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added Abdallah's non hermit davidson

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src/dav_general_mat/dav_ext_rout_nonsym_B1space.irp.f Normal file
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! ---
subroutine davidson_general_ext_rout_nonsym_b1space(u_in, H_jj, energies, sze, N_st, N_st_diag_in, converged, hcalc)
use mmap_module
BEGIN_DOC
! Generic modified-Davidson diagonalization
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!
! u_in : guess coefficients on the various states. Overwritten on exit by right eigenvectors
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! N_st_diag_in : Number of states in which H is diagonalized. Assumed > N_st
!
! 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_in
double precision, intent(in) :: H_jj(sze)
logical, intent(inout) :: converged
double precision, intent(inout) :: u_in(sze,N_st_diag_in)
double precision, intent(out) :: energies(N_st)
external hcalc
character*(16384) :: write_buffer
integer :: iter, N_st_diag
integer :: i, j, k, m
integer :: iter2, itertot
logical :: disk_based
integer :: shift, shift2, itermax
integer :: nproc_target
integer :: order(N_st_diag_in)
double precision :: to_print(2,N_st)
double precision :: r1, r2, alpha
double precision :: cpu, wall
double precision :: cmax
double precision :: energy_shift(N_st_diag_in*davidson_sze_max)
double precision, allocatable :: U(:,:)
double precision, allocatable :: y(:,:), h(:,:), lambda(:)
double precision, allocatable :: residual_norm(:)
integer :: i_omax
double precision :: lambda_tmp
double precision, allocatable :: U_tmp(:), overlap(:)
double precision, allocatable :: W(:,:)
!double precision, pointer :: W(:,:)
double precision, external :: u_dot_v, u_dot_u
include 'constants.include.F'
N_st_diag = N_st_diag_in
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, y, 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
provide threshold_nonsym_davidson
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 = sze
m=1
disk_based = .False.
call resident_memory(rss)
do
r1 = 8.d0 * &! bytes
( dble(sze)*(N_st_diag*itermax) &! U
+ 1.d0*dble(sze*m)*(N_st_diag*itermax) &! W
+ 2.d0*(N_st_diag*itermax)**2 &! h,y
+ 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 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*itermax) )
allocate( &
! Large
U(sze,N_st_diag*itermax), &
! Small
h(N_st_diag*itermax,N_st_diag*itermax), &
y(N_st_diag*itermax,N_st_diag*itermax), &
lambda(N_st_diag*itermax), &
residual_norm(N_st_diag) &
)
U = 0.d0
h = 0.d0
y = 0.d0
lambda = 0.d0
residual_norm = 0.d0
ASSERT (N_st > 0)
ASSERT (N_st_diag >= N_st)
ASSERT (sze > 0)
! Davidson iterations
! ===================
converged = .False.
! Initialize from N_st to N_st_diag with gaussian random numbers
! to be sure to have overlap with any eigenvectors
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
! Normalize all states
do k = 1, N_st_diag
call normalize(u_in(1,k), sze)
enddo
! Copy from the guess input "u_in" to the working vectors "U"
do k = 1, N_st_diag
do i = 1, sze
U(i,k) = u_in(i,k)
enddo
enddo
! ---
itertot = 0
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
! Gram-Schmidt to orthogonalize all new guess with the previous vectors
call ortho_qr(U, size(U, 1), sze, shift2)
call ortho_qr(U, size(U, 1), sze, shift2)
! W = H U
call hcalc(W(1,shift+1), U(1,shift+1), N_st_diag, sze)
else
! Already computed in update below
continue
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) )
! Diagonalize h y = lambda y
! ---------------------------
call diag_nonsym_right(shift2, h(1,1), size(h, 1), y(1,1), size(y, 1), lambda(1), size(lambda, 1))
! Express eigenvectors of h in the determinant basis:
! ---------------------------------------------------
! y(:,k) = rk
! U(:,k) = Bk
! U(:,shift2+k) = Rk = Bk x rk
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) )
do k = 1, N_st_diag
call normalize(U(1,shift2+k), sze)
enddo
! ---
! select the max overlap
!
