@Nate, I don't know all the details about this algorithm, but based on the tests I've performed here it requires much fewer function evaluations than dblquad or tplquad, since it is NOT a recursive call of 1D-integrands. It offers two refinement options: h-cubature which refines by including more integration points p-cubature which refines by increasing the approximation order (better for smooth functions) I will keep working on that and I hope to give you a better feedback very soon. Please, see more details here: http://ab-initio.mit.edu/wiki/index.php/Cubature Greetings, Saullo 2013/8/23 <scipy-dev-request@scipy.org>

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Today's Topics:

1. Re: Loss of precision using lsoda f2py interface or ode class (Joris Vankerschaver) 2. Re: Need some help to wrap the cubature package in scipy/integrate (Nathan Woods)

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Message: 1 Date: Fri, 23 Aug 2013 14:56:49 +0200 From: Joris Vankerschaver <jvankers@gmail.com> Subject: Re: [SciPy-Dev] Loss of precision using lsoda f2py interface or ode class To: SciPy Developers List <scipy-dev@scipy.org> Message-ID: <504DC808-6E3E-436B-A936-696B51834882@gmail.com> Content-Type: text/plain; charset=us-ascii

On 23-aug-2013, at 02:15, Juan Luis Cano wrote:

...

I fear odeint/ode bugs are starting to pile up (gh-1567, gh-1801, gh-1976, gh-2515, gh-2570), and as many have suggested in the past a rewrite or redesign would be quite helpful.

This may have been pointed out before, but one inconsistency that should be fixed in an eventual redesign is that scipy.integrate.ode expects an RHS of the form `f(t, y0, ...)` whereas odeint expects an RHS with the first two parameters reversed, i.e. of the form `f(y0, t, ...)`. The former convention is the standard in Matlab and Sage.

All the best, Joris

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Message: 2 Date: Fri, 23 Aug 2013 10:22:01 -0600 From: Nathan Woods <charlesnwoods@gmail.com> Subject: Re: [SciPy-Dev] Need some help to wrap the cubature package in scipy/integrate To: SciPy Developers List <scipy-dev@scipy.org> Message-ID: <-1837672449859755872@unknownmsgid> Content-Type: text/plain; charset="iso-8859-1"

We just had a multidimensional integrator (nquad) wrapped into the latest beta version of scipy. How does cubature compare? I've been kicking around the idea of improving the speed of nquad by moving more of the code to a compiled language. How would that compare?

Nate

On Aug 23, 2013, at 5:35 AM, Saullo Castro <saullogiovani@gmail.com> wrote:

I am wrapping the Cubature package for multi-dimensional integration that supports vector-valued functions and offers both fixed and adaptive integration schemes.

Please, see more details here: http://ab-initio.mit.edu/wiki/index.php/Cubature

I've forked the scipy repository and my current attempt can be directly accessed here:

https://github.com/saullocastro/scipy/blob/master/scipy/integrate/_cubature....

When compiling the cython code I am getting the error:

_cubature.obj : error LNK2019: unresolved external symbol hcubature referenced in function __pyx_pf_9_cubature_fhcubature C:\usr\scipy\scipy\integrate\_cubature.pyd : fatal error LNK1120: 1 unresolved externals error: command 'link.exe' failed with exit status 1120

Could you please have a look?

Thank you very much! Saullo

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