaluation. Expressions like a+b or a×b don’t return another matrix or vector; they return a placeholder object that only computes something on assignment. For complicated expressions this can be a huge win, e.g. r=a+b+c+d will read from a,b,c,d, compute sum of the 4 on the fly, and write into r without temporary copies in memory. However, also makes Eigen’s source code outright scary, and hard to debug or optimize. Anyway, based on the old pics there http://eigen.tuxfamily.org/index.php?title=Benchmark http://eigen.tuxfamily.org/index.php?title=Benchmark they are more or less comparable. Things like alpha·X+beta·Y were much faster in Eigen (probably due to that lazy evaluation thing), Hessenberg was much faster in MKL, in general they are close.