mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-12-23 04:43:45 +01:00
Merge branch 'dev' into features_pt2
This commit is contained in:
commit
b0f85476fe
@ -4,8 +4,8 @@ type units =
|
||||
| Angstrom
|
||||
;;
|
||||
|
||||
let angstrom_to_bohr = 1. /. 0.52917721092
|
||||
let bohr_to_angstrom = 0.52917721092
|
||||
let angstrom_to_bohr = 1. /. 0.52917721067121
|
||||
let bohr_to_angstrom = 0.52917721067121
|
||||
;;
|
||||
|
||||
|
||||
|
||||
@ -436,7 +436,7 @@ BEGIN_PROVIDER [ double precision, ao_two_e_integral_schwartz,(ao_num,ao_num) ]
|
||||
!$OMP SCHEDULE(dynamic)
|
||||
do i=1,ao_num
|
||||
do k=1,i
|
||||
ao_two_e_integral_schwartz(i,k) = dsqrt(ao_two_e_integral(i,k,i,k))
|
||||
ao_two_e_integral_schwartz(i,k) = dsqrt(ao_two_e_integral(i,i,k,k))
|
||||
ao_two_e_integral_schwartz(k,i) = ao_two_e_integral_schwartz(i,k)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
@ -287,9 +287,9 @@ subroutine ZMQ_pt2(E, pt2_data, pt2_data_err, relative_error, N_in)
|
||||
call omp_set_nested(.false.)
|
||||
|
||||
|
||||
print '(A)', '========== ================= =========== =============== =============== ================='
|
||||
print '(A)', ' Samples Energy Stat. Err Variance Norm^2 Seconds '
|
||||
print '(A)', '========== ================= =========== =============== =============== ================='
|
||||
print '(A)', '========== ======================= ===================== ===================== ==========='
|
||||
print '(A)', ' Samples Energy Variance Norm^2 Seconds'
|
||||
print '(A)', '========== ======================= ===================== ===================== ==========='
|
||||
|
||||
PROVIDE global_selection_buffer
|
||||
|
||||
@ -312,26 +312,30 @@ subroutine ZMQ_pt2(E, pt2_data, pt2_data_err, relative_error, N_in)
|
||||
!$OMP END PARALLEL
|
||||
call end_parallel_job(zmq_to_qp_run_socket, zmq_socket_pull, 'pt2')
|
||||
|
||||
print '(A)', '========== ================= =========== =============== =============== ================='
|
||||
print '(A)', '========== ======================= ===================== ===================== ==========='
|
||||
|
||||
do k=1,N_states
|
||||
pt2_overlap(pt2_stoch_istate,k) = pt2_data % overlap(k,pt2_stoch_istate)
|
||||
enddo
|
||||
! ! The overlap is not exactly zero because of the guiding function.
|
||||
! ! Remove the bias
|
||||
! do k=1,pt2_stoch_istate-1
|
||||
! pt2_overlap(k,pt2_stoch_istate) -= pt2_data % overlap(k,pt2_stoch_istate)
|
||||
! enddo
|
||||
print *, 'Overlap before orthogonalization'
|
||||
print *, pt2_overlap(:,pt2_stoch_istate)
|
||||
print *, 'Overlap after orthogonalization'
|
||||
print *, pt2_overlap(pt2_stoch_istate,:)
|
||||
print *, '-------'
|
||||
SOFT_TOUCH pt2_overlap
|
||||
|
||||
enddo
|
||||
FREE pt2_stoch_istate
|
||||
|
||||
! Symmetrize overlap
|
||||
do j=2,N_states
|
||||
do i=1,j-1
|
||||
pt2_overlap(i,j) = 0.5d0 * (pt2_overlap(i,j) + pt2_overlap(j,i))
|
||||
pt2_overlap(j,i) = pt2_overlap(i,j)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
print *, 'Overlap of perturbed states:'
|
||||
do k=1,N_states
|
||||
print *, pt2_overlap(k,:)
|
||||
enddo
|
||||
print *, '-------'
|
||||
|
||||
if (N_in > 0) then
|
||||
b%cur = min(N_in,b%cur)
|
||||
if (s2_eig) then
|
||||
@ -529,7 +533,14 @@ subroutine pt2_collector(zmq_socket_pull, E, relative_error, pt2_data, pt2_data_
|
||||
|
||||
if ((time - time1 > 1.d0) .or. (n==N_det_generators)) then
|
||||
time1 = time
|
||||
print '(G10.3, 2X, F16.10, 2X, G10.3, 2X, G14.6, 2X, G14.6, 2X, F10.4)', c, avg+E, eqt, avg2, avg3(pt2_stoch_istate), time-time0
|
||||
print '(I10, X, F12.6, X, G10.3, X, F10.6, X, G10.3, X, F10.6, X, G10.3, X, F10.4)', c, &
|
||||
pt2_data % pt2(pt2_stoch_istate) +E, &
|
||||
pt2_data_err % pt2(pt2_stoch_istate), &
|
||||
pt2_data % variance(pt2_stoch_istate), &
|
||||
pt2_data_err % variance(pt2_stoch_istate), &
|
||||
pt2_data % overlap(pt2_stoch_istate,pt2_stoch_istate), &
|
||||
pt2_data_err % overlap(pt2_stoch_istate,pt2_stoch_istate), &
|
||||
time-time0
|
||||
if (stop_now .or. ( &
|
||||
(do_exit .and. (dabs(pt2_data_err % pt2(pt2_stoch_istate)) / &
|
||||
(1.d-20 + dabs(pt2_data % pt2(pt2_stoch_istate)) ) <= relative_error))) ) then
|
||||
|
||||
@ -1,4 +1,3 @@
|
||||
|
||||
use bitmasks
|
||||
|
||||
BEGIN_PROVIDER [ double precision, pt2_match_weight, (N_states) ]
|
||||
@ -144,7 +143,6 @@ BEGIN_PROVIDER [ double precision, selection_weight, (N_states) ]
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
|
||||
subroutine get_mask_phase(det1, pm, Nint)
|
||||
use bitmasks
|
||||
implicit none
|
||||
@ -288,6 +286,7 @@ subroutine select_singles_and_doubles(i_generator,hole_mask,particle_mask,fock_d
|
||||
PROVIDE psi_bilinear_matrix_rows psi_det_sorted_order psi_bilinear_matrix_order
|
||||
PROVIDE psi_bilinear_matrix_transp_rows_loc psi_bilinear_matrix_transp_columns
|
||||
PROVIDE psi_bilinear_matrix_transp_order psi_selectors_coef_transp
|
||||
PROVIDE banned_excitation
|
||||
|
||||
monoAdo = .true.
|
||||
monoBdo = .true.
|
||||
@ -607,7 +606,8 @@ subroutine select_singles_and_doubles(i_generator,hole_mask,particle_mask,fock_d
|
||||
|
||||
h2 = hole_list(i2,s2)
|
||||
call apply_hole(pmask, s2,h2, mask, ok, N_int)
|
||||
banned = .false.
|
||||
banned(:,:,1) = banned_excitation(:,:)
|
||||
banned(:,:,2) = banned_excitation(:,:)
|
||||
do j=1,mo_num
|
||||
bannedOrb(j, 1) = .true.
|
||||
bannedOrb(j, 2) = .true.
