[Numpy-discussion] determinant of a scalar not handled

Skipper Seabold jsseabold@gmail....
Tue Jul 27 11:36:45 CDT 2010


On Tue, Jul 27, 2010 at 12:00 PM, Robert Kern <robert.kern@gmail.com> wrote:
> On Tue, Jul 27, 2010 at 07:51, Skipper Seabold <jsseabold@gmail.com> wrote:
>> On Mon, Jul 26, 2010 at 10:05 PM, Alan G Isaac <aisaac@american.edu> wrote:
>>> But I am still confused about the use case.
>>> What is the scalar- (or 1d-array-) returning procedure
>>> invokedbefore taking the determinant?
>>
>> Recently I ran into this trying to make the log-likelihood of a
>> multivariate and univariate autoregressive process use the same
>> function.  One has log(sigma_scalar) and one calls for
>> logdet(Sigma_matrix).  I also ran in to again yesterday working on the
>> Kalman filter, depending on the process being modeled and how the user
>> writes a function if the needed coefficient arrays depend on
>> parameters.  To be more general, I have to put in atleast_2d, even
>> though these checks are really in slogdet.
>
> Not necessarily. In this context, you are treating a scalar as a 1x1
> matrix. Or rather, in full generality, you have a 1x1 matrix and
> 1-element vectors and only doing operations on them that map fairly
> neatly onto a subset of scalar properties. Consequently, you can use
> scalars in their place without much problem (to add confusion, the
> scalar case was formulated first, then generalized to the multivariate
> case, but that doesn't change the mathematics unless if you believe
> certain ethnomathematicians).
>
> However, there are other contexts in which scalars are used where the
> determinant would come into play. For example, scalar-vector
> multiplication is defined. If you have an n-vector, then scalar-vector
> multiplication behaves like matrix-vector multiplication provided that
> the matrix is a diagonal matrix with the diagonal entries each being
> the scalar value. In this context, the determinant is not just the
> scalar value itself, but rather value**n.
>

Ok, but I'm not sure I see why this would make automatic handling of
scalars as 2d 1x1 arrays a bad idea.

> Many of the references you found stating that the "determinant of a
> scalar value is" the scalar itself were actually referring to 1x1
> matrices, not true scalars. 1x1 matrices behave like scalars, but not
> all scalars behave like 1x1 matrices. linalg.det() does not know the
> context in which you are treating the scalar, so it rightly complains.
>
> That said, I expect you will be running into this 1x1<->scalar special
> case reasonably frequently in statsmodels. Writing a dwim_logdet()
> utility function there that does what you want is a perfectly
> reasonable thing to do.
>

Fair enough.

Can someone mark the ticket invalid or won't fix then?  It doesn't
look like I can do it.

http://projects.scipy.org/numpy/ticket/1556

Skipper


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