I have a B \ A calculation I need to solve repeatedly (10^4–10^5 times) with the same B, ideally without allocation, that includes the result A is a mutable buffer I want to write to the elements of A may be ForwardDiff.Dual I narrowed down a solution that I like (factorize, go static), but I wou…

Can’t you horizontally stack all A and do a single solve?

Unfortunately not, it is an iterative problem (each iteration does this to calculate something, within a minimizer).

Check out FastLapackInterface Edit: Sorry, I initially missed the part where the elements of A may be ForwardDiff.Dual. FastLapackInterface isn’t applicable there.

Your 49x49 matrix is probably too big for StaticArrays to be effective. In general, StaticArrays loses most of its performance benefit (and can start to choke your compiler) as vectors/matrices start to grow above 100ish elements. I think everything you want is covered by ldiv!(B_lu,A). It’s alloca…

[image] mikmoore: Your 49x49 matrix is probably too big for StaticArrays to be effective. The benchmarks suggest otherwise. That said, I also find this puzzling since the relevant method ( StaticArrays._A_ldiv_B ) does not shortcut for “large” matrices, it is still a generated function which is…

I don’t have a solution, but if I understood correctly you could try to use the sweep operator instead of the \ which is available in two packages: SweepOperator.jl LinearRegressionKit.jl If you don’t need to compute any extra statistics (like the sum of squares). The package from Joshday will li…

If it is possible to work with A' instead of A, then you could just reinterpret the dual numbers as scalars to get an A matrix with more columns. Then apply B_lu and reinterpret back.

Here are my benchmarks, using your definitions from above: A_ss = SMatrix{n,m}(A) # no need to use MMatrix here Abuf = similar(A); @btime \($B_lu,$A); # 3.6us, 1 alloc # allocates new result @btime ldiv!($B_lu,$A); # 2.8us, 0 alloc # overwrites A with result @btime ldiv!($B_lu,copy!($Abuf,$A)); # 3…

Just to make this thread more searchable for other future users (This question arises from time to time), it is better to add Solve linear system to the title. @Tamas_Papp , Could you do that?

Solve linear system repeatedly without allocation

General Usage

lmiq July 7, 2022, 3:29pm 5

Maybe this helps: Non-allocating matrix inversion - #7 by stevengj

Topic		Replies	Views
Solving linear system without allocating Numerics	19	666	August 9, 2025
Solve a system of linear equations many times without allocating memory Numerics	18	2563	April 7, 2020
DifferentiationInterface+ForwardDiff unable to diff ldiv! (any other options to solve linear system w/o allocations and differentiate?) Performance question	34	429	July 28, 2025
Non-allocating matrix inversion Performance matrices	13	3763	April 23, 2022
Help with allocations (variable length least squares) New to Julia memory-allocation	10	1268	March 25, 2021

Solve linear system repeatedly without allocation

Related topics