I've tried to do timing of simple 2D integrals using sage/mpmath vs.
mathematica.
Example:
===================================================
sage: version()
'Sage Version 4.3.3, Release Date: 2010-02-21'
sage: %time quadgl(lambda x,y: sin(x)*cos(y)/(x**2+y**2+1),[-8, 10],
[-6,10])
CPU times: user 15.96 s, sys: 0.02 s, total: 15.98 s
******* Wall time: 16.00 s ********
mpf('-0.0043118150747524404')
sage: %time quadts(lambda x,y: sin(x)*cos(y)/(x**2+y**2+1),[-8, 10],
[-6,10])
CPU times: user 43.77 s, sys: 0.08 s, total: 43.85 s
****** Wall time: 43.86 s *********
mpf('-0.0043118140088211727')
========================================================
Mathematica Version 7.0.0
NIntegrate[Sin[x] Cos[y]/(x^2 + y^2 + 1), {x, -8, 10}, {y, -6, 10}] //
Timing
{
****** 2.7881739999999984` ********
, -0.004311814008789632`}
This is a typical result. Mathematica seems to be faster typically by
a factor of 5 and sometimes much more with no tweaking of the method
of integration. If I play with the method of integration more than an
order of magnitude of can be reached quite easily for mathematica ...
Am I doing this right? I.e. is this performance difference roughly
what I should expect for this kind of task?
Is there another way to do numerical integration in sage?
Regards,
wb
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