cipsi¶
CIPSI algorithm.
The run_stochastic_cipsi()
and run_cipsi()
subroutines start with a single
determinant, or with the wave function in the EZFIO database if
determinants read_wf
is true
.
The run_cipsi()
subroutine iteratively:
- Selects the most important determinants from the external space and adds them to the internal space
- If
determinants s2_eig
istrue
, it adds all the necessary determinants to allow the eigenstates of \(\hat H\) to be eigenstates of \(\widehat{S^2}\) - Diagonalizes \(\hat H\) in the enlarged internal space
- Computes the PT2 contribution to the energy stochastically [13]
or deterministically, depending on
perturbation do_pt2
- Extrapolates the variational energy by fitting \(E=E_\text{FCI} - \alpha\, E_\text{PT2}\)
The difference between run_stochastic_cipsi()
and run_cipsi()
is that
run_stochastic_cipsi()
selects the determinants on the fly with the computation
of the stochastic PT2 [13]. Hence, it is a semi-stochastic selection. It
- Selects the most important determinants from the external space and adds them to the internal space, on the fly with the computation of the PT2 with the stochastic algorithm presented in [13].
- If
determinants s2_eig
istrue
, it adds all the necessary determinants to allow the eigenstates of \(\hat H\) to be eigenstates of \(\widehat{S^2}\) - Extrapolates the variational energy by fitting \(E=E_\text{FCI} - \alpha\, E_\text{PT2}\)
- Diagonalizes \(\hat H\) in the enlarged internal space
The number of selected determinants at each iteration will be such that the
size of the wave function will double at every iteration. If determinants
s2_eig
is true
, then the number of selected determinants will be 1.5x the
current number, and then all the additional determinants will be added.
By default, the program will stop when more than one million determinants have been selected, or when the PT2 energy is below \(10^{-4}\).
The variational and PT2 energies of the iterations are stored in the EZFIO database, in the iterations module.
Computation of the PT2 energy¶
At each iteration, the PT2 energy is computed considering the Epstein-Nesbet zeroth-order Hamiltonian:
where the \(|\alpha \rangle\) determinants are generated by applying all the single and double excitation operators to all the determinants of the wave function \(\Psi_G\).
When the hybrid-deterministic/stochastic algorithm is chosen
(default), \(Psi_G = \Psi_S = \Psi\), the full wavefunction expanded in the
internal space.
When the deterministic algorithm is chosen (perturbation do_pt2
is set to false
), \(Psi_G\) is a truncation of \(|\Psi \rangle\) using
determinants threshold_generators
, and \(Psi_S\) is a truncation
of \(|\Psi \rangle\) using determinants threshold_selectors
, and re-weighted
by \(1/\langle \Psi_s | \Psi_s \rangle\).
At every iteration, while computing the PT2, the variance of the wave function is also computed:
The expression of the variance is the same as the expression of the PT2, with a denominator of 1. It measures how far the wave function is from the FCI solution. Note that the absence of denominator in the Heat-Bath selected CI method is selection method by minimization of the variance, whereas CIPSI is a selection method by minimization of the energy.
If perturbation do_pt2
is set to false
, then the stochastic
PT2 is not computed, and an approximate value is obtained from the CIPSI
selection. The calculation is faster, but the extrapolated FCI value is
less accurate. This way of running the code should be used when the only
goal is to generate a wave function, as for using CIPSI wave functions as
trial wave functions of QMC calculations for example.
The PT2 program reads the wave function of the EZFIO database and computes the energy and the PT2 contribution.
State-averaging¶
Extrapolated FCI energy¶
An estimate of the FCI energy is computed by extrapolating
This extrapolation is done for all the requested states, and excitation energies are printed as energy differences between the extrapolated energies of the excited states and the extrapolated energy of the ground state.
The extrapolations are given considering the 2 last points, the 3 last points, …, the 7 last points. The extrapolated value should be chosen such that the extrpolated value is stable with the number of points.
