I am a beginner in Julia. I would like to create a Julia code to send `Matrix{SMatrix{2,2,ComplexF64,4}}`

to a neighboring process in MPI parallel computation. Here is the code I am currently working on. Thank you in advance.

```
using StaticArrays
using LinearAlgebra
using MPI
# Set the grid size
L = 500
# Set the k-space mesh
k_mesh = range(-π, stop=π, length=L)
# Function to generate the Hamiltonian matrix
function Hamiltonian(kx, ky)
return @SMatrix [cos(kx) im*sin(ky); -im*sin(ky) cos(kx)]
end
# Main function
function main()
# Get the MPI communicator
comm = MPI.COMM_WORLD
# Get the rank of the current process
myrank = MPI.Comm_rank(comm)
# Get the total number of processes
size = MPI.Comm_size(comm)
# Helper function to calculate the split range
function start_and_end(N, comm)
nprocs = MPI.Comm_size(comm)
myrank = MPI.Comm_rank(comm)
if N % nprocs != 0
println("Error! N % number of processes must be 0.")
MPI.Abort(comm, 1) # Properly terminate MPI
end
# Calculate the range assigned to each process
nbun = div(N, nprocs)
ista = myrank * nbun + 1
iend = ista + nbun - 1
return ista, iend, nbun
end
# Calculate the rank of neighboring processes
dst = mod(myrank + 1, size)
src = mod(myrank - 1, size)
if src < 0
src += size
end
# Calculate the range assigned to the current process
ista, iend, nbun = start_and_end(L, comm)
# Extract the k-mesh for the assigned range
k_mesh_i = deepcopy(k_mesh[ista:iend])
# Generate the Hamiltonian matrix for each k-point
Ham_i = Hamiltonian.(k_mesh, k_mesh_i')
# Extract the first and last rows
Ham_upper = deepcopy(Ham_i[1, :])
Ham_downer = deepcopy(Ham_i[nbun, :])
# Convert SMatrix to standard Julia arrays for MPI communication
Ham_upper_array = reduce(vcat, [vec(h) for h in Ham_upper])
Ham_downer_array = reduce(vcat, [vec(h) for h in Ham_downer])
# Prepare buffers for receiving
Ham_upper_recv = similar(Ham_upper_array)
Ham_downer_recv = similar(Ham_downer_array)
# Start asynchronous communication with neighboring processes
rreq = MPI.Irecv!(Ham_upper_recv, comm, source=src, tag=src + 32)
sreq = MPI.Isend(Ham_downer_array, comm, dest=dst, tag=myrank + 32)
# Wait for communication to complete
MPI.Waitall([rreq, sreq])
# Reconstruct the received data back into SMatrix format
Ham_upper_received = [@SMatrix ComplexF64[Ham_upper_recv[i], Ham_upper_recv[i+1]; Ham_upper_recv[i+2], Ham_upper_recv[i+3]] for i in 1:4:length(Ham_upper_recv)]
# Output communication logs
println("$myrank: Sending $myrank -> $dst = $sreq")
println("$myrank: Received $src -> $myrank = $rreq")
end
# Initialize MPI
MPI.Init()
# Execute the main function
main()
# Finalize MPI
MPI.Finalize()
```