Re: TOMS748 question

From: Shriramana Sharma (samjnaa_at_[hidden])
Date: 2021-01-27 16:17:00

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