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239 lines (224 loc) · 9.13 KB
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module cg
use workingprecision
use matrixtools
use mpi
implicit none
! This module contains the conjugate gradient related functions and
! subroutines.
contains
function congrad(A, b) result(x)
! Simple sequential algorithm for the CG method.
real(kind=wp) :: A(:,:), b(:), x(size(b)), r(size(b))
real(kind=wp) :: AtA(size(A,1), size(A,2)), bt(size(b)), p(size(b))
real(kind=wp) :: Ap(size(A,1))
real(kind=wp) :: rsold, rsnew, alph
real(kind=wp), parameter :: tol = 1e-10
integer :: i, n
n = size(A,1)
x = 0_wp
AtA = matmul(transpose(A), A)
bt = matmul(transpose(A), b)
r = bt - matmul(AtA,x)
p = r
rsold = dot_product(r,r)
do i = 1, n
Ap = matmul(AtA,p)
alph = rsold/(sum(p*Ap))
x = x + alph*p
r = r - alph*Ap
rsnew = dot_product(r,r)
if (rsnew < epsilon(1.0)**2) then
print *, "Converged!"
exit
end if
p = r + rsnew/rsold*p
rsold = rsnew
end do
end function congrad
subroutine solve_cg(A, b, x)
! Use MPI to distribute the matrix multiplication
real(kind=wp), intent(in) :: A(:,:), b(:)
real(kind=wp), intent(out) :: x(size(b,1))
real(kind=wp), allocatable :: At(:,:), AtA(:,:), Atb(:)
real(kind=wp), allocatable :: Ap(:), bt(:), r(:), p(:)
real(kind=wp) :: rsnew, rsold, alph
integer, parameter :: from_master = 1, from_worker = 2
integer :: numtasks, id, numworkers, source, dest
integer :: m, n, rows, avgrow, extra, offset, i, k, ierr
integer :: status(MPI_STATUS_SIZE), mdata(2)
call MPI_COMM_RANK(MPI_COMM_WORLD, id, ierr)
call MPI_COMM_SIZE(MPI_COMM_WORLD, numtasks, ierr)
numworkers = numtasks - 1 ! Need one for master
if (numtasks < 2) then
print *, "Number of processors must be at least 2"
call MPI_FINALIZE(ierr)
stop
end if
m = size(A,1)
n = size(A,2)
if (size(b,1) /= m) then
print *, "Dimensions of A and b must agree"
call MPI_FINALIZE(ierr)
stop
end if
if (id == 0) then
allocate(At(n,m))
At = transpose(A)
! compute: AtA = matmul(At,A) and bt = matmul(At,b)
avgrow = n/numworkers ! Since we are working with transpose(A),
! rows = n
extra = mod(n,numworkers)
! Send data to workers:
offset = 1
do dest = 1, numworkers
if (dest <= extra) then
rows = avgrow + 1
else
rows = avgrow
end if
mdata(1) = offset
mdata(2) = rows
call MPI_SEND(mdata, 2, MPI_INTEGER, dest, from_master, &
MPI_COMM_WORLD, ierr)
if (wp == sp) then
call MPI_SEND(At(offset:offset+rows-1,:), rows*m, MPI_REAL, &
dest, from_master, MPI_COMM_WORLD, ierr)
else
call MPI_SEND(At(offset:offset+rows-1,:), rows*m, &
MPI_DOUBLE_PRECISION, dest, from_master, &
MPI_COMM_WORLD, ierr)
end if
offset = offset + rows
end do
! Get results
allocate(AtA(n,n),Atb(n))
do source = 1, numworkers
call MPI_RECV(mdata, 2, MPI_INTEGER, source, from_worker, &
MPI_COMM_WORLD, status, ierr)
offset = mdata(1)
rows = mdata(2)
if (wp == sp) then
call MPI_RECV(AtA(offset:offset+rows-1,:), rows*n, &
MPI_REAL, source, from_worker, MPI_COMM_WORLD, &
status, ierr)
call MPI_RECV(Atb(offset:offset+rows-1), rows, MPI_REAL, &
source, from_worker, MPI_COMM_WORLD, status, ierr)
else
