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pqdts.f90
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pqdts.f90
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!pqdts: parallel qauntum detector tomography solver
!MIT License
!
!Copyright (c) 2024 Paderborn University, Paderborn Center for Parallel Computing, Robert Schade
!
!Permission is hereby granted, free of charge, to any person obtaining a copy
!of this software and associated documentation files (the "Software"), to deal
!in the Software without restriction, including without limitation the rights
!to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
!copies of the Software, and to permit persons to whom the Software is
!furnished to do so, subject to the following conditions:
!
!The above copyright notice and this permission notice shall be included in all
!copies or substantial portions of the Software.
!
!THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
!IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
!FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
!AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
!LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
!OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
!SOFTWARE.
module basics
use omp_lib, only: omp_get_wtime
use iso_fortran_env, only: int8, int32, int64, real64
#ifdef MPI
use mpi_f08, ONLY: MPI_request, MPI_Barrier, MPI_COMM_WORLD, MPI_allreduce, MPI_DOUBLE, MPI_SUM, &
MPI_Status, MPI_STATUSES_IGNORE, MPI_RECV, MPI_MIN, mpi_in_place, mpi_long, mpi_max, MPI_Finalize
#endif
implicit none
integer(kind=int64) :: m, n, d, MB, MB1, MB2, NP1, NP2
integer(kind=int64) :: Fl, Pl
type :: dpline
integer(kind=int32) :: c = 0
logical :: isalloc = .False.
real(kind=real64), pointer, dimension(:) :: f
end type
type :: intline
integer(kind=int32) :: c = 0
integer(kind=int32), pointer, dimension(:) :: f
end type
#ifdef MPI
!stuff for MPI
integer(kind=int32) :: ierror
integer(kind=int32) :: ierr
TYPE(MPI_Request), pointer, dimension(:) :: requests
TYPE(dpline), pointer, dimension(:) :: requestsbuf
logical :: tbarrier
#endif
integer(kind=int32) :: rank
integer(kind=int32) :: num_proc
integer(kind=int64) :: localrows
integer(kind=int64) :: localrows0 !start of block of rows
integer(kind=int64) :: localrows1
type(intline), dimension(:), pointer :: block_red
type(intline), dimension(:), pointer :: block_red_steps
integer(int32) :: blocks_red
!timing
real(kind=real64), pointer, dimension(:) :: timingsum
real(kind=real64), pointer, dimension(:) :: timingt
integer(kind=int32), pointer, dimension(:) :: timingc
integer(kind=int32) :: timingid
character(len=20), pointer, dimension(:) :: timingn
logical :: time_io = .false.
!traffic
real(kind=real64), pointer, dimension(:) :: dsend
real(kind=real64), pointer, dimension(:) :: drecv
!F
integer(kind=int64), pointer, dimension(:) :: Fi, Fj
real(kind=real64), pointer, dimension(:) :: Fd
integer(kind=int64), pointer, dimension(:) :: Frow0
integer(kind=int64), pointer, dimension(:) :: Frow1
integer(kind=int64), pointer, dimension(:) :: Flocalrow0
integer(kind=int64), pointer, dimension(:) :: Flocalrow1
type(dpline), dimension(:), pointer :: Frows
!P
integer(kind=int64), pointer, dimension(:) :: Pi, Pj
real(kind=real64), pointer, dimension(:) :: Pd
!auxiliary variables
real(kind=real64), pointer, dimension(:, :) :: P
real(kind=real64), pointer, dimension(:, :) :: O
real(kind=real64), pointer, dimension(:, :) :: Xtmp, Xp, sn !,btmp,btmp2,btmp3
integer(kind=int8), pointer, dimension(:, :) :: ik
integer(kind=int32), pointer, dimension(:) :: maxr
!mode setting
integer(kind=int32) :: mode
logical :: tfullspace
!constants
real(kind=real64) :: M_PI = 4.D0*DATAN(1.D0)
real(kind=real64) :: gam = 0.0D0
contains
subroutine tstart(n)
implicit none
character(*), intent(in) :: n
logical :: found
integer(kind=int32) :: i, it
real(kind=real64) :: t
t = omp_get_wtime()
found = .false.
