372 KiB
CHAMP Jastrow Factor
- Introduction
- Context
- Computation
- Electron-electron component
- Electron-nucleus component
- Electron-electron-nucleus component
- Electron-electron rescaled distances in $J_\text{eeN}$
- Electron-electron rescaled distances derivatives in $J_\text{eeN}$
- Electron-nucleus rescaled distances in $J_\text{eeN}$
- Electron-nucleus rescaled distances derivatives in $J_\text{eeN}$
- Temporary arrays for electron-electron-nucleus Jastrow $f_{een}$
- Electron-electron-nucleus Jastrow $f_{een}$
- Electron-electron-nucleus Jastrow $f_{een}$ derivative
- Total Jastrow value
Introduction
The Jastrow factor depends on the electronic ($\mathbf{r}$) and nuclear ($\mathbf{R}$) coordinates. Its defined as $\exp(J(\mathbf{r},\mathbf{R}))$, where
\[ J(\mathbf{r},\mathbf{R}) = J_{\text{eN}}(\mathbf{r},\mathbf{R}) + J_{\text{ee}}(\mathbf{r}) + J_{\text{eeN}}(\mathbf{r},\mathbf{R}) \]
In the following, we use the notations $r_{ij} = |\mathbf{r}_i - \mathbf{r}_j|$ and $R_{i\alpha} = |\mathbf{r}_i - \mathbf{R}_\alpha|$.
$J_{\text{eN}}$ contains electron-nucleus terms:
\[ J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{\alpha=1}^{N_\text{nucl}} \sum_{i=1}^{N_\text{elec}} \frac{a_{1\,\alpha}\, f_\alpha(R_{i\alpha})}{1+a_{2\,\alpha}\, f_\alpha(R_{i\alpha})} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1\,\alpha}\, [f_\alpha(R_{i\alpha})]^p - J_{\text{eN}}^{\infty \alpha} \]
$J_{\text{ee}}$ contains electron-electron terms: \[ J_{\text{ee}}(\mathbf{r}) = \sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{\frac{1}{2}(1+\delta^{\uparrow\downarrow}_{ij}) b_1\, f_{\text{ee}}(r_{ij})}{1+b_2\, f_{\text{ee}}(r_{ij})} + \sum_{p=2}^{N_\text{ord}^b} b_{p+1}\, [f_{\text{ee}}(r_{ij})]^p - J_{ee}^\infty \]
and $J_{\text{eeN}}$ contains electron-electron-Nucleus terms:
\[ J_{\text{eeN}}(\mathbf{r},\mathbf{R}) = \sum_{\alpha=1}^{N_{\text{nucl}}} \sum_{i=1}^{N_{\text{elec}}} \sum_{j=1}^{i-1} \sum_{p=2}^{N_{\text{ord}}} \sum_{k=0}^{p-1} \sum_{l=0}^{p-k-2\delta_{k,0}} c_{lkp\alpha} \left[ g_\text{ee}({r}_{ij}) \right]^k \left[ \left[ g_\alpha({R}_{i\alpha}) \right]^l + \left[ g_\alpha({R}_{j\alpha}) \right]^l \right] \left[ g_\alpha({R}_{i\,\alpha}) \, g_\alpha({R}_{j\alpha}) \right]^{(p-k-l)/2} \]
$c_{lkp\alpha}$ are non-zero only when $p-k-l$ is even.
$f$ and $g$ are scaling function defined as
\[ f_\alpha(r) = \frac{1-e^{-\kappa_\alpha\, r}}{\kappa_\alpha} \text{ and } g_\alpha(r) = e^{-\kappa_\alpha\, r} = 1-\kappa_\alpha f_\alpha(r). \]
The terms $J_{\text{ee}}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that $J_{\text{ee}}$ and $J_{\text{eN}}$ have an asymptotic value of zero.
Context
The following data stored in the context:
Variable | Type | In/Out | Description |
---|---|---|---|
uninitialized |
int32_t |
in | Keeps bits set for uninitialized data |
rescale_factor_ee |
double |
in | The distance scaling factor |
rescale_factor_en |
double[type_nucl_num] |
in | The distance scaling factor |
aord_num |
int64_t |
in | The number of a coeffecients |
bord_num |
int64_t |
in | The number of b coeffecients |
cord_num |
int64_t |
in | The number of c coeffecients |
type_nucl_num |
int64_t |
in | Number of Nuclei types |
type_nucl_vector |
int64_t[nucl_num] |
in | IDs of types of Nuclei |
a_vector |
double[aord_num + 1][type_nucl_num] |
in | a polynomial coefficients |
b_vector |
double[bord_num + 1] |
in | b polynomial coefficients |
c_vector |
double[cord_num][type_nucl_num] |
in | c polynomial coefficients |
factor_ee |
double[walker.num] |
out | Jastrow factor: electron-electron part |
factor_ee_date |
uint64_t |
out | Jastrow factor: electron-electron part |
factor_en |
double[walker.num] |
out | Jastrow factor: electron-nucleus part |
factor_en_date |
uint64_t |
out | Jastrow factor: electron-nucleus part |
factor_een |
double[walker.num] |
out | Jastrow factor: electron-electron-nucleus part |
factor_een_date |
uint64_t |
out | Jastrow factor: electron-electron-nucleus part |
factor_ee_deriv_e |
double[4][nelec][walker.num] |
out | Derivative of the Jastrow factor: electron-electron-nucleus part |
factor_ee_deriv_e_date |
uint64_t |
out | Keep track of the date for the derivative |
factor_en_deriv_e |
double[4][nelec][walker.num] |
out | Derivative of the Jastrow factor: electron-electron-nucleus part |
factor_en_deriv_e_date |
uint64_t |
out | Keep track of the date for the en derivative |
factor_een_deriv_e |
double[4][nelec][walker.num] |
out | Derivative of the Jastrow factor: electron-electron-nucleus part |
factor_een_deriv_e_date |
uint64_t |
out | Keep track of the date for the een derivative |
Computed data:
Variable | Type | In/Out | |
---|---|---|---|
dim_c_vector |
int64_t |
Number of unique C coefficients | |
dim_c_vector_date |
uint64_t |
Number of unique C coefficients | |
asymp_jasa |
double[type_nucl_num] |
Asymptotic component | |
asymp_jasa_date |
uint64_t |
Ladt modification of the asymptotic component | |
asymp_jasb |
double[2] |
Asymptotic component (up- or down-spin) | |
asymp_jasb_date |
uint64_t |
Ladt modification of the asymptotic component | |
c_vector_full |
double[dim_c_vector][nucl_num] |
vector of non-zero coefficients | |
c_vector_full_date |
uint64_t |
Keep track of changes here | |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
Transform l,k,p, and m into consecutive indices | |
lkpm_combined_index_date |
uint64_t |
Transform l,k,p, and m into consecutive indices | |
tmp_c |
double[walker.num][cord_num][cord_num+1][nucl_num][elec_num] |
vector of non-zero coefficients | |
dtmp_c |
double[walker.num][elec_num][4][nucl_num][cord_num+1][cord_num] |
vector of non-zero coefficients | |
ee_distance_rescaled |
double[walker.num][num][num] |
Electron-electron rescaled distances | |
ee_distance_rescaled_date |
uint64_t |
Last modification date of the electron-electron distances | |
ee_distance_rescaled_deriv_e |
double[walker.num][4][num][num] |
Electron-electron rescaled distances derivatives | |
ee_distance_rescaled_deriv_e_date |
uint64_t |
Last modification date of the electron-electron distance derivatives | |
en_distance_rescaled |
double[walker.num][nucl_num][num] |
Electron-nucleus distances | |
en_distance_rescaled_date |
uint64_t |
Last modification date of the electron-electron distances | |
en_distance_rescaled_deriv_e |
double[walker.num][4][nucl_num][num] |
Electron-electron rescaled distances derivatives | |
en_distance_rescaled_deriv_e_date |
uint64_t |
Last modification date of the electron-electron distance derivatives | |
een_rescaled_n |
double[walker.num][cord_num+1][nucl_num][elec_num] |
The electron-electron rescaled distances raised to the powers defined by cord | |
een_rescaled_n_date |
uint64_t |
Keep track of the date of creation | |
een_rescaled_e_deriv_e |
double[walker.num][cord_num+1][elec_num][4][elec_num] |
The electron-electron rescaled distances raised to the powers defined by cord derivatives wrt electrons | |
een_rescaled_e_deriv_e_date |
uint64_t |
Keep track of the date of creation | |
een_rescaled_n_deriv_e |
