On 27 March 2010 20:24, Andrea Gavana <andrea.gavana@gmail.com> wrote:

Hi All,

I have an interpolation problem and I am having some difficulties in tackling it. I hope I can explain myself clearly enough.

Basically, I have a whole bunch of 3D fluid flow simulations (close to 1000), and they are a result of different combinations of parameters. I was planning to use the Radial Basis Functions in scipy, but for the moment let's assume, to simplify things, that I am dealing only with one parameter (x). In 1000 simulations, this parameter x has 1000 values, obviously. The problem is, the outcome of every single simulation is a vector of oil production over time (let's say 40 values per simulation, one per year), and I would like to be able to interpolate my x parameter (1000 values) against all the simulations (1000x40) and get an approximating function that, given another x parameter (of size 1x1) will give me back an interpolated production profile (of size 1x40).

If I understand your problem correctly, you have a function taking one value as input (or one 3D vector) and returning a vector of length 40. You want to know whether there are tools in scipy to support this. I'll say first that it's not strictly necessary for there to be: you could always just build 40 different interpolators, one for each component of the output. After all, there's no interaction in the calculations between the output coordinates. This is of course awkward, in that you'd like to just call F(x) and get back a vector of length 40, but that can be remedied by writing a short wrapper function that simply calls all 40 interpolators. A problem that may be more serious is that the python loop over the 40 interpolators can be slow, while a C implementation would give vector-valued results rapidly. To make this work, you're going to have to find a compiled-code interpolator that returns vector values. This is not in principle complicated, since they just need to run the same interpolator code on 40 sets of coefficients. But I don't think many of scipy's interpolators do this. The only ones I'm sure are able to do this are the polynomial interpolators I wrote, which work only on univariate inputs (and provide no kind of smoothing). If you're going to use these I recommend using scipy's spline functions to construct smoothing splines, which you'd then convert to a piecewise cubic. But I'd say, give the 40 interpolators a try. If they're slow, try interpolating many points at once: rather than giving just one x value, call the interpolators with a thousand (or however many you need) at a time. This will speed up scipy's interpolators, and it will make the overhead of a forty-element loop negligible. Anne

Something along these lines:

import numpy as np from scipy.interpolate import Rbf

# x.shape = (1000, 1) # y.shape = (1000, 40)

rbf = Rbf(x, y)

# New result with xi.shape = (1, 1) --> fi.shape = (1, 40) fi = rbf(xi)

Does anyone have a suggestion on how I could implement this? Sorry if it sounds confused... Please feel free to correct any wrong assumptions I have made, or to propose other approaches if you think RBFs are not suitable for this kind of problems.

Thank you in advance for your suggestions.

Andrea.

"Imagination Is The Only Weapon In The War Against Reality." http://xoomer.alice.it/infinity77/

==> Never *EVER* use RemovalGroup for your house removal. You'll regret it forever. http://thedoomedcity.blogspot.com/2010/03/removal-group-nightmare.html <== _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion