[Help-gsl] GSL 2.1 nonlinear least squares question

[viktor drobot]

Hello!


I'm working on application which determines some kinetic constants from
experimental data graph. Currently I use Nelder-Mead multidimensional
minimization algorithm to find the minimum of least squares functional. My
program computes the sum of squares directly from experimental data:

SS = sum (exp(time_i) - calc(time_i))^2

the calc() function solves the initial value problem for some predefined
ODE system which corresponds to the model under investigation and returns
the value of substance concentration at time point time_i. With this
approach I don't need Jacobians and this pretty good because for my case I
can't find the analytical form of Jacobi matrix.

Recently I've found that GSL 2.1 offers the Levenberg-Marquardt algorithm
with Tikhonov's regularization to solve the nonlinear least squares
problem. Also I've found that these routines can compute the Jacobian
internally with finite difference formulae without external manipulations.

But I've stucked with gsl_multifit_function_fdf routine. As I understood
the internal implementation of such routines require vector with
experimental data points (in GSL they are named as f_i). This drives me a
bit crazy because I not sure if I can pass the only one function f_i - the
previous SS. I don't want to pass over the whole vector of curve points
because sometimes I have enormous number of input files and so the final
vector size will be too large.

So I'm asking your, dear experts, what should I do to correctly implement
nonlinear least squares problem solver as described above. Can I pass only
the final sum of squares as the only f_i function or no?

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