cusparse<t>axpyi and cusparse<t>doti are function names in cuSPARSE, the CUDA sparse matrix library.
The naming conventions section explains <t> denotes data types, and axpyi, doti, roti all denote operations. However it does not further explain what the 'i' means in those names.
FYI, cusparse<t>axpyi performs a * x + y (so I guess 'axpy' means 'ax plus y').
cusparse<t>doti performs dot product of a sparse vector x and a dense vector y.
cusparse<t>roti performs rotations (actually I'm not clear on how that works either).