[Gretl-users] Re: vec() and vech(): row-major vs. column-major
Am 17.12.2020 um 21:38 schrieb Allin Cottrell:
On Thu, 17 Dec 2020, Sven Schreiber wrote:
> Am 17.12.2020 um 21:18 schrieb Allin Cottrell:
>> On Thu, 17 Dec 2020, Sven Schreiber wrote:
>>
>> What should the message say? Seems like it would have to be something
>> like: If your input matrix is not symmetric, make sure the upper
>> triangle is what it would be if the matrix were symmetric. But that
>> sounds kinda redundant to me.
>>
>>
> Well, maybe something like: "For the odd case of non-symmetric input M,
> to obtain the same result as the vech functions in Gauss or Octave or as
> per the Wikipedia definition, use the transpose of M to effectively work
> on its lower triangle."
OK, better than my attempt. But non-symmetry in itself is not the
decider. If the upper triangle is "right" and the rest is zeros (or
arbitrary), vech(M) is right and vech(M') wrong. The case where you
need vech(M') is just where the upper triangle is arbitrary, and what
you actually want is in the lower triangle.
Yes, I agree. The thing is just that gretl here seems to be the outlier,
"everybody" else --OK, haven't looked very hard-- seems to use the lower
triangle. And once you start departing from the convention, then from
the doc it isn't 100% clear that gretl's vech doesn't half-stack the
upper triangle by columns instead of rows. (Fortunately it doesn't, of
course.)
To be clear about the background:
The Gauss code I was looking at populated element by element the lower
triangle of a matrix M that would become a covariance matrix. Then it
did xpnd(vech(M)) to get the dense symmetric matrix. (Where xpnd is what
unvech is in gretl.) There the convention about the triangles obviously
matter, and again, I simply didn't expect gretl's variant.
thanks
sven