On 29/10/2010 6:35 a.m., Robert Kern wrote: > On Thu, Oct 28, 2010 at 12:33, Brennan Williams > <brennan.willi...@visualreservoir.com> wrote: >> On 29/10/2010 2:34 a.m., Robert Kern wrote: >>> On Thu, Oct 28, 2010 at 06:38, Brennan Williams >>> <brennan.willi...@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. > Right. Just as long as the problem is linear in the coefficients, the > design matrix can be derived however you like. > So I could optionally put log terms in if I thought it was linear in log(x) for example? >> 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. > Rbf doesn't like duplicate points. :-) OK, fair enough, I just need to add a bit of housekeeping to remove duplicate simulations. Thanks for the confirmation.
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