! start test ------------------------------------------------------------------------
!
!double precision, allocatable :: Utest(:,:), Otest(:)
!allocate( Utest(sze,shift2), Otest(shift2) )
!call dgemm( 'N', 'N', sze, shift2, shift2, 1.d0 &
! , U, size(U, 1), y, size(y, 1), 0.d0, Utest(1,1), size(Utest, 1) )
!do k = 1, shift2
! call normalize(Utest(1,k), sze)
!enddo
!do j = 1, sze
! write(455, '(100(1X, F16.10))') (Utest(j,k), k=1,shift2)
!enddo
!do k = 1, shift2
! Otest(k) = 0.d0
! do i = 1, sze
! Otest(k) += Utest(i,k) * u_in(i,1)
! enddo
! Otest(k) = dabs(Otest(k))
! print *, ' Otest =', k, Otest(k), lambda(k)
!enddo
!deallocate(Utest, Otest)
!
! end test ------------------------------------------------------------------------
!
allocate( overlap(N_st_diag) )
do k = 1, N_st_diag
overlap(k) = 0.d0
do i = 1, sze
overlap(k) = overlap(k) + U(i,shift2+k) * u_in(i,1)
enddo
overlap(k) = dabs(overlap(k))
!print *, ' overlap =', k, overlap(k)
enddo
lambda_tmp = 0.d0
do k = 1, N_st_diag
if(overlap(k) .gt. lambda_tmp) then
i_omax = k
lambda_tmp = overlap(k)
endif
enddo
deallocate(overlap)
if( lambda_tmp .lt. 0.8d0) then
print *, ' very small overlap..'
print*, ' max overlap = ', lambda_tmp, i_omax
stop
endif
! lambda_tmp = lambda(1)
! lambda(1) = lambda(i_omax)
! lambda(i_omax) = lambda_tmp
!
! allocate( U_tmp(sze) )
! do i = 1, sze
! U_tmp(i) = U(i,shift2+1)
! U(i,shift2+1) = U(i,shift2+i_omax)
! U(i,shift2+i_omax) = U_tmp(i)
! enddo
! deallocate(U_tmp)
!
! allocate( U_tmp(N_st_diag*itermax) )
! do i = 1, shift2
! U_tmp(i) = y(i,1)
! y(i,1) = y(i,i_omax)
! y(i,i_omax) = U_tmp(i)
! enddo
! deallocate(U_tmp)
! ---
!do k = 1, N_st_diag
! call normalize(U(1,shift2+k), sze)
!enddo
! ---
! y(:,k) = rk
! W(:,k) = H x Bk
! W(:,shift2+k) = H x Bk x rk
! = Wk
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) )
! ---
! 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)
! to_print(2,k) = residual_norm(k)
!endif
enddo
!$OMP END PARALLEL DO
residual_norm(1) = u_dot_u(U(1,shift2+i_omax), sze)
to_print(1,1) = lambda(i_omax)
to_print(2,1) = residual_norm(1)
if( (itertot > 1) .and. (iter == 1) ) then
!don't print
continue
else
write(*, '(1X, I3, 1X, 100(1X, F16.10, 1X, F16.10, 1X, F16.10))') 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_nonsym_davidson
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 ! loop over iter
! Re-contract U and update W
! --------------------------------
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
call ortho_qr(U, size(U, 1), sze, N_st_diag)
call ortho_qr(U, size(U, 1), sze, N_st_diag)
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)
enddo
endif
enddo
enddo ! loop over while
! ---
do k = 1, N_st
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(U, h, y, lambda, residual_norm)
FREE nthreads_davidson
end subroutine davidson_general_ext_rout_nonsym_b1space
! ---
