[Numpy-discussion] fixing diag() for matrices

Keith Goodman kwgoodman at gmail.com
Fri Jul 28 08:07:49 CDT 2006

Every time I want to make a diagonal matrix from a vector I have to do
a google search. So I'm with you Sven:

diag(NxN matrix) should return a Nx1 matrix
diag(Nx1 or 1xN matrix) should return a NxN matrix

instead of the current behavior:

diag(NxN matrix) returns an array
diag(Nx1 matrix) returns a 1x1 array

>> x

matrix([[ 0.43298158,  0.84572719],
        [ 0.1391546 ,  0.66412104]])
>> diag(x)
   array([ 0.43298158,  0.66412104])
>> diag(x[:,0])
   array([ 0.43298158])

On 7/28/06, Sven Schreiber <svetosch at gmx.net> wrote:
> Robert Kern schrieb:
> > Sven Schreiber wrote:
> >> That would be fine with me. However, I'd like to point out that after
> >> some bug-squashing currently all numpy functions deal with
> >> numpy-matrices correctly, afaik. The current behavior of numpy.diag
> >> could be viewed as a violation of that principle. (Because if x has
> >> shape (n,1), diag(x) returns only the first entry, which is pretty
> >> stupid for a diag-function operating on a vector.)
> >
> > I don't think so. It's operating exactly as it is documented to. It doesn't do
> > what you want, but it's not supposed to read your mind and guess that you are
> > treating (n,1) and (1,n) arrays as linear algebraic vectors and that you want to
> > form a diagonal matrix from that vector. It handles matrix objects just fine; it
> > does not obey a particular convention that you want to use, though. That's
> > neither broken nor a violation of the principle that most numpy functions should
> > accept matrix objects; it's just not what you want.
> Ok, let me get some facts straight:
> 1. If you're using numpy-matrices, algebraic vectors are *automatically*
> (n,1) or (1,n). I didn't make it up, and nobody has to read my mind to
> understand that; it's just a *fact* of numpy (and you knew that long
> before I was even aware of numpy's existence ;-).
> 2. I never claimed that the documentation of diag is wrong. I'm just
> questioning whether its behavior with vectors represented as
> numpy-matrices (which have shape (n,1) or (1,n) and are therefore always
> 2d in the numpy sense) is really intended, because I currently doubt
> that it's useful for *anyone*. (Of course you can prove me wrong there...)
> 3. The cited principle is not (only) about accepting matrices, it's
> about "honoring" them by either preserving their type for the output,
> and of course by doing the equivalent thing as for the equivalent
> numpy-array input. Currently, however, diag() is not providing the
> "vector-to-diagonal-matrix" functionality if you work with
> numpy-matrices (modulo some obvious workarounds). To me, that's a partly
> broken function, and it's *not* handling matrix objects "just fine".
> >
> > I don't want to introduce a backwards-compatibility-breaking special case to the
> > function. "Special cases aren't special enough to break the rules." Different
> > functionality should go into a different function.
> >
> I hope (but somehow doubt...) that I've convinced you that it's actually
> about applying the same logical rule to all input types, not about
> introducing a special case. I agree that in principle backwards
> compatibility could be an issue; however that would mean that people are
> actually using the strange behavior that diag() displays with (n,1) or
> (1,n) matrix-vectors (namely returning only the first element).
> Does anybody do that? I doubt it, but of course I can't prove it; does
> anybody on the list know of an example where it's used?
> Having said all that in this lengthy message, I don't want to push it
> too far. I believe that the right thing to do would be to fix diag()
> along the lines I suggested. If I haven't managed to convince you and/or
> the other developers, so be it, and I can live with a new
> numpy.matlib.diag() just fine.
> In the latter case, may I also suggest that a new numpy.matlib.diag()
> always return a numpy-matrix even when given a numpy-array? Background:
> Currently (and I think it's ok that way) the eig*() functions return the
> eigenvalues in a 1d-array, even for numpy-matrices as inputs. It is
> fairly usual to use a diagonal matrix with the eigenvalues on the
> diagonal in an algebraic formula. That could be achieved with
> n.matlib.diag(n.linalg.eig*(...)[0]) without an enclosing mat() call
> only if n.matlib.diag always returns a numpy-matrix.
> Thanks for reading until the end...
> cheers,
> Sven
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