[Numpy-discussion] determinant of a scalar not handled

[Charles R Harris]

On Mon, Jul 26, 2010 at 6:22 PM, Joshua Holbrook <josh.holbrook at gmail.com>wrote:

> 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
> > _______________________________________________
> > NumPy-Discussion mailing list
> > NumPy-Discussion at scipy.org
> > http://mail.scipy.org/mailman/listinfo/numpy-discussion
> >
>
> 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.
>
>
And the definition of a determinant is? There are several, but the common
form these days is an anti-symmetric multilinear form acting on a set of
column vectors and scaled so that applying it to the columns of the identity
matrix is one. In that case one would have to treat a scalar as a column
vector.

As a practical matter I don't have a problem with det handling scalars if it
is useful to do so.

Chuck
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