[Numpy-discussion] determinant of a scalar not handled

[Joshua Holbrook]

On Mon, Jul 26, 2010 at 4:18 PM, Skipper Seabold <jsseabold at gmail.com> wrote:
> On Mon, Jul 26, 2010 at 7:38 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
>>
>>
>> On Mon, Jul 26, 2010 at 5:05 PM, Skipper Seabold <jsseabold at gmail.com>
>> wrote:
>>>
>>> On Mon, Jul 26, 2010 at 5:48 PM, Alan G Isaac <aisaac at american.edu> wrote:
>>> > On 7/26/2010 12:45 PM, Skipper Seabold wrote:
>>> >> Right now np.linalg.det does not handle scalars or 1d (scalar) arrays.
>>> >
>>> > I don't have a real opinion on changing this, but I am curious
>>> > to know the use case, as the current behavior seems
>>>
>>> Use case is just so that I can have less atleast_2d's in my code,
>>> since checks are done in linalg.det anyway.
>>>
>>> > a) correct and b) to provide an error check.
>>> >
>>>
>>> Isn't the determinant defined for a scalar b such that det(b) ==
>>> det([b]) == det([[b]])?
>>>
>>
>> Well,  no  ;)  Matrices have determinants, scalars don't. Where are you
>> running into a problem? Is something returning a scalar where a square array
>> would be more appropriate?
>
> No, linalg.det always returns a scalar, and I, of course, could be
> more careful and always ensure that whatever the user supplies it
> becomes a 2d array, but I don't like putting atleast_2d everywhere if
> I don't need to.  I thought that the determinant of a scalar was by
> definition a scalar (e.g, google "determinant of a scalar is"), hence
>
> np.linalg.det(np.array([[2]]))
> #2.0
>
> which should either fail or if not, then I think np.linalg.det should
> handle scalars and scalars as 1d arrays.
>
> So instead of me having to do
>
> b = np.array([2])
> b = np.atleast_2d(b)
> np.linalg.det(b)
> #2.0
>
> I could just do
> b = np.array([2])
> np.linalg.det(b)
> #2.0
>
> Regardless, doing asarray, checking if something is 2d, and then
> checking if its square seems redundant and could be replaced by an
> atleast_2d in linalg.slogdet which 1) takes a view as an array, 2)
> ensures that the we have a 2d array, and 3) handles the scalar case.
> Then we check if it's square.  It doesn't really change much except
> keeping me from having to put atleast_2d's in my code.
>
> Skipper
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>

imo, the determinant of a scalar should be defined as itself, based on
the definition of the determinant. I don't have a vested interest in
linalg's behavior in this respect, though.

--Josh