do i = 1, 50
if (trim(n) .eq. timingn(i)) then
it = i
found = .true.
exit
end if
end do
if (.not. found) then
timingid = timingid + 1
it = timingid
end if
if (timingt(it) .ne. 0) then
print *, "timer ", it, "is already running"
stop
end if
timingt(it) = t
timingc(it) = timingc(it) + 1
timingn(it) = trim(n)
end subroutine
subroutine tstop(n)
implicit none
character(*), intent(in) :: n
logical :: found
integer(kind=int32) :: i, it
real(kind=real64) :: t
t = omp_get_wtime()
found = .false.
do i = 1, 50
if (trim(n) .eq. timingn(i)) then
it = i
found = .true.
exit
end if
end do
if (.not. found) then
print *, "timer ", trim(n), "has not been started"
stop
end if
timingsum(it) = timingsum(it) + t - timingt(it)
timingt(it) = 0
end subroutine
subroutine tprint(iter)
implicit none
integer(kind=int32), intent(in) :: iter
integer(kind=int32) :: i
Character(len=255) :: str
logical :: file_exists
if (.not. time_io) then
write (str, *) "timing_", rank, ".out"
str = adjustl(str)
INQUIRE (FILE=trim(str), EXIST=file_exists)
if (file_exists) then
if (iter .eq. 0) then
open (43, file=trim(str), status="replace", action="write")
else
open (43, file=trim(str), status="old", position="append", action="write")
end if
else
open (43, file=trim(str), status='new', action="write")
end if
time_io = .true.
end if
do i = 1, timingid
write (43, *) iter, timingn(i), timingc(i), timingsum(i)
end do
call flush (43)
end subroutine
subroutine fprob(x, mean, prob)
implicit none
real(kind=real64), intent(in) :: x
real(kind=real64), intent(in) :: mean
real(kind=real64), intent(out) :: prob
real(kind=real64) :: y, lf
if (mean .lt. 50) then
if (mean .eq. 0 .and. x .eq. 0) then
prob = 1.0D0
else
lf = LGAMMA(x + 1.0D0)
prob = exp(log(mean)*x - lf - mean)
end if
else
y = (x - mean)/sqrt(mean)
prob = exp(-0.5D0*y**2)/sqrt(mean)/sqrt(2*M_PI)
end if
end subroutine
subroutine Bdiag(BD)
!diagonal of Hessian H_ii
implicit none
real(kind=real64), intent(inout), dimension(:, :), pointer :: BD
integer(kind=int64) :: i, j
call tstart("Bdiag")
call pset(m, n, 0.0D0, BD)
!$OMP parallel DO private(i) schedule(static,1)
do j = 1, N
do i = 1, D
if (Flocalrow0(i) .ne. -1) then
BD(Flocalrow0(i):Flocalrow1(i), j) = BD(Flocalrow0(i):Flocalrow1(i), j) + 2.0*Frows(i)%f**2
end if
end do
end do
!$OMP end parallel DO
if (gam .ne. 0) then
call tstart("Biag_gam")
!$OMP parallel DO schedule(static,1)
do i = 1, N
BD(:localrows - 1, i) = BD(:localrows - 1, i) + 2.0D0*gam
BD(2:, i) = BD(2:, i) + 2.0D0*gam
end do
!$OMP end parallel DO
call tstop("Biag_gam")
end if
if (.not. tfullspace) then
call pscale(m, n, 2.0D0, BD)
! !$OMP parallel DO schedule(static,1)
! do j = 1, localrows
! BD(j, maxr(j)) = 0
! end do
! !$OMP end parallel DO
end if
call tstop("Bdiag")
end subroutine
subroutine BF(dd, BX)
!Hessian times vector: BX=H(X)*dd
