## Message chain

Write a simple program where every processor sends data to the next
one. Let ntasks be the number of the tasks, and myid the rank of the
current process. Your program should work as follows:

 - Every task with a rank less than ntasks-1 sends a message to task
myid+1.  For example, task 0 sends a message to task 1.

 - The message content is an integer array where each element is
   initialized to myid.

 - The message tag is the receiver’s id number.

 - The sender prints out the number of elements it sends and the tag
number.  All tasks with rank ≥ 1 receive messages.

- Each receiver prints out their myid, and the first element in the
  received array.

 a) Implement the program described above using `MPI_Send` and
 `MPI_Recv`. You may start from scratch or use as a starting point 
 [c/skeleton.c](c/skeleton.c), [fortran/skeleton.F90](fortran/skeleton.F90) or
 [python/skeleton.py](c/skeleton.py). Investigate the timings with different
 numbers of MPI tasks (e.g. 2, 4, 8, 16, ...), and pay attention especially to
 rank 0. Can you explain the behaviour?

 b) Rewrite the program using `MPI_Sendrecv` instead of `MPI_Send` and
`MPI_Recv`. Investigate again timings with different numbers of MPI 
tasks (e.g. 2, 4, 8, 16, ...). Can you explain the differences to case a)?

 c) Try to simplify the code by employing the `MPI_PROC_NULL` in treating the
 special cases of the first and last task in the chain.

 d) Rewrite the program using non-blocking communication (MPI_Isend and
 MPI_Irecv).

 c) Rewrite the program using persistent communication operations
 (MPI_Send_init, MPI_Recv_init, etc.).