I want to extend python and numpy by writing some modules in C or C++, using BLAS and LAPACK. I also want to be able to distribute the code as standalone C/C++ libraries. I would like this libraries to use both single and double precision float. Some examples of functions I will write are conjugate gradient for solving linear systems or accelerated first order methods. Some functions will need to call a Python function from the C/C++ code.
After playing a little with the Python/C API and the Numpy/C API, I discovered that many people advocate the use of Cython instead (see for example this question or this one). I am not an expert about Cython, but it seems that for some cases, you still need to use the Numpy/C API and know how it works. Given the fact that I already have (some little) knowledge about the Python/C API and none about Cython, I was wondering if it makes sense to keep on using the Python/C API, and if using this API has some advantages over Cython. In the future, I will certainly develop some stuff not involving numerical computing, so this question is not only about numpy. One of the thing I like about the Python/C API is the fact that I learn some stuff about how the Python interpreter is working.
Thanks.