double[walker.num][cord_num+1][nucl_num][4][elec_num] |
The electron-electron rescaled distances raised to the powers defined by cord derivatives wrt electrons | |
een_rescaled_n_deriv_e_date |
uint64_t |
Keep track of the date of creation | |
value |
double[walk_num] |
out | Value of the Jastrow factor |
value_date |
uint64_t |
out | Keep track of the date |
gl |
double[walk_num][4][elec_num] |
out | Gradient and Laplacian of the Jastrow factor |
value_date |
uint64_t |
out | Keep track of the date |
Data structure
typedef struct qmckl_jastrow_champ_struct{
int64_t * restrict lkpm_combined_index;
int64_t * restrict type_nucl_vector;
double * restrict asymp_jasa;
double * restrict asymp_jasb;
double * restrict a_vector;
double * restrict b_vector;
double * restrict c_vector;
double * restrict c_vector_full;
double * restrict dtmp_c;
double * restrict ee_distance_rescaled;
double * restrict ee_distance_rescaled_deriv_e;
double * restrict een_rescaled_e;
double * restrict een_rescaled_e_deriv_e;
double * restrict een_rescaled_n;
double * restrict een_rescaled_n_deriv_e;
double * restrict en_distance_rescaled;
double * restrict en_distance_rescaled_deriv_e;
double * restrict factor_ee;
double * restrict factor_ee_deriv_e;
double * restrict factor_een;
double * restrict factor_een_deriv_e;
double * restrict factor_en;
double * restrict factor_en_deriv_e;
double * restrict rescale_factor_en;
double * restrict tmp_c;
double * restrict value;
double * restrict gl;
int64_t aord_num;
int64_t bord_num;
int64_t cord_num;
int64_t dim_c_vector;
int64_t type_nucl_num;
uint64_t asymp_jasa_date;
uint64_t asymp_jasb_date;
uint64_t c_vector_full_date;
uint64_t dim_c_vector_date;
uint64_t dtmp_c_date;
uint64_t ee_distance_rescaled_date;
uint64_t ee_distance_rescaled_deriv_e_date;
uint64_t een_rescaled_e_date;
uint64_t een_rescaled_e_deriv_e_date;
uint64_t een_rescaled_n_date;
uint64_t een_rescaled_n_deriv_e_date;
uint64_t en_distance_rescaled_date;
uint64_t en_distance_rescaled_deriv_e_date;
uint64_t factor_ee_date;
uint64_t factor_ee_deriv_e_date;
uint64_t factor_een_date;
uint64_t factor_een_deriv_e_date;
uint64_t factor_en_date;
uint64_t factor_en_deriv_e_date;
uint64_t lkpm_combined_index_date;
uint64_t tmp_c_date;
uint64_t value_date;
uint64_t gl_date;
double rescale_factor_ee;
int32_t uninitialized;
bool provided;
} qmckl_jastrow_champ_struct;
The uninitialized
integer contains one bit set to one for each
initialization function which has not been called. It becomes equal
to zero after all initialization functions have been called. The
struct is then initialized and provided == true
.
Some values are initialized by default, and are not concerned by
this mechanism.
qmckl_exit_code qmckl_init_jastrow_champ(qmckl_context context);
qmckl_exit_code qmckl_init_jastrow_champ(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct*) context;
assert (ctx != NULL);
ctx->jastrow_champ.uninitialized = (1 << 10) - 1;
/* Default values */
ctx->jastrow_champ.aord_num = -1;
ctx->jastrow_champ.bord_num = -1;
ctx->jastrow_champ.cord_num = -1;
ctx->jastrow_champ.type_nucl_num = -1;
ctx->jastrow_champ.dim_c_vector = -1;
return QMCKL_SUCCESS;
}
Initialization functions
To prepare for the Jastrow and its derivative, all the following functions need to be called.
qmckl_exit_code qmckl_set_jastrow_champ_rescale_factor_ee (qmckl_context context, const double kappa_ee);
qmckl_exit_code qmckl_set_jastrow_champ_rescale_factor_en (qmckl_context context, const double* kappa_en, const int64_t size_max);
qmckl_exit_code qmckl_set_jastrow_champ_aord_num (qmckl_context context, const int64_t aord_num);
qmckl_exit_code qmckl_set_jastrow_champ_bord_num (qmckl_context context, const int64_t bord_num);
qmckl_exit_code qmckl_set_jastrow_champ_cord_num (qmckl_context context, const int64_t cord_num);
qmckl_exit_code qmckl_set_jastrow_champ_type_nucl_num (qmckl_context context, const int64_t type_nucl_num);
qmckl_exit_code qmckl_set_jastrow_champ_type_nucl_vector (qmckl_context context, const int64_t* type_nucl_vector, const int64_t nucl_num);
qmckl_exit_code qmckl_set_jastrow_champ_a_vector (qmckl_context context, const double * a_vector, const int64_t size_max);
qmckl_exit_code qmckl_set_jastrow_champ_b_vector (qmckl_context context, const double * b_vector, const int64_t size_max);
qmckl_exit_code qmckl_set_jastrow_champ_c_vector (qmckl_context context, const double * c_vector, const int64_t size_max);
#+NAME:pre2
#+NAME:post2
When the required information is completely entered, other data structures are computed to accelerate the calculations. The intermediates factors are precontracted using BLAS LEVEL 3 operations.
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_rescale_factor_ee (context, &
kappa_ee) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
double precision, intent(in), value :: kappa_ee
end function qmckl_set_jastrow_champ_rescale_factor_ee
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_rescale_factor_en (context, &
kappa_en, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(in) :: kappa_en(size_max)
end function qmckl_set_jastrow_champ_rescale_factor_en
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_aord_num (context, &
aord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: aord_num
end function qmckl_set_jastrow_champ_aord_num
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_bord_num (context, &
bord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: bord_num
end function qmckl_set_jastrow_champ_bord_num
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_cord_num (context, &
cord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: cord_num
end function qmckl_set_jastrow_champ_cord_num
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_type_nucl_num (context, &
type_nucl_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: type_nucl_num
end function qmckl_set_jastrow_champ_type_nucl_num
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_type_nucl_vector (context, &
type_nucl_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
integer(c_int64_t), intent(in) :: type_nucl_vector(size_max)
end function qmckl_set_jastrow_champ_type_nucl_vector
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_a_vector(context, &
a_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(in) :: a_vector(size_max)
end function qmckl_set_jastrow_champ_a_vector
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_b_vector(context, &
b_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(in) :: b_vector(size_max)
end function qmckl_set_jastrow_champ_b_vector
integer(qmckl_exit_code) function qmckl_set_jastrow_champ_c_vector(context, &
c_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(in) :: c_vector(size_max)
end function qmckl_set_jastrow_champ_c_vector
end interface
Access functions
Along with these core functions, calculation of the jastrow factor requires the following additional information to be set:
When all the data for the AOs have been provided, the following
function returns true
.
