LAPACKE_?larfb_work: bad work matrix layout

[vladimir-ch]

LAPACKE_?larfb_work passes work and ldwork to the Fortran routine unmodified even if the matrix layout is row major. This is extremely surprising bordering a bug because it means that the work matrix has to be column major while all the other matrices are treated as row major. Interestingly, LAPACKE_?larfb follows the game and the work matrix it allocates (due to ldwork it uses) is column major.

I might be wrong but the only reasonable solution I see is not to allocate work in LAPACKE_?larfb and allocate it in LAPACKE_?larfb_work instead while ignoring work and ldwork parameters passed to it.

It seems that LAPACKE_?tprfb_work and LAPACKE_?trsna_work suffer from the same problem.

[vladimir-ch]

Have you been able to confirm this? If you think it is a bug and if you agree with the solution I propose, I could submit a patch.

[vladimir-ch]

Recently I've been thinking about this issue again and even after this long time I'm still unsure whether lapacke should allocate a new work matrix or not. I lean towards yes. For example, LAPACKE_dlange_work does allocate a new work array in case of 1-norm (which translates to inf-norm for the Fortran call). This suggests that the author was aware that in a row-major implementation the work array is needed/useful in a different situation than in the Fortran implementation. However, this allocation does not happen in LAPACKE_dlantr_work (which has caused me a lot of pain in our Gonum interface before I figured it out). In other words, there is an inconsistence between LAPACKE_dlange_work, which allocates, and a bunch of other function, which don't and therefore cause surprises.