`bunchkaufman!` allocates much more memory than `lu!`

[juliohm]

Is this expected?

julia> using LinearAlgebra

julia> A = Symmetric(rand(1000, 1000))

julia> @allocated bunchkaufman!(A, check=false)
520208

julia> @allocated lu!(A, check=false)
8096

[juliohm]

According to this NASA paper, the Bunch-Kaufman should require less memory than LU. I didn't double check the minor details though: https://ntrs.nasa.gov/api/citations/19890018970/downloads/19890018970.pdf

[aravindh-krishnamoorthy]

This is the LAPACK working buffer, see here: https://netlib.org/lapack/explore-html/d8/d0e/group__hetrf_ga431b081d6c9c48af82ec003a7d3070ff.html

julia> using LinearAlgebra
julia> A = Symmetric(rand(1000, 1000));
julia> A1 = copy(A); @allocated LAPACK.sytrf!('U',A1.data)
4798424
julia> A1 = copy(A); @allocated LAPACK.sytrf!('U',A1.data)
520224

Here, $520224 \approx$ N $\times$ NB samples (see above link for LWORK) $= 1000\times 64$ elements (on my PC) $= 1000 \times 64 \times 8 = 512000$ bytes.

[juliohm]

Thank you @aravindh-krishnamoorthy for this additional information. What is not clear from your message is if this can be fixed on the Julia side. Are we already doing the best thing possible with the underlying LAPACK implementation?

[aravindh-krishnamoorthy]

Are we already doing the best thing possible with the underlying LAPACK implementation?

Unfortunately, this seems to be the case. LAPACK's sytrf, which is used for bunchkaufman!, requires additional N*NB (WORK) + N (ipiv) buffers, while dgetrf, which is used for lu!, is completely in place and requires only an N buffer for ipiv.

But, the other advantages of Bunch-Kaufman mentioned in the NASA article are still applicable.

[juliohm]

Thank you @aravindh-krishnamoorthy for the very helpful comments.

I will close the issue given that we can't fix the allocations in the Julia side.