[SciPy-User] The QR decomposition values returned by fsolve

[josef.pktd at gmail.com]

On Sun, Oct 28, 2012 at 8:15 PM, The Helmbolds <helmrp at yahoo.com> wrote:
> I think the following is the source of my confusion. SciPy's docstring for fsolve omits the following
> information found in the "User Guide for MINPACK" regarding HYBRD and HYBRDJ.
> The following is not a direct quote, but it's pretty close:
>
>     The initial value of the Jacobian is not updated
>     until the rank-1 method fails to produce satisfactory progress.
>
> I assume that the Jacobian gets updated intermittently, and only
> when the rank-1 method is not producing satisfactory progress.
> (So in fact it might never get updated!!)
>
> Because fsolve's QR-related outputs (`fjac`, `r`, and `qtf`) are based on the
> final value of fsolve's internal "approximate Jacobian", they may be quite wide
> of the mark, unless fsolve "just happens" to return right after the Jacobian
> has been updated.
>
> Accordingly -- unless there is some objection -- in my revision of fsolve's docstring, I'll
> add to the Notes section something like the following:
>
>     **Cautionary Note**: According to [the MINPACK User Guide], the
>     initial value of the program's "approximate Jacobian" is estimated
>     (or calculated if `fprime` is supplied by the user), but is updated
>     only when the rank-1 method is not producing satisfactory progress.
>     Because the program's QR-related outputs (`fjac`, `r`, and `qtf`)
>     are based on the program's internal "approximate Jacobian", they
>     should not be used in subsequent analysis unless their validity is
>     confirmed by independent computations.

Thanks, this is useful information.

What's not clear to me is what rank-1 method means, how often this
will occur, and whether mentioning rank-1 method is useful for users.
If I have to use my own Jacobian, then I don't care whether it's
rank-1 or rank-5 :), given that I'm not an expert in the details of
the algorithm.

Do you know if the same is true for leastsq?

Josef


>
> Bob H
>
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