On Sun, Mar 28, 2010 at 03:26, Anne Archibald <peridot.faceted@gmail.com> wrote:

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.

40 is not a bad number to loop over. The thing I would be worried about is the repeated calculation of the (1000, 1000) radial function evaluation. I think that a small modification of Rbf could be made to handle the vector-valued case. I leave that as an exercise to Andrea, of course. :-) -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco