For many of us mathematicians, we were taught to use MATLAB, and we were taught to vectorize everything. I mean obviously if we have matrices $$A$$, $$B$$, and $$C$$ and want to multiply element-wise (say to solve a reaction-equation at each point in space), then the optimal code is

A.*B.*C

No questions to ask, right? Actually, this code isn’t as optimized as you’d think. Lets dig deeper.

BLAS, Linpack, and MKL

The reason you are always told by “the lords of numerical math” to vectorize your code is because very smart programmers worked really hard on making basic things work well. Most of the “standardized” vectorized computations are calling subroutines from packages known as BLAS and LINPACK. To see what version your MATLAB is using, you can call