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dav_double_dress_ext_rout.irp.f

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Emmanuel Giner 2021-10-26 19:11:04 +02:00
parent 699f655b89
commit 1f0c48023d
3 changed files with 557 additions and 174 deletions
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520
src/dav_general_mat/dav_double_dress_ext_rout.irp.f Normal file
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@ -0,0 +1,520 @@
subroutine dav_double_dressed(u_in,H_jj,Dress_jj,Dressing_vec,idx_dress,energies,sze,N_st,N_st_diag,converged,hcalc)
use mmap_module
BEGIN_DOC
! Generic Davidson diagonalization with TWO DRESSING VECTORS
!
! Dress_jj : DIAGONAL DRESSING of the Hamiltonian
!
! Dressing_vec : COLUMN / LINE DRESSING VECTOR
!
! idx_dress : position of the basis function used to use the Dressing_vec (usually the largest coeff)
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!
! u_in : guess coefficients on the various states. Overwritten on exit
!
! sze : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! N_st_diag : Number of states in which H is diagonalized. Assumed > sze
!
! Initial guess vectors are not necessarily orthonormal
!
! hcalc subroutine to compute W = H U (see routine hcalc_template for template of input/output)
END_DOC
implicit none
integer, intent(in) :: sze, N_st, N_st_diag, idx_dress
double precision, intent(in) :: H_jj(sze),Dress_jj(sze),Dressing_vec(sze,N_st)
double precision, intent(inout) :: u_in(sze,N_st_diag)
double precision, intent(out) :: energies(N_st_diag)
logical, intent(out) :: converged
external hcalc
double precision, allocatable :: H_jj_tmp(:)
ASSERT (N_st > 0)
ASSERT (sze > 0)
allocate(H_jj_tmp(sze))
do i=1,sze
H_jj_tmp(i) = H_jj(i) + Dress_jj(i)
enddo
do k=1,N_st
do i=1,sze
H_jj_tmp(i) += u_in(i,k) * Dressing_vec(i,k)
enddo
enddo
integer :: iter
integer :: i,j,k,l,m
double precision, external :: u_dot_v, u_dot_u
integer :: k_pairs, kl
integer :: iter2, itertot
double precision, allocatable :: y(:,:), h(:,:), lambda(:)
double precision, allocatable :: s_tmp(:,:)
double precision, allocatable :: residual_norm(:),inv_c_idx_dress_vec(:)
character*(16384) :: write_buffer
double precision :: to_print(2,N_st),inv_c_idx_dress
double precision :: cpu, wall
integer :: shift, shift2, itermax, istate
double precision :: r1, r2, alpha
logical :: state_ok(N_st_diag*davidson_sze_max)
integer :: nproc_target
integer :: order(N_st_diag)
double precision :: cmax
double precision, allocatable :: U(:,:), overlap(:,:)
double precision, pointer :: W(:,:)
logical :: disk_based
double precision :: energy_shift(N_st_diag*davidson_sze_max)
allocate(inv_c_idx_dress_vec(N_st))
inv_c_idx_dress = 1.d0/u_in(idx_dress,1)
do i = 1, N_st
inv_c_idx_dress_vec(i) = 1.d0/u_in(idx_dress,i)
enddo
include 'constants.include.F'
integer :: N_st_diag_in
N_st_diag_in = N_st_diag
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, y, h, lambda
if (N_st_diag_in*3 > sze) then
print *, 'error in Davidson :'
print *, 'Increase n_det_max_full to ', N_st_diag_in*3
stop -1
endif
itermax = max(2,min(davidson_sze_max, sze/N_st_diag_in))+1
itertot = 0
if (state_following) then
allocate(overlap(N_st_diag_in*itermax, N_st_diag_in*itermax))
else
allocate(overlap(1,1)) ! avoid 'if' for deallocate
endif
overlap = 0.d0
call write_time(6)
write(6,'(A)') ''
write(6,'(A)') 'Davidson Diagonalization'
write(6,'(A)') '------------------------'
write(6,'(A)') ''
! Find max number of cores to fit in memory
! -----------------------------------------
nproc_target = nproc
double precision :: rss
integer :: maxab
maxab = max(N_det_alpha_unique, N_det_beta_unique)+1
m=1
disk_based = .False.
call resident_memory(rss)
do
r1 = 8.d0 * &! bytes
( dble(sze)*(N_st_diag_in*itermax) &! U
+ 1.0d0*dble(sze*m)*(N_st_diag_in*itermax) &! W
+ 3.0d0*(N_st_diag_in*itermax)**2 &! h,y,s_tmp
+ 1.d0*(N_st_diag_in*itermax) &! lambda
+ 1.d0*(N_st_diag_in) &! residual_norm
! In H_u_0_nstates_zmq
+ 2.d0*(N_st_diag_in*N_det) &! u_t, v_t, on collector
+ 2.d0*(N_st_diag_in*N_det) &! u_t, v_t, on slave
+ 0.5d0*maxab &! idx0 in H_u_0_nstates_openmp_work_*
+ nproc_target * &! In OMP section
( 1.d0*(N_int*maxab) &! buffer
+ 3.5d0*(maxab) ) &! singles_a, singles_b, doubles, idx
) / 1024.d0**3
if (nproc_target == 0) then
call check_mem(r1,irp_here)
nproc_target = 1
exit
endif
if (r1+rss < qp_max_mem) then
exit
endif
if (itermax > 4) then
itermax = itermax - 1
else if (m==1.and.disk_based_davidson) then
m=0
disk_based = .True.
itermax = 6
else
nproc_target = nproc_target - 1
endif
enddo
nthreads_davidson = nproc_target
TOUCH nthreads_davidson
call write_int(6,N_st,'Number of states')
call write_int(6,N_st_diag_in,'Number of states in diagonalization')
call write_int(6,sze,'Number of basis functions ')
call write_int(6,nproc_target,'Number of threads for diagonalization')
call write_double(6, r1, 'Memory(Gb)')
if (disk_based) then
print *, 'Using swap space to reduce RAM'
endif
!---------------
write(6,'(A)') ''
write_buffer = '====='
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ==========='
enddo
write(6,'(A)') write_buffer(1:6+41*N_st)
write_buffer = 'Iter'
do i=1,N_st
write_buffer = trim(write_buffer)//' Energy Residual '
enddo
write(6,'(A)') write_buffer(1:6+41*N_st)
write_buffer = '====='
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ==========='
enddo
write(6,'(A)') write_buffer(1:6+41*N_st)
allocate(W(sze,N_st_diag_in*itermax))
allocate( &
! Large
U(sze,N_st_diag_in*itermax), &
! Small
h(N_st_diag_in*itermax,N_st_diag_in*itermax), &
y(N_st_diag_in*itermax,N_st_diag_in*itermax), &
s_tmp(N_st_diag_in*itermax,N_st_diag_in*itermax), &
residual_norm(N_st_diag_in), &
lambda(N_st_diag_in*itermax))
h = 0.d0
U = 0.d0
y = 0.d0
s_tmp = 0.d0
ASSERT (N_st > 0)
ASSERT (N_st_diag_in >= N_st)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
! Davidson iterations
! ===================
converged = .False.
do k=N_st+1,N_st_diag_in
do i=1,sze
call random_number(r1)
call random_number(r2)
r1 = dsqrt(-2.d0*dlog(r1))
r2 = dtwo_pi*r2
u_in(i,k) = r1*dcos(r2) * u_in(i,k-N_st)
enddo
u_in(k,k) = u_in(k,k) + 10.d0
enddo
do k=1,N_st_diag_in
call normalize(u_in(1,k),sze)
enddo
do k=1,N_st_diag_in
do i=1,sze
U(i,k) = u_in(i,k)
enddo
enddo
do while (.not.converged)
itertot = itertot+1
if (itertot == 8) then
exit
endif
do iter=1,itermax-1
shift = N_st_diag_in*(iter-1)
shift2 = N_st_diag_in*iter
if ((iter > 1).or.(itertot == 1)) then
! Compute |W_k> = \sum_i |i><i|H|u_k>
! -----------------------------------
call hcalc(W(1,shift+1),U(1,shift+1),N_st_diag_in,sze)
! Compute then the DIAGONAL PART OF THE DRESSING
! <i|W_k> += Dress_jj(i) * <i|U>
call dressing_diag_uv(W(1,shift+1),U(1,shift+1),Dress_jj,N_st_diag_in,sze)
else
! Already computed in update below
continue
endif
if (N_st == 1) then
l = idx_dress
double precision :: f
f = inv_c_idx_dress
do istate=1,N_st_diag_in
do i=1,sze
W(i,shift+istate) += Dressing_vec(i,1) *f * U(l,shift+istate)
W(l,shift+istate) += Dressing_vec(i,1) *f * U(i,shift+istate)
enddo
enddo
else
print*,'dav_double_dressed routine not yet implemented for N_st > 1'
!
