662 lines
18 KiB
Fortran
662 lines
18 KiB
Fortran
BEGIN_PROVIDER [ integer, davidson_iter_max ]
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implicit none
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BEGIN_DOC
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! Max number of Davidson iterations
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END_DOC
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davidson_iter_max = 100
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END_PROVIDER
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BEGIN_PROVIDER [ integer, davidson_sze_max ]
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implicit none
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BEGIN_DOC
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! Max number of Davidson sizes
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END_DOC
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ASSERT (davidson_sze_max <= davidson_iter_max)
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davidson_sze_max = max(8,2*N_states_diag)
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END_PROVIDER
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subroutine davidson_diag(dets_in,u_in,energies,dim_in,sze,N_st,Nint,iunit)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Davidson diagonalization.
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!
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! dets_in : bitmasks corresponding to determinants
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!
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! u_in : guess coefficients on the various states. Overwritten
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! on exit
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!
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! dim_in : leftmost dimension of u_in
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!
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! sze : Number of determinants
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!
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! N_st : Number of eigenstates
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!
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! iunit : Unit number for the I/O
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!
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! Initial guess vectors are not necessarily orthonormal
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END_DOC
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integer, intent(in) :: dim_in, sze, N_st, Nint, iunit
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integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
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double precision, intent(inout) :: u_in(dim_in,N_st)
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double precision, intent(out) :: energies(N_st)
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double precision, allocatable :: H_jj(:)
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double precision :: diag_h_mat_elem
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integer :: i
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ASSERT (N_st > 0)
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ASSERT (sze > 0)
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ASSERT (Nint > 0)
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ASSERT (Nint == N_int)
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PROVIDE mo_bielec_integrals_in_map
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allocate(H_jj(sze))
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(sze,H_jj,dets_in,Nint) &
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!$OMP PRIVATE(i)
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!$OMP DO SCHEDULE(guided)
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do i=1,sze
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H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call davidson_diag_hjj(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,Nint,iunit)
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deallocate (H_jj)
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end
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logical function det_inf(key1, key2, Nint)
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use bitmasks
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implicit none
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integer,intent(in) :: Nint
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integer(bit_kind),intent(in) :: key1(Nint, 2), key2(Nint, 2)
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integer :: i,j
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det_inf = .false.
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do i=1,2
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do j=Nint,1,-1
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if(key1(j,i) < key2(j,i)) then
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det_inf = .true.
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return
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else if(key1(j,i) > key2(j,i)) then
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return
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end if
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end do
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end do
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end function
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subroutine tamiser(key, idx, no, n, Nint, N_key)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Uncodumented : TODO
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END_DOC
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integer,intent(in) :: no, n, Nint, N_key
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integer(bit_kind),intent(inout) :: key(Nint, 2, N_key)
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integer,intent(inout) :: idx(N_key)
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integer :: k,j,tmpidx
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integer(bit_kind) :: tmp(Nint, 2)
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logical :: det_inf
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integer :: ni
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k = no
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j = 2*k
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do while(j <= n)
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if(j < n) then
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if (det_inf(key(1,1,j), key(1,1,j+1), Nint)) then
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j = j+1
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endif
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endif
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if(det_inf(key(1,1,k), key(1,1,j), Nint)) then
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do ni=1,Nint
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tmp(ni,1) = key(ni,1,k)
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tmp(ni,2) = key(ni,2,k)
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key(ni,1,k) = key(ni,1,j)
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key(ni,2,k) = key(ni,2,j)
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key(ni,1,j) = tmp(ni,1)
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key(ni,2,j) = tmp(ni,2)
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enddo
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tmpidx = idx(k)
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idx(k) = idx(j)
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idx(j) = tmpidx
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k = j
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j = k+k
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else
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return
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endif
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enddo
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end subroutine
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subroutine sort_dets_ba_v(key_in, key_out, idx, shortcut, version, N_key, Nint)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Uncodumented : TODO
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END_DOC
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integer, intent(in) :: Nint, N_key
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integer(bit_kind),intent(in) :: key_in(Nint,2,N_key)
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integer(bit_kind),intent(out) :: key_out(Nint,N_key)
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integer,intent(out) :: idx(N_key)
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integer,intent(out) :: shortcut(0:N_key+1)