bool qmckl_jastrow_champ_provided (const qmckl_context context);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_rescale_factor_ee (context, &
kappa_ee) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
double precision, intent(out) :: kappa_ee
end function qmckl_get_jastrow_champ_rescale_factor_ee
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_rescale_factor_en (context, &
kappa_en, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: kappa_en(size_max)
end function qmckl_get_jastrow_champ_rescale_factor_en
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_aord_num (context, &
aord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(out) :: aord_num
end function qmckl_get_jastrow_champ_aord_num
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_bord_num (context, &
bord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(out) :: bord_num
end function qmckl_get_jastrow_champ_bord_num
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_cord_num (context, &
cord_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(out) :: cord_num
end function qmckl_get_jastrow_champ_cord_num
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_type_nucl_num (context, &
type_nucl_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(out) :: type_nucl_num
end function qmckl_get_jastrow_champ_type_nucl_num
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_type_nucl_vector (context, &
type_nucl_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context), intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
integer(c_int64_t), intent(out) :: type_nucl_vector(size_max)
end function qmckl_get_jastrow_champ_type_nucl_vector
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_a_vector(context, &
a_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: a_vector(size_max)
end function qmckl_get_jastrow_champ_a_vector
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_b_vector(context, &
b_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: b_vector(size_max)
end function qmckl_get_jastrow_champ_b_vector
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_c_vector(context, &
c_vector, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in) , value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: c_vector(size_max)
end function qmckl_get_jastrow_champ_c_vector
end interface
Test
/* Reference input data */
int64_t walk_num = n2_walk_num;
int64_t elec_num = n2_elec_num;
int64_t elec_up_num = n2_elec_up_num;
int64_t elec_dn_num = n2_elec_dn_num;
int64_t nucl_num = n2_nucl_num;
double rescale_factor_ee = 1.0;
double rescale_factor_en[2] = { 1.0, 1.0 };
double* elec_coord = &(n2_elec_coord[0][0][0]);
const double* nucl_charge = n2_charge;
double* nucl_coord = &(n2_nucl_coord[0][0]);
int64_t size_max;
/* Provide Electron data */
qmckl_exit_code rc;
assert(!qmckl_electron_provided(context));
rc = qmckl_check(context,
qmckl_set_electron_num (context, elec_up_num, elec_dn_num)
);
assert(rc == QMCKL_SUCCESS);
assert(qmckl_electron_provided(context));
rc = qmckl_check(context,
qmckl_set_electron_coord (context, 'N', walk_num, elec_coord, walk_num*3*elec_num)
);
assert(rc == QMCKL_SUCCESS);
double elec_coord2[walk_num*3*elec_num];
rc = qmckl_check(context,
qmckl_get_electron_coord (context, 'N', elec_coord2, walk_num*3*elec_num)
);
assert(rc == QMCKL_SUCCESS);
for (int64_t i=0 ; i<3*elec_num ; ++i) {
assert( elec_coord[i] == elec_coord2[i] );
}
/* Provide Nucleus data */
assert(!qmckl_nucleus_provided(context));
rc = qmckl_check(context,
qmckl_set_nucleus_num (context, nucl_num)
);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_nucleus_provided(context));
double nucl_coord2[3*nucl_num];
rc = qmckl_get_nucleus_coord (context, 'T', nucl_coord2, 3*nucl_num);
assert(rc == QMCKL_NOT_PROVIDED);
rc = qmckl_check(context,
qmckl_set_nucleus_coord (context, 'T', &(nucl_coord[0]), 3*nucl_num)
);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_nucleus_provided(context));
rc = qmckl_check(context,
qmckl_get_nucleus_coord (context, 'N', nucl_coord2, nucl_num*3)
);
assert(rc == QMCKL_SUCCESS);
for (int64_t k=0 ; k<3 ; ++k) {
for (int64_t i=0 ; i<nucl_num ; ++i) {
assert( nucl_coord[nucl_num*k+i] == nucl_coord2[3*i+k] );
}
}
rc = qmckl_check(context,
qmckl_get_nucleus_coord (context, 'T', nucl_coord2, nucl_num*3)
);
assert(rc == QMCKL_SUCCESS);
for (int64_t i=0 ; i<3*nucl_num ; ++i) {
assert( nucl_coord[i] == nucl_coord2[i] );
}
double nucl_charge2[nucl_num];
rc = qmckl_get_nucleus_charge(context, nucl_charge2, nucl_num);
assert(rc == QMCKL_NOT_PROVIDED);
rc = qmckl_check(context,
qmckl_set_nucleus_charge(context, nucl_charge, nucl_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_get_nucleus_charge(context, nucl_charge2, nucl_num)
);
assert(rc == QMCKL_SUCCESS);
for (int64_t i=0 ; i<nucl_num ; ++i) {
assert( nucl_charge[i] == nucl_charge2[i] );
}
assert(qmckl_nucleus_provided(context));
Computation
The computed data is stored in the context so that it can be reused by different kernels. To ensure that the data is valid, for each computed data the date of the context is stored when it is computed. To know if some data needs to be recomputed, we check if the date of the dependencies are more recent than the date of the data to compute. If it is the case, then the data is recomputed and the current date is stored.
Electron-electron component
Asymptotic component
Calculate the asymptotic component asymp_jasb
to be substracted from the
electron-electron jastrow factor \(J_{\text{ee}}\). Two values are
computed. The first one is for antiparallel spin pairs, and the
second one for parallel spin pairs.
\[ J_{\text{ee}}^{\infty} = \frac{\frac{1}{2}(1+\delta^{\uparrow \downarrow})\,b_1 \kappa_\text{ee}^{-1}}{1 + b_2\, \kappa_\text{ee}^{-1}} + \sum_{p=2}^{N_\text{ord}^b} b_{p+1}\, \kappa_\text{ee}^{-p} \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_asymp_jasb(qmckl_context context,
double* const asymp_jasb,
const int64_t size_max);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_asymp_jasb(context, &
asymp_jasb, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: asymp_jasb(size_max)
end function qmckl_get_jastrow_champ_asymp_jasb
end interface
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
bord_num |
int64_t |
in | Order of the polynomial |
b_vector |
double[bord_num+1] |
in | Values of b |
rescale_factor_ee |
double |
in | Electron coordinates |
asymp_jasb |
double[2] |
out | Asymptotic value |
integer function qmckl_compute_jastrow_champ_asymp_jasb_doc_f(context, bord_num, b_vector, rescale_factor_ee, asymp_jasb) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: bord_num
double precision , intent(in) :: b_vector(bord_num + 1)
double precision , intent(in) :: rescale_factor_ee
double precision , intent(out) :: asymp_jasb(2)
integer*8 :: i, p
double precision :: kappa_inv, x, asym_one
kappa_inv = 1.0d0 / rescale_factor_ee
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (bord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
asym_one = b_vector(1) * kappa_inv / (1.0d0 + b_vector(2) * kappa_inv)
asymp_jasb(:) = (/asym_one, 0.5d0 * asym_one/)
do i = 1, 2
x = kappa_inv
do p = 2, bord_num
x = x * kappa_inv
asymp_jasb(i) = asymp_jasb(i) + b_vector(p + 1) * x
end do
end do
end function qmckl_compute_jastrow_champ_asymp_jasb_doc_f
qmckl_exit_code
qmckl_compute_jastrow_champ_asymp_jasb_hpc (const qmckl_context context,
const int64_t bord_num,
const double* b_vector,
const double rescale_factor_ee,
double* const asymp_jasb )
{
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (bord_num < 0) {
return QMCKL_INVALID_ARG_2;
}
const double kappa_inv = 1.0 / rescale_factor_ee;
const double asym_one = b_vector[0] * kappa_inv / (1.0 + b_vector[1] * kappa_inv);
asymp_jasb[0] = asym_one;
asymp_jasb[1] = 0.5 * asym_one;
for (int i = 0 ; i<2 ; ++i) {
double x = kappa_inv;
for (int p = 1; p < bord_num; ++p) {
x *= kappa_inv;
asymp_jasb[i] += b_vector[p+1]*x;
}
}
return QMCKL_SUCCESS;
}
qmckl_exit_code qmckl_compute_jastrow_champ_asymp_jasb (
const qmckl_context context,
const int64_t bord_num,
const double* b_vector,
const double rescale_factor_ee,
double* const asymp_jasb )
{
#ifdef HAVE_HPC
return qmckl_compute_jastrow_champ_asymp_jasb_hpc (context,
bord_num, b_vector, rescale_factor_ee, asymp_jasb);
#else
return qmckl_compute_jastrow_champ_asymp_jasb_doc (context,
bord_num, b_vector, rescale_factor_ee, asymp_jasb);
#endif
}
Test
assert(qmckl_electron_provided(context));
int64_t type_nucl_num = n2_type_nucl_num;
int64_t* type_nucl_vector = &(n2_type_nucl_vector[0]);
int64_t aord_num = n2_aord_num;
int64_t bord_num = n2_bord_num;
int64_t cord_num = n2_cord_num;
double* a_vector = &(n2_a_vector[0][0]);
double* b_vector = &(n2_b_vector[0]);
double* c_vector = &(n2_c_vector[0][0]);
int64_t dim_c_vector=0;
assert(!qmckl_jastrow_champ_provided(context));
/* Set the data */
rc = qmckl_check(context,
qmckl_set_jastrow_champ_aord_num(context, aord_num)
);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_bord_num(context, bord_num)
);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_cord_num(context, cord_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_type_nucl_num(context, type_nucl_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_type_nucl_vector(context, type_nucl_vector, nucl_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_a_vector(context, a_vector,(aord_num+1)*type_nucl_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_b_vector(context, b_vector,(bord_num+1))
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_get_jastrow_champ_dim_c_vector(context, &dim_c_vector)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_c_vector(context, c_vector,dim_c_vector*type_nucl_num)
);
assert(rc == QMCKL_SUCCESS);
double k_ee = 0.;
double k_en[2] = { 0., 0. };
rc = qmckl_check(context,
qmckl_set_jastrow_champ_rescale_factor_en(context, rescale_factor_en, type_nucl_num)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_set_jastrow_champ_rescale_factor_ee(context, rescale_factor_ee)
);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
qmckl_get_jastrow_champ_rescale_factor_ee (context, &k_ee)
);
assert(rc == QMCKL_SUCCESS);
assert(k_ee == rescale_factor_ee);
rc = qmckl_check(context,
qmckl_get_jastrow_champ_rescale_factor_en (context, &(k_en[0]), type_nucl_num)
);
assert(rc == QMCKL_SUCCESS);
for (int i=0 ; i<type_nucl_num ; ++i) {
assert(k_en[i] == rescale_factor_en[i]);
}
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
double asymp_jasb[2];
rc = qmckl_get_jastrow_champ_asymp_jasb(context, asymp_jasb,2);
// calculate asymp_jasb
assert(fabs(asymp_jasb[0]-0.5323750557252571) < 1.e-12);
assert(fabs(asymp_jasb[1]-0.31567342786262853) < 1.e-12);
Electron-electron component
Calculate the electron-electron jastrow component factor_ee
using the asymp_jasb
component and the electron-electron rescaled distances ee_distance_rescaled
.