! call dgemm('T','N', N_st, N_st_diag_in, sze, 1.d0, &
! psi_coef, size(psi_coef,1), &
! U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
!
! call dgemm('N','N', sze, N_st_diag_in, N_st, 1.0d0, &
! Dressing_vec, size(Dressing_vec,1), s_tmp, size(s_tmp,1), &
! 1.d0, W(1,shift+1), size(W,1))
!
!
! call dgemm('T','N', N_st, N_st_diag_in, sze, 1.d0, &
! Dressing_vec, size(Dressing_vec,1), &
! U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
!
! call dgemm('N','N', sze, N_st_diag_in, N_st, 1.0d0, &
! psi_coef, size(psi_coef,1), s_tmp, size(s_tmp,1), &
! 1.d0, W(1,shift+1), size(W,1))
!
endif
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
! -------------------------------------------
call dgemm('T','N', shift2, shift2, sze, &
1.d0, U, size(U,1), W, size(W,1), &
0.d0, h, size(h,1))
call dgemm('T','N', shift2, shift2, sze, &
1.d0, U, size(U,1), U, size(U,1), &
0.d0, s_tmp, size(s_tmp,1))
! Diagonalize h
! ---------------
integer :: lwork, info
double precision, allocatable :: work(:)
y = h
lwork = -1
allocate(work(1))
call dsygv(1,'V','U',shift2,y,size(y,1), &
s_tmp,size(s_tmp,1), lambda, work,lwork,info)
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call dsygv(1,'V','U',shift2,y,size(y,1), &
s_tmp,size(s_tmp,1), lambda, work,lwork,info)
deallocate(work)
if (info /= 0) then
stop 'DSYGV Diagonalization failed'
endif
! Compute Energy for each eigenvector
! -----------------------------------
call dgemm('N','N',shift2,shift2,shift2, &
1.d0, h, size(h,1), y, size(y,1), &
0.d0, s_tmp, size(s_tmp,1))
call dgemm('T','N',shift2,shift2,shift2, &
1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
0.d0, h, size(h,1))
do k=1,shift2
lambda(k) = h(k,k)
enddo
if (state_following) then
overlap = -1.d0
do k=1,shift2
do i=1,shift2
overlap(k,i) = dabs(y(k,i))
enddo
enddo
do k=1,N_st
cmax = -1.d0
do i=1,N_st
if (overlap(i,k) > cmax) then
cmax = overlap(i,k)
order(k) = i
endif
enddo
do i=1,N_st_diag_in
overlap(order(k),i) = -1.d0
enddo
enddo
overlap = y
do k=1,N_st
l = order(k)
if (k /= l) then
y(1:shift2,k) = overlap(1:shift2,l)
endif
enddo
do k=1,N_st
overlap(k,1) = lambda(k)
enddo
endif
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
call dgemm('N','N', sze, N_st_diag_in, shift2, &
1.d0, U, size(U,1), y, size(y,1), 0.d0, U(1,shift2+1), size(U,1))
call dgemm('N','N', sze, N_st_diag_in, shift2, &
1.d0, W, size(W,1), y, size(y,1), 0.d0, W(1,shift2+1), size(W,1))
! Compute residual vector and davidson step
! -----------------------------------------
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,k)
do k=1,N_st_diag_in
do i=1,sze
U(i,shift2+k) = &
(lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) &
/max(H_jj_tmp(i) - lambda (k),1.d-2)
enddo
if (k <= N_st) then
residual_norm(k) = u_dot_u(U(1,shift2+k),sze)
to_print(1,k) = lambda(k)
to_print(2,k) = residual_norm(k)
endif
enddo
!$OMP END PARALLEL DO
if ((itertot>1).and.(iter == 1)) then
!don't print
continue
else
write(*,'(1X,I3,1X,100(1X,F16.10,1X,E11.3))') iter-1, to_print(1:2,1:N_st)
endif
! Check convergence
if (iter > 1) then
converged = dabs(maxval(residual_norm(1:N_st))) < threshold_davidson
endif
do k=1,N_st
if (residual_norm(k) > 1.d8) then
print *, 'Davidson failed'
stop -1
endif
enddo
if (converged) then
exit
endif
logical, external :: qp_stop
if (qp_stop()) then
converged = .True.