implicit none
real(kind=real64), intent(inout), dimension(:, :), pointer :: dd, BX
integer(kind=int64) :: i, j
!call pset(m,n,0.0D0,btmp)
!call dl(btmp,btmp2)
!call dl(dd,btmp3)
!BX=btmp3-btmp2
!return
call tstart("BF")
call tstart("BF_prep")
if (.not. tfullspace) then
call pcopy(m, n, dd, bx)
!$OMP parallel DO schedule(static,1)
do j = 1, localrows
Bx(j, maxr(j)) = -(sum(dd(j, :)) - dd(j, maxr(j)))
end do
!$OMP end parallel DO
end if
call tstop("BF_prep")
call tstart("BF_O")
if (.not. tfullspace) then
call redO(Bx, .true., O)
else
call redO(dd, .true., O)
end if
call pset(m, n, 0.0D0, BX)
call tstop("BF_O")
call tstart("BF_BX")
!$OMP parallel DO private(i) schedule(static,1)
do j = 1, N
do i = 1, D
if (Flocalrow0(i) .ne. -1) then
BX(Flocalrow0(i):Flocalrow1(i), j) = BX(Flocalrow0(i):Flocalrow1(i), j) + 2.0*Frows(i)%f*(O(j, i))
end if
end do
end do
!$OMP end parallel DO
call tstop("BF_BX")
if (gam .ne. 0) then
call tstart("BF_gam")
if (.not. tfullspace) then
!$OMP parallel DO schedule(static,1) private(j)
do i = 1, N
do j = 1, localrows
if (j .lt. localrows) then
BX(j, i) = BX(j, i) + 2.0D0*gam*(dd(j, i) - dd(j + 1, i))
if (i .eq. maxr(j)) then
BX(j, i) = BX(j, i) + 2.0D0*gam*(-dd(j, i) - (sum(dd(j, :)) - dd(j, maxr(j))))
end if
if (i .eq. maxr(j + 1)) then
BX(j, i) = BX(j, i) + 2.0D0*gam*(+dd(j + 1, i) + (sum(dd(j + 1, :)) - dd(j + 1, maxr(j + 1))))
end if
end if
if (j .gt. 1) then
BX(j, i) = BX(j, i) - 2.0D0*gam*(dd(j - 1, i) - dd(j, i))
if (i .eq. maxr(j - 1)) then
BX(j, i) = BX(j, i) - 2.0D0*gam*(-dd(j - 1, i) - (sum(dd(j - 1, :)) - dd(j - 1, maxr(j - 1))))
end if
if (i .eq. maxr(j)) then
BX(j, i) = BX(j, i) - 2.0D0*gam*(+dd(j, i) + (sum(dd(j, :)) - dd(j, maxr(j))))
end if
end if
end do
end do
!$OMP end parallel DO
else
!$OMP parallel DO schedule(static,1) private(j)
do i = 1, N
do j = 1, localrows
if (j .lt. localrows) then
BX(j, i) = BX(j, i) + 2.0D0*gam*(dd(j, i) - dd(j + 1, i))
end if
if (j .gt. 1) then
BX(j, i) = BX(j, i) - 2.0D0*gam*(dd(j - 1, i) - dd(j, i))
end if
end do
end do
!$OMP end parallel DO
end if
call tstop("BF_gam")
end if
if (.not. tfullspace) then
!$OMP parallel DO schedule(static,1)
do j = 1, localrows
BX(j, :) = BX(j, :) - BX(j, maxr(j))
end do
!$OMP end parallel DO
end if
call tstop("BF")
end subroutine
subroutine Lalpha_min(X, S, tproj, alpha, dlalpha)
implicit none
real(kind=real64), intent(inout), dimension(:, :) :: X, S
logical, intent(in) :: tproj
real(kind=real64), intent(out) :: alpha, dlalpha
real(kind=real64) :: df, dx, Lm, Lp, L0, alphamin
integer(kind=int64) :: i
call tstart("Lalpha_min")
!backtracking
dx = 1e-5
alpha = 0.0D0
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, L0)
call pgaxpy2(m, n, 1.0D0, x, alpha + dx, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, Lp)
df = (Lp - L0)/(dx)
dlalpha = df