|
||||
@ -674,7 +674,8 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
|
||||
logical :: ok
|
||||
integer :: s1, s2, p1, p2, ib, j, istate, jstate
|
||||
integer(bit_kind) :: mask(N_int, 2), det(N_int, 2)
|
||||
double precision :: e_pert, delta_E, val, Hii, w, tmp, alpha_h_psi, coef(N_states)
|
||||
double precision :: e_pert(N_states), coef(N_states)
|
||||
double precision :: delta_E, val, Hii, w, tmp, alpha_h_psi
|
||||
double precision, external :: diag_H_mat_elem_fock
|
||||
double precision :: E_shift
|
||||
|
||||
@ -682,7 +683,12 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
|
||||
double precision, allocatable :: values(:)
|
||||
integer, allocatable :: keys(:,:)
|
||||
integer :: nkeys
|
||||
|
||||
double precision :: s_weight(N_states,N_states)
|
||||
do jstate=1,N_states
|
||||
do istate=1,N_states
|
||||
s_weight(istate,jstate) = dsqrt(selection_weight(istate)*selection_weight(jstate))
|
||||
enddo
|
||||
enddo
|
||||
|
||||
if(sp == 3) then
|
||||
s1 = 1
|
||||
@ -763,23 +769,59 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
|
||||
! call occ_pattern_of_det(det,occ,N_int)
|
||||
! call occ_pattern_to_dets_size(occ,n,elec_alpha_num,N_int)
|
||||
|
||||
e_pert = 0.d0
|
||||
coef = 0.d0
|
||||
logical :: do_diag
|
||||
do_diag = .False.
|
||||
|
||||
do istate=1,N_states
|
||||
delta_E = E0(istate) - Hii + E_shift
|
||||
alpha_h_psi = mat(istate, p1, p2)
|
||||
if (alpha_h_psi == 0.d0) cycle
|
||||
|
||||
val = alpha_h_psi + alpha_h_psi
|
||||
tmp = dsqrt(delta_E * delta_E + val * val)
|
||||
if (delta_E < 0.d0) then
|
||||
tmp = -tmp
|
||||
endif
|
||||
e_pert = 0.5d0 * (tmp - delta_E)
|
||||
e_pert(istate) = 0.5d0 * (tmp - delta_E)
|
||||
if (dabs(alpha_h_psi) > 1.d-4) then
|
||||
coef(istate) = e_pert / alpha_h_psi
|
||||
coef(istate) = e_pert(istate) / alpha_h_psi
|
||||
else
|
||||
coef(istate) = alpha_h_psi / delta_E
|
||||
endif
|
||||
enddo
|
||||
|
||||
do_diag = sum(dabs(coef)) > 0.001d0
|
||||
|
||||
double precision :: eigvalues(N_states+1)
|
||||
double precision :: work(1+6*(N_states+1)+2*(N_states+1)**2)
|
||||
integer :: iwork(3+5*(N_states+1)), info, k ,n
|
||||
|
||||
if (do_diag) then
|
||||
double precision :: pt2_matrix(N_states+1,N_states+1)
|
||||
pt2_matrix(N_states+1,N_states+1) = Hii+E_shift
|
||||
do istate=1,N_states
|
||||
pt2_matrix(:,istate) = 0.d0
|
||||
pt2_matrix(istate,istate) = E0(istate)
|
||||
pt2_matrix(istate,N_states+1) = mat(istate,p1,p2)
|
||||
pt2_matrix(N_states+1,istate) = mat(istate,p1,p2)
|
||||
enddo
|
||||
|
||||
call DSYEVD( 'V', 'U', N_states+1, pt2_matrix, N_states+1, eigvalues, &
|
||||
work, size(work), iwork, size(iwork), info )
|
||||
if (info /= 0) then
|
||||
print *, 'error in '//irp_here
|
||||
stop -1
|
||||
endif
|
||||
pt2_matrix = dabs(pt2_matrix)
|
||||
iwork(1:N_states+1) = maxloc(pt2_matrix,DIM=1)
|
||||
do k=1,N_states
|
||||
e_pert(iwork(k)) = eigvalues(k) - E0(iwork(k))
|
||||
enddo
|
||||
endif
|