exit
endif
enddo
! Re-contract U and update W
! --------------------------------
call dgemm('N','N', sze, N_st_diag_in, shift2, 1.d0, &
W, size(W,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
do k=1,N_st_diag_in
do i=1,sze
W(i,k) = u_in(i,k)
enddo
enddo
call dgemm('N','N', sze, N_st_diag_in, shift2, 1.d0, &
U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
do k=1,N_st_diag_in
do i=1,sze
U(i,k) = u_in(i,k)
enddo
enddo
enddo
call nullify_small_elements(sze,N_st_diag_in,U,size(U,1),threshold_davidson_pt2)
do k=1,N_st_diag_in
do i=1,sze
u_in(i,k) = U(i,k)
enddo
enddo
do k=1,N_st_diag_in
energies(k) = lambda(k)
enddo
write_buffer = '======'
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ==========='
enddo
write(6,'(A)') trim(write_buffer)
write(6,'(A)') ''
call write_time(6)
deallocate(W)
deallocate ( &
residual_norm, &
U, overlap, &
h, y, s_tmp, &
lambda &
)
FREE nthreads_davidson
end
subroutine dressing_diag_uv(v,u,dress_diag,N_st,sze)
implicit none
BEGIN_DOC
! Routine that computes the diagonal part of the dressing
!
! v(i) += u(i) * dress_diag(i)
!
! !!!!!!!! WARNING !!!!!!!! the vector v is not initialized
!
! !!!!!!!! SO MAKE SURE THERE ARE SOME MEANINGFUL VALUES IN THERE
END_DOC
integer, intent(in) :: N_st,sze
double precision, intent(in) :: u(sze,N_st),dress_diag(sze)
double precision, intent(inout) :: v(sze,N_st)
integer :: i,istate
do istate = 1, N_st
do i = 1, sze
v(i,istate) += dress_diag(i) * u(i,istate)
enddo
enddo
end

2
src/dav_general_mat/dav_ext_rout.irp.f
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@ -3,7 +3,7 @@ subroutine davidson_general_ext_rout(u_in,H_jj,energies,sze,N_st,N_st_diag_in,co
use mmap_module
implicit none
BEGIN_DOC
! Davidson diagonalization with specific diagonal elements of the H matrix
! Generic Davidson diagonalization
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!

209
src/utils/sort.irp.f
View File

@ -38,7 +38,15 @@ BEGIN_TEMPLATE
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer, external :: omp_get_num_threads
call rec_$X_quicksort(x,iorder,isize,1,isize,nproc)
if (omp_get_num_threads() == 1) then
!$OMP PARALLEL DEFAULT(SHARED)
!$OMP SINGLE
call rec_$X_quicksort(x,iorder,isize,1,isize,nproc)
!$OMP END SINGLE
!$OMP END PARALLEL
else
call rec_$X_quicksort(x,iorder,isize,1,isize,nproc)
endif
end
recursive subroutine rec_$X_quicksort(x, iorder, isize, first, last, level)
@ -49,7 +57,7 @@ BEGIN_TEMPLATE
$type :: c, tmp
integer :: itmp
integer :: i, j
if(isize<2)return
c = x( shiftr(first+last,1) )
@ -81,11 +89,16 @@ BEGIN_TEMPLATE
endif
else
if (first < i-1) then
!$OMP TASK DEFAULT(SHARED) FIRSTPRIVATE(isize,first,i,level)
call rec_$X_quicksort(x, iorder, isize, first, i-1,level/2)
!$OMP END TASK
endif
if (j+1 < last) then
!$OMP TASK DEFAULT(SHARED) FIRSTPRIVATE(isize,last,j,level)
call rec_$X_quicksort(x, iorder, isize, j+1, last,level/2)
!$OMP END TASK
endif
!$OMP TASKWAIT
endif
end
@ -249,60 +262,7 @@ SUBST [ X, type ]
i2 ; integer*2 ;;
END_TEMPLATE
!---------------------- INTEL
IRP_IF INTEL
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
use intel
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
character, allocatable :: tmp(:)
if (isize < 2) return
call ippsSortRadixIndexGetBufferSize(isize, $ippsz, n)
allocate(tmp(n))
call ippsSortRadixIndexAscend_$ityp(x, $n, iorder, isize, tmp)
deallocate(tmp)
iorder(1:isize) = iorder(1:isize)+1
call $Xset_order(x,iorder,isize)
end
subroutine $Xsort_noidx(x,isize)
use intel
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer :: n
character, allocatable :: tmp(:)
if (isize < 2) return