if (mode .eq. 2) then
alpha = 1.0D0
else
alpha = 100.0D0
end if
lm = huge(lm)
alphamin = 0
do i = 1, 100
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, Lp)
if (lp .lt. lm) then
lm = lp
alphamin = alpha
end if
if (rank .eq. 0) print *, "line search", i, "L=", Lp, "alpha=", alpha, "df(0)=", df
if (Lp .gt. L0 + 0.1D0*alpha*df) then
alpha = alpha*0.75D0
else
exit
end if
end do
alpha = alphamin
if (lm .gt. l0) alpha = 0
call tstop("Lalpha_min")
end subroutine
subroutine Lalpha_min2(X, S, tproj, alpha, dlalpha)
implicit none
real(kind=real64), intent(inout), dimension(:, :) :: X, S
logical, intent(in) :: tproj
real(kind=real64), intent(out) :: alpha, dlalpha
real(kind=real64) :: df, dx, Lm, Lp, L0, alphamin, xmin
integer(kind=int64) :: i
call tstart("Lalpha_min")
!backtracking
dx = 1e-5
alpha = 0.0D0
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
if (tproj) call doproj2(Xtmp, xmin)
call L(Xtmp, L0)
call pgaxpy2(m, n, 1.0D0, x, alpha + dx, s, xtmp)
if (tproj) call doproj2(Xtmp, xmin)
call L(Xtmp, Lp)
df = (Lp - L0)/(dx)
dlalpha = df
alpha = 1.0D0
lm = huge(lm)
alphamin = 0
do i = 1, 100
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
call doproj2(Xtmp, xmin)
call L(Xtmp, Lp)
if (lp .lt. lm .and. xmin .ge. -1e-12) then
lm = lp
alphamin = alpha
end if
if (rank .eq. 0) print *, "line search", i, "L=", Lp, "alpha=", alpha, "df(0)=", df, "min(X)=", xmin
if (Lp .gt. L0 + 0.1D0*alpha*df .or. xmin .lt. -1e-12) then
alpha = alpha*0.75D0
else
exit
end if
end do
alpha = alphamin
call tstop("Lalpha_min")
end subroutine
subroutine Lalpha_min_auglag(X, S, tproj, alpha, dlalpha)
implicit none
real(kind=real64), intent(inout), dimension(:, :) :: X, S
logical, intent(in) :: tproj
real(kind=real64), intent(out) :: alpha, dlalpha
real(kind=real64) :: df, dx, Lm, Lp, L0, alphamin
integer(kind=int64) :: i
call tstart("Lalpha_min")
!backtracking
dx = 1e-5
alpha = 0.0D0
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, L0)
call pgaxpy2(m, n, 1.0D0, x, alpha + dx, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, Lp)
df = (Lp - L0)/(dx)
dlalpha = df
alpha = 1.0D0
lm = huge(lm)
alphamin = 0
do i = 1, 100
call pgaxpy2(m, n, 1.0D0, x, alpha, s, xtmp)
if (tproj) call doproj(Xtmp)
call L(Xtmp, Lp)
if (lp .lt. lm) then
lm = lp
alphamin = alpha
end if
if (rank .eq. 0) print *, "line search", i, "L=", Lp, "alpha=", alpha, "df(0)=", df
if (Lp .gt. L0 + 0.1D0*alpha*df) then
alpha = alpha*0.75D0
else
exit
end if
end do
alpha = alphamin
call tstop("Lalpha_min")
end subroutine
subroutine paxpy(m, n, alpha, x, y)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x, y
real(kind=real64), intent(in) :: alpha
integer(kind=int64) :: i
call tstart("paxpy")
!$OMP parallel DO schedule(static,1)
do i = 1, N
y(:, i) = y(:, i) + alpha*x(:, i)
end do
!$OMP end parallel DO
