Leaving my old answer below for historical reference, however as of version 11.2.0 (currently available on Wolfram Cloud and soon to be released as a desktop product) the low-level linear algebra functions have been documented, see
The comments by both Michael E2 and J....
I can partially answer to my own questions. Amazingly, but it is easier to use the internal MKL. Let us consider my question about multiplication a band matrix by a dense matrix. The corresponding function is mkl_zdiamm.
I wrote the following code (diamm.c)
How should I know the correct order of arguments without trying several times?
You can't, usually. A lot of the undocumented usage that you see on this site will have been worked out by trial and error. Sometimes it is fruitless - I have explored plenty of interesting-sounding internal functions and got nowhere.
Are there detailed usage information of ...
I think these three comments make a pretty good answer:
Alexey is talking about (effective) memory bandwidth, which will be hugely influenced by relative cache sizes and speeds. And even if MKL may not be optimal on AMD processors, it's still faster than ACML (AMD's own equivalent) and every other math library apart (perhaps, and even then very debatable) ...