[Octave-bug-tracker] [bug #62412] quadcc does not warn when quadrature fails to converge

[Nicholas Jankowski]

Follow-up Comment #11, bug #62412 (project octave):

"It would be nice if in addition, when called from integral, the different
called quadrature functions could be muted, and the estimated returned error
compared within integral to return a warning that is formatted agnostically to
which integrator is used, but this is not necessary."

the 7.1.0 release version now routes complex integrands to quadgk after bug
#58636, which supposedly can intelligently(?) handle them. Do you think there
may be a better way to process that? 

I agree that a single , uniform error estimate would be best.  quadv currently
doesn't have a typical estimate as an output, though. just an evaluation
count, which can sort-of be used as an arbirtrarily scaled convergence metric.
I'm sure it has an internal error metric, but I haven't looked that closely. 
It would be just as easy to add an optional third output with that metric
without breaking compatability if it was available as a simple scalar. Since
it was the only integrator we had that could handle vector-valued functions,
its inclusion was needed to maximize the wrapper's compatability.

for better algorithm documentation:

quadcc: states it provides "an estimate of the absolute integration error",
and doesn't describe how it handles sigularities or inf limits but does
provide the reference for Gonnet where a better definition could be extracted
if its not obvious from the code (after verifying we correctly followed the
method). 
quadgk: describes error as "ERR is an approximate bound on the error in the
integral 'abs (Q - I)', where I is the exact value of the integral.", but it
could probably better describe how that's calculated. Also no informatino
given on transformations but reference to Shampine is given. 
quadv: neither is given, nor a reference, but it says it's Simpsons with 
recursive subdivision.

Of course, Octave's integral wrapper itself was really meant to just be a
bandaid pending an actual integral rewrite. From the matlab help for integral,
"quadgk and integral use essentially the same integration method" it looks
like they just expanded quadgk to add array valued function handling, as
almost all other options are the same. Maybe we over complicated things trying
to keep quadcc for performance. 


    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?62412>

_______________________________________________
  Message sent via Savannah
  https://savannah.gnu.org/