Thanks for the feedback on quadpack and any potential
interface.
You write:
------------------------
>> over the interval (x,2,3) by using the default epsabs=0.0,
>> epsrel = 1.0e-8, so only epsrel plays a role, but I get
>I don't think that's true. If you set epsabs to 0, then you are telling
>quadpack that you want to get an absolute error of 0. I don't recall
>how epsabs and epsrel interact, though.
---------------------------------------------------
You will get the default options settings if you use
an integrand containing an undefined symbol, in which
case quad_qags (for example) returns a noun form:
(%i3) quad_qags(a*x,x,0,1);
(%o3) quad_qags(a x, x, 0, 1, epsrel = 1.0E-8, epsabs = 0.0, limit = 200)
It is clear that this set of defaults is not meant to ask for an
answer with zero absolute error (which is also not possible usually
in any floating point calculation).
The example I used, in fact, showed that a more accurate answer
is returned by using epsabs=0.0, in which case the relative error
criterion is the complete decider on precision goals being met.
Detailed examples and comparisons of the effects, in practice,
of using one or the other of these parameters to control the
calculation are included in Ch. 8, Numerical Integration
(Maxima by Example).
You later write:
----------------------------------------
>For the standard quadpack interface, I can see where it might be useful
>to turn off the messages because the return code is part of the answer
>so you can tell if the integration was apparently ok or not. But with
>your nint (which reminds of Fortran nint/aint, not numerical
>integration), there's no indication that anything went wrong, except if
>quadpack prints out the error message.
--------------------------------------------------
The current version of nint always writes
an error message to the console screen whenever the error number
is not 0.
Hence nint satisfies your justified desire to be warned of
anything not going right. And because I automatically write an
error message to the screen, I would like to have a way to locally
turn off the automatic slatec error message reporting to the
screen.
That being said, I don't understand error number 1 being declared
for my example. It seems counterintuitive that slatec complains
with the progress using a choice of options that leads to the
most accurate answer.
As to the weird name, nint is just a
short easily typed placeholder for a better name. As the archives
reveal, there was a long and passionate exchange of views
long ago about another proposed numerical integration
packager function, which I think was called nintegrate. There
were complaints about that name as well, and the whole effort
was lost(?) in the mists of history.
My attitude is that providing students etc with a less than perfect
packaged numerical integrator is still a useful thing to do.
Ted Woollett