How to determine MPI rank/process number local to a socket/node

It depends on the MPI implementation - and there is no standard for this particular problem.

Open MPI has some environment variables that can help. OMPI_COMM_WORLD_LOCAL_RANK will give you the local rank within a node - ie. this is the process number which you are looking for. A call to getenv will therefore answer your problem - but this is not portable to other MPI implementations.

See this for the (short) list of variables in OpenMPI.

I don't know of a corresponding "node number".

This exact problem is discussed on Markus Wittmann's Blog, MPI Node-Local Rank determination.

There, three strategies are suggested:

1. A naive, portable solution employs MPI_Get_processor_name or gethostname to create an unique identifier for the node and performs an MPI_Alltoall on it. [...]
2. [Method 2] relies on MPI_Comm_split, which provides an easy way to split a communicator into subgroups (sub-communicators). [...]
3. Shared memory can be utilized, if available. [...]

For some working code (presumably LGPL licensed?), Wittmann links to MpiNodeRank.cpp from the APSM library.

I believe you can achieve that with MPI-3 in this manner:

MPI_Comm shmcomm;
MPI_Comm_split_type(MPI_COMM_WORLD, MPI_COMM_TYPE_SHARED, 0,
                    MPI_INFO_NULL, &shmcomm);
int shmrank;
MPI_Comm_rank(shmcomm, &shmrank);