Solve a system of linear equations many times without allocating memory

[MartinOtter]

@MartinOtter

@MartinOtter

So, it is clear that lu! always allocates memory.

Not if you disable pivoting. You may be looking for

Alu = lu!(A, Val(false))
ldiv!(Alu, b)

Note, however, that you may worried about something that is unlikely to be relevant: if A is large, then the computation itself will dominate timing, if A is small, you should using StaticArrays which again do not allocate.

Also, please do read the docstrings ( ?lu! , ?ldiv! ) instead of programming by trial and error. Most of these things are documented.

Disabling pivoting is no alternativ, because a solution of a regular system may fail.

I am contributing to a generic modeling and simulation system (Modia/Modia3D/ModiaMath) and depending on user models a few or many, small or large linear equation systems will appear.

My summary of the remarks is: In Julia there is currently no generic library function available to solve repeately a (small or large) linear equation system without allocating memory in every iteration. For the time being I will just use lu! and ldiv! and at some time in the future provide a special library function that either uses LAPACK functions directly (for Float64) and otherwise uses lu! and ldiv!.