Can I parallelize my program? - cuda

Question

This is my program:
program test
implicit none
integer n,m,k,i,j,Errorflag
real :: Yabs(39,39),angle(39,39)
real ,dimension(67,1) :: deltaA,A
real :: V(1,39),d(1,39),v1(29,1),d1(38,1),Ps(1,38),Qs(1,39),Jac(67,67),invJac(67,67)
real :: B1(1,38),B2(1,29),MF(1,67),trnsMF(67,1),P0(1,39),Q0(1,39)
real, dimension(38,38) :: dia1,offdia1,J1
real, dimension(29,29) :: dia2,dia3,dia4,offdia4,J4
real,dimension(38,29) ::offdia2,J2
real,dimension(29,38) ::offdia3,J3
real p,p1,q,q1
n=39;m=9
MF(1,1)=10
open(unit=3,file="ybus.dat",status="old")
open(unit=4,file="angle.dat",status="old")
do i=1,39
read(3,*) Yabs(i,1:39)
read(4,*)angle(i,1:39)
end do
close(3)
close(4)
open(unit=5,file="activepower.dat",status="old")
open(unit=8,file="reactivepower.dat",status="old")
read(5,*)Ps(1,1:38)
read(8,*)Qs(1,1:29)
close(5)
close(8)
do i=1,67
deltaA(i,1)=0
end do
v1(1:29,1)=1
d1(1:38,1)=0
A(1:38,1)=d1(1:38,1)
A(39:67,1)=v1(1:29,1)
!call cpu_time(t1)
do while(maxval(abs(MF))>0.0001)
V(1,1)=0.982
V(1,2:30)=v1(1:29,1)
V(1,31)=1.03
V(1,32)=0.9831
V(1,33)=1.0123
V(1,34)=0.9972
V(1,35)=1.0493
V(1,36)=1.0635
V(1,37)=1.0278
V(1,38)=1.0265
V(1,39)=1.0475
d(1,1)=0
d(1,2:39)=d1(1:38,1)
! % % % %------Active Power Calculation-----%
p1=0;p=0
do i=2,n
do j=1,n
p1=(V(i)*V(j)*Yabs(i,j)*cos(angle(i,j)-d(i)+d(j)))
p=p1+p
end do
P0(i-1)=p
p=0
end do
! % % % %------Reactive Power Calculation-----%
p=0;p1=0
do i=2,(n-m)
do j=1,n
p1=-(V(i)*V(j)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j)))
p=p1+p
end do
Q0(i-1)=p
p=0
end do
!!!!!!!!!!!mismatch factor
do i=1,(n-1)
B1(i)=Ps(i)-P0(i)
end do
do i=1,(n-m-1)
B2(i)=Qs(i)-Q0(i)
end do
MF(1,1:38)=B1(1,1:38)
MF(1,39:67)=B2(1,1:29)
!!!!!!!!jacobian calculation for preddictor step
!!!!!!!!!!!!!!!!!!!!!!dia of j1
p=0;p1=0
do i=2,n
do j=1,n
if(j .ne. i)then
p1=V(i)*V(j)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j))
!print*,p1
p=p1+p
end if
end do
i=i-1
dia1(i,i)=p
p=0
i=i+1
end do
!!!!!!!!!!!!!!off dia. of j1
q=0;q1=0;
do k=2,n
i=k
do j=2,n
if(j .ne. i)then
q1=V(i)*V(j)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j))
end if
i=i-1;j=j-1
offdia1(i,j)=-q1
q1=0
i=i+1;j=j+1
end do
end do
do i=1,38
do j=1,38
J1(i,j)=offdia1(i,j)+dia1(i,j)
end do
end do
!!!!!!!!!!!!!!!!!!!dia. of j2
p=0;p1=0
do i=2,(n-m)
do j=1,n
if(j .ne. i)then
p1=V(j)*Yabs(i,j)*cos(angle(i,j)-d(i)+d(j))
p=p1+p
end if
end do
dia2(i-1,i-1)=p+(2*V(i)*Yabs(i,i)*cos(angle(i,i)))
p=0;
end do
!!!!!!!!!!!!!!!!!!off dia. of j2
p1=0;
do k=2,n
i=k
do j=2,(n-m)
if(j .ne. i)then
p1=V(i)*Yabs(i,j)*cos(angle(i,j)-d(i)+d(j));
end if
i=i-1;j=j-1
offdia2(i,j)=p1
p1=0;
i=i+1;j=j+1
end do
end do
do i=1,(n-m-1)
offdia2(i,i)=dia2(i,i)
end do
J2=offdia2
!!!!!!!!!!!!!!!!!!!!dia. of j3
p=0;p1=0
do i=2,(n-m)
do j=1,n
if(j .ne. i)then
p1=V(i)*V(j)*Yabs(i,j)*cos(angle(i,j)-d(i)+d(j))
p=p1+p;
end if
end do
i=i-1;
dia3(i,i)=p
p=0;
i=i+1;
end do
!!!!!!!!!!!!!!off dia of j3
p=0;p1=0
do k=2,(n-m)
i=k;
do j=2,n
if(j .ne. i)then
p1=V(i)*V(j)*Yabs(i,j)*cos(angle(i,j)-d(i)+d(j))
end if
i=i-1;j=j-1
offdia3(i,j)=-p1;
p1=0;
i=i+1;j=j+1
end do
end do
do i=1,(n-m-1)
offdia3(i,i)=dia3(i,i)
end do
J3=offdia3
!!!!!!!!!!dia of j4
p=0;p1=0
do i=2,(n-m)
do j=1,n
if(j .ne. i)then
p1=V(j)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j))
p=p1+p
end if
end do
dia4(i-1,i-1)=-(2*V(i)*Yabs(i,i)*sin(angle(i,i)))-p
p=0;p1=0
end do
!!!!!!!!!!!!!!!off dia of j4
p1=0;p=0
do k=2,(n-m)
i=k;
do j=2,(n-m)
if(j .ne. i)then
p1=V(i)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j))
end if
i=i-1;j=j-1
offdia4(i,j)=-p1
p1=0;
i=i+1;j=j+1
end do
end do
do i=1,(n-m-1)
offdia4(i,i)=dia4(i,i);
end do
J4=offdia4
!!!!!!!
!!!!!!!!!!!!!!!!!!!formation of final jacobian!!!!!!!!!!
Jac( 1:38, 1:38) = J1 (1:38,1:38)
Jac( 1:38,39:67) = J2 (1:38,1:29)
Jac(39:67, 1:38) = J3 (1:29,1:38)
Jac(39:67,39:67) = J4 (1:29,1:29)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!print*,Jac(23,21)
CALL FindInv(Jac,invJac ,67, ErrorFlag)
trnsMF=transpose(MF)
deltaA=matmul( invJac, trnsMF)
do i=1,67
A(i)=A(i)+deltaA(i)
end do
!!!!!!!!!!!!updating values
do i=1,(n-1)
d1(i)=A(i)
end do
k=0
do i=n,(2*n-2-m)
k=1+k
v1(k)=A(i)
end do
end do
end program test
The array "Ps" contains some values. Now if I increase value of Ps(15) by Ps(15)+1 so for both values can I parallelize this code to get answer quickly.
I am using PGI compiler for CUDA FORTRAN.