call ippsSortRadixIndexGetBufferSize(isize, $ippsz, n)
allocate(tmp(n))
call ippsSortRadixAscend_$ityp_I(x, isize, tmp)
deallocate(tmp)
end
SUBST [ X, type, ityp, n, ippsz ]
; real ; 32f ; 4 ; 13 ;;
i ; integer ; 32s ; 4 ; 11 ;;
i2 ; integer*2 ; 16s ; 2 ; 7 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
@ -329,12 +289,12 @@ BEGIN_TEMPLATE
endif
end subroutine $Xsort
SUBST [ X, type ]
d ; double precision ;;
SUBST [ X, type, Y ]
; real ; i ;;
d ; double precision ; i8 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
@ -346,112 +306,8 @@ BEGIN_TEMPLATE
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
call sorted_$Xnumber(x,isize,n)
if (isize == n) then
return
endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
call $Xradix_sort(x,iorder,isize,-1)
endif
end subroutine $Xsort
SUBST [ X, type ]
i8 ; integer*8 ;;
END_TEMPLATE
!---------------------- END INTEL
IRP_ELSE
!---------------------- NON-INTEL
BEGIN_TEMPLATE
subroutine $Xsort_noidx(x,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer, allocatable :: iorder(:)
integer :: i
allocate(iorder(isize))
do i=1,isize
iorder(i)=i
enddo
call $Xsort(x,iorder,isize)
deallocate(iorder)
end subroutine $Xsort_noidx
SUBST [ X, type ]
; real ;;
d ; double precision ;;
i ; integer ;;
i8 ; integer*8 ;;
i2 ; integer*2 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
! call sorted_$Xnumber(x,isize,n)
! if (isize == n) then
! return
! endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
! call heap_$Xsort(x,iorder,isize)
call quick_$Xsort(x,iorder,isize)
endif
end subroutine $Xsort
SUBST [ X, type ]
; real ;;
d ; double precision ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
call sorted_$Xnumber(x,isize,n)
if (isize == n) then
return
endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
call $Xradix_sort(x,iorder,isize,-1)
endif
! call $Xradix_sort(x,iorder,isize,-1)
call quick_$Xsort(x,iorder,isize)
end subroutine $Xsort
SUBST [ X, type ]
@ -460,11 +316,6 @@ SUBST [ X, type ]
i2 ; integer*2 ;;
END_TEMPLATE
IRP_ENDIF
!---------------------- END NON-INTEL
BEGIN_TEMPLATE
subroutine $Xset_order(x,iorder,isize)
implicit none
@ -562,12 +413,10 @@ SUBST [ X, type ]
i2; integer*2 ;;
END_TEMPLATE
BEGIN_TEMPLATE
recursive subroutine $Xradix_sort$big(x,iorder,isize,iradix)
recursive subroutine $Xradix_sort$big(x,iorder,isize,iradix)
implicit none
BEGIN_DOC
! Sort integer array x(isize) using the radix sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
@ -703,14 +552,24 @@ recursive subroutine $Xradix_sort$big(x,iorder,isize,iradix)
endif
! !$OMP PARALLEL DEFAULT(SHARED) if (isize > 1000000)
! !$OMP SINGLE
if (i3>1_$int_type) then
! !$OMP TASK FIRSTPRIVATE(iradix_new,i3) SHARED(x,iorder) if(i3 > 1000000)
call $Xradix_sort$big(x,iorder,i3,iradix_new-1)
! !$OMP END TASK
endif
if (isize-i3>1_$int_type) then
! !$OMP TASK FIRSTPRIVATE(iradix_new,i3) SHARED(x,iorder) if(isize-i3 > 1000000)
call $Xradix_sort$big(x(i3+1_$int_type),iorder(i3+1_$int_type),isize-i3,iradix_new-1)
! !$OMP END TASK
endif
! !$OMP TASKWAIT
! !$OMP END SINGLE
! !$OMP END PARALLEL
return
endif
@ -765,11 +624,16 @@ recursive subroutine $Xradix_sort$big(x,iorder,isize,iradix)
if (i1>1_$int_type) then
!$OMP TASK FIRSTPRIVATE(i0,iradix,i1) SHARED(x,iorder) if(i1 >1000000)
call $Xradix_sort$big(x(i0+1_$int_type),iorder(i0+1_$int_type),i1,iradix-1)
!$OMP END TASK
endif
if (i0>1) then
!$OMP TASK FIRSTPRIVATE(i0,iradix) SHARED(x,iorder) if(i0 >1000000)
call $Xradix_sort$big(x,iorder,i0,iradix-1)
!$OMP END TASK
endif
!$OMP TASKWAIT
end
@ -782,4 +646,3 @@ SUBST [ X, type, integer_size, is_big, big, int_type ]
END_TEMPLATE