I'm new to the world of machine learning and data fitting and I'm currently trying to transfer some Matlab code to Python. In this code my goal is to fit a surface to a given set of datapoints which have (x,y,z) coordinates. The Matlab code looks like the following:
[xData, yData, zData] = prepareSurfaceData( X0, Y0, ZPhi0 );
% Type of polynom
ft = fittype( 'poly44' );
% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft );
[x0,y0]=meshgrid(x,y);
And I obtain the values that solve the following expression:
Linear model Poly44:
val(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 +
p21*x^2*y + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y
+ p22*x^2*y^2 + p13*x*y^3 + p04*y^4
However, I've been looking for a way to replicate this in Python but it seems as if all the functions available are only meant for 2D. My initial approach has been to use numpy.polynomial.polifit, but I'm stuck as I would like something along the lines:
xData = X0.T
yData = Y0.T
zData = Zphi0.T
pol_degree = 44
coefs, stats = poly.polynomial.polyfit((xData, yData), zData, pol_degree, full=True)
This of course does not work and I've tried other packages but haven't got any results. I've seen a post suggesting that a good way to do this would be to separate the dimensions and fit xy an xz for example, like this:
coefsxy = poly.polynomial.polyfit(xData, yData, pol_degree)
coefsxz = poly.polynomial.polyfit(xData, zData, pol_degree)
But I don't see how can I join these two expressions and obtain the surface that I need.
Can somebody explain me what would be the best way to transfer this Matlab code to Python?