Answer 1

Your code is fairly straightforward with lots of independent parallel loops. These parallel loops appear to be wrapped in an outer convergence do while loop, so as long as you keep the data on the device for all iterations of the convergence loop, you won't be bottlenecked by transfers.
I would recommend starting with compiler directives for this code rather than diving in to CUDA Fortran. Compiler directives work well for simple independent loops like these -- they are simple hints that you place in code comments that tell the compiler which loops to parallelize, which data to copy, etc.
You can first try OpenMP to accelerate to multiple CPU cores. Then you can use GPU directives such as OpenACC, which is going to be available soon in compilers from PGI, Cray, and CAPS. To get a head start, you could download a free trial of the PGI compiler and use their "Accelerator" directives. Accelerator is very similar in syntax to OpenACC.

Answer 2

Yes, you can use the PGI compiler to write CUDA kernels and make CUDA API calls.
PGI Fortran CUDA Homepage
The question, I think, you mean to ask is "Should I parallelize this code?"
My answer would be that yes you could see some mild benefits to parallelization, at a glance.
For example, segments like:
do i=2,n
do j=1,n
if(j .ne. i)then
p1=V(i)*V(j)*Yabs(i,j)*sin(angle(i,j)-d(i)+d(j))
!print*,p1
p=p1+p
end if
end do
i=i-1
dia1(i,i)=p
p=0
i=i+1
end do
Are an N^2 set of independent calculations (in this case you set n=39, but I assume it could change). Thus you're dealing with at least a couple hundred calculations. While ideally you'd want even MORE calculations in terms of parallelization, you're at least in good shape in terms of that many of your loops appear to be doing identical independent work # each step -- ideal for a threaded application.
Thus you could see some mild benefit to writing CUDA kernels to replace your looping code segments in your data post-processing algorithms. Beware, the latencies of the PCI bus in terms of memory transfers do nullify some of the performance gains, particularly for small systems.
Thus I would say, yes, by all means you can and should try this if you're game, but don't expect it to be 100x faster... maybe like 2-10x faster, if you code it well, depending on your loop bound size and level of divergence within the particular loops.
Worst case scenario you see no gains, or even see slowdown, but at least you've learned something!!