\[ f_\text{ee} = \sum_{i,j<i} \left[ \frac{\delta_{ij}^{\uparrow\downarrow} B_0\, C_{ij}}{1 - B_1\, C_{ij}} + \sum_{k=2}^{n_\text{ord}} B_k\, C_{ij}^k - {J_{\text{ee}}^{\infty}}_{ij} \right] \]
$\delta$ is the spin factor, $B$ is the vector of $b$ parameters, $C$ is the array of rescaled distances.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_ee(qmckl_context context,
double* const factor_ee,
const int64_t size_max);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_factor_ee (context, &
factor_ee, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: factor_ee(size_max)
end function qmckl_get_jastrow_champ_factor_ee
end interface
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
up_num |
int64_t |
in | Number of alpha electrons |
bord_num |
int64_t |
in | Number of coefficients |
b_vector |
double[bord_num+1] |
in | List of coefficients |
ee_distance_rescaled |
double[walk_num][elec_num][elec_num] |
in | Electron-electron distances |
asymp_jasb |
double[2] |
in | Asymptotic value of the Jastrow |
factor_ee |
double[walk_num] |
out | $f_{ee}$ |
integer function qmckl_compute_factor_ee_doc_f(context, walk_num, elec_num, up_num, bord_num, &
b_vector, ee_distance_rescaled, asymp_jasb, factor_ee) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, bord_num, up_num
double precision , intent(in) :: b_vector(bord_num + 1)
double precision , intent(in) :: ee_distance_rescaled(elec_num, elec_num, walk_num)
double precision , intent(in) :: asymp_jasb(2)
double precision , intent(out) :: factor_ee(walk_num)
integer*8 :: i, j, p, ipar, nw
double precision :: x, power_ser, spin_fact
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (bord_num < 0) then
info = QMCKL_INVALID_ARG_4
return
endif
factor_ee = 0.0d0
do nw =1, walk_num
do j = 1, elec_num
do i = 1, j - 1
x = ee_distance_rescaled(i,j,nw)
power_ser = 0.0d0
spin_fact = 1.0d0
ipar = 1
do p = 2, bord_num
x = x * ee_distance_rescaled(i,j,nw)
power_ser = power_ser + b_vector(p + 1) * x
end do
if(j <= up_num .or. i > up_num) then
spin_fact = 0.5d0
ipar = 2
endif
factor_ee(nw) = factor_ee(nw) + spin_fact * b_vector(1) * &
ee_distance_rescaled(i,j,nw) / &
(1.0d0 + b_vector(2) * &
ee_distance_rescaled(i,j,nw)) &
+ power_ser - asymp_jasb(ipar)
end do
end do
end do
end function qmckl_compute_factor_ee_doc_f
qmckl_exit_code qmckl_compute_factor_ee_hpc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* asymp_jasb,
double* const factor_ee ) {
int ipar;
double x, x1, spin_fact, power_ser;
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (walk_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (elec_num <= 0) {
return QMCKL_INVALID_ARG_3;
}
if (bord_num < 0) {
return QMCKL_INVALID_ARG_4;
}
for (int nw = 0; nw < walk_num; ++nw) {
factor_ee[nw] = 0.0; // put init array here.
size_t ishift = nw * elec_num * elec_num;
for (int i = 0; i < elec_num; ++i ) {
for (int j = 0; j < i; ++j) {
x = ee_distance_rescaled[j + i * elec_num + ishift];
x1 = x;
power_ser = 0.0;
spin_fact = 1.0;
ipar = 0; // index of asymp_jasb
for (int p = 1; p < bord_num; ++p) {
x = x * x1;
power_ser += b_vector[p + 1] * x;
}
if(i < up_num || j >= up_num) {
spin_fact = 0.5;
ipar = 1;
}
factor_ee[nw] += spin_fact * b_vector[0] *
x1 / (1.0 + b_vector[1] * x1)
- asymp_jasb[ipar] + power_ser;
}
}
}
return QMCKL_SUCCESS;
}
qmckl_exit_code
qmckl_compute_factor_ee (const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* asymp_jasb,
double* const factor_ee )
{
#ifdef HAVE_HPC
return qmckl_compute_factor_ee_hpc(context, walk_num, elec_num,
up_num, bord_num, b_vector, ee_distance_rescaled, asymp_jasb,
factor_ee);
#else
return qmckl_compute_factor_ee_doc(context, walk_num, elec_num,
up_num, bord_num, b_vector, ee_distance_rescaled, asymp_jasb,
factor_ee);
#endif
}
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
double factor_ee[walk_num];
rc = qmckl_check(context,
qmckl_get_jastrow_champ_factor_ee(context, factor_ee, walk_num)
);
// calculate factor_ee
printf("%e\n%e\n\n",factor_ee[0],-4.282760865958113 );
assert(fabs(factor_ee[0]+4.282760865958113) < 1.e-12);
Derivative
The derivative of factor_ee
is computed using the ee_distance_rescaled
and
the electron-electron rescaled distances derivatives ee_distance_rescaled_deriv_e
.
There are four components, the gradient which has 3 components in the \(x, y, z\)
directions and the laplacian as the last component.