||||
|
||||
|
||||
! ! Gram-Schmidt using input overlap matrix
|
||||
! do istate=1,N_states
|
||||
! do jstate=1,istate-1
|
||||
@ -791,14 +833,13 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
|
||||
do istate=1, N_states
|
||||
|
||||
alpha_h_psi = mat(istate, p1, p2)
|
||||
e_pert = coef(istate) * alpha_h_psi
|
||||
|
||||
do jstate=1,N_states
|
||||
pt2_data % overlap(jstate,istate) += coef(jstate) * alpha_h_psi
|
||||
enddo
|
||||
|
||||
pt2_data % variance(istate) += alpha_h_psi * alpha_h_psi
|
||||
pt2_data % pt2(istate) += e_pert
|
||||
pt2_data % pt2(istate) += e_pert(istate)
|
||||
|
||||
!!!DEBUG
|
||||
! delta_E = E0(istate) - Hii + E_shift
|
||||
@ -823,14 +864,29 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
|
||||
|
||||
case(5)
|
||||
! Variance selection
|
||||
w = w - alpha_h_psi * alpha_h_psi * selection_weight(istate)
|
||||
! w = w - alpha_h_psi * alpha_h_psi * s_weight(istate,istate)
|
||||
w = min(w, - alpha_h_psi * alpha_h_psi * s_weight(istate,istate))
|
||||
! do jstate=1,N_states
|
||||
! if (istate == jstate) cycle
|
||||
! w = w + dabs(alpha_h_psi*mat(jstate,p1,p2)) * s_weight(istate,jstate)
|
||||
! enddo
|
||||
|
||||
case(6)
|
||||
w = w - coef(istate) * coef(istate) * selection_weight(istate)
|
||||
! w = w - coef(istate) * coef(istate) * s_weight(istate,istate)
|
||||
w = min(w,- coef(istate) * coef(istate) * s_weight(istate,istate))
|
||||
! do jstate=1,N_states
|
||||
! if (istate == jstate) cycle
|
||||
! w = w + dabs(coef(istate)*coef(jstate)) * s_weight(istate,jstate)
|
||||
! enddo
|
||||
|
||||
case default
|
||||
! Energy selection
|
||||
w = w + e_pert * selection_weight(istate)
|
||||
! w = w + e_pert(istate) * s_weight(istate,istate)
|
||||
w = min(w, e_pert(istate) * s_weight(istate,istate))
|
||||
! do jstate=1,N_states
|
||||
! if (istate == jstate) cycle
|
||||
! w = w + dabs(X(istate)*X(jstate)) * s_weight(istate,jstate)
|
||||
! enddo
|
||||
|
||||
end select
|
||||
end do
|
||||
|
||||
@ -141,6 +141,12 @@ subroutine ZMQ_selection(N_in, pt2_data)
|
||||
enddo
|
||||
|
||||
pt2_overlap(:,:) = pt2_data % overlap(:,:)
|
||||
|
||||
print *, 'Overlap of perturbed states:'
|
||||
do l=1,N_states
|
||||
print *, pt2_overlap(l,:)
|
||||
enddo
|
||||
print *, '-------'
|
||||
SOFT_TOUCH pt2_overlap
|
||||
call update_pt2_and_variance_weights(pt2_data, N_states)
|
||||
|
||||
|
||||
@ -8,7 +8,7 @@ default: 1.e-10
|
||||
type: logical
|
||||
doc: Thresholds of Davidson's algorithm is set to E(rPT2)*threshold_davidson_from_pt2
|
||||
interface: ezfio,provider,ocaml
|
||||
default: true
|
||||
default: false
|
||||
|
||||
[n_states_diag]
|
||||
type: States_number
|
||||
|
||||
@ -44,7 +44,7 @@ default: 2
|
||||
type: integer
|
||||
doc: Weight used in the selection. 0: input state-average weight, 1: 1./(c_0^2), 2: rPT2 matching, 3: variance matching, 4: variance and rPT2 matching, 5: variance minimization and matching, 6: CI coefficients 7: input state-average multiplied by variance and rPT2 matching 8: input state-average multiplied by rPT2 matching 9: input state-average multiplied by variance matching
