Hi,

can the Levenberg-Marquart (or nonlinear optimization) module of Eigen be used in 3 dimension (surface fitting)? All of its examples are in 2d. But I have to fit a surface and I don't know how to do that. I have a set of experimental data, which are function of two independent variable. So the matrices would not be the same, dimensionally.

It's a very urgent case. Please help.

Of course, the LevenbergMarquardt can be used in any dimension! Which kind of mathematical model do you wanna fit?

I have a set of data, which are function of two independent vaiables "phi" and "theta". I want to fit a surface, which is a simple multiplication of two Gaussian function:
psi = [1/(S_phi*sqrt(2*pi))*exp(-0.5*((phi-phi_m)/S_phi)^2)] * [1/(S_theta*sqrt(2*pi))*exp(-0.5*((theta-theta_m)/S_theta)^2)].
The unknown parameters are "S_phi" and "S_theta".

hm, why not simply computing the value of the variances from the variances of the data?

Anyway, using LM for that model is direct, you simply have to write a functor filling the value vector with psi(phi,theta) evaluated at each sample, and the Jacobian matrix containing the partial derivatives of psi(phi,theta) wrt psi and theta for each sample.

in 3d the psi is no more vector, it's a matrix. Is it okay, if I define it as a matrix?

Regardless of the physical dimension of your problem, at the end you're minimizing a sum of square terms "sum_i ( f_i(x_1,...,x_n) )^2". The functor you have to provide simply fill a 1D vector with values f_i evaluated for the current unknown values x_j...

I've tried to convert it to a 1D vector, but its impossible. Actually the summation, which I have, ist not only over "i", but also over "j", because the variables "phi" and "theta" are independent.