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integer(bit_kind),intent(out) :: version(Nint,N_key+1)
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integer(bit_kind), allocatable :: key(:,:,:)
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integer :: i,ni
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allocate ( key(Nint,2,N_key) )
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do i=1,N_key
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do ni=1,Nint
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key(ni,1,i) = key_in(ni,2,i)
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key(ni,2,i) = key_in(ni,1,i)
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enddo
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enddo
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call sort_dets_ab_v(key, key_out, idx, shortcut, version, N_key, Nint)
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deallocate ( key )
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end subroutine
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subroutine sort_dets_ab_v(key_in, key_out, idx, shortcut, version, N_key, Nint)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Uncodumented : TODO
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END_DOC
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integer, intent(in) :: Nint, N_key
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integer(bit_kind),intent(in) :: key_in(Nint,2,N_key)
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integer(bit_kind),intent(out) :: key_out(Nint,N_key)
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integer,intent(out) :: idx(N_key)
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integer,intent(out) :: shortcut(0:N_key+1)
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integer(bit_kind),intent(out) :: version(Nint,N_key+1)
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integer(bit_kind), allocatable :: key(:,:,:)
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integer(bit_kind) :: tmp(Nint, 2)
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integer :: tmpidx,i,ni
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allocate (key(Nint,2,N_key))
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do i=1,N_key
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do ni=1,Nint
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key(ni,1,i) = key_in(ni,1,i)
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key(ni,2,i) = key_in(ni,2,i)
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enddo
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idx(i) = i
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end do
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do i=N_key/2,1,-1
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call tamiser(key, idx, i, N_key, Nint, N_key)
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end do
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do i=N_key,2,-1
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do ni=1,Nint
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tmp(ni,1) = key(ni,1,i)
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tmp(ni,2) = key(ni,2,i)
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key(ni,1,i) = key(ni,1,1)
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key(ni,2,i) = key(ni,2,1)
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key(ni,1,1) = tmp(ni,1)
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key(ni,2,1) = tmp(ni,2)
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enddo
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tmpidx = idx(i)
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idx(i) = idx(1)
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idx(1) = tmpidx
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call tamiser(key, idx, 1, i-1, Nint, N_key)
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end do
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shortcut(0) = 1
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shortcut(1) = 1
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do ni=1,Nint
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version(ni,1) = key(ni,1,1)
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enddo
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do i=2,N_key
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do ni=1,nint
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if(key(ni,1,i) /= key(ni,1,i-1)) then
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shortcut(0) = shortcut(0) + 1
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shortcut(shortcut(0)) = i
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version(:,shortcut(0)) = key(:,1,i)
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exit
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end if
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end do
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end do
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shortcut(shortcut(0)+1) = N_key+1
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do i=1,N_key
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do ni=1,Nint
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key_out(ni,i) = key(ni,2,i)
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enddo
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enddo
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deallocate (key)
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end subroutine
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subroutine sort_dets_ab(key, idx, shortcut, N_key, Nint)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Uncodumented : TODO
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END_DOC
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integer, intent(in) :: Nint, N_key
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integer(bit_kind),intent(inout) :: key(Nint,2,N_key)
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integer,intent(inout) :: idx(N_key)
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integer,intent(inout) :: shortcut(0:N_key+1)
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integer(bit_kind) :: tmp(Nint, 2)
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integer :: tmpidx,i,ni
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do i=1,N_key
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idx(i) = i
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end do
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do i=N_key/2,1,-1
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call tamiser(key, idx, i, N_key, Nint, N_key)
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end do
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do i=N_key,2,-1
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do ni=1,Nint
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tmp(ni,1) = key(ni,1,i)
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tmp(ni,2) = key(ni,2,i)
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key(ni,1,i) = key(ni,1,1)
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key(ni,2,i) = key(ni,2,1)
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key(ni,1,1) = tmp(ni,1)
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key(ni,2,1) = tmp(ni,2)
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enddo
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tmpidx = idx(i)
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idx(i) = idx(1)
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idx(1) = tmpidx
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call tamiser(key, idx, 1, i-1, Nint, N_key)
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end do
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shortcut(0) = 1
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shortcut(1) = 1
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do i=2,N_key
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do ni=1,nint
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if(key(ni,1,i) /= key(ni,1,i-1)) then
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shortcut(0) = shortcut(0) + 1
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shortcut(shortcut(0)) = i
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exit
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end if
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end do
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end do
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shortcut(shortcut(0)+1) = N_key+1
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end subroutine
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subroutine davidson_diag_hjj(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,Nint,iunit)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Davidson diagonalization with specific diagonal elements of the H matrix
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!
