[Octave-bug-tracker] [bug #52074] Missing integration functions integral2, integral3

[Nicholas Jankowski]

Follow-up Comment #1, bug #52074 (project octave):

I started a wrapper to dblquad similar to that done for integral. I'm now
recalling what issues popped up last time I looked at this.

In order to have full compatibility:
1 - integral2 needs y-limits to be able to be functions of x. dblquad can only
handle scalar limits (rectangular integration region.) it may be able to do a
mask function overlay to 'zero out'  certain regions for non-rectangular
domains, but that seems pretty inefficient (matlab agrees in it's public help
for integral2). but it may be a decent initial compatibility hack. (ylim as a
function is not available in matlab's dblquad either, so it's not a dblquad
incompatibility)

2 - integral2 takes a 'method' parameter that lets you select between 'tiled'
(or patch integration a la quad2d, not yet implemented in Octave) and
'iterated' (what it seems dblquad currently does). if a quad2d gets
implemented could probably have the wrapper call quad2d or dblquad as
specified. for now, can't do it. 

3 - only other parameters are reltol and abstol.  the problem is that dblquad
only takes abstol. it will pass parameters to the integrating function, but it
will only pass the limits and abstol to the underlying integrator. So even
though I could have it use quadgk which can take a reltol, I don't have any
way of pass the reltol value to it.  So, another parameter that can't be used
if integral2 is a simple wrapper.

a minimal, not fully compatible wrapper should be trivial. issue 2 should be
trivial once a quad2d appears. issue 1 should be able  to be satisfied with a
masking hack.  issue 3... no idea without fully reimplementing a 2-d
integration routine. (I think all the integral, integral2, integral3 functions
will need that to get full compatibility.)

will try for a minimal integral2 wrapper this weekend.

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