Re: About diagonal matrices

[John W. Eaton]

On 20-Feb-2009, Jaroslav Hajek wrote:

| On Fri, Feb 20, 2009 at 5:45 PM, John W. Eaton <address@hidden> wrote:
| 
| > But I think there are also some bugs.  Shouldn't the following return
| > full matrices with the zero elements replaced by NaN (or -0, in the
| > case of dividing by -Inf)?
| >
| >  diag ([1,2,3]) / 0
| >  diag ([1,2,3]) / NaN
| >  diag ([1,2,3]) / -Inf
| >  diag ([1,2,3]) * NaN
| >  diag ([1,2,3]) * Inf
| >
| 
| I think it's better in the current manner. I don't like the idea that
| the memory can suddenly explode just because the multiplier happened
| to be Inf. Right now, scalar * diag gives invariantly diag. This is
| somewhat analogous to how sparse matrices behave.

I see

  octave:3> speye (3)*Inf
  ans =

  Compressed Column Sparse (rows = 3, cols = 3, nnz = 3 [33%])
  )

    (1, 1) -> Inf
    (2, 2) -> Inf
    (3, 3) -> Inf

  octave:4> speye (3)/0
  warning: division by zero
  ans =

     Inf   NaN   NaN
     NaN   Inf   NaN
     NaN   NaN   Inf


So there seems to be some disagreement here, even within Octave.

I'm not sure what is best here, but I don't like it that we produce
numerically incorrect or incompatible answers just because of a
storage scheme.

BTW, for the two examples above, Matlab appears to keep the sparse
storage scheme, but does now fill with NaN values.  If I recall
correctly, some previous versions did not do the operations on the
zero values at all.

For sparse matrices, I don't mind switching the storage scheme, though
I can imagine some cases where that would not be desirable either.

For diagonal matrices, we can't fill in the zero values and keep the
diagonal matrix storage scheme.  But we could convert back to diagonal
if the off diagonal elements become zero.  Should we be doing that?
It doesn't appear to be implemented now.

jwe