[Numpy-discussion] quadratic function

[Brennan Williams]

  On 29/10/2010 2:34 a.m., Robert Kern wrote:
> On Thu, Oct 28, 2010 at 06:38, Brennan Williams
> <brennan.williams at visualreservoir.com>  wrote:
>>   I have used both linear least squares and radial basis functions as a
>> proxy equation, calculated from the results of computer simulations
>> which are calculating some objective function value based on a number of
>> varied input parameters.
>>
>> As an alternative option I want to add a quadratic function so if there
>> are parameters/variables x,y,z then rather than just having a linear
>> function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to
>> have the option not to include all the different second order terms.
> A = np.column_stack([
>      np.ones_like(x),
>      x, y, z,
>      x*x, y*y, z*z,
>      x*y, y*z, x*z,
> ])
> x, res, rank, s = np.linalg.lstsq(A, f)
>
OK, so in other words, you can use linalg.lstsq for whatever higher 
order terms you want to include or exclude. Very nice. Thanks.

On a related topic I also use the Rbf radial basis function as a proxy 
equation. I have one set of data that it fails to return an Rbf for and 
I've just realised that in my set of simulations that are used to build 
the proxy equation I have some duplicate equations. I'm wondering if Rbf 
doesn't like duplicate points? It obviously doesn't affect linalg.lstsq.

Brennan