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 general parameters the functions are defined by the following data types:

gsl_multifit_function

Data Type

This data type defines a general system of functions with 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 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 vectors x. void * params a pointer to the parameters of the function.

gsl_multifit_function_fdf

Data Type

This data type defines a general system of functions with 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 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 matrix result J_ij = d f_i(x,params) / d x_j in J for argument x and 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 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 vectors x. void * params a pointer to the parameters of the function.