subroutine diag_nonsym_right(n, A, A_ldim, V, V_ldim, energy, E_ldim)
implicit none
integer, intent(in) :: n, A_ldim, V_ldim, E_ldim
double precision, intent(in) :: A(A_ldim,n)
double precision, intent(out) :: energy(E_ldim), V(V_ldim,n)
character*1 :: JOBVL, JOBVR, BALANC, SENSE
integer :: i, j
integer :: ILO, IHI, lda, ldvl, ldvr, LWORK, INFO
double precision :: ABNRM
integer, allocatable :: iorder(:), IWORK(:)
double precision, allocatable :: WORK(:), SCALE_array(:), RCONDE(:), RCONDV(:)
double precision, allocatable :: Atmp(:,:), WR(:), WI(:), VL(:,:), VR(:,:), Vtmp(:)
double precision, allocatable :: energy_loc(:), V_loc(:,:)
allocate( Atmp(n,n), WR(n), WI(n), VL(1,1), VR(n,n) )
do i = 1, n
do j = 1, n
Atmp(j,i) = A(j,i)
enddo
enddo
JOBVL = "N" ! computes the left eigenvectors
JOBVR = "V" ! computes the right eigenvectors
BALANC = "B" ! Diagonal scaling and Permutation for optimization
SENSE = "V" ! Determines which reciprocal condition numbers are computed
lda = n
ldvr = n
ldvl = 1
allocate( WORK(1), SCALE_array(n), RCONDE(n), RCONDV(n), IWORK(2*n-2) )
LWORK = -1 ! to ask for the optimal size of WORK
call dgeevx( BALANC, JOBVL, JOBVR, SENSE & ! CHARACTERS
, n, Atmp, lda & ! MATRIX TO DIAGONALIZE
, WR, WI & ! REAL AND IMAGINARY PART OF EIGENVALUES
, VL, ldvl, VR, ldvr & ! LEFT AND RIGHT EIGENVECTORS
, ILO, IHI, SCALE_array, ABNRM, RCONDE, RCONDV & ! OUTPUTS OF OPTIMIZATION
, WORK, LWORK, IWORK, INFO )
if(INFO .ne. 0) then
print*, 'dgeevx failed !!', INFO
stop
endif
LWORK = max(int(work(1)), 1) ! this is the optimal size of WORK
deallocate(WORK)
allocate(WORK(LWORK))
call dgeevx( BALANC, JOBVL, JOBVR, SENSE &
, n, Atmp, lda &
, WR, WI &
, VL, ldvl, VR, ldvr &
, ILO, IHI, SCALE_array, ABNRM, RCONDE, RCONDV &
, WORK, LWORK, IWORK, INFO )
if(INFO .ne. 0) then
print*, 'dgeevx failed !!', INFO
stop
endif
deallocate( WORK, SCALE_array, RCONDE, RCONDV, IWORK )
deallocate( VL, Atmp )
allocate( energy_loc(n), V_loc(n,n) )
energy_loc = 0.d0
V_loc = 0.d0
i = 1
do while(i .le. n)
! print*, i, WR(i), WI(i)
if( dabs(WI(i)) .gt. 1e-7 ) then
print*, ' Found an imaginary component to eigenvalue'
print*, ' Re(i) + Im(i)', i, WR(i), WI(i)
energy_loc(i) = WR(i)
do j = 1, n
V_loc(j,i) = WR(i) * VR(j,i) - WI(i) * VR(j,i+1)
enddo
energy_loc(i+1) = WI(i)
do j = 1, n
V_loc(j,i+1) = WR(i) * VR(j,i+1) + WI(i) * VR(j,i)
enddo
i = i + 2
else
energy_loc(i) = WR(i)
do j = 1, n
V_loc(j,i) = VR(j,i)
enddo
i = i + 1
endif
enddo
deallocate(WR, WI, VR)
! ordering
! do j = 1, n
! write(444, '(100(1X, F16.10))') (V_loc(j,i), i=1,5)
! enddo
allocate( iorder(n) )
do i = 1, n
iorder(i) = i
enddo
call dsort(energy_loc, iorder, n)
do i = 1, n
energy(i) = energy_loc(i)
do j = 1, n
V(j,i) = V_loc(j,iorder(i))
enddo
enddo
deallocate(iorder)
! do j = 1, n
! write(445, '(100(1X, F16.10))') (V_loc(j,i), i=1,5)
! enddo
deallocate(V_loc, energy_loc)
end subroutine diag_nonsym_right
! ---