Re: TOMS748 question

From: Shriramana Sharma (samjnaa_at_[hidden])
Date: 2021-01-27 16:29:37

https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L335

Couldn't `if(boost::math::sign(fa) * boost::math::sign(fb) > 0)` be
simplified to `if (fa * fb > 0)` or is it just a case of being generic
and Boost-ish templatable?

https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L105

Is this test of `if((b - a) < 2 * tol * a)` where tol is 2×epsilon
meaningful given that eps_tolerance has a minimum of 4×epsilon? I
would have thought that tol(a, b) will catch this before it ever
arrives here.

Or is it needed because that is relative tolerance and this is absolute?

On Wed, Jan 27, 2021 at 9:47 PM Shriramana Sharma <samjnaa_at_[hidden]> wrote:
>
> Thanks for replying. Will ask here if I have any further questions.
>
>
> On Wed, Jan 27, 2021 at 6:38 PM John Maddock via Boost-users
> <boost-users_at_[hidden]> wrote:
> >
> > On 26/01/2021 15:46, Shriramana Sharma via Boost-users wrote:
> > > Namaste.
> > >
> > > This is wrt the TOMS748 math root finding implementation:
> > >
> > > Given that `if(fa == 0)` is handled at:
> > >
> > > https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L325
> > >
> > > … and the function returns in case of the above condition, it is not
> > > clear to me what the need is for the `if (fa != 0)` at:
> > >
> > > https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L342
> >
> > You're quite right - it's superfluous, will fix.
> >
> > > Now I also note similar checks at:
> > >
> > > https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L352
> > > https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L366
> > >
> > > … but regarding those lines, while I can understand the need for
> > > checking there after more bracketing work is done, it is not clear to
> > > me why `(fa == 0)` is alone checked for, and not `(fb == 0)` as well.
> > > I would have thought the algorithm is not biased towards a or b.
> >
> > When bracket() is called, it updates either fa or fb with the next value
> > (fc), and when fc is zero then fa is always set to zero, and the result
> > is always a.  So checking fb == 0 is unnecessary after a bracket() call.
> >
> > > Indeed, in the last steps from:
> > >
> > > https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L465,
> > >
> > > … both the conditions are checked for,
> >
> > Somewhat different situation - at this point the loop has terminated,
> > and we're just tightening up our interval in the case that one of a or b
> > is right on the root.  This is a nicety not required by the algorithm as
> > such, and indeed the fb == 0 branch *may* be superfluous, but I would
> > want to think very carefully indeed before changing it ;)
> >
> > Best, John Maddock.
> >
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> Shriramana Sharma ஶ்ரீரமணஶர்மா श्रीरमणशर्मा 𑀰𑁆𑀭𑀻𑀭𑀫𑀡𑀰𑀭𑁆𑀫𑀸

-- 
Shriramana Sharma ஶ்ரீரமணஶர்மா श्रीरमणशर्मा 𑀰𑁆𑀭𑀻𑀭𑀫𑀡𑀰𑀭𑁆𑀫𑀸