\[ \nabla_i f_\text{ee} = \frac{1}{2}\sum_{j} \left[\frac{\delta_{ij}^{\uparrow\downarrow} B_0\, \nabla_i C_{ij}}{(1 - B_1\, C_{ij})^2} + \sum^{n_\text{ord}}_{k=2} B_k\, k\, C_{ij}^{k-1} \nabla C_{ij} \right] \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_ee_deriv_e(qmckl_context context,
double* const factor_ee_deriv_e,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
up_num |
int64_t |
in | Number of alpha electrons |
bord_num |
int64_t |
in | Number of coefficients |
b_vector |
double[bord_num+1] |
in | List of coefficients |
ee_distance_rescaled |
double[walk_num][elec_num][elec_num] |
in | Electron-electron distances |
ee_distance_rescaled_deriv_e |
double[walk_num][4][elec_num][elec_num] |
in | Electron-electron distances |
factor_ee_deriv_e |
double[walk_num][4][elec_num] |
out | Electron-electron distances |
integer function qmckl_compute_factor_ee_deriv_e_doc_f( &
context, walk_num, elec_num, up_num, bord_num, &
b_vector, ee_distance_rescaled, ee_distance_rescaled_deriv_e, &
factor_ee_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, bord_num, up_num
double precision , intent(in) :: b_vector(bord_num + 1)
double precision , intent(in) :: ee_distance_rescaled(elec_num, elec_num,walk_num)
double precision , intent(in) :: ee_distance_rescaled_deriv_e(4,elec_num, elec_num,walk_num) !TODO
double precision , intent(out) :: factor_ee_deriv_e(elec_num,4,walk_num)
integer*8 :: i, j, p, nw, ii
double precision :: x, spin_fact, y
double precision :: den, invden, invden2, invden3, xinv
double precision :: lap1, lap2, lap3, third
double precision, dimension(3) :: pow_ser_g
double precision, dimension(4) :: dx
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (bord_num < 0) then
info = QMCKL_INVALID_ARG_4
return
endif
factor_ee_deriv_e = 0.0d0
third = 1.0d0 / 3.0d0
do nw =1, walk_num
do j = 1, elec_num
do i = 1, elec_num
x = ee_distance_rescaled(i,j,nw)
if(abs(x) < 1.0d-18) cycle
pow_ser_g = 0.0d0
spin_fact = 1.0d0
den = 1.0d0 + b_vector(2) * x
invden = 1.0d0 / den
invden2 = invden * invden
invden3 = invden2 * invden
xinv = 1.0d0 / (x + 1.0d-18)
dx(1) = ee_distance_rescaled_deriv_e(1, i, j, nw)
dx(2) = ee_distance_rescaled_deriv_e(2, i, j, nw)
dx(3) = ee_distance_rescaled_deriv_e(3, i, j, nw)
dx(4) = ee_distance_rescaled_deriv_e(4, i, j, nw)
if((i <= up_num .and. j <= up_num ) .OR. &
(i > up_num .and. j > up_num)) then
spin_fact = 0.5d0
endif
lap1 = 0.0d0
lap2 = 0.0d0
lap3 = 0.0d0
do ii = 1, 3
x = ee_distance_rescaled(i, j, nw)
if(abs(x) < 1.0d-18) cycle
do p = 2, bord_num
y = p * b_vector(p + 1) * x
pow_ser_g(ii) = pow_ser_g(ii) + y * dx(ii)
lap1 = lap1 + (p - 1) * y * xinv * dx(ii) * dx(ii)
lap2 = lap2 + y
x = x * ee_distance_rescaled(i, j, nw)
end do
lap3 = lap3 - 2.0d0 * b_vector(2) * dx(ii) * dx(ii)
factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) &
+ spin_fact * b_vector(1) * dx(ii) * invden2 + pow_ser_g(ii)
end do
ii = 4
lap2 = lap2 * dx(ii) * third
lap3 = lap3 + den * dx(ii)
lap3 = lap3 * (spin_fact * b_vector(1) * invden3)
factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) + lap1 + lap2 + lap3
end do
end do
end do
end function qmckl_compute_factor_ee_deriv_e_doc_f
qmckl_exit_code qmckl_compute_factor_ee_deriv_e_hpc(
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* ee_distance_rescaled_deriv_e,
double* const factor_ee_deriv_e ) {
double pow_ser_g[3];
double dx[4];
double x, spin_fact, y;
double den, invden, invden2, invden3, xinv;
double lap1, lap2, lap3, third;
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (walk_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (elec_num <= 0) {
return QMCKL_INVALID_ARG_3;
}
if (bord_num < 0) {
return QMCKL_INVALID_ARG_4;
}
for (int nw = 0; nw < walk_num; ++nw) {
for (int ii = 0; ii < 4; ++ii) {
for (int j = 0; j < elec_num; ++j) {
factor_ee_deriv_e[j + ii * elec_num + nw * elec_num * 4] = 0.0;
}
}
}
third = 1.0 / 3.0;
for (int nw = 0; nw < walk_num; ++nw) {
for (int i = 0; i < elec_num; ++i) {
for (int j = 0; j < elec_num; ++j) {
x = ee_distance_rescaled[j + i * elec_num + nw * elec_num * elec_num];
if (fabs(x) < 1.0e-18) continue;
for (int ii = 0; ii < 3; ++ii){
pow_ser_g[ii] = 0.0;
}
spin_fact = 1.0;
den = 1.0 + b_vector[1] * x;
invden = 1.0 / den;
invden2 = invden * invden;
invden3 = invden2 * invden;
xinv = 1.0 / (x + 1.0e-18);
dx[0] = ee_distance_rescaled_deriv_e[0 \
+ j * 4 + i * 4 * elec_num \
+ nw * 4 * elec_num * elec_num];
dx[1] = ee_distance_rescaled_deriv_e[1 \
+ j * 4 + i * 4 * elec_num \
+ nw * 4 * elec_num * elec_num];
dx[2] = ee_distance_rescaled_deriv_e[2 \
+ j * 4 + i * 4 * elec_num \
+ nw * 4 * elec_num * elec_num];
dx[3] = ee_distance_rescaled_deriv_e[3 \
+ j * 4 + i * 4 * elec_num \
+ nw * 4 * elec_num * elec_num];
if((i <= (up_num-1) && j <= (up_num-1) ) || (i > (up_num-1) && j > (up_num-1))) {
spin_fact = 0.5;
}
lap1 = 0.0;
lap2 = 0.0;
lap3 = 0.0;
for (int ii = 0; ii < 3; ++ii) {
x = ee_distance_rescaled[j + i * elec_num + nw * elec_num * elec_num];
if (fabs(x) < 1.0e-18) continue;
for (int p = 2; p < bord_num+1; ++p) {
y = p * b_vector[(p-1) + 1] * x;
pow_ser_g[ii] = pow_ser_g[ii] + y * dx[ii];
lap1 = lap1 + (p - 1) * y * xinv * dx[ii] * dx[ii];
lap2 = lap2 + y;
x = x * ee_distance_rescaled[j + i * elec_num + nw * elec_num * elec_num];
}
lap3 = lap3 - 2.0 * b_vector[1] * dx[ii] * dx[ii];
factor_ee_deriv_e[i + ii * elec_num + nw * elec_num * 4 ] += \
+ spin_fact * b_vector[0] * dx[ii] * invden2 \
+ pow_ser_g[ii] ;
}
int ii = 3;
lap2 = lap2 * dx[ii] * third;
lap3 = lap3 + den * dx[ii];
lap3 = lap3 * (spin_fact * b_vector[0] * invden3);
factor_ee_deriv_e[i + ii*elec_num + nw * elec_num * 4] += lap1 + lap2 + lap3;
}
}
}
return QMCKL_SUCCESS;
}
qmckl_exit_code qmckl_compute_factor_ee_deriv_e_hpc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* ee_distance_rescaled_deriv_e,
double* const factor_ee_deriv_e );
qmckl_exit_code qmckl_compute_factor_ee_deriv_e_doc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* ee_distance_rescaled_deriv_e,
double* const factor_ee_deriv_e );
qmckl_exit_code qmckl_compute_factor_ee_deriv_e (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t bord_num,
const double* b_vector,
const double* ee_distance_rescaled,
const double* ee_distance_rescaled_deriv_e,
double* const factor_ee_deriv_e ) {
#ifdef HAVE_HPC
return qmckl_compute_factor_ee_deriv_e_hpc(context, walk_num, elec_num, up_num, bord_num, b_vector, ee_distance_rescaled, ee_distance_rescaled_deriv_e, factor_ee_deriv_e );
#else
return qmckl_compute_factor_ee_deriv_e_doc(context, walk_num, elec_num, up_num, bord_num, b_vector, ee_distance_rescaled, ee_distance_rescaled_deriv_e, factor_ee_deriv_e );
#endif
}
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
// calculate factor_ee_deriv_e
double factor_ee_deriv_e[walk_num][4][elec_num];
rc = qmckl_get_jastrow_champ_factor_ee_deriv_e(context, &(factor_ee_deriv_e[0][0][0]),walk_num*4*elec_num);
// check factor_ee_deriv_e
assert(fabs(factor_ee_deriv_e[0][0][0]-0.16364894652107934) < 1.e-12);
assert(fabs(factor_ee_deriv_e[0][1][0]+0.6927548119830084 ) < 1.e-12);
assert(fabs(factor_ee_deriv_e[0][2][0]-0.073267755223968 ) < 1.e-12);
assert(fabs(factor_ee_deriv_e[0][3][0]-1.5111672803213185 ) < 1.e-12);
Electron-electron rescaled distances
ee_distance_rescaled
stores the matrix of the rescaled distances between all
pairs of electrons:
\[ C_{ij} = \frac{ 1 - e^{-\kappa r_{ij}}}{\kappa} \]
where \(r_{ij}\) is the matrix of electron-electron distances.
