better cumulative integration routines (like cumtrapz)
Hi, I'm wondering if anyone can recommend a routine for one-dimensional cumulative numerical integrals. Obviously there is scipy.integrate.cumtrapz, but I was wondering if anyone knows of an implementation of a more sophisticated numerical integration algorithm that can take not just end points, but a whole series of points, and efficiently approximate the definite integral at each point. In other words, I have a function f(x), and want the value of the definite integral from x0 to [x1, x2, x3, x4, ...] Ideally I would want to be able to specify the desired precision of the results, and also get an estimate of the achieved precision. Essentially I'm asking for scipy.integrate.quad, but optimized for a whole set of points. For the most part my functions are well behaved, so I don't need fancy singularity-handling, though built-in infinite-limit handling is great. The obvious hack is to compute the definite integral separately for each interval in my series of points, then add them together, but I was wondering if anyone knows of an algorithm/implementation that does this efficiently. I'd be willing to work on implementing something myself, if you have pointers to an algorithm. Thanks! -Roban
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Roban Hultman Kramer