mirror of
https://github.com/LCPQ/quantum_package
synced 2024-09-16 17:35:42 +02:00
399 lines
17 KiB
ReStructuredText
399 lines
17 KiB
ReStructuredText
=============
|
|
BiInts Module
|
|
=============
|
|
|
|
Here, all bi-electronic integrals (:math:`1/r_{12}`) are computed. As they have
|
|
4 indices and many are zero, they are stored in a map, as defined in
|
|
``Utils/map_module.f90``. To fetch an AO integral, use the
|
|
``get_ao_bielec_integral(i,j,k,l,ao_integrals_map)`` function, and to fetch and
|
|
MO integral, use ``get_mo_bielec_integral(i,j,k,l,mo_integrals_map)`` or
|
|
``mo_bielec_integral(i,j,k,l)``.
|
|
|
|
The conventions are:
|
|
|
|
* For AO integrals : (ik|jl) = (11|22)
|
|
* For MO integrals : <ij|kl> = <12|12>
|
|
|
|
|
|
|
|
Needed Modules
|
|
==============
|
|
|
|
.. Do not edit this section It was auto-generated
|
|
.. by the `update_README.py` script.
|
|
|
|
.. image:: tree_dependency.png
|
|
|
|
* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
|
|
* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
|
|
|
|
Needed Modules
|
|
==============
|
|
.. Do not edit this section It was auto-generated
|
|
.. by the `update_README.py` script.
|
|
|
|
|
|
.. image:: tree_dependency.png
|
|
|
|
* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
|
|
* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
|
|
* `ZMQ <http://github.com/LCPQ/quantum_package/tree/master/src/ZMQ>`_
|
|
|
|
Documentation
|
|
=============
|
|
.. Do not edit this section It was auto-generated
|
|
.. by the `update_README.py` script.
|
|
|
|
|
|
`add_integrals_to_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L40>`_
|
|
Adds integrals to tha MO map according to some bitmask
|
|
|
|
|
|
`ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1>`_
|
|
integral of the AO basis <ik|jl> or (ij|kl)
|
|
i(r1) j(r1) 1/r12 k(r2) l(r2)
|
|
|
|
|
|
`ao_bielec_integral_schwartz <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L414>`_
|
|
Needed to compute Schwartz inequalities
|
|
|
|
|
|
`ao_bielec_integral_schwartz_accel <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L106>`_
|
|
integral of the AO basis <ik|jl> or (ij|kl)
|
|
i(r1) j(r1) 1/r12 k(r2) l(r2)
|
|
|
|
|
|
`ao_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L328>`_
|
|
Map of Atomic integrals
|
|
i(r1) j(r2) 1/r12 k(r1) l(r2)
|
|
|
|
|
|
`ao_bielec_integrals_in_map_collector <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L123>`_
|
|
Collects results from the AO integral calculation
|
|
|
|
|
|
`ao_bielec_integrals_in_map_slave <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L72>`_
|
|
Computes a buffer of integrals
|
|
|
|
|
|
`ao_bielec_integrals_in_map_slave_inproc <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L11>`_
|
|
Computes a buffer of integrals. i is the ID of the current thread.
|
|
|
|
|
|
`ao_bielec_integrals_in_map_slave_tcp <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L1>`_
|
|
Computes a buffer of integrals. i is the ID of the current thread.