call tstop("paxpy")
end subroutine
subroutine pgaxpy(m, n, alpha, x, beta, y)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x, y
real(kind=real64), intent(in) :: alpha, beta
integer(kind=int64) :: i
call tstart("gpaxpy")
!$OMP parallel DO schedule(static,1)
do i = 1, N
y(:, i) = beta*y(:, i) + alpha*x(:, i)
end do
!$OMP end parallel DO
call tstop("gpaxpy")
end subroutine
subroutine pgaxpy2(m, n, alpha, x, beta, y, z)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x, y, z
real(kind=real64), intent(in) :: alpha, beta
integer(kind=int64) :: i
call tstart("pgpaxpy2")
!$OMP parallel DO schedule(static,1)
do i = 1, N
z(:, i) = beta*y(:, i) + alpha*x(:, i)
end do
!$OMP end parallel DO
call tstop("pgpaxpy2")
end subroutine
subroutine pset(m, n, alpha, x)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(in) :: alpha
real(kind=real64), intent(inout), dimension(:, :) :: x
integer(kind=int64) :: i
call tstart("pset")
!$OMP parallel DO schedule(static,1)
do i = 1, N
x(:, i) = alpha
end do
!$OMP end parallel DO
call tstop("pset")
end subroutine
subroutine pcopy(m, n, x, y)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x, y
integer(kind=int64) :: i
call tstart("pcopy")
!$OMP parallel DO schedule(static,1)
do i = 1, N
y(:, i) = x(:, i)
end do
!$OMP end parallel DO
call tstop("pcopy")
end subroutine
subroutine pscale(m, n, alpha, x)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x
real(kind=real64), intent(in) :: alpha
integer(kind=int64) :: i
call tstart("pscale")
!$OMP parallel DO schedule(static,1)
do i = 1, N
x(:, i) = x(:, i)*alpha
end do
!$OMP end parallel DO
call tstop("pscale")
end subroutine
subroutine pcopy_scale(m, n, alpha, x, y)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :) :: x, y
real(kind=real64), intent(in) :: alpha
integer(kind=int64) :: i
call tstart("pcopy_scale")
!$OMP parallel DO schedule(static,1)
do i = 1, N
y(:, i) = x(:, i)*alpha
end do
!$OMP end parallel DO
call tstop("pcopy_scale")
end subroutine
subroutine pdot(m, n, x, y, val)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :), pointer :: x, y
real(kind=real64), intent(out) :: val
real(kind=real64), external :: ddot
integer(kind=int64) :: i
#ifdef MPI
integer(kind=int32) :: ierr
#endif
call tstart("pdot")
call tstart("pdot_red")
val = 0
!$OMP parallel DO schedule(static,1) reduction(+:val)
do i = 1, N
val = val + sum(x(:, i)*y(:, i))
end do
!$OMP end parallel DO
call tstop("pdot_red")
#ifdef MPI
call tstart("pdot_comm")
call MPI_ALLREDUCE(MPI_IN_PLACE, val, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD, ierr)
call tstop("pdot_comm")
#endif
call tstop("pdot")
end subroutine
subroutine pmin(m, n, x, val)
implicit none
integer(kind=int64), intent(in) :: n, m
real(kind=real64), intent(inout), dimension(:, :), pointer :: x
real(kind=real64), intent(out) :: val