Providers¶
-
initialize_pt2_e0_denominator
¶ File :
cipsi/energy.irp.f
logical :: initialize_pt2_e0_denominator
If true, initialize pt2_E0_denominator
Needed by:
-
nthreads_pt2
¶ File :
cipsi/environment.irp.f
integer :: nthreads_pt2
Number of threads for Davidson
Needs:
-
pt2_collector:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
subroutine pt2_collector(zmq_socket_pull, E, relative_error, pt2, error, &
variance, norm, b, N_)
Needs:
pt2_j
pt2_stoch_istate
n_states
Called by:
zmq_pt2()
Calls:
add_to_selection_buffer()
check_mem()
create_selection_buffer()
delete_selection_buffer()
end_zmq_to_qp_run_socket()
pull_pt2_results()
sleep()
sort_selection_buffer()
wall_time()
-
pt2_cw
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1)
Needs:
Needed by:
-
pt2_e0_denominator
¶ File :
cipsi/energy.irp.f
double precision, allocatable :: pt2_e0_denominator (N_states)
E0 in the denominator of the PT2
Needs:
mpi_master
n_states
-
pt2_f
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer, allocatable :: pt2_f (N_det_generators) integer :: pt2_n_tasks_max
Needs:
n_states
psi_det_sorted_gen
-
pt2_j
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer, allocatable :: pt2_j (N_det_generators) integer, allocatable :: pt2_r (N_det_generators)
Needs:
-
pt2_mindetinfirstteeth
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer :: pt2_n_teeth integer :: pt2_mindetinfirstteeth
Needs:
Needed by:
-
pt2_n_0
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1)
Needs:
Needed by:
-
pt2_n_tasks
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer :: pt2_n_tasks
Number of parallel tasks for the Monte Carlo
Needs:
Needed by:
-
pt2_n_tasks_max
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer, allocatable :: pt2_f (N_det_generators) integer :: pt2_n_tasks_max
Needs:
n_states
psi_det_sorted_gen
-
pt2_n_teeth
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer :: pt2_n_teeth integer :: pt2_mindetinfirstteeth
Needs:
Needed by:
-
pt2_r
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer, allocatable :: pt2_j (N_det_generators) integer, allocatable :: pt2_r (N_det_generators)
Needs:
-
pt2_stoch_istate
¶ File :
cipsi/pt2_stoch_routines.irp.f
integer :: pt2_stoch_istate
State for stochatsic PT2
Needed by:
-
pt2_u
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_u (N_det_generators)
Needs:
Needed by:
-
pt2_u_0
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1)
Needs:
Needed by:
-
pt2_w
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1)
Needs:
Needed by:
-
pt2_w_t
¶ File :
cipsi/pt2_stoch_routines.irp.f
double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1)
Needs:
Needed by:
Subroutines / functions¶
-
add_to_selection_buffer:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine add_to_selection_buffer(b, det, val)
Needs:
Called by:
fill_buffer_double()
pt2_collector()
selection_collector()
Calls:
sort_selection_buffer()
-
bitstring_to_list_in_selection:
()¶ File :
cipsi/selection.irp.f
subroutine bitstring_to_list_in_selection( string, list, n_elements, Nint)
Gives the inidices(+1) of the bits set to 1 in the bit string
Called by:
splash_pq()
spot_isinwf()
-
create_selection_buffer:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine create_selection_buffer(N, siz_, res)
Needs:
Called by:
pt2_collector()
run_pt2_slave()
run_selection_slave()
selection_collector()
zmq_pt2()
zmq_selection()
Calls:
check_mem()
-
delete_selection_buffer:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine delete_selection_buffer(b)
Called by:
pt2_collector()
run_pt2_slave()
run_selection_slave()
selection_collector()
zmq_pt2()
zmq_selection()
-
fill_buffer_double:
()¶ File :
cipsi/selection.irp.f
subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_diag_tmp, E0, pt2, variance, norm, mat, buf)
Needs:
n_states
n_int
psi_det_hii
Called by:
select_singles_and_doubles()
Calls:
add_to_selection_buffer()
apply_holes()
apply_particles()
-
get_d0:
()¶ File :
cipsi/selection.irp.f
subroutine get_d0(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs)
Needs:
n_states
n_int
Called by:
splash_pq()
Calls:
apply_particles()
get_mo_two_e_integrals()
i_h_j()
-
get_d1:
()¶ File :
cipsi/selection.irp.f
subroutine get_d1(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs)
Needs:
n_states
n_int
Called by:
splash_pq()
Calls:
apply_particles()
get_mo_two_e_integrals()
i_h_j()
-
get_d2:
()¶ File :
cipsi/selection.irp.f
subroutine get_d2(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs)
Needs:
n_states
Called by:
splash_pq()
-
get_mask_phase:
()¶ File :
cipsi/selection.irp.f
subroutine get_mask_phase(det1, pm, Nint)
Called by:
splash_pq()
-
get_phase_bi:
()¶ File :
cipsi/selection.irp.f
double precision function get_phase_bi(phasemask, s1, s2, h1, p1, h2, p2, Nint)
-
make_selection_buffer_s2:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine make_selection_buffer_s2(b)
Needs:
elec_alpha_num
Called by:
zmq_pt2()
zmq_selection()
Calls:
check_mem()
dsort()
i8sort()
occ_pattern_to_dets()
occ_pattern_to_dets_size()
-
merge_selection_buffers:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine merge_selection_buffers(b1, b2)
Merges the selection buffers b1 and b2 into b2
Needs:
Called by:
run_pt2_slave()
run_selection_slave()
Calls:
check_mem()
-
past_d1:
()¶ File :
cipsi/selection.irp.f
subroutine past_d1(bannedOrb, p)
Needs:
Called by:
splash_pq()
-
past_d2:
()¶ File :
cipsi/selection.irp.f
subroutine past_d2(banned, p, sp)
Needs:
Called by:
splash_pq()
-
provide_everything:
()¶ File :
cipsi/slave_cipsi.irp.f
subroutine provide_everything
Needs:
threshold_generators
psi_det_sorted_bit
n_states
h_apply_buffer_allocated
n_det_generators
psi_det_generators
n_int
psi_det_generators
Called by:
run_slave_cipsi()
-
pt2_find_sample:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
integer function pt2_find_sample(v, w)
Needs:
-
pt2_find_sample_lr:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
integer function pt2_find_sample_lr(v, w, l_in, r_in)
Needs:
-
pt2_slave_inproc:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
subroutine pt2_slave_inproc(i)
Needs:
Called by:
zmq_pt2()
Calls:
run_pt2_slave()
-
pull_pt2_results:
()¶ File :
cipsi/run_pt2_slave.irp.f
subroutine pull_pt2_results(zmq_socket_pull, index, pt2, variance, norm, task_id, n_tasks, b)
Needs:
n_states
Called by:
pt2_collector()
-
pull_selection_results:
()¶ File :
cipsi/run_selection_slave.irp.f
subroutine pull_selection_results(zmq_socket_pull, pt2, variance, norm, val, det, N, task_id, ntask)
Needs:
n_states
Called by:
selection_collector()
-
push_pt2_results:
()¶ File :
cipsi/run_pt2_slave.irp.f
subroutine push_pt2_results(zmq_socket_push, index, pt2, variance, norm, b, task_id, n_tasks)
Needs:
n_states
Called by:
run_pt2_slave()
-
push_selection_results:
()¶ File :
cipsi/run_selection_slave.irp.f
subroutine push_selection_results(zmq_socket_push, pt2, variance, norm, b, task_id, ntask)
Needs:
n_states
Called by:
run_selection_slave()
-
remove_duplicates_in_selection_buffer:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine remove_duplicates_in_selection_buffer(b)
Needs:
Called by:
zmq_pt2()
Calls:
check_mem()
i8sort()
-
run_cipsi:
()¶ File :
cipsi/cipsi.irp.f
subroutine run_cipsi
Selected Full Configuration Interaction with deterministic selection and stochastic PT2.