Get
qmckl_exit_code qmckl_get_jastrow_champ_ee_distance_rescaled(qmckl_context context, double* const distance_rescaled);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
elec_num |
int64_t |
in | Number of electrons |
rescale_factor_ee |
double |
in | Factor to rescale ee distances |
walk_num |
int64_t |
in | Number of walkers |
coord |
double[3][walk_num][elec_num] |
in | Electron coordinates |
ee_distance |
double[walk_num][elec_num][elec_num] |
out | Electron-electron rescaled distances |
integer function qmckl_compute_ee_distance_rescaled_f(context, elec_num, rescale_factor_ee, walk_num, &
coord, ee_distance_rescaled) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
double precision , intent(in) :: rescale_factor_ee
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: coord(elec_num,walk_num,3)
double precision , intent(out) :: ee_distance_rescaled(elec_num,elec_num,walk_num)
integer*8 :: k
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
do k=1,walk_num
info = qmckl_distance_rescaled(context, 'T', 'T', elec_num, elec_num, &
coord(1,k,1), elec_num * walk_num, &
coord(1,k,1), elec_num * walk_num, &
ee_distance_rescaled(1,1,k), elec_num, rescale_factor_ee)
if (info /= QMCKL_SUCCESS) then
exit
endif
end do
end function qmckl_compute_ee_distance_rescaled_f
Test
assert(qmckl_electron_provided(context));
double ee_distance_rescaled[walk_num * elec_num * elec_num];
rc = qmckl_get_jastrow_champ_ee_distance_rescaled(context, ee_distance_rescaled);
// (e1,e2,w)
// (0,0,0) == 0.
assert(ee_distance_rescaled[0] == 0.);
// (1,0,0) == (0,1,0)
assert(ee_distance_rescaled[1] == ee_distance_rescaled[elec_num]);
// value of (1,0,0)
assert(fabs(ee_distance_rescaled[1]-0.5502278003524018) < 1.e-12);
// (0,0,1) == 0.
assert(ee_distance_rescaled[5*elec_num + 5] == 0.);
// (1,0,1) == (0,1,1)
assert(ee_distance_rescaled[5*elec_num+6] == ee_distance_rescaled[6*elec_num+5]);
// value of (1,0,1)
assert(fabs(ee_distance_rescaled[5*elec_num+6]-0.3622098222364193) < 1.e-12);
Electron-electron rescaled distance gradients and Laplacian with respect to electron coordinates
The rescaled distances, represented by $C_{ij} = (1 - e^{-\kappa_\text{e} r_{ij}})/\kappa_\text{e}$
are differentiated with respect to the electron coordinates.
This information is stored in the tensor
ee_distance_rescaled_deriv_e
. The initial three sequential
elements of this three-dimensional tensor provide the $x$, $y$, and $z$
direction derivatives, while the fourth index corresponds to the Laplacian.
Get
qmckl_exit_code qmckl_get_jastrow_champ_ee_distance_rescaled_deriv_e(qmckl_context context, double* const distance_rescaled_deriv_e);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
elec_num |
int64_t |
in | Number of electrons |
rescale_factor_ee |
double |
in | Factor to rescale ee distances |
walk_num |
int64_t |
in | Number of walkers |
coord |
double[3][walk_num][elec_num] |
in | Electron coordinates |
ee_distance_deriv_e |
double[walk_num][4][elec_num][elec_num] |
out | Electron-electron rescaled distance derivatives |
integer function qmckl_compute_ee_distance_rescaled_deriv_e_f(context, elec_num, rescale_factor_ee, walk_num, &
coord, ee_distance_rescaled_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
double precision , intent(in) :: rescale_factor_ee
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: coord(elec_num,walk_num,3)
double precision , intent(out) :: ee_distance_rescaled_deriv_e(4,elec_num,elec_num,walk_num)
integer*8 :: k
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
do k=1,walk_num
info = qmckl_distance_rescaled_deriv_e(context, 'T', 'T', elec_num, elec_num, &
coord(1,k,1), elec_num*walk_num, &
coord(1,k,1), elec_num*walk_num, &
ee_distance_rescaled_deriv_e(1,1,1,k), elec_num, rescale_factor_ee)
if (info /= QMCKL_SUCCESS) then
exit
endif
end do
end function qmckl_compute_ee_distance_rescaled_deriv_e_f
Test
assert(qmckl_electron_provided(context));
double ee_distance_rescaled_deriv_e[4 * walk_num * elec_num * elec_num];
rc = qmckl_get_jastrow_champ_ee_distance_rescaled_deriv_e(context, ee_distance_rescaled_deriv_e);
// TODO: Get exact values
//// (e1,e2,w)
//// (0,0,0) == 0.
//assert(ee_distance[0] == 0.);
//
//// (1,0,0) == (0,1,0)
//assert(ee_distance[1] == ee_distance[elec_num]);
//
//// value of (1,0,0)
//assert(fabs(ee_distance[1]-7.152322512964209) < 1.e-12);
//
//// (0,0,1) == 0.
//assert(ee_distance[elec_num*elec_num] == 0.);
//
//// (1,0,1) == (0,1,1)
//assert(ee_distance[elec_num*elec_num+1] == ee_distance[elec_num*elec_num+elec_num]);
//
//// value of (1,0,1)
//assert(fabs(ee_distance[elec_num*elec_num+1]-6.5517646321055665) < 1.e-12);
Electron-nucleus component
Asymptotic component for
Calculate the asymptotic component asymp_jasa
to be substracted from the final
electron-nucleus jastrow factor \(J_{\text{eN}}\). The asymptotic component is calculated
via the a_vector
and the electron-nucleus rescale factors rescale_factor_en
.
\[ J_{\text{en}}^{\infty \alpha} = \frac{a_1 \kappa_\alpha^{-1}}{1 + a_2 \kappa_\alpha^{-1}} \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_asymp_jasa(qmckl_context context,
double* const asymp_jasa,
const int64_t size_max);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_asymp_jasa(context, &
asymp_jasa, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: asymp_jasa(size_max)
end function qmckl_get_jastrow_champ_asymp_jasa
end interface
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
aord_num |
int64_t |
in | Order of the polynomial |
type_nucl_num |
int64_t |
in | Number of nucleus types |
a_vector |
double[type_nucl_num][aord_num+1] |
in | Values of a |
rescale_factor_en |
double[type_nucl_num] |
in | Electron nucleus distances |
asymp_jasa |
double[type_nucl_num] |
out | Asymptotic value |
integer function qmckl_compute_jastrow_champ_asymp_jasa_f(context, aord_num, type_nucl_num, a_vector, &
rescale_factor_en, asymp_jasa) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: aord_num
integer*8 , intent(in) :: type_nucl_num
double precision , intent(in) :: a_vector(aord_num + 1, type_nucl_num)
double precision , intent(in) :: rescale_factor_en(type_nucl_num)
double precision , intent(out) :: asymp_jasa(type_nucl_num)
integer*8 :: i, j, p
double precision :: kappa_inv, x, asym_one
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (aord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
do i=1,type_nucl_num
kappa_inv = 1.0d0 / rescale_factor_en(i)
asymp_jasa(i) = a_vector(1,i) * kappa_inv / (1.0d0 + a_vector(2,i) * kappa_inv)
x = kappa_inv
do p = 2, aord_num
x = x * kappa_inv
asymp_jasa(i) = asymp_jasa(i) + a_vector(p+1, i) * x
end do
end do
end function qmckl_compute_jastrow_champ_asymp_jasa_f
/*
qmckl_exit_code qmckl_compute_jastrow_champ_asymp_jasa (
const qmckl_context context,
const int64_t aord_num,
const int64_t type_nucl_num,
const double* a_vector,
double* const rescale_factor_en,
double* const asymp_jasa ) {
if (context == QMCKL_NULL_CONTEXT){
return QMCKL_INVALID_CONTEXT;
}
if (aord_num < 0) {
return QMCKL_INVALID_ARG_2;
}
for (int i = 0 ; i <= type_nucl_num; ++i) {
const double kappa_inv = 1.0 / rescale_factor_en[i];
asymp_jasa[i] = a_vector[aord_num*i] * kappa_inv / (1.0 + a_vector[1 + aord_num*i] * kappa_inv);
double x = kappa_inv;
for (int p = 1; p < aord_num; ++p){
x *= kappa_inv;
asymp_jasa[i] = asymp_jasa[i] + a_vector[p + 1 + aord_num*i] * x;
}
}
return QMCKL_SUCCESS;
}
*/
qmckl_exit_code qmckl_compute_jastrow_champ_asymp_jasa (
const qmckl_context context,
const int64_t aord_num,
const int64_t type_nucl_num,
const double* a_vector,
const double* rescale_factor_en,
double* const asymp_jasa );
Test
double asymp_jasa[2];
rc = qmckl_get_jastrow_champ_asymp_jasa(context, asymp_jasa, type_nucl_num);
// calculate asymp_jasb
printf("%e %e\n", asymp_jasa[0], -0.548554);
assert(fabs(-0.548554 - asymp_jasa[0]) < 1.e-12);
Electron-nucleus component
Calculate the electron-electron jastrow component factor_en
using the a_vector
coeffecients and the electron-nucleus rescaled distances en_distance_rescaled
.
