What is the algorithm? You know the various diagonal elements, and thus the set of indexes for those diagonals and various super/sub diagonals. Stuff the values into those entries.
In MATLAB, this would involve a final call to sparse. If you are writing the code in C, you know (in theory, if you understand sparse matrices) what order to stuff the entries into the array to be efficient.
If you want to know the EXACT algorithm specifics of what spdiags does, then just do this:
type spdiags
and read the code.