Needs:
correlation_energy_ratio_max
n_iter
psi_energy_with_nucl_rep
psi_occ_pattern
n_det_max
n_states
h_apply_buffer_allocated
n_det
s2_eig
do_pt2
psi_energy
pt2_relative_error
ref_bitmask_energy
psi_det
n_states_diag
psi_coef
psi_det_sorted
pt2_max
threshold_generators
Called by:
fci()
Calls:
check_mem()
diagonalize_ci()
ezfio_get_hartree_fock_energy()
ezfio_has_hartree_fock_energy()
make_s2_eigenfunction()
print_extrapolated_energy()
print_summary()
save_energy()
save_iterations()
save_wavefunction()
write_double()
zmq_pt2()
zmq_selection()
Touches:
psi_det_sorted_bit
psi_occ_pattern
pt2_stoch_istate
state_average_weight
threshold_generators
-
run_pt2_slave:
()¶ File :
cipsi/run_pt2_slave.irp.f
subroutine run_pt2_slave(thread,iproc,energy)
Needs:
n_states_diag
n_states
Called by:
pt2_slave_inproc()
run_slave_main()
Calls:
check_mem()
create_selection_buffer()
delete_selection_buffer()
end_zmq_push_socket()
end_zmq_to_qp_run_socket()
merge_selection_buffers()
push_pt2_results()
select_connected()
sleep()
sort_selection_buffer()
wall_time()
-
run_selection_slave:
()¶ File :
cipsi/run_selection_slave.irp.f
subroutine run_selection_slave(thread,iproc,energy)
Needs:
Called by:
run_slave_main()
selection_slave_inproc()
Calls:
create_selection_buffer()
delete_selection_buffer()
end_zmq_push_socket()
end_zmq_to_qp_run_socket()
merge_selection_buffers()
push_selection_results()
select_connected()
sleep()
sort_selection_buffer()
-
run_slave_cipsi:
()¶ File :
cipsi/slave_cipsi.irp.f
subroutine run_slave_cipsi
Helper program for distributed parallelism
Needs:
read_wf
distributed_davidson
Called by:
fci()
pt2()
Calls:
omp_set_nested()
provide_everything()
run_slave_main()
switch_qp_run_to_master()
Touches:
distributed_davidson
pt2_e0_denominator
pt2_stoch_istate
read_wf
state_average_weight
threshold_generators
-
run_slave_main:
()¶ File :
cipsi/slave_cipsi.irp.f
subroutine run_slave_main
Needs:
n_det_generators
psi_det
n_states_diag
zmq_context
threshold_generators
Called by:
run_slave_cipsi()
Calls:
davidson_slave_tcp()
mpi_print()
omp_set_nested()
run_pt2_slave()
run_selection_slave()
sleep()
wait_for_states()
wall_time()
write_double()
Touches:
threshold_generators
-
run_stochastic_cipsi:
()¶ File :
cipsi/stochastic_cipsi.irp.f
subroutine run_stochastic_cipsi
Selected Full Configuration Interaction with Stochastic selection and PT2.