|
||||
interface: ezfio,provider,ocaml
|
||||
default: 2
|
||||
default: 1
|
||||
|
||||
[threshold_generators]
|
||||
type: Threshold
|
||||
|
||||
@ -99,6 +99,10 @@ double precision function get_two_e_integral(i,j,k,l,map)
|
||||
type(map_type), intent(inout) :: map
|
||||
real(integral_kind) :: tmp
|
||||
PROVIDE mo_two_e_integrals_in_map mo_integrals_cache
|
||||
if (banned_excitation(i,k) .or. banned_excitation(j,l)) then
|
||||
get_two_e_integral = 0.d0
|
||||
return
|
||||
endif
|
||||
ii = l-mo_integrals_cache_min
|
||||
ii = ior(ii, k-mo_integrals_cache_min)
|
||||
ii = ior(ii, j-mo_integrals_cache_min)
|
||||
@ -159,6 +163,11 @@ subroutine get_mo_two_e_integrals(j,k,l,sze,out_val,map)
|
||||
! return
|
||||
!DEBUG
|
||||
|
||||
out_val(1:sze) = 0.d0
|
||||
if (banned_excitation(j,l)) then
|
||||
return
|
||||
endif
|
||||
|
||||
ii0 = l-mo_integrals_cache_min
|
||||
ii0 = ior(ii0, k-mo_integrals_cache_min)
|
||||
ii0 = ior(ii0, j-mo_integrals_cache_min)
|
||||
@ -172,6 +181,7 @@ subroutine get_mo_two_e_integrals(j,k,l,sze,out_val,map)
|
||||
q = q+shiftr(s*s-s,1)
|
||||
|
||||
do i=1,sze
|
||||
if (banned_excitation(i,k)) cycle
|
||||
ii = ior(ii0, i-mo_integrals_cache_min)
|
||||
if (iand(ii, -128) == 0) then
|
||||
ii_8 = ior( shiftl(ii0_8,7), int(i,8)-mo_integrals_cache_min_8)
|
||||
@ -272,6 +282,29 @@ subroutine get_mo_two_e_integrals_exch_ii(k,l,sze,out_val,map)
|
||||
|
||||
end
|
||||
|
||||
BEGIN_PROVIDER [ logical, banned_excitation, (mo_num,mo_num) ]
|
||||
implicit none
|
||||
use map_module
|
||||
BEGIN_DOC
|
||||
! If true, the excitation is banned in the selection. Useful with local MOs.
|
||||
END_DOC
|
||||
banned_excitation = .False.
|
||||
integer :: i,j
|
||||
integer(key_kind) :: idx
|
||||
double precision :: tmp
|
||||
! double precision :: buffer(mo_num)
|
||||
do j=1,mo_num
|
||||
do i=1,j-1
|
||||
call two_e_integrals_index(i,j,j,i,idx)
|
||||
!DIR$ FORCEINLINE
|
||||
call map_get(mo_integrals_map,idx,tmp)
|
||||
banned_excitation(i,j) = dabs(tmp) < 1.d-15
|
||||
banned_excitation(j,i) = banned_excitation(i,j)
|
||||
enddo
|
||||
enddo
|
||||
END_PROVIDER
|
||||
|
||||
|
||||
|
||||
integer*8 function get_mo_map_size()
|
||||
implicit none
|
||||
|
||||
@ -17,7 +17,7 @@ program molden
|
||||
|
||||
write(i_unit_output,'(A)') '[Molden Format]'
|
||||
|
||||
write(i_unit_output,'(A)') '[Atoms] ANGSTROM'
|
||||
write(i_unit_output,'(A)') '[Atoms] Angs'
|
||||
do i = 1, nucl_num
|
||||
write(i_unit_output,'(A2,2X,I4,2X,I4,3(2X,F15.10))') &
|
||||
trim(element_name(int(nucl_charge(i)))), &
|
||||
|
||||
@ -11,7 +11,7 @@ subroutine svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
|
||||
integer, intent(in) :: LDA, LDU, LDVt, m, n
|
||||
double precision, intent(in) :: A(LDA,n)
|
||||
double precision, intent(out) :: U(LDU,m)