|
|
|
|
|
|
`ao_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L123>`_
|
|
Cache of AO integrals for fast access
|
|
|
|
|
|
`ao_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L113>`_
|
|
Min and max values of the AOs for which the integrals are in the cache
|
|
|
|
|
|
`ao_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L112>`_
|
|
Min and max values of the AOs for which the integrals are in the cache
|
|
|
|
|
|
`ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L6>`_
|
|
AO integrals
|
|
|
|
|
|
`ao_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L44>`_
|
|
If |<pq|rs>| < ao_integrals_threshold then <pq|rs> is zero
|
|
|
|
|
|
`ao_l4 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L278>`_
|
|
Computes the product of l values of i,j,k,and l
|
|
|
|
|
|
`bench_maps <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/test_integrals.irp.f#L1>`_
|
|
Performs timing benchmarks on integral access
|
|
|
|
|
|
`bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L19>`_
|
|
Undocumented
|
|
|
|
|
|
`bielec_integrals_index_reverse <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L36>`_
|
|
Undocumented
|
|
|
|
|
|
`clear_ao_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L273>`_
|
|
Frees the memory of the AO map
|
|
|
|
|
|
`clear_mo_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L514>`_
|
|
Frees the memory of the MO map
|
|
|
|
|
|
`compute_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L289>`_
|
|
Compute AO 1/r12 integrals for all i and fixed j,k,l
|
|
|
|
|
|
`compute_ao_integrals_jl <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1174>`_
|
|
Parallel client for AO integrals
|
|
|
|
|
|
`disk_access_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L25>`_
|
|
Read/Write AO integrals from/to disk [ Write | Read | None ]
|
|
|
|
|
|
`disk_access_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L63>`_
|
|
Read/Write MO integrals from/to disk [ Write | Read | None ]
|
|
|
|
|
|
`do_direct_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L6>`_
|
|
Compute integrals on the fly
|
|
|
|
|
|
`dump_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_667#L3>`_
|
|
Save to disk the $ao integrals
|
|
|
|
|
|
`dump_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_667#L137>`_
|
|
Save to disk the $ao integrals
|
|
|
|
|
|
`eri <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L577>`_
|
|
ATOMIC PRIMTIVE bielectronic integral between the 4 primitives ::
|
|
primitive_1 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2)
|
|
primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2)
|
|
primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2)
|
|
primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * r2**2)
|
|
|
|
|
|
`gauleg <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L29>`_
|
|
Gauss-Legendre
|
|
|
|
|
|
`gauleg_t2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L10>`_
|
|
t_w(i,1,k) = w(i)
|
|
t_w(i,2,k) = t(i)
|
|
|
|
|
|
`gauleg_w <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L11>`_
|
|
t_w(i,1,k) = w(i)
|
|
t_w(i,2,k) = t(i)
|
|
|
|
|
|
`general_primitive_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L439>`_
|
|
Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
|
|
|
|
|
|
`get_ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L155>`_
|
|
Gets one AO bi-electronic integral from the AO map
|
|
|
|
|
|
`get_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L194>`_
|
|
Gets multiple AO bi-electronic integral from the AO map .
|
|
All i are retrieved for j,k,l fixed.
|
|
|
|
|
|
`get_ao_bielec_integrals_non_zero <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L222>`_
|
|
Gets multiple AO bi-electronic integral from the AO map .
|
|
All non-zero i are retrieved for j,k,l fixed.
|
|
|
|
|
|
`get_ao_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L264>`_
|
|
Returns the number of elements in the AO map
|
|
|
|
|
|
`get_mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L374>`_
|
|
Returns one integral <ij|kl> in the MO basis
|
|
|
|
|
|
`get_mo_bielec_integral_schwartz <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L405>`_
|
|
Returns one integral <ij|kl> in the MO basis
|
|
|
|
|
|
`get_mo_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L438>`_
|
|
Returns multiple integrals <ij|kl> in the MO basis, all
|
|
i for j,k,l fixed.
|
|
|
|
|
|
`get_mo_bielec_integrals_ij <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L469>`_
|
|
Returns multiple integrals <ij|kl> in the MO basis, all
|
|
i(1)j(2) 1/r12 k(1)l(2)
|
|
i, j for k,l fixed.
