Re: surface fitting question

*To*: mathgroup at smc.vnet.net*Subject*: [mg61336] Re: surface fitting question*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 16 Oct 2005 00:17:52 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <diprth$hpc$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ralph Smith wrote: > 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. > > thanks, > Ralph > > > Hi Ralph, You must provide to *Fit* a list of three coordinates for each points as in the following example: In[1]:= data = Flatten[Table[Table[{i, j, Random[Real, {0, 2500}]}, {j, 17}], {i, 26}], 1]; In[2]:= myFit = Fit[data, {x^3, x^2, x, 1, y^3, y^2, y}, {x, y}] Out[2]= 901.9358457174038 + 69.00000405849856*x - 4.965777107187227*x^2 + 0.11341669401419147*x^3 - 18.948955500363553*y + 5.111441786546051*y^2 - 0.23474750193421623*y^3 In[3]:= Plot3D[myFit, {x, 1, 26}, {y, 1, 17}]; Best regards, /J.M.