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quantum_package/src/Davidson/diagonalization_hs2.irp.f

436 lines
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Fortran
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subroutine davidson_diag_hs2(dets_in,u_in,dim_in,energies,sze,N_st,N_st_diag,Nint,iunit)
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
!
! iunit : Unit number for the I/O
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint, iunit
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)
double precision, allocatable :: H_jj(:), S2_jj(:)
double precision :: diag_h_mat_elem
integer :: i
ASSERT (N_st > 0)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
PROVIDE mo_bielec_integrals_in_map
allocate(H_jj(sze), S2_jj(sze))
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(sze,H_jj,S2_jj, dets_in,Nint) &
!$OMP PRIVATE(i)
!$OMP DO SCHEDULE(guided)
do i=1,sze
H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
call get_s2(dets_in(1,1,i),dets_in(1,1,i),Nint,S2_jj(i))
enddo
!$OMP END DO
!$OMP END PARALLEL
call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
deallocate (H_jj,S2_jj)
end
subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
use bitmasks
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_jj : specific diagonal S^2 matrix elements
!
! 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 : Number of states in which H is diagonalized. Assumed > sze
!
! iunit : Unit for the I/O
!
! 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(in) :: H_jj(sze), S2_jj(sze)
integer, intent(in) :: iunit
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
double precision, intent(out) :: energies(N_st_diag)
integer :: sze_8
integer :: iter
integer :: i,j,k,l,m
logical :: converged
double precision :: u_dot_v, u_dot_u
integer, allocatable :: kl_pairs(:,:)
integer :: k_pairs, kl
integer :: iter2
double precision, allocatable :: W(:,:), U(:,:), R(:,:), S(:,:)
double precision, allocatable :: y(:,:), h(:,:), lambda(:), s2(:)
double precision, allocatable :: c(:), 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
include 'constants.include.F'
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, S, y, h, lambda
if (N_st_diag > sze) then
stop 'error in Davidson : N_st_diag > sze'
endif
PROVIDE nuclear_repulsion
call write_time(iunit)
call wall_time(wall)
call cpu_time(cpu)
write(iunit,'(A)') ''
write(iunit,'(A)') 'Davidson Diagonalization'
write(iunit,'(A)') '------------------------'
write(iunit,'(A)') ''
call write_int(iunit,N_st,'Number of states')
call write_int(iunit,N_st_diag,'Number of states in diagonalization')
call write_int(iunit,sze,'Number of determinants')
write(iunit,'(A)') ''
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ =========== ==========='
enddo
write(iunit,'(A)') trim(write_buffer)
write_buffer = ' Iter'
do i=1,N_st
write_buffer = trim(write_buffer)//' Energy S^2 Residual'
enddo
write(iunit,'(A)') trim(write_buffer)
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ =========== ==========='
enddo
write(iunit,'(A)') trim(write_buffer)
integer, external :: align_double
sze_8 = align_double(sze)
allocate( &
kl_pairs(2,N_st_diag*(N_st_diag+1)/2), &
W(sze_8,N_st_diag*davidson_sze_max), &
U(sze_8,N_st_diag*davidson_sze_max), &
R(sze_8,N_st_diag), &
S(sze_8,N_st_diag*davidson_sze_max), &
h(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
y(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
s_(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
s_tmp(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
residual_norm(N_st_diag), &
c(N_st_diag*davidson_sze_max), &
s2(N_st_diag*davidson_sze_max), &
lambda(N_st_diag*davidson_sze_max))
h = 0.d0
s_ = 0.d0
s_tmp = 0.d0
c = 0.d0
U = 0.d0
S = 0.d0
R = 0.d0
y = 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=1,N_st
call normalize(u_in(1,k),sze)
enddo
do k=N_st+1,N_st_diag
do i=1,sze
double precision :: r1, r2
call random_number(r1)
call random_number(r2)
u_in(i,k) = dsqrt(-2.d0*dlog(r1))*dcos(dtwo_pi*r2)
enddo
! Gram-Schmidt
! ------------
call dgemv('T',sze,k-1,1.d0,u_in,size(u_in,1), &
u_in(1,k),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,u_in,size(u_in,1), &
c,1,1.d0,u_in(1,k),1)
