[SciPy-User] multidimensional polynomial fit

David Goldsmith d.l.goldsmith@gmail....
Sun Jun 13 17:15:15 CDT 2010

On Sun, Jun 13, 2010 at 2:29 PM, Oscar Gerardo Lazo Arjona <
algebraicamente@gmail.com> wrote:

> David Goldsmith <d.l.goldsmith <at> gmail.com> writes:
> > Whatever you do, before submission, please ensure that your function has
> a
> complete, Standard-conforming docstring (and, though this is not "my
> department," so to speak, most would probably join me in also asking that
> it be
> accompanied by a pretty complete suite of unit tests, esp. something as
> mathematically complicated as this - my off-the-cuff would be that it
> should
> have at least three, preferably at least five non-trivial or semi-trivial
> tests,
> by which I mean tests which pass when a non-trivial solution consisting of
> simple, e.g., integer, values is produced exactly [to within, say, 9
> sigfigs],
> for at least two degrees above 2, one even and one odd - just my $0.02).DG
> I implemented the function so that it returns a sage[1] symbolic
> expression.
> Although it could also return a list of coefficients. Within sage's command
> propt, it can be used like this:
> sage: var('x y z')
> (x, y, z)
> sage: G=-2*y^3*x +x^2 + x*y  -5*z -1
> sage: pg=[(i,j,k,G.subs(x=i,y=j,z=k)) for i in srange(-1,1.5,0.5) for j in
> srange(-1,1.5,0.5) for k in srange(-1,1.5,0.5)]
> sage: load('/myhome/polynomial_fit.py')
> sage: Pg=polynomial_fit(pg,[2,3,1],[x,y,z],depreciation=True)
> -2.0*x*y^3 + x^2 + x*y - 5.0*z - 1.0
> It reconstructs the original polynomial without *any error*.

So the number of data _must_ equal the number of terms in the polynomial?
(Anything else will be over- or under-determined and require either some
sort of error minimizing fit.)  What's your use case; just curious.


> Notice the
> depreciation option which depreciates coefficients that are smaller than
> 10e-10
> so that they do not appear in the resulting polynomial.
> So, if I understood you correctly, this passes your propposed requirement
> ;) .I
> haven't written a docstring, but in the mean time, how do I make my
> submission?
> I also did not understand what you meant by unit tests...
> Oscar
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