Hi @lanast,
I have been through many of the Fortran options at http://www.autodiff.org, and as others have mentioned, the vast majority of them are no longer available or are limited to old subsets of Fortran.
May I ask which form of AD you require, Forward or Backward? For Forward mode, there are several OO libraries available, such as in flibs.
The only option for Backward mode that I am aware of is Tapenade which I can recommend highly. It is robust and works well with a wide-subset of modern Fortran. I can confirm that it can be integrated with a makefile quite nicely when installed locally. Moreover, the source-code transformation approach to AD will always provide the best performance since you can exploit compiler optimization of derivative code. Tapenade used to be closed-source and licensed for commercial use, but it now looks like it’s open source under MIT which is brilliant!
May I ask which BLAS/LAPACK operations you need derivatives for @ivanpribec? My understanding of this is that it isn’t usually a good idea to differentiate such routines, rather it is better to use the normal BLAS/LAPACK operations to implement the analytic derivative. I would recommend the following report on this topic: An extended collection of matrix derivative results for forward and reverse mode algorithmic differentiation. I’ve applied this successfully in a simple MATLAB potential flow solver to get reverse mode derivatives from the matrix inverse op.