integer(kind=int64) :: i
#ifdef MPI
integer(kind=int32) :: ierr
#endif
call tstart("pmin")
call tstart("pmin_red")
val = 0
!$OMP parallel DO schedule(static,1) reduction(min:val)
do i = 1, N
val = minval(X(:, i))
end do
!$OMP end parallel DO
call tstop("pmin_red")
#ifdef MPI
call tstart("pmin_comm")
call MPI_ALLREDUCE(MPI_IN_PLACE, val, 1, MPI_DOUBLE, MPI_MIN, MPI_COMM_WORLD, ierr)
call tstop("pmin_comm")
#endif
call tstop("pmin")
end subroutine
recursive subroutine butterfly(N, rank, offset, level, send, recv)
implicit none
integer(kind=int32), intent(in) :: N
integer(kind=int32), intent(in) :: offset, level, rank
integer(kind=int64), intent(inout), pointer, dimension(:, :) :: send, recv
integer(kind=int32) :: N1, N2, a1, a2
integer(kind=int32) :: i
if (N .eq. 1) return
!halves, N1<=N2
N1 = N/2
N2 = N - N1
!print*,N,offset,level,N1,N2
!everyone from half 1 needs to send to half 2
do i = 1, N1
a1 = i + offset
a2 = N1 + i + offset
if (a1 .ne. a2) then
!print*,"send1",level,a1,a2
if (a1 .eq. rank + 1) then
if (send(level, 1) .eq. -1) then
send(level, 1) = a2 - 1
else
send(level, 2) = a2 - 1
end if
end if
if (a2 .eq. rank + 1) then
if (recv(level, 1) .eq. -1) then
recv(level, 1) = a1 - 1
else
recv(level, 2) = a1 - 1
end if
end if
end if
end do
call butterfly(N1, rank, offset, level + 1, send, recv)
!everyone from half 2 needs to send to half 1
do i = N1 + 1, N
a1 = i + offset
a2 = mod(i + N1 + 1, N1) + 1 + offset
if (a1 .ne. a2) then
!print*,"send2",level,a1,a2
if (a1 .eq. rank + 1) then
if (send(level, 1) .eq. -1) then
send(level, 1) = a2 - 1
else
send(level, 2) = a2 - 1
end if
end if
if (a2 .eq. rank + 1) then
if (recv(level, 1) .eq. -1) then
recv(level, 1) = a1 - 1
else
recv(level, 2) = a1 - 1
end if
end if
end if
end do
call butterfly(N2, rank, offset + N1, level + 1, send, recv)
end subroutine
subroutine redO(X, allreduce, O)
implicit none
real(kind=real64), pointer, intent(in), dimension(:, :) :: X
logical, intent(in) :: allreduce
real(kind=real64), pointer, intent(in), dimension(:, :) :: O
integer(kind=int64) :: i, j
#ifdef MPI
TYPE(MPI_Status) :: stat
logical :: found
integer(kind=int32) :: ierr, rc
real(kind=real64), allocatable, dimension(:) :: tmpf
integer(kind=int64), pointer, dimension(:, :) :: send, recv
integer(kind=int64) :: iop
integer(kind=int32) :: k
integer(kind=int32) :: lmax, level, lm, rcm, rankl
#endif
call tstart("redO_O")
!$OMP parallel DO private(j) schedule(static,1)
do i = 1, D
if (Flocalrow0(i) .ne. -1) then
do J = 1, N
O(j, i) = sum(Frows(i)%f*X(Flocalrow0(i):Flocalrow1(i), j))
end do
else
O(:, i) = 0.0D0
end if
end do
!$OMP end parallel DO
call tstop("redO_O")
#ifdef MPI
call tstart("redO_comm")
!reduce O where necessary
rc = 0
if (.true.) then
!send
do i = 1, D
if (block_red(i)%c .gt. 1) then
found = .false.