call normalize(u_in(1,k),sze)
enddo
do while (.not.converged)
do k=1,N_st_diag
do i=1,sze
U(i,k) = u_in(i,k)
enddo
enddo
do iter=1,davidson_sze_max-1
shift = N_st_diag*(iter-1)
shift2 = N_st_diag*iter
! Compute |W_k> = \sum_i |i><i|H|u_k>
! -----------------------------------------
call H_S2_u_0_nstates(W(1,shift+1),S(1,shift+1),U(1,shift+1),H_jj,S2_jj,sze,dets_in,Nint,N_st_diag,sze_8)
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
! -------------------------------------------
! do l=1,N_st_diag
! do k=1,N_st_diag
! do iter2=1,iter-1
! h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l,iter),sze)
! h(k,iter,l,iter2) = h(k,iter2,l,iter)
! enddo
! enddo
! do k=1,l
! h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l,iter),sze)
! h(l,iter,k,iter) = h(k,iter,l,iter)
! enddo
! enddo
call dgemm('T','N', shift2, N_st_diag, sze, &
1.d0, U, size(U,1), W(1,shift+1), size(W,1), &
0.d0, h(1,shift+1), size(h,1))
call dgemm('T','N', shift2, N_st_diag, sze, &
1.d0, U, size(U,1), S(1,shift+1), size(S,1), &
0.d0, s_(1,shift+1), size(s_,1))
! Diagonalize h
! -------------
call lapack_diag(lambda,y,h,size(h,1),shift2)
! 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 (s2_eig) then
logical :: state_ok(N_st_diag*davidson_sze_max)
do k=1,shift2
state_ok(k) = (dabs(s2(k)-expected_s2) < 0.6d0)
enddo
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
endif
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
! do k=1,N_st_diag
! do i=1,sze
! U(i,shift2+k) = 0.d0
! W(i,shift2+k) = 0.d0
! S(i,shift2+k) = 0.d0
! enddo
! do l=1,N_st_diag*iter
! do i=1,sze
! U(i,shift2+k) = U(i,shift2+k) + U(i,l)*y(l,k)
! W(i,shift2+k) = W(i,shift2+k) + W(i,l)*y(l,k)
! S(i,shift2+k) = S(i,shift2+k) + S(i,l)*y(l,k)
! enddo
! enddo
! enddo
!
!
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))
call dgemm('N','N', sze, N_st_diag, shift2, &
1.d0, S, size(S,1), y, size(y,1), 0.d0, S(1,shift2+1), size(S,1))
! Compute residual vector
! -----------------------
! do k=1,N_st_diag
! print *, s2(k)
! s2(k) = u_dot_v(U(1,shift2+k), S(1,shift2+k), sze) + S_z2_Sz
! print *, s2(k)
! print *, ''
! pause
! enddo
do k=1,N_st_diag
do i=1,sze
R(i,k) = (lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) &
* (1.d0 + s2(k) * U(i,shift2+k) - S(i,shift2+k) - S_z2_Sz)
enddo
if (k <= N_st) then
residual_norm(k) = u_dot_u(R(1,k),sze)
to_print(1,k) = lambda(k) + nuclear_repulsion
to_print(2,k) = s2(k)
to_print(3,k) = residual_norm(k)
if (residual_norm(k) > 1.e9) then
stop 'Davidson failed'
endif
endif
enddo
write(iunit,'(X,I3,X,100(X,F16.10,X,F11.6,X,E11.3))') iter, to_print(:,1:N_st)
call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
if (converged) then
exit
endif
! Davidson step
! -------------
do k=1,N_st_diag
do i=1,sze
U(i,shift2+k) = - R(i,k)/max(H_jj(i) - lambda(k),1.d-2)
enddo
enddo
! Gram-Schmidt
! ------------
do k=1,N_st_diag
! do l=1,N_st_diag*iter
! c(1) = u_dot_v(U(1,shift2+k),U(1,l),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,l)
! enddo
! enddo
!
call dgemv('T',sze,N_st_diag*iter,1.d0,U,size(U,1), &
U(1,shift2+k),1,0.d0,c,1)
call dgemv('N',sze,N_st_diag*iter,-1.d0,U,size(U,1), &
c,1,1.d0,U(1,shift2+k),1)
!
! do l=1,k-1
! c(1) = u_dot_v(U(1,shift2+k),U(1,shift2+l),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,shift2+l)
! enddo
! enddo
!
call dgemv('T',sze,k-1,1.d0,U(1,shift2+1),size(U,1), &
U(1,shift2+k),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,U(1,shift2+1),size(U,1), &
c,1,1.d0,U(1,shift2+k),1)
call normalize( U(1,shift2+k), sze )
enddo
enddo
if (.not.converged) then
iter = davidson_sze_max-1
endif
! Re-contract to u_in
! -----------
do k=1,N_st_diag
energies(k) = lambda(k)
enddo
! do k=1,N_st_diag
! do i=1,sze
! do l=1,iter*N_st_diag
! u_in(i,k) += U(i,l)*y(l,k)
! enddo
! enddo
! enddo
! enddo
call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, 1.d0, &
U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
enddo
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ =========== ==========='
enddo
write(iunit,'(A)') trim(write_buffer)
write(iunit,'(A)') ''
call write_time(iunit)
deallocate ( &
kl_pairs, &
W, residual_norm, &
U, &
R, c, S, &
h, &
y, s_, s_tmp, &
lambda &
)
end
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