On Tue, Jul 27, 2010 at 11:36, Skipper Seabold <jsseab...@gmail.com> wrote: > On Tue, Jul 27, 2010 at 12:00 PM, Robert Kern <robert.k...@gmail.com> wrote: >> On Tue, Jul 27, 2010 at 07:51, Skipper Seabold <jsseab...@gmail.com> wrote: >>> On Mon, Jul 26, 2010 at 10:05 PM, Alan G Isaac <ais...@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.
Because scalars might not be representing 1x1 matrices but rather NxN diagonal matrices. >> 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 Done. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
