Re: surface fitting question

*To*: mathgroup at smc.vnet.net*Subject*: [mg61330] Re: [mg61328] surface fitting question*From*: "David Annetts" <davidannetts at aapt.net.au>*Date*: Sun, 16 Oct 2005 00:17:46 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi Ralph, > I have this data in a file. It is a 2D table that 26 rows and > 17 columns. > | > -------------------------------------------------------------- > --------- > | 0.000 0.000 0.000 ... 0.000 0.000 0.000 > | 0.050 0.050 0.155 ... 16.409 19.375 20.156 > | . > | . > | . > | 47.500 50.000 55.000 ... 2017.500 2075.580 2182.765 > -------------------------------------------------------------- > --------- > | > > I would like to find an equation that describes this surface > using mathematica. I think that 3rd degree polynomials would > be what I'm looking for. So, maybe > data[x,y] = ax^3 + bx^2 + cx + d + ey^3 + fy^2 + gy > > I've seen and example that uses Fit[], so I think this can be > done, but I'm a novice at mathematica and don't know how to > set this problem up. I have been able to fit a polynomial to > curve data, but now I need to fit a surface. This sort of thing is described by online help. You can use Fit[], or any of the ?*Regress options from Statistics`. As an example, (* geneate some data *) data = Table[{x, y, 10 x^3 + 5 x^2 + 6 x + 10 - 5y^3 - 5y^2 - 10y}, {x, -5, 5, .5}, {y, -5, 5, .5}]; (* try and fit these data *) Needs["Statistics`"] NonlinearFit[Partition[Flatten[data], 3], a x^3 + b x ^2 + c x + d + e y^3 + f y^2 + g y, {x, y}, {{a, 1}, {b, 1}, {c, 1}, {d, 1}, {e, 1}, {f, 1}, {g, 1}}] To get a better idea of the fit (obviously not needed here), change Fit to Regress. Regards, Dave.