\[ f_{\alpha}(R_{i\alpha}) = \sum_{i,j<i} \left\{ \frac{ A_0 C_{ij}}{1 - A_1 C_{ij}} + \sum^{N^\alpha_{\text{ord}}}_{k}A_k C_{ij}^k \right\} \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_en(qmckl_context context,
double* const factor_en,
const int64_t size_max);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_factor_en (context, &
factor_en, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: factor_en(size_max)
end function qmckl_get_jastrow_champ_factor_en
end interface
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
type_nucl_num |
int64_t |
in | Number of unique nuclei |
type_nucl_vector |
int64_t[nucl_num] |
in | IDs of unique nuclei |
aord_num |
int64_t |
in | Number of coefficients |
a_vector |
double[aord_num+1][type_nucl_num] |
in | List of coefficients |
en_distance_rescaled |
double[walk_num][nucl_num][elec_num] |
in | Electron-nucleus distances |
asymp_jasa |
double[type_nucl_num] |
in | Type of nuclei |
factor_en |
double[walk_num] |
out | Electron-nucleus jastrow |
integer function qmckl_compute_factor_en_doc_f( &
context, walk_num, elec_num, nucl_num, type_nucl_num, &
type_nucl_vector, aord_num, a_vector, &
en_distance_rescaled, asymp_jasa, factor_en) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, aord_num, nucl_num, type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
double precision , intent(in) :: a_vector(aord_num + 1, type_nucl_num)
double precision , intent(in) :: en_distance_rescaled(elec_num, nucl_num, walk_num)
double precision , intent(in) :: asymp_jasa(type_nucl_num)
double precision , intent(out) :: factor_en(walk_num)
integer*8 :: i, a, p, nw
double precision :: x, power_ser
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (aord_num < 0) then
info = QMCKL_INVALID_ARG_7
return
endif
do nw =1, walk_num
factor_en(nw) = 0.0d0
do a = 1, nucl_num
do i = 1, elec_num
x = en_distance_rescaled(i, a, nw)
factor_en(nw) = factor_en(nw) + a_vector(1, type_nucl_vector(a)) * x / &
(1.0d0 + a_vector(2, type_nucl_vector(a)) * x) - asymp_jasa(type_nucl_vector(a))
do p = 2, aord_num
x = x * en_distance_rescaled(i, a, nw)
factor_en(nw) = factor_en(nw) + a_vector(p + 1, type_nucl_vector(a)) * x
end do
end do
end do
end do
end function qmckl_compute_factor_en_doc_f
/*
qmckl_exit_code qmckl_compute_factor_en (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t aord_num,
const double* a_vector,
const double* en_distance_rescaled,
const double* asymp_jasa,
double* const factor_en ) {
double x, x1, power_ser;
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (walk_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (elec_num <= 0) {
return QMCKL_INVALID_ARG_3;
}
if (nucl_num <= 0) {
return QMCKL_INVALID_ARG_4;
}
if (type_nucl_num <= 0) {
return QMCKL_INVALID_ARG_5;
}
if (type_nucl_vector == NULL) {
return QMCKL_INVALID_ARG_6;
}
if (aord_num < 0) {
return QMCKL_INVALID_ARG_7;
}
if (a_vector == NULL) {
return QMCKL_INVALID_ARG_8;
}
if (en_distance_rescaled == NULL) {
return QMCKL_INVALID_ARG_9;
}
if (factor_en == NULL) {
return QMCKL_INVALID_ARG_10;
}
for (int nw = 0; nw < walk_num; ++nw ) {
// init array
factor_en[nw] = 0.0;
for (int a = 0; a < nucl_num; ++a ) {
for (int i = 0; i < elec_num; ++i ) {
x = en_distance_rescaled[i + a * elec_num + nw * (elec_num * nucl_num)];
x1 = x;
power_ser = 0.0;
for (int p = 2; p < aord_num+1; ++p) {
x = x * x1;
power_ser = power_ser + a_vector[p+ (type_nucl_vector[a]-1) * aord_num] * x;
}
factor_en[nw] = factor_en[nw] + a_vector[0 + (type_nucl_vector[a]-1)*aord_num] * x1 / \
(1.0 + a_vector[1 + (type_nucl_vector[a]-1) * aord_num] * x1) + \
power_ser;
}
factor_en[nw] = factor_en[nw] + asymp_jasa[type_nucl_vector[a];
}
}
return QMCKL_SUCCESS;
}
*/
qmckl_exit_code qmckl_compute_factor_en (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t aord_num,
const double* a_vector,
const double* en_distance_rescaled,
const double* asymp_jasa,
double* const factor_en );
qmckl_exit_code qmckl_compute_factor_en_doc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t aord_num,
const double* a_vector,
const double* en_distance_rescaled,
const double* asymp_jasa,
double* const factor_en );
qmckl_exit_code qmckl_compute_factor_en (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t aord_num,
const double* a_vector,
const double* en_distance_rescaled,
const double* asymp_jasa,
double* const factor_en )
{
#ifdef HAVE_HPC
return qmckl_compute_factor_en_doc (context, walk_num, elec_num, nucl_num, type_nucl_num,
type_nucl_vector, aord_num, a_vector, en_distance_rescaled,
asymp_jasa, factor_en );
#else
return qmckl_compute_factor_en_doc (context, walk_num, elec_num, nucl_num, type_nucl_num,
type_nucl_vector, aord_num, a_vector, en_distance_rescaled,
asymp_jasa, factor_en );
#endif
}
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
double factor_en[walk_num];
rc = qmckl_get_jastrow_champ_factor_en(context, factor_en,walk_num);
// calculate factor_en
assert(fabs(5.1052574308112755 - factor_en[0]) < 1.e-12);
Derivative
Calculate the electron-electron jastrow component factor_en_deriv_e
derivative
with respect to the electron coordinates using the en_distance_rescaled
and
en_distance_rescaled_deriv_e
which are already calculated previously.
