On Wed, 28 Nov 2012 15:47:08 +0100, Sébastien Villemot wrote:
>
> I have tested the three BLAS implementations available in Debian (netlib
> BLAS, ATLAS and OpenBLAS), and they all give the same result (bad from
> your point of view).
>
> So I am not sure this is a bug. Maybe this is on purpose. If one
> considers this operation to be invalid (as I do), then it makes sense to
> do nothing.
If the operation is considered invalid, then it should return an error
instead of doing nothing silently.
However, I insist that the operation is perfectly valid from a
mathematical point of view. Indeed, in mathematics, ∑_{i ∈ ∅} a_i = 0.
Therefore, A * x = 0 when A has dimensions M×0. This corner case is
also useful in practice. For a problem I have, I needed to compute
t ↦ f(t₀ y + ∑ t_i a_i)
where a_i are vectors and t_i real numbers. It so happens that in
some circumstances, the sum may be empty leading to a constant
function instead of the correct t ↦ f(t₀ y). A very bad surprise
IMHO, incoherent with the semantics of the operation.
> Does the documentation clearly states that BLAS supports operations on
> objects with one dimension equal to zero?
Not the man pages. To the contrary, for N, the man page clearly
includes the possibility that N = 0:
N - INTEGER.
On entry, N specifies the number of columns of the matrix A. N
must be at least zero. Unchanged on exit.
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