[SciPy-Dev] vectorized scipy.integrate.quad

[Christoph Groth]

Nathan Woods wrote:

> Unless I'm mistaken, though, integration of a python function seems
> unlikely to take advantage of a vectorized C integrator, so the speed
> ups would be limited to those calling quad with ctypes functions.

What I proposed is making it possible that the integrand gets called
with a sequence of x-values instead of a single x-value at a time.  It
would be then up to the user-specified integrand function to perform the
computation.  I can think of at least three ways that can provide speed-ups:

• vectorized evaluation using vectorized numpy operations (it should be faster
  to call np.sin(x) once with x being an array of 21 elements than to
  call math.sin(x) 21 times).

• concurrent.futures

• MPI

Is there a problem that I fail to see?

> Also, I think breaking the API would be a bad idea, but you could, for
> instance, allow quad to accept both numbers and sequences, and then
> wrap the number in an array before sending it on to the
> integrator. This would preserve the API, while allowing the desired
> vectorization.

Of course breaking the API is a bad idea.  That’s why I have in mind
keeping scipy.integrate.quad as it is, and adding a sibling that could
be called scipy.integrate.vectorized_quad.  If the algorithm of
vectorized_quad remains the same (as planned), quad could be eventually
implemented as a thin wrapper around vectorized_quad.  This would allow
to remove the unomodified QUADPACK from scipy.

I am sorry, I do not understand your proposal for extending the API in a
backwards-compatible way without introducing a new function.  Could you
please explain it in more detail?

Christoph
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