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! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
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!
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! dets_in : bitmasks corresponding to determinants
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!
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! u_in : guess coefficients on the various states. Overwritten
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! on exit
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!
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! dim_in : leftmost dimension of u_in
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!
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! sze : Number of determinants
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!
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! N_st : Number of eigenstates
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!
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! iunit : Unit for the I/O
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!
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! Initial guess vectors are not necessarily orthonormal
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END_DOC
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integer, intent(in) :: dim_in, sze, N_st, Nint
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integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
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double precision, intent(in) :: H_jj(sze)
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integer, intent(in) :: iunit
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double precision, intent(inout) :: u_in(dim_in,N_st)
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double precision, intent(out) :: energies(N_st)
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integer :: sze_8
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integer :: iter
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integer :: i,j,k,l,m
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logical :: converged
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double precision :: overlap(N_st,N_st)
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double precision :: u_dot_v, u_dot_u
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integer, allocatable :: kl_pairs(:,:)
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integer :: k_pairs, kl
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integer :: iter2
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double precision, allocatable :: W(:,:,:), U(:,:,:), R(:,:), Wt(:)
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double precision, allocatable :: y(:,:,:,:), h(:,:,:,:), lambda(:)
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double precision :: diag_h_mat_elem
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double precision :: residual_norm(N_st)
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character*(16384) :: write_buffer
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double precision :: to_print(2,N_st)
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double precision :: cpu, wall
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, Wt, y, h, lambda
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call write_time(iunit)
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call wall_time(wall)
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call cpu_time(cpu)
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write(iunit,'(A)') ''
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write(iunit,'(A)') 'Davidson Diagonalization'
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write(iunit,'(A)') '------------------------'
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write(iunit,'(A)') ''
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call write_int(iunit,N_st,'Number of states')
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call write_int(iunit,sze,'Number of determinants')
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write(iunit,'(A)') ''
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write_buffer = '===== '
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ================'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write_buffer = ' Iter'
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do i=1,N_st
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write_buffer = trim(write_buffer)//' Energy Residual'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write_buffer = '===== '
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ================'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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integer, external :: align_double
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sze_8 = align_double(sze)
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allocate( &
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kl_pairs(2,N_st*(N_st+1)/2), &
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W(sze_8,N_st,davidson_sze_max), &
