[Help-gsl] Usage of gsl_multiroot_function_fdf

[Gerald I. Evenden]

This function gsl_multiroot_function_fdf requires three function entries: the 
basic function, the derivative of the function and a sequential call to the 
first two.

The operation of *_fdf (last function listed in gsl_multiroot_function_fdf) is 
clear in that a sequence of a call to the function followed by a derivative 
call guarantees that elements of the computation of the basic function may be 
carried over to the derivative call.  What is not clear, because of the 
independently passed derivative call, is whether it is guarantee that the 
basic function will always be called (with the same arguments) before the 
derivative funtion.  If this sequence were true, it would appear that the 
second function (derivative) argument in gsl_multiroot_function_fdf would not 
be necessary.

What I am concerned with is: can I depend upon a call to the basic function 
prior to a call to the derivative function---each with the same vector x 
argument.

Comments appreciated.  Thank-you.

PS: Current usage works assuming without carrying over computations but some 
speed up should occur if I can use previously computed elements in the 
derivatives.
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