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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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37.3 Providing the Function to be Minimized

You must provide n functions of p variables for the minimization algorithms to operate on. In order to allow for arbitrary parameters the functions are defined by the following data types:

Data Type: gsl_multifit_function
This data type defines a general system of functions with arbitrary parameters.
int (* f) (const gsl_vector * x, void * params, gsl_vector * f)
this function should store the vector result f(x,params) in f for argument x and arbitrary parameters params, returning an appropriate error code if the function cannot be computed.
size_t n
the number of functions, i.e. the number of components of the vector f.
size_t p
the number of independent variables, i.e. the number of components of the vector x.
void * params
a pointer to the arbitrary parameters of the function.
Data Type: gsl_multifit_function_fdf
This data type defines a general system of functions with arbitrary parameters and the corresponding Jacobian matrix of derivatives,
int (* f) (const gsl_vector * x, void * params, gsl_vector * f)
this function should store the vector result f(x,params) in f for argument x and arbitrary parameters params, returning an appropriate error code if the function cannot be computed.
int (* df) (const gsl_vector * x, void * params, gsl_matrix * J)
this function should store the n-by-p Jacobian matrix result J_ij = d f_i(x,params) / d x_j in J for argument x and arbitrary parameters params, returning an appropriate error code if the function cannot be computed.
int (* fdf) (const gsl_vector * x, void * params, gsl_vector * f, gsl_matrix * J)
This function should set the values of the f and J as above, for arguments x and arbitrary parameters params. This function provides an optimization of the separate functions for f(x) and J(x)---it is always faster to compute the function and its derivative at the same time.
size_t n
the number of functions, i.e. the number of components of the vector f.
size_t p
the number of independent variables, i.e. the number of components of the vector x.
void * params
a pointer to the arbitrary parameters of the function.

Note that when fitting a non-linear model against experimental data, the data is passed to the functions above using the params argument and the trial best-fit parameters through the x argument.

ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition