Re: new gsvd function incompatible w/Matlab

[Daniel J Sebald]

On 08/17/2016 10:28 AM, Rik wrote:
> All,
>
> I don't want to look a gift horse in the mouth, but the new gsvd function
> doesn't calculate the same values as Matlab.  This is a shame, because no
> one with existing Matlab gsvd code will switch to Octave unless it is clear
> that they can get the same results.  I filed a bug report about it here
> (https://savannah.gnu.org/bugs/index.php?48807).
>
> If we are lucky, it is simply a matter of recombining the outputs in a
> different format, but I am not a linear algebra expert so I haven't tried.
>
> --Rik

What is not the same?  (I haven't looked closely.)  Is it something like 
the order of generalized eigenvalues/vectors?

What is important is that the function is consistent.  There is an 
example in the documentation:

> > a = hilb (3);
> > b = [1 2 3; 3 2 1];
> > [u, v, c, s, x, r] = gsvd (a, b);
> > u' * a * x
ans =

  -1.4093e-01  -1.2434e+00   4.3737e-01
  -1.3878e-17  -4.0950e-01   2.7068e-01
   5.5511e-17  -1.8486e-17  -8.0222e-03

> > [1 0 0; [0;0] c] * [r]
ans =

  -0.14093  -1.24345   0.43737
   0.00000  -0.40950   0.27068
   0.00000   0.00000  -0.00802

The two sides of the equation seem correct.

Note, the following error messages don't seem accurately descriptive:

> > demo gsvd
warning: demo: no function gsvd found
warning: called from
    demo at line 117 column 5

[No function gsvd found?  I just called it.]

> > test gsvd
????? gsvd is a built-in function

[Built-in functions don't have tests?]

Dan