I need help optimising a piece of code which involves the computation of many small vectors and matrices. I have a list of vectors and matrices, given by mu_i and S_i respectively. I need to calculate nu_i = A*mu_i + b and P_i = A*S_i*A' + R, where A, b and R are all the correct size. This operation…

I changed your code to use static arrays, the timing of devectorized is printed in the bottom using LinearAlgebra, BenchmarkTools, StaticArrays # De-vectorised code function devectorised!(mu, S, A, ATranspose, R, simulationLength, u) n = length(mu) for i = 1:simulationLength for j =…

Your second path of keeping things as large arrays seems like a good one to me. I haven’t completely decoded it, but one thing you can do for speed is to re-use caches, permutedims!(_S, S, ...) and mul! etc. You can probably also write the whole thing in two lines using TensorOperations.jl, which w…

[image] scj: Furthermore, is Julia appropriate for real-time operation? I’ve previously used heavily vectorised Matlab code for real-time operation and it worked well enough; Julia should perform just as well. It always depends on how strict you are when you are talking about realtime. We hav…

[image] scj: I’ve previously used heavily vectorised Matlab code for real-time operation By the way, heavily vectorized matlab is extremely wasteful with allocations. Did you run the matlab code in the matlab runtime or you used it to compile C-code or mex-functions? If you ran the matlab nat…

I ran it using the Matlab runtime. I’m very new to Julia – I’ve been using it less than a week – and I’m far from a Matlab expert. To add some context, I wrote a multi-sensor multi-target tracking algorithm in Matlab and vectorised the code, it obtained real-time results for a moderate number of sen…

Ok, yeah vectorizing the code is not always the best strategy in Julia, although the broadcasting machinery will get you further (faster) than what you can do with matlab. Writing the loops manually in julia gives you the potential to achieve fortran/C speed, but you must of course follow the perfor…

If I get your code correctly, your d=6 is small enough to potentially see benefits from StaticArrays . TensorOperations as mentioned above is also worth pursuing, as you tight loop is currently allocating tons of memory (every slice x[:,:,i] is allocating a matrix).

This is a huge improvement, thank you for the help.

A while ago I asked a similar question, which you might find a useful read: [image] Multiply many-matrices by many-vectors Performance All, I have a critical portion of code that essentially involves the multiplication of many pre-computed matrices by many pre-computed v…

[image] scj: A = [Array(1.0I, 3, 3) T*Array(1.0I, 3, 3); zeros(3, 3) Array(1.0I, 3, 3)] By the way, in recent versions of julia, this can be written Matrix([I(3) T*I(3); 0I I]) # alternatively diagm(ones(6)) + diagm(T=>4ones(3)) I(6) + diagm(3=>4ones(3))

Apologies to enter this thread with another topic. I have a problem which might be close to this one. I’d like to kindly ask if anyone has experienced or could look into it. It is performance of loops with larger matrices and multiplication. For loop in function and multiplication of larger matrice…

Optimising code: Multiplying a list of matrices by a matrix

New to Julia

GregVernon November 21, 2019, 8:51pm 10

A while ago I asked a similar question, which you might find a useful read:

Topic		Replies	Views
Multiply many-matrices by many-vectors Performance matlab , parallel , multithreading , tensors	33	6925	December 14, 2018
Julia is significantly slower (~18 x) than Matlab in vector and matrix algebra New to Julia	32	2213	June 25, 2023
Speeding up the multiplying, adding, subtracting of 3D matrices Numerics question	16	820	June 24, 2023
Julia matrix-multiplication performance Performance linearalgebra	20	9112	October 30, 2022
Acceleration of a function Performance question	16	1042	November 16, 2020

Optimising code: Multiplying a list of matrices by a matrix

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