|
|
|
|
|
|
`get_mo_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L523>`_
|
|
Return the number of elements in the MO map
|
|
|
|
|
|
`give_polynom_mult_center_x <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L791>`_
|
|
subroutine that returns the explicit polynom in term of the "t"
|
|
variable of the following polynomw :
|
|
I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q)
|
|
|
|
|
|
`i_x1_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L710>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x1_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L854>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x1_pol_mult_a1 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L974>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x1_pol_mult_a2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1028>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x1_pol_mult_recurs <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L888>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x2_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L746>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`i_x2_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1090>`_
|
|
recursive function involved in the bielectronic integral
|
|
|
|
|
|
`insert_into_ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L299>`_
|
|
Create new entry into AO map
|
|
|
|
|
|
`insert_into_mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L313>`_
|
|
Create new entry into MO map, or accumulate in an existing entry
|
|
|
|
|
|
`integrale_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L634>`_
|
|
calculate the integral of the polynom ::
|
|
I_x1(a_x+b_x, c_x+d_x,p,q) * I_x1(a_y+b_y, c_y+d_y,p,q) * I_x1(a_z+b_z, c_z+d_z,p,q)
|
|
between ( 0 ; 1)
|
|
|
|
|
|
`load_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_667#L89>`_
|
|
Read from disk the $ao integrals
|
|
|
|
|
|
`load_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_667#L223>`_
|
|
Read from disk the $ao integrals
|
|
|
|
|
|
`mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L425>`_
|
|
Returns one integral <ij|kl> in the MO basis
|
|
|
|
|
|
`mo_bielec_integral_jj <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L445>`_
|
|
mo_bielec_integral_jj(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange(i,j) = K_ij
|
|
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_jj_anti <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L447>`_
|
|
mo_bielec_integral_jj(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange(i,j) = K_ij
|
|
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_jj_anti_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L313>`_
|
|
mo_bielec_integral_jj_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_jj_exchange <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L446>`_
|
|
mo_bielec_integral_jj(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange(i,j) = K_ij
|
|
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_jj_exchange_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L312>`_
|
|
mo_bielec_integral_jj_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_jj_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L311>`_
|
|
mo_bielec_integral_jj_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
|
|
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
|
|
|
|
|
|
`mo_bielec_integral_mipi <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L472>`_
|
|
<mi|pi> and <mi|pi> - <mi|ip>. Indices are (i,m,p)
|
|
|
|
|
|
`mo_bielec_integral_mipi_anti <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L473>`_
|
|
<mi|pi> and <mi|pi> - <mi|ip>. Indices are (i,m,p)
|
|
|
|
|
|
`mo_bielec_integral_schwartz <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L497>`_
|
|
Needed to compute Schwartz inequalities
|
|
|
|
|
|
`mo_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L22>`_
|
|
If True, the map of MO bielectronic integrals is provided
|
|
|
|
|
|
`mo_bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1>`_
|
|
Computes an unique index for i,j,k,l integrals
|
|
|
|
|
|
`mo_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L340>`_
|
|
Cache of MO integrals for fast access
|
|
|
|
|
|
`mo_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L330>`_
|
|
Min and max values of the MOs for which the integrals are in the cache
|
|
|
|
|
|
`mo_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L329>`_
|
|
Min and max values of the MOs for which the integrals are in the cache
|
|
|
|
|
|
`mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L286>`_
|
|
MO integrals
|
|
|
|
|
|
`mo_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L82>`_
|
|
If |<ij|kl>| < ao_integrals_threshold then <pq|rs> is zero
|
|
|
|
|
|
`n_pt_max_integrals_16 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L1>`_
|
|
Aligned n_pt_max_integrals
|
|
|
|
|
|
`n_pt_sup <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L777>`_
|
|
Returns the upper boundary of the degree of the polynomial involved in the
|
|
bielctronic integral :
|
|
Ix(a_x,b_x,c_x,d_x) * Iy(a_y,b_y,c_y,d_y) * Iz(a_z,b_z,c_z,d_z)
|
|
|
|
|
|
`provide_all_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L526>`_
|
|
Undocumented
|
|
|
|
|
|
`push_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L21>`_
|
|
Push integrals in the push socket
|
|
|
|
|
|
`qp_ao_ints <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/qp_ao_ints.irp.f#L1>`_
|
|
Increments a running calculation to compute AO integrals
|
|
|
|
|
|
`read_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L1>`_
|
|
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
|
|
|
|
|
|
`read_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L2>`_
|
|
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
|
|
|
|
|
|
`write_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L3>`_
|
|
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
|
|
|
|
|
|
`write_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L4>`_
|
|
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
|
|
|