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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.