Needs:
correlation_energy_ratio_max
n_iter
psi_energy_with_nucl_rep
psi_occ_pattern
n_det_max
n_states
h_apply_buffer_allocated
n_det
s2_eig
psi_energy
pt2_relative_error
ref_bitmask_energy
psi_det
n_states_diag
psi_coef
psi_det_sorted
pt2_max
threshold_generators
Called by:
fci()
Calls:
check_mem()
copy_h_apply_buffer_to_wf()
diagonalize_ci()
ezfio_get_hartree_fock_energy()
ezfio_has_hartree_fock_energy()
make_s2_eigenfunction()
print_extrapolated_energy()
print_summary()
save_energy()
save_iterations()
save_wavefunction()
write_double()
zmq_pt2()
Touches:
psi_det_sorted_bit
psi_occ_pattern
pt2_stoch_istate
state_average_weight
threshold_generators
-
select_connected:
()¶ File :
cipsi/selection.irp.f
subroutine select_connected(i_generator,E0,pt2,variance,norm,b,subset,csubset)
Needs:
n_states
n_int
Called by:
run_pt2_slave()
run_selection_slave()
Calls:
build_fock_tmp()
select_singles_and_doubles()
-
select_singles_and_doubles:
()¶ File :
cipsi/selection.irp.f
subroutine select_singles_and_doubles(i_generator,hole_mask,particle_mask,fock_diag_tmp,E0,pt2,variance,norm,buf,subset,csubset)
WARNING /!: It is assumed that the generators and selectors are psi_det_sorted
Needs:
Called by:
select_connected()
Calls:
apply_hole()
bitstring_to_list_ab()
check_mem()
fill_buffer_double()
get_excitation_degree_spin()
isort()
splash_pq()
spot_isinwf()
-
selection_collector:
()¶ File :
cipsi/zmq_selection.irp.f
subroutine selection_collector(zmq_socket_pull, b, N, pt2, variance, norm)
Needs:
n_states
Called by:
zmq_selection()
Calls:
add_to_selection_buffer()
check_mem()
create_selection_buffer()
delete_selection_buffer()
end_zmq_to_qp_run_socket()
pull_selection_results()
sort_selection_buffer()
-
selection_slave_inproc:
()¶ File :
cipsi/zmq_selection.irp.f
subroutine selection_slave_inproc(i)
Needs:
Called by:
zmq_selection()
Calls:
run_selection_slave()
-
sort_selection_buffer:
()¶ File :
cipsi/selection_buffer.irp.f
subroutine sort_selection_buffer(b)
Needs:
Called by:
add_to_selection_buffer()
pt2_collector()
run_pt2_slave()
run_selection_slave()
selection_collector()
Calls:
check_mem()
dsort()
-
splash_pq:
()¶ File :
cipsi/selection.irp.f
subroutine splash_pq(mask, sp, det, i_gen, N_sel, bannedOrb, banned, mat, interesting)
Needs:
psi_selectors_coef_transp
n_states
Called by:
select_singles_and_doubles()
Calls:
bitstring_to_list_in_selection()
get_d0()
get_d1()
get_d2()
get_mask_phase()
past_d1()
past_d2()
-
spot_isinwf:
()¶ File :
cipsi/selection.irp.f
subroutine spot_isinwf(mask, det, i_gen, N, banned, fullMatch, interesting)
Needs:
Called by:
select_singles_and_doubles()
Calls:
bitstring_to_list_in_selection()
-
testteethbuilding:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
logical function testTeethBuilding(minF, N)
Needs:
Calls:
check_mem()
-
zmq_pt2:
()¶ File :
cipsi/pt2_stoch_routines.irp.f
subroutine ZMQ_pt2(E, pt2,relative_error, error, variance, norm, N_in)
Needs:
psi_bilinear_matrix_transp_values
state_average_weight
mo_num
nthreads_pt2
psi_bilinear_matrix_values
mo_one_e_integrals
elec_alpha_num
nproc
psi_bilinear_matrix_columns_loc
threshold_generators
psi_det_beta_unique
Called by:
run_cipsi()
run_stochastic_cipsi()
Calls:
check_mem()
create_selection_buffer()
delete_selection_buffer()
end_parallel_job()
fill_h_apply_buffer_no_selection()
make_selection_buffer_s2()
new_parallel_job()
omp_set_nested()
pt2_collector()
pt2_slave_inproc()
remove_duplicates_in_selection_buffer()
resident_memory()
write_double()
write_int()
zmq_selection()
Touches:
-
zmq_selection:
()¶ File :
cipsi/zmq_selection.irp.f
subroutine ZMQ_selection(N_in, pt2, variance, norm)
Needs:
state_average_weight
psi_bilinear_matrix_values
pt2_e0_denominator
do_pt2
nproc
s2_eig
threshold_generators
psi_det_beta_unique
Called by:
run_cipsi()
zmq_pt2()
Calls:
copy_h_apply_buffer_to_wf()
create_selection_buffer()
delete_selection_buffer()
end_parallel_job()
fill_h_apply_buffer_no_selection()
make_selection_buffer_s2()
new_parallel_job()
save_wavefunction()
selection_collector()
selection_slave_inproc()
write_double()
Touches: