Static matrix equation solve in-place?

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1

I’m using static arrays to solve a 3x3 matrix equation that has to be solved repeatedly. Is there a function for solving these equations in place with static arrays (SMatrix, SVector)? I see all the in-place BLAS routines, but I’m not sure if that will defeat the purpose of using static arrays. So far, A\b is considerably faster without decomposing the matrix first for this small system.

2

I think what you want is ldiv!

3

I gave that a try and got

julia> ldiv!(A, b)
ERROR: MethodError: no method matching ldiv!(::SArray{Tuple{3,3},Float64,2,9}, ::MArray{Tuple{3},Float64,1,3})

The docs for ldiv! also say " The argument A should not be a matrix," so I’m unsure about applicability to an unfactorized static matrix.

4

If the arrays are static, what’s the purpose of the in-place solve? I believe StaticArrays have custom methods for 3x3 solves that do not allocate anything?

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5

Is that the case? I could be confused, but does repeated execution of x = A\b somehow compile to an in-place operation with x? How can there be zero allocation for the result of A\b?

6

The cool thing with StaticArrays is that non-inplace methods don’t have to allocate (on the heap) since you know exactly how much memory it will need.

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7

Ok, so there is no reason to fret about where the result of A\b goes, because it’s basically just a tuple and will not cause any slowdown?

3 Likes
8

Right.

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