Re: Meaning of * (mtimes) for nd-arrays

[Marco Atzeri]

On 16/02/2016 20:13, Nicholas Jankowski wrote:
>     one(1,1,3) is not the same as one(1,3). I never said the oposite. The
>     behavior when multiplying by a vector is what is equivalent (it seems
>     only in Octave). You see, a singleton left dimension is rather
>     useless...but I grant that one could stick to that. But as Jordi
>     mentioned many times there are plenty of generalizations, e.g.
>     if (n x 1) * (1 x m) gives n x m, then  (n x 1) * (1 x 1 x m) gives (1
>     x n x m), or (n x 1 x m), or (n x m)? note, tat the last one is the
>     "squeeze" of the first one and it seems what the programmer chose.
>
>     So I guess we will have to stick to matlab idiosyncrasy and fix this
>     to give an error... anyways, is this the results of broadcasting? No
>     way of checking the Octave:broadcast warning anymore, but I wouldn't
>     think so.
>
>
> Yes, sorry I was being a bit pedantic on that. I figured you knew the
> difference but I was just being explicit.
>
> In any case, I'd argue that a singleton left dimension is not completely
> useless. I put a model together last year that made heavy use of
> n-vectors to orthogonalize the process. Combined with broadcasting, it
> made bookkeeping rather straight forward with dims 1 and 2 being the 2x2
> transfer functions, 3 being the spatial degree of freedom, 4 being the
> eigenvalue d.o.f., 5 being ... something else.
>
> In any case, almost no basic matrix functions accept anything with ndims
> ~= 2. I think some people have written n-D array functions, but the base
> * should throw an error rather than squeeze the user's data for them. I
> wouldn't think broadcasting would be to blame here, as it shouldn't come
> up without invoking .*  , should it?
>
> nickj

It seems a curious extension of broadcasting
always having max two dimension as output

octave:15> ones(2,3)*ones(3,1)
ans =

   3
   3

octave:16> ones(2,3)*ones(3,1,2)
ans =

   3   3
   3   3

octave:17> ones(2,3)*ones(3,1,2,2)
ans =

   3   3   3   3
   3   3   3   3

octave:18> ones(2,3)*ones(3,1,2,2,2)
ans =

   3   3   3   3   3   3   3   3
   3   3   3   3   3   3   3   3


The error messages gives a hint on what is happening:

octave:34> ones(2,2,3)*ones(3,2,2,2)
error: operator *: nonconformant arguments (op1 is 2x6, op2 is 3x8)
octave:34> ones(2,2,3)*ones(3,2,2)
error: operator *: nonconformant arguments (op1 is 2x6, op2 is 3x4)
octave:34> ones(2,2,2)*ones(2,2,2)
error: operator *: nonconformant arguments (op1 is 2x4, op2 is 2x4)