|
||||
double precision, intent(out) :: U(LDU,min(m,n))
|
||||
double precision,intent(out) :: Vt(LDVt,n)
|
||||
double precision,intent(out) :: D(min(m,n))
|
||||
double precision,allocatable :: work(:)
|
||||
@ -19,19 +19,19 @@ subroutine svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
|
||||
double precision,allocatable :: A_tmp(:,:)
|
||||
allocate (A_tmp(LDA,n))
|
||||
A_tmp = A
|
||||
A_tmp(:,:) = A(:,:)
|
||||
|
||||
! Find optimal size for temp arrays
|
||||
allocate(work(1))
|
||||
lwork = -1
|
||||
call dgesvd('A','A', m, n, A_tmp, LDA, &
|
||||
call dgesvd('S','S', m, n, A_tmp, LDA, &
|
||||
D, U, LDU, Vt, LDVt, work, lwork, info)
|
||||
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
|
||||
lwork = max(int(work(1)), 5*MIN(M,N))
|
||||
deallocate(work)
|
||||
|
||||
allocate(work(lwork))
|
||||
call dgesvd('A','A', m, n, A_tmp, LDA, &
|
||||
call dgesvd('S','S', m, n, A_tmp, LDA, &
|
||||
D, U, LDU, Vt, LDVt, work, lwork, info)
|
||||
deallocate(work,A_tmp)
|
||||
|
||||
@ -42,6 +42,128 @@ subroutine svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
|
||||
end
|
||||
|
||||
subroutine eigSVD(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Algorithm 3 of https://arxiv.org/pdf/1810.06860.pdf
|
||||
!
|
||||
! A(m,n) = U(m,n) D(n) Vt(n,n) with m>n
|
||||
END_DOC
|
||||
integer, intent(in) :: LDA, LDU, LDVt, m, n
|
||||
double precision, intent(in) :: A(LDA,n)
|
||||
double precision, intent(out) :: U(LDU,n)
|
||||
double precision,intent(out) :: Vt(LDVt,n)
|
||||
double precision,intent(out) :: D(n)
|
||||
|
||||
integer :: i,j,k
|
||||
|
||||
if (m<n) then
|
||||
stop -1
|
||||
call svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
return
|
||||
endif
|
||||
|
||||
double precision, allocatable :: B(:,:), V(:,:)
|
||||
allocate(B(n,n))
|
||||
! B = - At . A
|
||||
call dgemm('T','N',n,n,m,-1.d0,A,size(A,1),A,size(A,1),0.d0,B,size(B,1))
|
||||
|
||||
! V, D = eig(B)
|
||||
allocate(V(n,n))
|
||||
call lapack_diagd(D,V,B,n,n)
|
||||
deallocate(B)
|
||||
do j=1,n
|
||||
do i=1,n
|
||||
Vt(i,j) = V(j,i)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! S = sqrt(-D)
|
||||
! U = A.V.S^-1
|
||||
! U = A.(S^-1.vt)t
|
||||
|
||||
do k=1,n
|
||||
if (D(k) >= 0.d0) then
|
||||
exit
|
||||
endif
|
||||
D(k) = dsqrt(-D(k))
|
||||
call dscal(n, 1.d0/D(k), V(1,k), 1)
|
||||
enddo
|
||||
D(k:n) = 0.d0
|
||||
k=k-1
|
||||
call dgemm('N','N',m,n,k,1.d0,A,size(A,1),V,size(V,1),0.d0,U,size(U,1))
|
||||
|
||||
end
|
||||
|
||||
|
||||
subroutine randomized_svd(A,LDA,U,LDU,D,Vt,LDVt,m,n,q,r)
|
||||
implicit none
|
||||
include 'constants.include.F'
|
||||
BEGIN_DOC
|
||||
! Randomized SVD: rank r, q power iterations
|
||||
!
|
||||
! 1. Sample column space of A with P: Z = A.P where P is random with r+p columns.
|
||||
!
|
||||
! 2. Power iterations : Z <- X . (Xt.Z)
|
||||
!
|
||||
! 3. Z = Q.R
|
||||
!
|
||||
! 4. Compute SVD on projected Qt.X = U' . S. Vt
|
||||
!
