On Sun, Mar 28, 2010 at 4:47 PM, Andrea Gavana <andrea.gavana@gmail.com> wrote:

HI All,

On 28 March 2010 19:22, Robert Kern wrote:

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. :-)

It seems like this whole interpolation stuff is not working as I thought. In particular, considering scalar-valued interpolation (i.e., looking at the final oil recovery only and not the time-based oil production profile), interpolation with RBFs is giving counter-intuitive and meaningless answers. The issues I am seeing are basically these:

# Interpolate the cumulative oil production rbf = Rbf(x1, x2, x3, x4, x5, x6, final_oil_recovery)

# Try to use existing combination of parameters to get back # the original result (more or less) possible_recovery = rbf(x1[10], x2[10], x3[10], x4[10], x5[10], x6[10])

1) If I attempt to use the resulting interpolation function ("rbf"), inputting a single value for each x1, x2, ..., x6 that is *already present* in the original x1, x2, ..., x6 vectors, I get meaningless results (i.e., negative oil productions, 1000% error, and so on) in all cases with some (rare) exceptions when using the "thin-plate" interpolation option; 2) Using a combination of parameters x1, x2, ..., x6 that is *not* in the original set, I get non-physical (i.e., unrealistic) results: it appears that RBFs think that if I increase the number of production wells I get less oil recovered (!), sometimes by a factor of 10.

I am pretty sure I am missing something in this whole interpolation thing (I am no expert at all), but honestly it is the first time I get such counter-intuitive results in my entire Python numerical life ;-)

The interpolation with a large number of points can be pretty erratic. Did you use all 1000 points in the RBF? Do see what's going on you could try 2 things: 1) Use only a few points (10 to 100) 2) Use gaussian with a large negative smooth I had problems in the past with rbf in examples, and in one case I switched to using neighborhood points only (e.g. with scipy.spatial, KDTree) Josef

Andrea.

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

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