Replace do loop with array notation in fortran - fortran

Question

I would like to replace the following do loop with FORTRAN's intrinsic functions and array notations.
do i=2, n
do j=2, n
a=b(j)-b(j-1)
c(i,j)=a*c(i-1,j)+d(i,j)
end do
end do
However, as c(i,j) depends on c(i-1,j) none of following trials worked. Because they do not update c(i,j)
!FORALL(i = 2:n , j = 2:n ) c(i,j)=c(i-1,j)*(b(j)-b(j-1))+d(i,j)
!FORALL(i = 2:n) c(i,2:n)=c(i-1,2:n)*(b(2:n)-b(1:n-1))+d(i,2:n)
!c(2:n,2:n)=RESHAPE( (/(c(i-1,2:n)*(b(2:n)-b(1:n-1))+d(i,2:n),i=2,n)/), (/n-1, n-1/))
!c(2:n,2:n)=RESHAPE((/(((b(j)-b(j-1)) *c(i-1,j)+d(i,j) ,j=2,n),i=2,n)/), (/n-1, n-1/))
!c(2:n,2:n)=spread(b(2:n)-b(1:n-1),ncopies = n-1,dim=1) * c(1:n-1,2:n) +d(2:n,2:n)
This is the best I can get. But it still has a do loop
do i=2, n
c(i,2:n)=c(i-1,2:n)*(b(2:n)-b(1:n-1))+d(i,2:n)
end do
Could all do loops be replaced by intrinsic functions and array notation. Or could this one be replaced somehow ?

Answer 1

In my experience, nothing beats the traditional do-loop. All the extension intrinsics create memory and CPU overhead by copying stuff to temporary space (on the stack usually), reshaping and the sort. If you're manipulating large arrays, you may encounter out-of-memory issues with the intrinsic functions.
Your best option is to stick to a 2-d loop that has the indexes correctly laid out:
do i=2, n
e = c(1:n,i-1)
do j=2, n
a=b(j)-b(j-1)
c(j,i)=a*e(j)+d(j,i)
end do
end do
By replacing the indexes (and making sure your dimension declarations follow), you are saving on the memory paging. c(j,i) and d(j,i) references travel column-wise inside memory while c(j,i-1) would have cut across columns (and produced paging overhead). So we copy it to a temporary e array.
I think this will be the fastest....

Answer 2

Starting with
do i=2, n
do j=2, n
a=b(j)-b(j-1)
c(i,j)=a*c(i-1,j)+d(i,j)
end do
end do
we can quickly eliminate the do loops with some nifty use of SIZE, SPREAD and EOSHIFT:
res = SPREAD(b - EOSHIFT(b,-1),2,SIZE(c,2))*EOSHIFT(c,-1) + d
Aha, turns out that the error I was receiving (V1) was due to my using RESHAPE rather than SPREAD. I fixed this in the current version (V2) and it compiles & works with both ifort and gfortran.