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Wt(sze), &
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U(sze_8,N_st,davidson_sze_max), &
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R(sze_8,N_st), &
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h(N_st,davidson_sze_max,N_st,davidson_sze_max), &
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y(N_st,davidson_sze_max,N_st,davidson_sze_max), &
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lambda(N_st*davidson_sze_max))
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ASSERT (N_st > 0)
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ASSERT (sze > 0)
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ASSERT (Nint > 0)
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ASSERT (Nint == N_int)
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! Initialization
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! ==============
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if (N_st > 1) then
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k_pairs=0
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do l=1,N_st
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do k=1,l
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k_pairs+=1
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kl_pairs(1,k_pairs) = k
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kl_pairs(2,k_pairs) = l
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enddo
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enddo
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(U,sze,N_st,overlap,kl_pairs,k_pairs, &
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!$OMP Nint,dets_in,u_in) &
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!$OMP PRIVATE(k,l,kl)
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! Orthonormalize initial guess
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! ============================
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!$OMP DO
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do kl=1,k_pairs
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k = kl_pairs(1,kl)
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l = kl_pairs(2,kl)
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if (k/=l) then
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overlap(k,l) = u_dot_v(U_in(1,k),U_in(1,l),sze)
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overlap(l,k) = overlap(k,l)
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else
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overlap(k,k) = u_dot_u(U_in(1,k),sze)
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endif
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call ortho_lowdin(overlap,size(overlap,1),N_st,U_in,size(U_in,1),sze)
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else
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overlap(1,1) = u_dot_u(U_in(1,1),sze)
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double precision :: f
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f = 1.d0 / dsqrt(overlap(1,1))
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do i=1,sze
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U_in(i,1) = U_in(i,1) * f
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enddo
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endif
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! Davidson iterations
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! ===================
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converged = .False.
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do while (.not.converged)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(k,i) SHARED(U,u_in,sze,N_st)
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do k=1,N_st
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!$OMP DO
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do i=1,sze
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U(i,k,1) = u_in(i,k)
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enddo
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!$OMP END DO
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enddo
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!$OMP END PARALLEL
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do iter=1,davidson_sze_max-1
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! Compute W_k = H |u_k>
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! ----------------------
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do k=1,N_st
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call H_u_0(W(1,k,iter),U(1,k,iter),H_jj,sze,dets_in,Nint)
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enddo
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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do l=1,N_st
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do k=1,N_st
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do iter2=1,iter-1
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h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l,iter),sze)
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h(k,iter,l,iter2) = h(k,iter2,l,iter)
