I think specifying the exact size of HQ would be good (I gather HQ.shape will be (n, n, p) ?

Similarly, could you say what the size of Tau will be? (this one I couldn't guess)

HQ.shape is the same shape as input A. Minimum is (max(n, 1), max(n, 1), p) but could be larger.
Tau.shape is (max(1, n-1), p)

Isn't it worth adding this to the docstring?

If n < min(A.shape[:2]), HQ would still have the same size as A? Would the n: rows and columns of HQ then be uninitialized?

Yes that's the way many of the SLICOT routines do it. Adding this to the docstring and rebasing once more.

We have a bunch of different docstring styles for the various functions. Opening another issue for that.

Thank you. Do you agree with this, from #88 (comment):

 So should that be "upper diagonal (or Hessenberg) in [:ilo-1]" ?

Agree. General rule is:

• Python-index = Fortran-index - 1
• Python-slice-start = Fortran-slice-start-1
• Python-slice-end:Fortran-slice-end

Or put differently:
A(x,y) = A[x-1,y-1]
A(a:b,c:d) = A[a-1:b,c-1:d]

Fix committed