[Octave-bug-tracker] [bug #57113] fminunc return wrong Hessian matrix

[Giuseppe]

Follow-up Comment #2, bug #57113 (project octave):

Hi! I don’t need symbolic solution. I was using the maximul likelihood
method in order to estimates parameters for the pdf of experimental data and
looking at the hessian, I noted there was incorrect results. So I tried with
the paraboloid and I saw that the function return the totally incorrect
result.
I think that there are some errors in the functions for the optimization of
multi variable functions, in fact I also noted that fminsearch often diverges
despite a good starting point.

Bye!
[comment #1 comment #1:]
> Thank you for your bug report.  Please note, that Octave "primarily intended
for numerical computations".  It it not a computer algebra system
https://en.wikipedia.org/wiki/Computer_algebra_system.  Octave uses some
adapted BFGS (a quasi-Newton) method in "fminunc" (see "edit fminunc") and
only provides approximations of the Hessian matrix.
> 
> 
> >> [x, fval, info, output, grad, hess] = fminunc (@(x) sum (x.^2),
ones(2,1))
> x =
> 
>   -0.0000000058530
>   -0.0000000058530
> 
> fval =    6.8516e-17
> info =  2
> output =
> 
>   scalar structure containing the fields:
> 
>     iterations =  16
>     successful =  7
>     funcCount =  29
> 
> grad =
> 
>   -0.000000026607
>   -0.000000026607
> 
> hess =
> 
>    1.50000   0.50000
>    0.50000   1.50000
> 
> 
> If you want to get a symbolic solution, please use the symbolic toolbox of
Octave, which does a great job for this toy problem:
> 
> 
> >> pkg load symbolic
> >> syms x y
> >> f(x, y) = x^2 + y^2
> f(x, y) = (symfun)
> 
>    2    2
>   x  + y
> 
> >> grad(x, y) = [diff(f, x); diff(f, y)]
> grad(x, y) = (symfun)
> 
>   ⎡2⋅x⎤
>   ⎢   ⎥
>   ⎣2⋅y⎦
> 
> >> hess(x, y) = [diff(f, x, 2), diff(diff (f, x), y); diff(diff (f, y), x),
diff(f, y, 2)]
> hess(x, y) = (symfun)
> 
>   ⎡2  0⎤
>   ⎢    ⎥
>   ⎣0  2⎦
> 

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