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diagonalization_hs2_dressed.irp.f
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diagonalization_hs2_dressed.irp.f
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BEGIN_PROVIDER [ character*(64), diag_algorithm ]
implicit none
BEGIN_DOC
! Diagonalization algorithm (Davidson or Lapack)
END_DOC
if (N_det > N_det_max_full) then
diag_algorithm = "Davidson"
else
diag_algorithm = "Lapack"
endif
if (N_det < N_states) then
diag_algorithm = "Lapack"
endif
END_PROVIDER
BEGIN_PROVIDER [ double precision, threshold_davidson_pt2 ]
implicit none
BEGIN_DOC
! Threshold of Davidson's algorithm, using PT2 as a guide
END_DOC
threshold_davidson_pt2 = threshold_davidson
END_PROVIDER
BEGIN_PROVIDER [ integer, dressed_column_idx, (N_states) ]
implicit none
BEGIN_DOC
! Index of the dressed columns
END_DOC
integer :: i
double precision :: tmp
integer, external :: idamax
do i=1,N_states
dressed_column_idx(i) = idamax(N_det, psi_coef(1,i), 1)
enddo
END_PROVIDER
subroutine davidson_diag_hs2(dets_in,u_in,s2_out,dim_in,energies,sze,N_st,N_st_diag,Nint,dressing_state,converged)
use bitmasks
implicit none
BEGIN_DOC
! Davidson diagonalization.
!
! dets_in : bitmasks corresponding to determinants
!
! u_in : guess coefficients on the various states. Overwritten
! on exit
!
! dim_in : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
double precision, intent(out) :: energies(N_st_diag), s2_out(N_st_diag)
integer, intent(in) :: dressing_state
logical, intent(out) :: converged
double precision, allocatable :: H_jj(:)
double precision, external :: diag_H_mat_elem, diag_S_mat_elem
integer :: i,k
ASSERT (N_st > 0)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
PROVIDE mo_two_e_integrals_in_map
allocate(H_jj(sze))
H_jj(1) = diag_h_mat_elem(dets_in(1,1,1),Nint)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(sze,H_jj, dets_in,Nint) &
!$OMP PRIVATE(i)
!$OMP DO SCHEDULE(static)
do i=2,sze
H_jj(i) = diag_H_mat_elem(dets_in(1,1,i),Nint)
enddo
!$OMP END DO
!$OMP END PARALLEL
if (dressing_state > 0) then
do k=1,N_st
do i=1,sze
H_jj(i) += u_in(i,k) * dressing_column_h(i,k)
enddo
enddo
endif
call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_out,energies,dim_in,sze,N_st,N_st_diag,Nint,dressing_state,converged)
deallocate (H_jj)
end
subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,s2_out,energies,dim_in,sze,N_st,N_st_diag_in,Nint,dressing_state,converged)
use bitmasks
use mmap_module
implicit none
BEGIN_DOC
! Davidson diagonalization with specific diagonal elements of the H matrix
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!
! S2_out : Output : s^2
!
! dets_in : bitmasks corresponding to determinants
!
! u_in : guess coefficients on the various states. Overwritten
! on exit
!
