Re: fsolve test failure

[Jaroslav Hajek]

On Tue, Jan 27, 2009 at 5:31 PM, John W. Eaton <address@hidden> wrote:
> After updating and rebuilding today, the following test is failing for
> me:
>
>  function retval = f (p)
>    x = p(1);
>    y = p(2);
>    z = p(3);
>    w = p(4);
>    retval = zeros (4, 1);
>    retval(1) = 3*x + 4*y + exp (z + w) - 1.007;
>    retval(2) = 6*x - 4*y + exp (3*z + w) - 11;
>    retval(3) = x^4 - 4*y^2 + 6*z - 8*w - 20;
>    retval(4) = x^2 + 2*y^3 + z - w - 4;
>  endfunction
>
>  test
>   x_opt = [ -0.767297326653401, 0.590671081117440, 1.47190018629642, 
> -1.52719341133957 ];
>   tol = 1.0e-5;
>   [x, fval, info] = fsolve (@f, [-1, 1, 2, -1]);
>   assert (info > 0);
>   assert (norm (x - x_opt, Inf) < tol);
>   assert (norm (fval) < tol);
>
>  octave> info
>  info =  1
>  octave> norm (x - x_opt, Inf), tol
>  ans =  1.6079e-05
>  tol =  1.0000e-05
>  octave> norm (fval), tol
>  ans =  1.0665e-04
>  tol =  1.0000e-05
>

That's weird, because I get something different:
octave:5> info
info =  1
octave:6> norm(x-x_opt, Inf)
ans =  4.1002e-07
octave:7> norm (fval)
ans =  3.4606e-06

Do you have qrupdate linked to Octave? That could maybe explain the
differences...
otherwise, we can check per line where the numbers start diverting.

> I'm not sure, but it looks like this line
>
>  ## Replace fun with a guarded version.
>  fun = @(x) guarded_eval (fun, x);
>
> should be
>
>  ## Replace fun with a guarded version.
>  fcn = @(x) guarded_eval (fcn, x);
>
> as fun is not defined before this point, or used after it.
>

OK, of course.

> Also, in the default settings section
>
>    x = optimset ("MaxIter", 400, "MaxFunEvals", Inf, \
>    "Jacobian", "off", "TolX", 1e-7, "TolF", 1e-7,
>    "OutputFcn", [], "Updating", "on", "FunValCheck", "off");
>    return;
>
> wouldn't it be better to set the default tolerances based on something
> like sqrt (eps (class (x))?  Or, if fsolve should still work when
> passed integer matrices, maybe something like
>
>  if (isa (x, "single"))
>    tol = sqrt (eps, "single");
>  else
>    tol = sqrt (eps);
>  endif
>

Originally, I used default settings exactly like this. However, I was
not sure how to reflect this in the default options, so I changed it
to fixed tolerances. If you have a better idea...

cheers

-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz