How to build a restriction or interpolation matrices for 2-d problem for V-cycle multigrid. I read a lot of references about it, they only shows the coefficients matrix like following. $$ \begin{matrix} 1/16 & 1/8 & 1/16 \\ 1/8 & 1/4 & 1/8 \\ 1/16 & 1/8 & 1/4 \\ \end{matrix} $$ For 1-d cases, I can easily build a interpolation matrix like(3 to 5): $$ \begin{matrix} 1 & & \\ 2 & & \\ 1 & 1 & \\ &2 & \\ & 1 & \\ \end{matrix} $$
and do the transpose to get the restriction matrix and get the coarser mesh by A2h = RAI. And that only work for 1-D case. Here's the python code I used to do the multigrid example: https://people.sc.fsu.edu/~jburkardt/py_src/gmgsolve/gmgsolve.py
For the 2-d case, I think I am supposed to use bilinear interpolation. But I don't know what the restriction and interpolation matrix look like. Does any one could show me a example, just like 9 to 5 restriction for 2-d case?