! dim_in : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! N_st_diag_in : Number of states in which H is diagonalized. Assumed > sze
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, N_st_diag_in, Nint
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(in) :: H_jj(sze)
integer, intent(in) :: dressing_state
double precision, intent(inout) :: s2_out(N_st_diag_in)
double precision, intent(inout) :: u_in(dim_in,N_st_diag_in)
double precision, intent(out) :: energies(N_st_diag_in)
integer :: iter, N_st_diag
integer :: i,j,k,l,m
logical, intent(inout) :: converged
double precision, external :: u_dot_v, u_dot_u
integer :: k_pairs, kl
integer :: iter2, itertot
double precision, allocatable :: y(:,:), h(:,:), h_p(:,:), lambda(:), s2(:)
real, allocatable :: y_s(:,:)
double precision, allocatable :: s_(:,:), s_tmp(:,:)
double precision :: diag_h_mat_elem
double precision, allocatable :: residual_norm(:)
character*(16384) :: write_buffer
double precision :: to_print(3,N_st)
double precision :: cpu, wall
integer :: shift, shift2, itermax, istate
double precision :: r1, r2, alpha
logical :: state_ok(N_st_diag_in*davidson_sze_max)
integer :: nproc_target
integer :: order(N_st_diag_in)
double precision :: cmax
double precision, allocatable :: U(:,:), overlap(:,:), S_d(:,:)
double precision, pointer :: W(:,:)
real, pointer :: S(:,:)
logical :: disk_based
double precision :: energy_shift(N_st_diag_in*davidson_sze_max)
include 'constants.include.F'
N_st_diag = N_st_diag_in
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, y_s, S_d, h, lambda
if (N_st_diag*3 > sze) then
print *, 'error in Davidson :'
print *, 'Increase n_det_max_full to ', N_st_diag*3
stop -1
endif
itermax = max(2,min(davidson_sze_max, sze/N_st_diag))+1
itertot = 0
if (state_following) then
allocate(overlap(N_st_diag*itermax, N_st_diag*itermax))
else
allocate(overlap(1,1)) ! avoid 'if' for deallocate
endif
overlap = 0.d0
PROVIDE nuclear_repulsion expected_s2 psi_bilinear_matrix_order psi_bilinear_matrix_order_reverse threshold_davidson_pt2
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*itermax) &! U
+ 1.5d0*dble(sze*m)*(N_st_diag*itermax) &! W,S
+ 1.d0*dble(sze)*(N_st_diag) &! S_d
+ 4.5d0*(N_st_diag*itermax)**2 &! h,y,y_s,s_,s_tmp
+ 2.d0*(N_st_diag*itermax) &! s2,lambda
+ 1.d0*(N_st_diag) &! residual_norm
! In H_S2_u_0_nstates_zmq
+ 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on collector
+ 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on slave
+ 0.5d0*maxab &! idx0 in H_S2_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,'Number of states in diagonalization')
call write_int(6,sze,'Number of determinants')
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 S^2 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)
if (disk_based) then
! Create memory-mapped files for W and S
type(c_ptr) :: ptr_w, ptr_s
integer :: fd_s, fd_w
call mmap(trim(ezfio_work_dir)//'davidson_w', (/int(sze,8),int(N_st_diag*itermax,8)/),&
8, fd_w, .False., ptr_w)
call mmap(trim(ezfio_work_dir)//'davidson_s', (/int(sze,8),int(N_st_diag*itermax,8)/),&
4, fd_s, .False., ptr_s)
call c_f_pointer(ptr_w, w, (/sze,N_st_diag*itermax/))
call c_f_pointer(ptr_s, s, (/sze,N_st_diag*itermax/))
else
allocate(W(sze,N_st_diag*itermax), S(sze,N_st_diag*itermax))
endif
allocate( &
! Large
U(sze,N_st_diag*itermax), &
S_d(sze,N_st_diag), &
! Small
h(N_st_diag*itermax,N_st_diag*itermax), &
h_p(N_st_diag*itermax,N_st_diag*itermax), &
y(N_st_diag*itermax,N_st_diag*itermax), &
s_(N_st_diag*itermax,N_st_diag*itermax), &
s_tmp(N_st_diag*itermax,N_st_diag*itermax), &
residual_norm(N_st_diag), &
s2(N_st_diag*itermax), &
y_s(N_st_diag*itermax,N_st_diag*itermax), &
lambda(N_st_diag*itermax))
h = 0.d0
U = 0.d0
y = 0.d0
s_ = 0.d0
s_tmp = 0.d0
ASSERT (N_st > 0)
ASSERT (N_st_diag >= N_st)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
! Davidson iterations
! ===================
converged = .False.
do k=N_st+1,N_st_diag
u_in(k,k) = 10.d0
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)
enddo
enddo
do k=1,N_st_diag
call normalize(u_in(1,k),sze)
enddo
do k=1,N_st_diag
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*(iter-1)
shift2 = N_st_diag*iter
if ((iter > 1).or.(itertot == 1)) then
! Compute |W_k> = \sum_i |i><i|H|u_k>
! -----------------------------------
if (disk_based) then
call ortho_qr_unblocked(U,size(U,1),sze,shift2)
call ortho_qr_unblocked(U,size(U,1),sze,shift2)
else
call ortho_qr(U,size(U,1),sze,shift2)
call ortho_qr(U,size(U,1),sze,shift2)
endif
if ((sze > 100000).and.distributed_davidson) then
call H_S2_u_0_nstates_zmq (W(1,shift+1),S_d,U(1,shift+1),N_st_diag,sze)
else
call H_S2_u_0_nstates_openmp(W(1,shift+1),S_d,U(1,shift+1),N_st_diag,sze)
endif
S(1:sze,shift+1:shift+N_st_diag) = real(S_d(1:sze,1:N_st_diag))
else
! Already computed in update below
continue
endif
if (dressing_state > 0) then
if (N_st == 1) then
l = dressed_column_idx(1)
double precision :: f
f = 1.0d0/psi_coef(l,1)
do istate=1,N_st_diag
do i=1,sze
W(i,shift+istate) += dressing_column_h(i,1) *f * U(l,shift+istate)
W(l,shift+istate) += dressing_column_h(i,1) *f * U(i,shift+istate)
S(i,shift+istate) += real(dressing_column_s(i,1) *f * U(l,shift+istate))
S(l,shift+istate) += real(dressing_column_s(i,1) *f * U(i,shift+istate))
enddo
enddo
else
call dgemm('T','N', N_st, N_st_diag, 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, N_st, 1.0d0, &
dressing_column_h, size(dressing_column_h,1), s_tmp, size(s_tmp,1), &
1.d0, W(1,shift+1), size(W,1))
call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, &
dressing_column_s, size(dressing_column_s,1), s_tmp, size(s_tmp,1), &
1.d0, S_d, size(S_d,1))
call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, &
dressing_column_h, size(dressing_column_h,1), &
U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
call dgemm('N','N', sze, N_st_diag, 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))
call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, &
dressing_column_s, size(dressing_column_s,1), &
U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, &
psi_coef, size(psi_coef,1), s_tmp, size(s_tmp,1), &
1.d0, S_d, size(S_d,1))
endif
endif
! Compute s_kl = <u_k | S_l> = <u_k| S2 |u_l>
! -------------------------------------------
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,j,k) COLLAPSE(2)
do j=1,shift2
do i=1,shift2
s_(i,j) = 0.d0
do k=1,sze
s_(i,j) = s_(i,j) + U(k,i) * dble(S(k,j))
enddo
enddo
enddo
!$OMP END PARALLEL DO
! 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_p,1))
! Penalty method
! --------------
if (s2_eig) then
h_p = s_
do k=1,shift2
h_p(k,k) = h_p(k,k) + S_z2_Sz - expected_s2
enddo
if (only_expected_s2) then
alpha = 0.1d0
h_p = h + alpha*h_p
else
alpha = 0.0001d0
h_p = h + alpha*h_p
endif
else
h_p = h
alpha = 0.d0
endif
! Diagonalize h_p
! ---------------
call lapack_diag(lambda,y,h_p,size(h_p,1),shift2)
! 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
! Compute S2 for each eigenvector
! -------------------------------
call dgemm('N','N',shift2,shift2,shift2, &
1.d0, s_, size(s_,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, s_, size(s_,1))
do k=1,shift2
s2(k) = s_(k,k) + S_z2_Sz
enddo
if (only_expected_s2) then
do k=1,shift2
state_ok(k) = (dabs(s2(k)-expected_s2) < 0.6d0)
enddo
else
do k=1,size(state_ok)
state_ok(k) = .True.
enddo
endif
do k=1,shift2
if (.not. state_ok(k)) then
do l=k+1,shift2
if (state_ok(l)) then
call dswap(shift2, y(1,k), 1, y(1,l), 1)
call dswap(1, s2(k), 1, s2(l), 1)
call dswap(1, lambda(k), 1, lambda(l), 1)
state_ok(k) = .True.
state_ok(l) = .False.
exit
endif
enddo
endif
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
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)
overlap(k,2) = s2(k)
enddo
do k=1,N_st
l = order(k)
if (k /= l) then
lambda(k) = overlap(l,1)
s2(k) = overlap(l,2)
endif
enddo
endif
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
call dgemm('N','N', sze, N_st_diag, 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, shift2, &
1.d0, W, size(W,1), y, size(y,1), 0.d0, W(1,shift2+1), size(W,1))
y_s(:,:) = real(y(:,:))
call sgemm('N','N', sze, N_st_diag, shift2, &
1., S, size(S,1), y_s, size(y_s,1), 0., S(1,shift2+1), size(S,1))
! Compute residual vector and davidson step
! -----------------------------------------
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,k)
do k=1,N_st_diag
do i=1,sze
U(i,shift2+k) = &
(lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) &
/max(H_jj(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) + nuclear_repulsion
to_print(2,k) = s2(k)
to_print(3,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,F11.6,1X,E11.3))') iter-1, to_print(1:3,1:N_st)
endif
! Check convergence
if (iter > 1) then
converged = dabs(maxval(residual_norm(1:N_st))) < threshold_davidson_pt2
endif
do k=1,N_st
if (residual_norm(k) > 1.e8) 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 S and W
! --------------------------------
call sgemm('N','N', sze, N_st_diag, shift2, 1., &
S, size(S,1), y_s, size(y_s,1), 0., S(1,shift2+1), size(S,1))
do k=1,N_st_diag
do i=1,sze
S(i,k) = S(i,shift2+k)
enddo
enddo
call dgemm('N','N', sze, N_st_diag, 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
do i=1,sze
W(i,k) = u_in(i,k)
enddo
enddo
call dgemm('N','N', sze, N_st_diag, 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
do i=1,sze
U(i,k) = u_in(i,k)
enddo
enddo
if (disk_based) then
call ortho_qr_unblocked(U,size(U,1),sze,N_st_diag)
call ortho_qr_unblocked(U,size(U,1),sze,N_st_diag)
else
call ortho_qr(U,size(U,1),sze,N_st_diag)
call ortho_qr(U,size(U,1),sze,N_st_diag)
endif
do j=1,N_st_diag
k=1
do while ((k<sze).and.(U(k,j) == 0.d0))
k = k+1
enddo
if (U(k,j) * u_in(k,j) < 0.d0) then
do i=1,sze
W(i,j) = -W(i,j)
S(i,j) = -S(i,j)
enddo
endif
enddo
do j=1,N_st_diag
do i=1,sze
S_d(i,j) = dble(S(i,j))
enddo
enddo
enddo
do k=1,N_st_diag
energies(k) = lambda(k)
s2_out(k) = s2(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)
if (disk_based)then
! Remove temp files
integer, external :: getUnitAndOpen
call munmap( (/int(sze,8),int(N_st_diag*itermax,8)/), 8, fd_w, ptr_w )
fd_w = getUnitAndOpen(trim(ezfio_work_dir)//'davidson_w','r')
close(fd_w,status='delete')
call munmap( (/int(sze,8),int(N_st_diag*itermax,8)/), 4, fd_s, ptr_s )
fd_s = getUnitAndOpen(trim(ezfio_work_dir)//'davidson_s','r')
close(fd_s,status='delete')
else
deallocate(W,S)
endif
deallocate ( &
residual_norm, &
U, overlap, &
h, y_s, S_d, &
y, s_, s_tmp, &
lambda &
)
FREE nthreads_davidson
end