I'm trying to break up a 4D array over the third dimension, and send to each node using MPI. Basically, I'm computing derivatives of a matrix, Cpq, with respect to atom positions in each of the three cartesian directions. Cpq is of size nat_sl x nat_sl, so dCpqdR is of size nat_sl x nat_sl x nat x 3. At the end of the day, for ever s,i pair, I have to compute the matrix product of dCpqdR between the transpose of the eigenvectors of Cpq and the eigenvectors of Cpq like so:
temp = MATMUL(TRANSPOSE(Cpq), MATMUL(dCpqdR(:, :, s, i), Cpq))
This is fine, but as it turns out, the loop over s and i is now by far the slow part of my code. Because each can be done independently, I was hoping that I could break up dCpqdR, and give each task it's own s, i to compute the derivative of. That is, I'd like task 1 to get dCpqdR(:,:,1,1), task 2 to get dCpqdR(:,:,1,2), etc.
I've got this working in some sense by using a buffered send/recv pair of calls. The root node allocates a temporary array, fills it, sends to the relevant nodes, and the relevant nodes do their computations as they wish. This is fine, but can be slow and memory inefficient. I'd ideally like to break it up in a more memory efficient way.
The logical thing to do, then, is to use mpi_scatterv, but here is where I start running into trouble, as I'm having trouble figuring out the memory layout for this. I've written this, so far:
call mpi_type_create_subarray(4, (/ nat_sl, nat_sl, nat, 3 /), (/nat_sl, nat_sl, n_pairs(me_image+1), 3/),&
(/0, 0, 0, 0/), mpi_order_fortran, mpi_double_precision, subarr_typ, ierr)
call mpi_type_commit(subarr_typ, ierr)
call mpi_scatterv(dCpqdR, n_pairs(me_image+1), f_displs, subarr_typ,&
my_dCpqdR, 3*nat_sl*3*nat_sl*3*n_pairs(me_image+1), subarr_typ,&
root_image, intra_image_comm, ierr)
I've computed n_pairs using this subroutine:
subroutine mbdvdw_para_init_int_forces()
implicit none
integer :: p, s, i, counter, k, cpu_ind
integer :: num_unique_rpq, n_pairs_per_proc, cpu
real(dp) :: Rpq(3), Rpq_norm, current_val
num_pairs = nat
if(.not.allocated(f_cpu_id)) allocate(f_cpu_id(nat, 3))
n_pairs_per_proc = floor(dble(num_pairs)/nproc_image)
cpu = 0
n_pairs = 0
counter = 1
p = 1
do counter = 0, num_pairs-1, 1
n_pairs(modulo(counter, nproc_image)+1) = n_pairs(modulo(counter, nproc_image)+1) + 1
end do
do s = 1, nat, 1
f_cpu_id(s) = cpu
if((counter.lt.num_pairs)) then
if(p.eq.n_pairs(cpu+1)) then
cpu = cpu + 1
p = 0
end if
end if
p = p + 1
end do
call mp_set_displs( n_pairs, f_displs, num_pairs, nproc_image)
f_displs = f_displs*nat_sl*nat_sl*3
end subroutine mbdvdw_para_init_int_forces
and the full method for the matrix multiplication is
subroutine mbdvdw_interacting_energy(energy, forcedR, forcedh, forcedV)
implicit none
real(dp), intent(out) :: energy
real(dp), dimension(nat, 3), intent(out) :: forcedR
real(dp), dimension(3,3), intent(out) :: forcedh
real(dp), dimension(nat), intent(out) :: forcedV
real(dp), dimension(3*nat_sl, 3*nat_sl) :: temp
real(dp), dimension(:,:,:,:), allocatable :: my_dCpqdR
integer :: num_negative, i_atom, s, i, j, counter
integer, parameter :: eigs_check = 200
integer :: subarr_typ, ierr
! lapack work variables
integer :: LWORK, errorflag
real(dp) :: WORK((3*nat_sl)*(3+(3*nat_sl)/2)), eigenvalues(3*nat_sl)
call start_clock('mbd_int_energy')
call mp_sum(Cpq, intra_image_comm)
eigenvalues = 0.0_DP
forcedR = 0.0_DP
energy = 0.0_DP
num_negative = 0
forcedV = 0.0_DP
errorflag=0
LWORK=3*nat_sl*(3+(3*nat_sl)/2)
call DSYEV('V', 'U', 3*nat_sl, Cpq, 3*nat_sl, eigenvalues, WORK, LWORK, errorflag)
if(errorflag.eq.0) then
do i_atom=1, 3*nat_sl, 1
!open (unit=eigs_check, file="eigs.tmp",action="write",status="unknown",position="append")
! write(eigs_check, *) eigenvalues(i_atom)
!close(eigs_check)
if(eigenvalues(i_atom).ge.0.0_DP) then
energy = energy + dsqrt(eigenvalues(i_atom))
else
num_negative = num_negative + 1
end if
end do
if(num_negative.ge.1) then
write(stdout, '(3X," WARNING: Found ", I3, " Negative Eigenvalues.")'), num_negative
end if
else
end if
energy = energy*nat/nat_sl
!!!!!!!!!!!!!!!!!!!!
! Forces below here. There's going to be some long parallelization business.
!!!!!!!!!!!!!!!!!!!!
call start_clock('mbd_int_forces')
if(.not.allocated(my_dCpqdR)) allocate(my_dCpqdR(nat_sl, nat_sl, n_pairs(me_image+1), 3)), my_dCpqdR = 0.0_DP
if(mbd_vdw_forces) then
do s=1,nat,1
if(me_image.eq.(f_cpu_id(s)+1)) then
do i=1,3,1
temp = MATMUL(TRANSPOSE(Cpq), MATMUL(my_dCpqdR(:, :, counter, i), Cpq))
do j=1,3*nat_sl,1
if(eigenvalues(j).ge.0.0_DP) then
forcedR(s, i) = forcedR(s, i) + 1.0_DP/(2.0_DP*dsqrt(eigenvalues(j)))*temp(j,j)
end if
end do
end do
counter = counter + 1
end if
end do
forcedR = forcedR*nat/nat_sl
do s=1,3,1
do i=1,3,1
temp = MATMUL(TRANSPOSE(Cpq), MATMUL(dCpqdh(:, :, s, i), Cpq))
do j=1,3*nat_sl,1
if(eigenvalues(j).ge.0.0_DP) then
forcedh(s, i) = forcedh(s, i) + 1.0_DP/(2.0_DP*dsqrt(eigenvalues(j)))*temp(j,j)
end if
end do
end do
end do
forcedh = forcedh*nat/nat_sl
call mp_sum(forcedR, intra_image_comm)
call mp_sum(forcedh, intra_image_comm)
end if
call stop_clock('mbd_int_forces')
call stop_clock('mbd_int_energy')
return
end subroutine mbdvdw_interacting_energy
But when run, it's complaining that
[MathBook Pro:58100] *** An error occurred in MPI_Type_create_subarray
[MathBook Pro:58100] *** reported by process [2560884737,2314885530279477248]
[MathBook Pro:58100] *** on communicator MPI_COMM_WORLD
[MathBook Pro:58100] *** MPI_ERR_ARG: invalid argument of some other kind
[MathBook Pro:58100] *** MPI_ERRORS_ARE_FATAL (processes in this communicator will now abort,
[MathBook Pro:58100] *** and potentially your MPI job)
so something is going wrong, but I have no idea what. I know my description is somewhat sparse to start with, so please let me know what information would be necessary to help.
