I'll put some comments inline to the code, and in the end add a complete implementation of the program, with various changes to improve the execution.
program BA
implicit none
integer, parameter :: N = 20
For real numbers it is advisable to introduce a real kind with selected_real_kind:
integer, parameter :: rk = selected_real_kind(15)
integer :: A(n,n)
Use the real kind introduced above, to declare the reals:
real(kind=rk) :: r, p, r2(2), pj
real(kind=rk) :: sumA_q
integer :: sumA
integer :: m0, i, j, L0, N1, t, jnod, k, di
Often it is better to use more than single characters for variables (for example something like `iNode` or `iEdge`, this makes it visible what the iterator is actually used for.
integer :: edge_number, ii, ie, je, degree
A = 0
m0 = 5 ! initial nodes
L0 = 4 ! initial edges
ii = 0
! adding m0 nodes with random connections
rand_cnx: do ! while is actually deprecated, you anyway use 'if exit' in the
! loop, so I'd stick to that one. Using a block label to allow
! the identification of the loop in the exit statement.
do ie = 1, m0
call random_number(r)
You could create a bunch of `m0` random numbers all at once here, and use them then subsequently. That might be a little faster, but probably has no really big impact.
je = r * (m0 - 1) + 1
if (A(ie,je) == 0 ) then
A(ie,je) = 1
A(je,ie) = 1
ii = ii + 1
if (ii>=L0) EXIT rand_cnx
No need to compute another random number here, if the limit was reached, leave the loop. Use a block label to directly leave the outer loop.
end if
end do
end do rand_cnx
edge_number = L0
N1 = m0
degree = m0
! Precompute sum of submatrix up to m0-1
sumA = sum(A(1:m0-1, 1:m0-1))
! adding remaining nodes with pereferential attachment
do t = 1,N-m0
di = 0
N1 = m0 + t
The summation over the subarray does not depend on the random numbers (only entries outside the subarray at N1 are modified, if I am not mistaken) and can be pre-computed. As N1 is linearly increasing, we can update the sum of the submatrix up to N1, by just adding the newly filled column and row from the previous iteration.
! Update sum of submatrix with the previously computed column and row.
sumA = sumA + sum(A(1:N1-1,N1-1)) + sum(A(N1-1,1:N1-2))
sumA_q = 1.0_rk / real(sumA, kind=rk)
do
call random_number(r)
jnod = r * (N1-2)+1
pj = sum(A(jnod,1:N1-1))*sumA_q
call random_number(r)
if ( r<pj .and. A(N1,jnod)==0 ) then
A(N1,jnod) = 1
A(jnod,N1) = 1
edge_number = edge_number + 1
di = sum(A(N1,1:N1))
if (di >= degree) EXIT
end if
end do
end do
do i = 1,N
write(12,"(*(I5))") (A(i,j),j=1,N)
end do
end program BA
With a little more memory effort, you could also precompute all `sum(A(jnod,1:N1-1))`, use them for the summation of the complete submatrix and in the computation of `pj`, instead of recalculating the sum everytime the random number picks a specific `jnod`. This would result in turning the `di` into an array of length `N`. Implementing this led be to find that the first additional node has to be connected to all previous nodes, as you set `degree=m0`. In this case no randomness seems to be involved? I catch this special case in the implementation below:
program BA
implicit none
integer, parameter :: N = 20
integer, parameter :: rk = selected_real_kind(15)
integer :: A(n,n)
real(kind=rk) :: r, pj
real(kind=rk) :: sumA_q
integer :: sumA
integer :: m0, i, j, L0, N1, t, jnod
integer :: di(N)
integer :: edge_number, ii, ie, je, degree
A = 0
di = 0
m0 = 5 ! initial nodes
L0 = 4 ! initial edges
! adding m0 nodes with random connections
ii = 0
rand_cnx: do
do ie = 1, m0
call random_number(r)
je = nint(r * (m0 - 1)) + 1
if (A(ie,je) == 0 ) then
A(ie,je) = 1
A(je,ie) = 1
di(ie) = di(ie) + 1
di(je) = di(je) + 1
ii = ii + 1
if (ii>=L0) EXIT rand_cnx
end if
end do
end do rand_cnx
edge_number = L0
N1 = m0
degree = m0
! Precompute sum of submatrix up to m0-1
sumA = sum(di(:m0-1)) - sum(A(:m0-1,m0))
! adding remaining nodes with pereferential attachment
do t = 1,N-m0
N1 = m0 + t
! Update sum of submatrix with the previously computed column and row.
sumA = sumA + sum(A(:N1-2,N1-1)) + di(N1-1)
sumA_q = 1.0_rk / real(sumA, kind=rk)
need_all: if (N1-1 == degree) then
! Need all nodes to fulfill degree, no randomness required?
A(N1,:N1-1) = 1
A(:N1-1,N1) = 1
edge_number = edge_number + N1-1
di(:N1-1) = di(:N1-1) + 1
di(N1) = di(N1) + N1-1
else need_all
do
call random_number(r)
jnod = nint(r * (N1-2))+1
! Only consider not yet connected nodes.
if (A(jnod,N1) == 0) then
pj = di(jnod)*sumA_q
call random_number(r)
if ( r<pj ) then
A(N1,jnod) = 1
A(jnod,N1) = 1
edge_number = edge_number + 1
di(N1) = di(N1)+1
di(jnod) = di(jnod) + 1
if (di(N1) >= degree) EXIT
end if
end if
end do
end if need_all
end do
do i = 1,N
write(12,"(*(I5))") (A(i,j),j=1,N)
end do
end program BA
No guarantees, that this is in any way correct. I guess, this could be further increased by just picking the random nodes out of the not yet connected ones. This would imply that you need to keep an index list of all 0 values for the current node, and then use `jnod` to pick out of those. This would be more involved book-keeping but would reduce the number of guesses, you need to do.