|
||||
! 5. U = Q U'
|
||||
END_DOC
|
||||
|
||||
integer, intent(in) :: LDA, LDU, LDVt, m, n, q, r
|
||||
double precision, intent(in) :: A(LDA,n)
|
||||
double precision, intent(out) :: U(LDU,r)
|
||||
double precision,intent(out) :: Vt(LDVt,r)
|
||||
double precision,intent(out) :: D(r)
|
||||
integer :: i, j, k
|
||||
|
||||
double precision,allocatable :: Z(:,:), P(:,:), Y(:,:), UY(:,:)
|
||||
double precision :: r1,r2
|
||||
allocate(P(n,r), Z(m,r))
|
||||
|
||||
! P is a normal random matrix (n,r)
|
||||
do k=1,r
|
||||
do i=1,n
|
||||
call random_number(r1)
|
||||
call random_number(r2)
|
||||
r1 = dsqrt(-2.d0*dlog(r1))
|
||||
r2 = dtwo_pi*r2
|
||||
P(i,k) = r1*dcos(r2)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Z(m,r) = A(m,n).P(n,r)
|
||||
call dgemm('N','N',m,r,n,1.d0,A,size(A,1),P,size(P,1),0.d0,Z,size(Z,1))
|
||||
|
||||
! Power iterations
|
||||
do k=1,q
|
||||
! P(n,r) = At(n,m).Z(m,r)
|
||||
call dgemm('T','N',n,r,m,1.d0,A,size(A,1),Z,size(Z,1),0.d0,P,size(P,1))
|
||||
! Z(m,r) = A(m,n).P(n,r)
|
||||
call dgemm('N','N',m,r,n,1.d0,A,size(A,1),P,size(P,1),0.d0,Z,size(Z,1))
|
||||
enddo
|
||||
|
||||
deallocate(P)
|
||||
|
||||
! QR factorization of Z
|
||||
call ortho_svd(Z,size(Z,1),m,r)
|
||||
|
||||
allocate(Y(r,n), UY(r,r))
|
||||
! Y(r,n) = Zt(r,m).A(m,n)
|
||||
call dgemm('T','N',r,n,m,1.d0,Z,size(Z,1),A,size(A,1),0.d0,Y,size(Y,1))
|
||||
|
||||
! SVD of Y
|
||||
call svd(Y,size(Y,1),UY,size(UY,1),D,Vt,size(Vt,1),r,n)
|
||||
deallocate(Y)
|
||||
|
||||
! U(m,r) = Z(m,r).UY(r,r)
|
||||
call dgemm('N','N',m,r,r,1.d0,Z,size(Z,1),UY,size(UY,1),0.d0,U,size(U,1))
|
||||
deallocate(UY,Z)
|
||||
|
||||
end
|
||||
|
||||
subroutine svd_complex(A,LDA,U,LDU,D,Vt,LDVt,m,n)
|
||||
implicit none
|
||||
@ -807,6 +929,33 @@ subroutine ortho_canonical(overlap,LDA,N,C,LDC,m,cutoff)
|
||||
end
|
||||
|
||||
|
||||
subroutine ortho_svd(A,LDA,m,n)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Orthogonalization via fast SVD
|
||||
!
|
||||
! A : matrix to orthogonalize
|
||||
!
|
||||
! LDA : leftmost dimension of A
|
||||
!
|
||||
! m : Number of rows of A
|
||||
!
|
||||
! n : Number of columns of A
|
||||
!
|
||||
END_DOC
|
||||
integer, intent(in) :: m,n, LDA
|
||||
double precision, intent(inout) :: A(LDA,n)
|
||||
if (m < n) then
|
||||
call ortho_qr(A,LDA,m,n)
|
||||
endif
|
||||
double precision, allocatable :: U(:,:), D(:), Vt(:,:)
|
||||
allocate(U(m,n), D(n), Vt(n,n))
|
||||
call SVD(A,LDA,U,size(U,1),D,Vt,size(Vt,1),m,n)
|
||||
A(1:m,1:n) = U(1:m,1:n)
|
||||
deallocate(U,D, Vt)
|
||||
|
||||
end
|
||||
|
||||
subroutine ortho_qr(A,LDA,m,n)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
|
||||
Loading…
Reference in New Issue
Block a user