[Numpy-discussion] Interpolation question

[Brennan Williams]

Andrea Gavana wrote:
> On 29 March 2010 00:34, Robert Kern wrote:
>   
>> On Sun, Mar 28, 2010 at 18:30, Andrea Gavana <andrea.gavana at gmail.com> wrote:
>>     
>>> Hi Friedrich & All,
>>>
>>> On 28 March 2010 23:51, Friedrich Romstedt wrote:
>>>       
>>>> 2010/3/28 Andrea Gavana <andrea.gavana at gmail.com>:
>>>>         
>>>>> Example 1
>>>>>
>>>>> # o2 and o3 are the number of production wells, split into 2
>>>>> # different categories
>>>>> # inj is the number of injection wells
>>>>> # fomts is the final oil recovery
>>>>>
>>>>> rbf = Rbf(oilPlateau, gasPlateau, gasInjPlateau, o2, o3, inj, fomts)
>>>>>
>>>>> op = [50380]
>>>>> gp = [103014000]
>>>>> gi = [53151000]
>>>>> o2w = [45]
>>>>> o3w = [20]
>>>>> inw = [15]
>>>>>
>>>>> fi = rbf(op, gp, gi, o2w, o3w, inw)
>>>>>
>>>>> # I => KNOW <= the answer to be close to +3.5e8
>>>>>
>>>>> print fi
>>>>>
>>>>> [ -1.00663296e+08]
>>>>>
>>>>> (yeah right...)
>>>>>
>>>>>
>>>>> Example 2
>>>>>
>>>>> Changing o2w from 45 to 25 (again, the answer should be close to 3e8,
>>>>> less wells => less production)
>>>>>
>>>>> fi = rbf(op, gp, gi, o2w, o3w, inw)
>>>>>
>>>>> print fi
>>>>>
>>>>> [  1.30023424e+08]
>>>>>
>>>>> And keep in mind, that nowhere I have such low values of oil recovery
>>>>> in my data... the lowest one are close to 2.8e8...
>>>>>           
>>>> I want to put my2 cents in, fwiw ...
>>>>
>>>> What I see from
>>>> http://docs.scipy.org/doc/scipy-0.7.x/reference/generated/scipy.interpolate.Rbf.html#scipy.interpolate.Rbf
>>>> are three things:
>>>>
>>>> 1. Rbf uses some weighting based on the radial functions.
>>>> 2. Rbf results go through the nodal points without *smooth* set to
>>>> some value != 0
>>>> 3. Rbf is isotropic
>>>>
>>>> (3.) is most important.  I see from your e-mail that the values you
>>>> pass in to Rbf are of very different order of magnitude.  But the
>>>> default norm used in Rbf is for sure isotropic, i.e., it will result
>>>> in strange and useless "mean distances" in R^N where there are N
>>>> parameters.  You have to either pass in a *norm* which weights the
>>>> coords according to their extent, or to scale the data such that the
>>>> aspect ratios of the hypecube's edges are sensible.
>>>>         
>>> I believe I need a technical dictionary to properly understand all
>>> that... :-D . Sorry, I am no expert at all, really, just an amateur
>>> with some imagination, but your suggestion about the different
>>> magnitude of the matrix is a very interesting one. Although I have
>>> absolutely no idea on how to re-scale them properly to avoid RBFs
>>> going crazy.
>>>       
>> Scaling each axis by its standard deviation is a typical first start.
>> Shifting and scaling the values such that they each go from 0 to 1 is
>> another useful thing to try.
>>     
>
> Ah, magnifico! Thank you Robert and Friedrich, it seems to be working
> now... I get reasonable values for various combinations of parameters
> by scaling the input data using the standard deviation of each of
> them. It seems also that the other interpolation schemes are much less
> erratic now, and in fact (using input values equal to the original
> data) I get these range of errors for the various schemes:
>
> inverse multiquadric -15.6098482614 15.7194674906
> linear                        -1.76157336073e-010 1.24949181055e-010
> cubic                        -0.000709860285963 0.018385394661
> gaussian                  -293.930336611 282.058111404
> quintic                      -0.176381494531 5.37780806549
> multiquadric             -30.9515933446 58.3786105046
> thin-plate                  -7.06755391536e-006 8.71407169821e-005
>
> In percentage. Some of them are still off the mark, but you should
> have seen them before ;-) .
>
>   
That's great news. Going to give it a try myself.
Interesting that the linear scheme gives the lowest error range.
> I'll do some more analysis tomorrow, and if it works I am going to try
> the bigger profile-over-time interpolation. Thank you so much guys 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 <==
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