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enddo
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enddo
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do k=1,l
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h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l,iter),sze)
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h(l,iter,k,iter) = h(k,iter,l,iter)
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enddo
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enddo
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!DEBUG H MATRIX
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!do i=1,iter
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! print '(10(x,F16.10))', h(1,i,1,1:i)
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!enddo
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!print *, ''
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!END
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! Diagonalize h
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! -------------
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call lapack_diag(lambda,y,h,N_st*davidson_sze_max,N_st*iter)
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! Express eigenvectors of h in the determinant basis
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! --------------------------------------------------
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(k,i,l,iter2) SHARED(U,W,R,y,iter,lambda,N_st,sze)
|
|
do k=1,N_st
|
|
!$OMP DO
|
|
do i=1,sze
|
|
U(i,k,iter+1) = 0.d0
|
|
W(i,k,iter+1) = 0.d0
|
|
do l=1,N_st
|
|
do iter2=1,iter
|
|
U(i,k,iter+1) = U(i,k,iter+1) + U(i,l,iter2)*y(l,iter2,k,1)
|
|
W(i,k,iter+1) = W(i,k,iter+1) + W(i,l,iter2)*y(l,iter2,k,1)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
enddo
|
|
!$OMP END PARALLEL
|
|
|
|
! Compute residual vector
|
|
! -----------------------
|
|
|
|
do k=1,N_st
|
|
do i=1,sze
|
|
R(i,k) = lambda(k) * U(i,k,iter+1) - W(i,k,iter+1)
|
|
enddo
|
|
residual_norm(k) = u_dot_u(R(1,k),sze)
|
|
to_print(1,k) = lambda(k) + nuclear_repulsion
|
|
to_print(2,k) = residual_norm(k)
|
|
enddo
|
|
|
|
write(iunit,'(X,I3,X,100(X,F16.10,X,E16.6))') 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
|
|
do i=1,sze
|
|
U(i,k,iter+1) = -1.d0/max(H_jj(i) - lambda(k),1.d-2) * R(i,k)
|
|
enddo
|
|
enddo
|
|
|
|
! Gram-Schmidt
|
|
! ------------
|
|
|
|
double precision :: c
|
|
do k=1,N_st
|
|
do iter2=1,iter
|
|
do l=1,N_st
|
|
c = u_dot_v(U(1,k,iter+1),U(1,l,iter2),sze)
|
|
do i=1,sze
|
|
U(i,k,iter+1) -= c * U(i,l,iter2)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
do l=1,k-1
|
|
c = u_dot_v(U(1,k,iter+1),U(1,l,iter+1),sze)
|
|
do i=1,sze
|
|
U(i,k,iter+1) -= c * U(i,l,iter+1)
|
|
enddo
|
|
enddo
|
|
call normalize( U(1,k,iter+1), sze )
|
|
enddo
|
|
|
|
!DEBUG : CHECK OVERLAP
|
|
!print *, '==='
|
|
!do k=1,iter+1
|
|
! do l=1,k
|
|
! c = u_dot_v(U(1,1,k),U(1,1,l),sze)
|
|
! print *, k,l, c
|
|
! enddo
|
|
!enddo
|
|
!print *, '==='
|
|
!pause
|
|
!END DEBUG
|
|
|
|
|
|
enddo
|
|
|
|
if (.not.converged) then
|
|
iter = davidson_sze_max-1
|
|
endif
|
|
|
|
! Re-contract to u_in
|
|
! -----------
|
|
|
|
do k=1,N_st
|
|
energies(k) = lambda(k)
|
|
do i=1,sze
|
|
u_in(i,k) = 0.d0
|
|
do iter2=1,iter
|
|
do l=1,N_st
|
|
u_in(i,k) += U(i,l,iter2)*y(l,iter2,k,1)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
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, &
|
|
Wt, &
|
|
U, &
|
|
R, &
|
|
h, &
|
|
y, &
|
|
lambda &
|
|
)
|
|
end
|
|
|
|
BEGIN_PROVIDER [ character(64), davidson_criterion ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! Can be : [ energy | residual | both | wall_time | cpu_time | iterations ]
|
|
END_DOC
|
|
davidson_criterion = 'residual'
|
|
END_PROVIDER
|
|
|
|
subroutine davidson_converged(energy,residual,wall,iterations,cpu,N_st,converged)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! True if the Davidson algorithm is converged
|
|
END_DOC
|
|
integer, intent(in) :: N_st, iterations
|
|
logical, intent(out) :: converged
|
|
double precision, intent(in) :: energy(N_st), residual(N_st)
|
|
double precision, intent(in) :: wall, cpu
|
|
double precision :: E(N_st), time
|
|
double precision, allocatable, save :: energy_old(:)
|
|
|
|
if (.not.allocated(energy_old)) then
|
|
allocate(energy_old(N_st))
|
|
energy_old = 0.d0
|
|
endif
|
|
|
|
E = energy - energy_old
|
|
energy_old = energy
|
|
if (davidson_criterion == 'energy') then
|
|
converged = dabs(maxval(E(1:N_st))) < threshold_davidson
|
|
else if (davidson_criterion == 'residual') then
|
|
converged = dabs(maxval(residual(1:N_st))) < threshold_davidson
|
|
else if (davidson_criterion == 'both') then
|
|
converged = dabs(maxval(residual(1:N_st))) + dabs(maxval(E(1:N_st)) ) &
|
|
< threshold_davidson
|
|
else if (davidson_criterion == 'wall_time') then
|
|
call wall_time(time)
|
|
converged = time - wall > threshold_davidson
|
|
else if (davidson_criterion == 'cpu_time') then
|
|
call cpu_time(time)
|
|
converged = time - cpu > threshold_davidson
|
|
else if (davidson_criterion == 'iterations') then
|
|
converged = iterations >= int(threshold_davidson)
|
|
endif
|
|
end
|