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .eq. rank) then
found = .true.
exit
end if
end do
if (found) then
if (allreduce) then
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .ne. rank) then
rc = rc + 1
if (.not. requestsbuf(rc)%isalloc) then
allocate (requestsbuf(rc)%f(N))
requestsbuf(rc)%isalloc = .true.
end if
requestsbuf(rc)%f(:) = O(:, i)
call MPI_ISEND(requestsbuf(rc)%f, int(N, kind=int32), MPI_DOUBLE, &
block_red(i)%f(k), int(i, kind=int32), MPI_COMM_WORLD, requests(rc), ierr)
! dsend(block_red(i)%f(k))=dsend(block_red(i)%f(k))+N*8
end if
end do
else
if (block_red(i)%f(1) .ne. rank) then
rc = rc + 1
if (.not. requestsbuf(rc)%isalloc) then
allocate (requestsbuf(rc)%f(N))
requestsbuf(rc)%isalloc = .true.
end if
requestsbuf(rc)%f = O(:, i)
! print*,rank,"MPI_ISEND",i,rank,block_red(i)%f(1)
call MPI_ISEND(requestsbuf(rc)%f, int(N, kind=int32), MPI_DOUBLE, &
block_red(i)%f(1), int(i, kind=int32), MPI_COMM_WORLD, requests(rc), ierr)
! dsend(block_red(i)%f(1))=dsend(block_red(i)%f(1))+N*8
end if
end if
end if
end if
end do
!receive
allocate (tmpf(N))
do i = 1, D
if (block_red(i)%c .gt. 1) then
found = .false.
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .eq. rank) then
found = .true.
exit
end if
end do
if (found) then
if (allreduce) then
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .ne. rank) then
! print*,rank,"MPI_RECV",i,block_red(i)%f(k),rank
call MPI_RECV(tmpf, int(N, kind=int32), MPI_DOUBLE, block_red(i)%f(k), &
int(i, kind=int32), MPI_COMM_WORLD, stat, ierr)
O(:, i) = O(:, i) + tmpf
! drecv(block_red(i)%f(k))=drecv(block_red(i)%f(k))+N*8
end if
end do
else
if (block_red(i)%f(1) .eq. rank) then
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .ne. rank) then
! print*,rank,"MPI_RECV",i,block_red(i)%f(k),rank
call MPI_RECV(tmpf, int(N, kind=int32), MPI_DOUBLE, block_red(i)%f(k), &
int(i, kind=int32), MPI_COMM_WORLD, stat, ierr)
O(:, i) = O(:, i) + tmpf
! drecv(block_red(i)%f(1))=drecv(block_red(i)%f(1))+N*8
end if
end do
end if
end if
end if
end if
end do
call mpi_waitall(rc, requests, MPI_STATUSES_IGNORE, ierr)
deallocate (tmpf)
else
!butterfly communication for reduction
allocate (tmpf(N))
lm = 0
do i = 1, D
if (block_red(i)%c .le. 1) cycle
lmax = bit_size(block_red(i)%c - 1) - leadz(block_red(i)%c - 1)
lm = max(lm, lmax)
end do
allocate (send(lm, 2))
allocate (recv(lm, 2))
rcm = 0
do level = 1, lm
rc = 0
do i = 1, D
!check if this line needs a reduction
if (block_red(i)%c .eq. 1) cycle
!perform butterfly reduction
lmax = bit_size(block_red(i)%c - 1) - leadz(block_red(i)%c - 1)
if (level .gt. lmax) cycle
!check if this rank is involved in the reduction
found = .false.
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .eq. rank) then
found = .true.
rankl = k - 1
exit
end if
end do
if (.not. found) cycle
send(:, :) = -1
recv(:, :) = -1
call butterfly(block_red(i)%c, rankl, 0, 1, send, recv)
do iop = 1, 2
if (send(level, iop) .eq. -1) cycle
rc = rc + 1
if (.not. requestsbuf(rc)%isalloc) then
allocate (requestsbuf(rc)%f(N))
requestsbuf(rc)%isalloc = .true.
end if
requestsbuf(rc)%f(:) = O(:, i)
call MPI_ISEND(requestsbuf(rc)%f, int(N, kind=int32), MPI_DOUBLE, &
block_red(i)%f(send(level, iop) + 1), int(i, kind=int32), MPI_COMM_WORLD, requests(rc), ierr)
end do
end do
do i = 1, D
!check if this line needs a reduction
if (block_red(i)%c .eq. 1) cycle
!perform butterfly reduction
lmax = bit_size(block_red(i)%c - 1) - leadz(block_red(i)%c - 1)
if (level .gt. lmax) cycle
!check if this rank is involved in the reduction
found = .false.