call MPI_RECV(AtA(offset:offset+rows-1,:), rows*n, &
MPI_DOUBLE_PRECISION, source, from_worker, &
MPI_COMM_WORLD, status, ierr)
call MPI_RECV(Atb(offset:offset+rows-1), rows, &
MPI_DOUBLE_PRECISION, source, from_worker, &
MPI_COMM_WORLD, status, ierr)
end if
end do
allocate(Ap(n), r(n), p(n))
x = 0_wp
r = Atb
p = r
rsold = dot_product(r,r)
do i = 1, n
do dest = 1, numworkers
call MPI_SEND(1, 1, MPI_INTEGER, dest, from_master, &
MPI_COMM_WORLD, ierr)
if (wp == sp) then
call MPI_SEND(p, n, MPI_REAL, dest, from_master, &
MPI_COMM_WORLD, ierr)
else
call MPI_SEND(p, n, MPI_DOUBLE_PRECISION, dest, &
from_master, MPI_COMM_WORLD, ierr)
end if
end do
do source = 1, numworkers
call MPI_RECV(mdata, 2, MPI_INTEGER, source, from_worker, &
MPI_COMM_WORLD, status, ierr)
offset = mdata(1)
rows = mdata(2)
if (wp == sp) then
call MPI_RECV(Ap(offset:offset+rows-1), rows, &
MPI_REAL, source, from_worker, MPI_COMM_WORLD, &
status, ierr)
else
call MPI_RECV(Ap(offset:offset+rows-1), rows, &
MPI_DOUBLE_PRECISION, source, from_worker, &
MPI_COMM_WORLD, status, ierr)
end if
end do
alph = rsold/dot_product(p,Ap)
x = x + alph*p
r = r - alph*Ap
rsnew = dot_product(r,r)
if (rsnew < epsilon(1.0)**2) then
do dest = 1, numworkers
call MPI_SEND(0, 1, MPI_INTEGER, dest, from_master, &
MPI_COMM_WORLD, ierr)
end do
print *, "Converged!"
exit
end if
p = r + rsnew/rsold*p
rsold = rsnew
end do
else ! workers
! Compute AtA = matmul(At,A) and bt = matmul(At,b)
call MPI_RECV(mdata, 2, MPI_INTEGER, 0, from_master, &
MPI_COMM_WORLD, status, ierr)
offset = mdata(1)
rows = mdata(2)
allocate(At(rows,m))
if (wp == sp) then
call MPI_RECV(At, rows*m, MPI_REAL, 0, from_master, &
MPI_COMM_WORLD, status, ierr)
else
call MPI_RECV(At, rows*m, MPI_DOUBLE_PRECISION, 0, &
from_master, MPI_COMM_WORLD, status, ierr)
end if
allocate(AtA(rows,n), bt(rows))
AtA = matmul(At,A)
bt = matmul(At,b)
! Send results back
call MPI_SEND(mdata, 2, MPI_INTEGER, 0, from_worker, &
MPI_COMM_WORLD, ierr)
if (wp == sp) then
call MPI_SEND(AtA, rows*n, MPI_REAL, 0, from_worker, &
MPI_COMM_WORLD, ierr)
call MPI_SEND(bt, rows, MPI_REAL, 0, from_worker, &
MPI_COMM_WORLD, ierr)
else
call MPI_SEND(AtA, rows*n, MPI_DOUBLE_PRECISION, 0, &
from_worker, MPI_COMM_WORLD, ierr)
call MPI_SEND(bt, rows, MPI_DOUBLE_PRECISION, 0, &
from_worker, MPI_COMM_WORLD, ierr)
end if
allocate(p(n))
do i = 1, n
! If we send 0, shut down this process.
call MPI_RECV(k, 1, MPI_INTEGER, 0, from_master, &
MPI_COMM_WORLD, status, ierr)
if (k == 0) then
call MPI_FINALIZE(ierr)
stop
end if
if (wp == sp) then
call MPI_RECV(p, n, MPI_REAL, 0, from_master, &
MPI_COMM_WORLD, status, ierr)
else
call MPI_RECV(p, n, MPI_DOUBLE_PRECISION, 0, from_master, &
MPI_COMM_WORLD, status, ierr)
end if
bt = matmul(AtA,p)
call MPI_SEND(mdata, 2, MPI_INTEGER, 0, from_worker, &
MPI_COMM_WORLD, ierr)
if (wp == sp) then
call MPI_SEND(bt, rows, MPI_REAL, 0, from_worker, &
MPI_COMM_WORLD, ierr)
else
call MPI_SEND(bt, rows, MPI_DOUBLE_PRECISION, 0, &
from_worker, MPI_COMM_WORLD, ierr)
end if
end do
call MPI_FINALIZE(ierr)
stop
end if
end subroutine solve_cg
end module cg