William Stein wrote:
>> Should we phase GSL out of numerical_integral too? Should we replace it
>> with the equivalent scipy call (which would make it massively shorter
>> and simpler)?
>
> Yes, it is very tempting to do so. One thing is that each function
> evaluation
> could in theory be much faster with the GSL version, since GSL takes
> as input a C-level callback function, whereas I think scipy's quadpack
> wrapper doesn't.
Using the example from this thread:
sage: timeit('quad(ff, 0, 18)')
625 loops, best of 3: 157 µs per loop
sage: timeit('numerical_integral(ff, 0, 18)')
625 loops, best of 3: 78.4 µs per loop
So GSL is twice as fast.
A few more examples pulled from thin air:
sage: f=250*cos(pi*x/180)^1.8 + 170.35*sin(x*pi)+log(1+x)
sage: ff = fast_float(f, 'x')
sage: timeit('quad(ff, 0, 18)')
625 loops, best of 3: 136 µs per loop
sage: timeit('numerical_integral(ff, 0, 18)')
625 loops, best of 3: 104 µs per loop
sage: f=250*cos(pi*x/180)^1.8 +
170.35*sin(x*pi)+log(1+x)+1/sqrt(1+x)+x^(0.3)
sage: ff = fast_float(f, 'x')
sage: timeit('quad(ff, 0, 18)')
625 loops, best of 3: 699 µs per loop
sage: timeit('numerical_integral(ff, 0, 18)')
625 loops, best of 3: 142 µs per loop
In each case, GSL is better or way better.
>
> Jason said:
>
>> Both GSL and scipy call quadpack.
>
> I'm not sure exactly what this means, since probably scipy's quadpack
> is a fortran library, but GSL is definitely built 100% fortran free
> (there's no fortran code in gsl and no fortran dependencies). Maybe
> GSL has a C port of quadpack, or some other sort of translation of the
> code. So I suspect GSL and scipy are calling into separate separate
> code that is compiled using a different compiler, so there could be
> differences in performance and capabilities.
Sorry; from the GSL docs:
The library reimplements the algorithms used in quadpack, a numerical
integration package written by Piessens, Doncker-Kapenga, Uberhuber and
Kahaner. Fortran code for quadpack is available on Netlib.
So you're right, there could be performance differences in the library
alone.
Jason
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