I am trying to use the trust-region methods w/in mkl 11 and have a couple of questions :
a) what is the layout of the jacobian matrix ?
I expect it to be fortran style matrix with m (mapped -f- dimension) rows and n columns ( x dimension). Is this correct ?
b) concerning the jacobian calculations :
1) can I completely ignore the provided interface and provide instead with my own evaluation ? Is the jacobian matrix all that I am interested ?
(Unfortunately the examples provided are not very illuminating as far as the part of the API concerning the jacobian valuations. As a result, I still do not understand what it does, besides the obvious/expected )
2) if I provide with a NULL pointer, will the jacobian be calculated internally, using numerical differentiation ? -leaving aside for the moment questions of efficiency. I believe not, because a) it is not mentioned in the notes and b) because there is no place to insert the function pointer for the function valuation ( wouldn't that simplify a lot the interface ? The RCI use here seems quite typical, as far as the examples show, at least) - the question still is valid though, since, in this case, the code could request for function values, no ?
3) when calculating the jacobian, one of the inputs is the function values at the point of valuation. As far as I see, from the examples, there is no accompanying evaluation of the function values. Is this always the case, and I, therefore, can use as fvec input the one held by the pointer passed in the solver routines ?
Finally, is there a more detailed write-up than the one provided in the reference manual ? ( the reference Conn00 comes with a rather heafty toll ;-) ).
Thank you very much in advance, for your help,