do k = 1, block_red(i)%c
if (block_red(i)%f(k) .eq. rank) then
found = .true.
rankl = k - 1
exit
end if
end do
if (.not. found) cycle
send(:, :) = -1
recv(:, :) = -1
call butterfly(block_red(i)%c, rankl, 0, 1, send, recv)
!recv
do iop = 1, 2
if (recv(level, iop) .eq. -1) cycle
call MPI_RECV(tmpf, int(N, kind=int32), MPI_DOUBLE, &
block_red(i)%f(recv(level, iop) + 1), int(i, kind=int32), MPI_COMM_WORLD, stat, ierr)
O(:, i) = O(:, i) + tmpf(:)
end do
end do
rcm = max(rcm, rc)
end do
call mpi_waitall(rc, requests, MPI_STATUSES_IGNORE, ierr)
deallocate (send)
deallocate (recv)
deallocate (tmpf)
end if
if (tbarrier) call MPI_Barrier(MPI_COMM_WORLD, ierr)
call tstop("redO_comm")
#endif
end subroutine
subroutine L(X, val)
implicit none
real(kind=real64), pointer, intent(in), dimension(:, :) :: X
real(kind=real64), intent(out) :: val
integer(kind=int64) :: i, j
#ifdef MPI
integer(kind=int32) :: ierr
#endif
call tstart("L")
call tstart("L_prep")
!reconstruct max column
if (.not. tfullspace) then
!$OMP parallel DO schedule(static,1)
do j = 1, localrows
X(j, maxr(j)) = 1.0D0 - (sum(X(j, :)) - X(j, maxr(j)))
end do
!$OMP end parallel DO
end if
call tstop("L_prep")
call tstart("L_O")
call redO(X, .true., O)
call tstop("L_O")
call tstart("L_red")
call tstart("L_red_calc")
val = 0.0D0
!$OMP parallel DO reduction(+:val) schedule(static,1)
do i = 1, D
if (block_red(i)%c .gt. 0) then
if (block_red(i)%f(1) .eq. rank) then
val = val + sum((O(:, i) - P(:, i))**2)
end if
end if
end do
!$OMP end parallel DO
call tstop("L_red_calc")
if (gam .ne. 0) then
call tstart("L_gam")
!$OMP parallel DO reduction(+:val) schedule(static,1) private(j)
do i = 1, N
do j = 1, localrows - 1
val = val + gam*(X(j, i) - X(j + 1, i))**2
end do
end do
!$OMP end parallel DO
call tstop("L_gam")
end if
#ifdef MPI
call tstart("L_red_comm")
call MPI_ALLREDUCE(MPI_IN_PLACE, val, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD, ierr)
call tstop("L_red_comm")
#endif
call tstop("L_red")
call tstop("L")
end subroutine
subroutine dL(X, dLdX)
implicit none
real(kind=real64), pointer, intent(in), dimension(:, :) :: X
real(kind=real64), pointer, intent(inout), dimension(:, :) :: dLdX
integer(kind=int64) :: i, j
call tstart("dL")
call tstart("dL_prep")
!reconstruct max column
if (.not. tfullspace) then
!$OMP parallel DO schedule(static,1)
do j = 1, localrows
X(j, maxr(j)) = 1.0D0 - (sum(X(j, :)) - X(j, maxr(j)))
end do
!$OMP end parallel DO
end if
call pset(M, N, 0.0D0, dldx)
call tstop("dL_prep")
call tstart("dL_O")
call redO(X, .true., O)
call tstop("dL_O")
call tstart("dL_dLdX")
!$OMP parallel DO private(i) schedule(static,1)
do j = 1, N
do i = 1, D