TODO: write equations.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_en_deriv_e(qmckl_context context,
double* const factor_en_deriv_e,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
type_nucl_num |
int64_t |
in | Number of unique nuclei |
type_nucl_vector |
int64_t[nucl_num] |
in | IDs of unique nuclei |
aord_num |
int64_t |
in | Number of coefficients |
a_vector |
double[aord_num+1][type_nucl_num] |
in | List of coefficients |
en_distance_rescaled |
double[walk_num][nucl_num][elec_num] |
in | Electron-nucleus distances |
en_distance_rescaled_deriv_e |
double[walk_num][4][nucl_num][elec_num] |
in | Electron-nucleus distance derivatives |
factor_en_deriv_e |
double[walk_num][4][elec_num] |
out | Electron-nucleus jastrow |
integer function qmckl_compute_factor_en_deriv_e_f( &
context, walk_num, elec_num, nucl_num, type_nucl_num, &
type_nucl_vector, aord_num, a_vector, &
en_distance_rescaled, en_distance_rescaled_deriv_e, factor_en_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, aord_num, nucl_num, type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
double precision , intent(in) :: a_vector(aord_num + 1, type_nucl_num)
double precision , intent(in) :: en_distance_rescaled(elec_num, nucl_num, walk_num)
double precision , intent(in) :: en_distance_rescaled_deriv_e(4, elec_num, nucl_num, walk_num)
double precision , intent(out) :: factor_en_deriv_e(elec_num,4,walk_num)
integer*8 :: i, a, p, ipar, nw, ii
double precision :: x, den, invden, invden2, invden3, xinv
double precision :: y, lap1, lap2, lap3, third
double precision, dimension(3) :: power_ser_g
double precision, dimension(4) :: dx
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (aord_num < 0) then
info = QMCKL_INVALID_ARG_7
return
endif
factor_en_deriv_e = 0.0d0
third = 1.0d0 / 3.0d0
do nw =1, walk_num
do a = 1, nucl_num
do i = 1, elec_num
x = en_distance_rescaled(i,a,nw)
if(abs(x) < 1.0d-18) continue
power_ser_g = 0.0d0
den = 1.0d0 + a_vector(2, type_nucl_vector(a)) * x
invden = 1.0d0 / den
invden2 = invden * invden
invden3 = invden2 * invden
xinv = 1.0d0 / x
do ii = 1, 4
dx(ii) = en_distance_rescaled_deriv_e(ii,i,a,nw)
end do
lap1 = 0.0d0
lap2 = 0.0d0
lap3 = 0.0d0
do ii = 1, 3
x = en_distance_rescaled(i, a, nw)
do p = 2, aord_num
y = p * a_vector(p + 1, type_nucl_vector(a)) * x
power_ser_g(ii) = power_ser_g(ii) + y * dx(ii)
lap1 = lap1 + (p - 1) * y * xinv * dx(ii) * dx(ii)
lap2 = lap2 + y
x = x * en_distance_rescaled(i, a, nw)
end do
lap3 = lap3 - 2.0d0 * a_vector(2, type_nucl_vector(a)) * dx(ii) * dx(ii)
factor_en_deriv_e(i, ii, nw) = factor_en_deriv_e(i, ii, nw) + a_vector(1, type_nucl_vector(a)) &
,* dx(ii) * invden2 &
+ power_ser_g(ii)
end do
ii = 4
lap2 = lap2 * dx(ii) * third
lap3 = lap3 + den * dx(ii)
lap3 = lap3 * a_vector(1, type_nucl_vector(a)) * invden3
factor_en_deriv_e(i, ii, nw) = factor_en_deriv_e(i, ii, nw) + lap1 + lap2 + lap3
end do
end do
end do
end function qmckl_compute_factor_en_deriv_e_f
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
// calculate factor_en_deriv_e
double factor_en_deriv_e[walk_num][4][elec_num];
rc = qmckl_get_jastrow_champ_factor_en_deriv_e(context, &(factor_en_deriv_e[0][0][0]),walk_num*4*elec_num);
// check factor_en_deriv_e
assert(fabs(factor_en_deriv_e[0][0][0]-0.11609919541763383) < 1.e-12);
assert(fabs(factor_en_deriv_e[0][1][0]+0.23301394780804574) < 1.e-12);
assert(fabs(factor_en_deriv_e[0][2][0]-0.17548337641865783) < 1.e-12);
assert(fabs(factor_en_deriv_e[0][3][0]+0.9667363412285741 ) < 1.e-12);
Electron-nucleus rescaled distances
en_distance_rescaled
stores the matrix of the rescaled distances between
electrons and nuclei.
\[ C_{i\alpha} = \frac{ 1 - e^{-\kappa_\alpha R_{i\alpha}}}{\kappa_\alpha} \]
where \(R_{i\alpha}\) is the matrix of electron-nucleus distances.
Get
qmckl_exit_code qmckl_get_electron_en_distance_rescaled(qmckl_context context, double* distance_rescaled);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
type_nucl_num |
int64_t |
in | Number of types of nuclei |
type_nucl_vector |
int64_t[nucl_num] |
in | Number of types of nuclei |
rescale_factor_en |
double[type_nucl_num] |
in | The factor for rescaled distances |
walk_num |
int64_t |
in | Number of walkers |
elec_coord |
double[3][walk_num][elec_num] |
in | Electron coordinates |
nucl_coord |
double[3][elec_num] |
in | Nuclear coordinates |
en_distance_rescaled |
double[walk_num][nucl_num][elec_num] |
out | Electron-nucleus distances |
integer function qmckl_compute_en_distance_rescaled_f(context, elec_num, nucl_num, type_nucl_num, &
type_nucl_vector, rescale_factor_en, walk_num, elec_coord, &
nucl_coord, en_distance_rescaled) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
double precision , intent(in) :: rescale_factor_en(type_nucl_num)
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: elec_coord(elec_num,walk_num,3)
double precision , intent(in) :: nucl_coord(nucl_num,3)
double precision , intent(out) :: en_distance_rescaled(elec_num,nucl_num,walk_num)
integer*8 :: i, k
double precision :: coord(3)
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_5
return
endif
do i=1, nucl_num
coord(1:3) = nucl_coord(i,1:3)
do k=1,walk_num
info = qmckl_distance_rescaled(context, 'T', 'T', elec_num, 1_8, &
elec_coord(1,k,1), elec_num*walk_num, coord, 1_8, &
en_distance_rescaled(1,i,k), elec_num, rescale_factor_en(type_nucl_vector(i)))
if (info /= QMCKL_SUCCESS) then
return
endif
end do
end do
end function qmckl_compute_en_distance_rescaled_f
Test
assert(qmckl_electron_provided(context));
assert(qmckl_nucleus_provided(context));
double en_distance_rescaled[walk_num][nucl_num][elec_num];
rc = qmckl_check(context,
qmckl_get_electron_en_distance_rescaled(context, &(en_distance_rescaled[0][0][0]))
);
assert (rc == QMCKL_SUCCESS);
// (e,n,w) in Fortran notation
// (1,1,1)
assert(fabs(en_distance_rescaled[0][0][0] - 0.4435709484118112) < 1.e-12);
// (1,2,1)
assert(fabs(en_distance_rescaled[0][1][0] - 0.8993601506374442) < 1.e-12);
// (2,1,1)
assert(fabs(en_distance_rescaled[0][0][1] - 0.46760219699910477) < 1.e-12);
// (1,1,2)
assert(fabs(en_distance_rescaled[0][0][5] - 0.1875631834682101) < 1.e-12);
// (1,2,2)
assert(fabs(en_distance_rescaled[0][1][5] - 0.8840716589810682) < 1.e-12);
// (2,1,2)
assert(fabs(en_distance_rescaled[0][0][6] - 0.42640469987268914) < 1.e-12);
Electron-electron rescaled distance gradients and Laplacian with respect to electron coordinates
The rescaled distances, represented by $C_{i\alpha} = (1 - e^{-\kappa_\alpha R_{i\alpha}})/\kappa$
are differentiated with respect to the electron coordinates.
This information is stored in the tensor
en_distance_rescaled_deriv_e
. The initial three sequential
elements of this three-index tensor provide the $x$, $y$, and $z$
direction derivatives, while the fourth index corresponds to the Laplacian.
Get
qmckl_exit_code qmckl_get_electron_en_distance_rescaled_deriv_e(qmckl_context context, double* distance_rescaled_deriv_e);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
type_nucl_num |
int64_t |
in | Number of nucleus types |
type_nucl_vector |
int64_t[nucl_num] |
in | Array of nucleus types |
rescale_factor_en |
double[nucl_num] |
in | The factors for rescaled distances |
walk_num |
int64_t |
in | Number of walkers |
elec_coord |
double[3][walk_num][elec_num] |
in | Electron coordinates |
nucl_coord |
double[3][elec_num] |
in | Nuclear coordinates |
en_distance_rescaled_deriv_e |
double[walk_num][nucl_num][elec_num][4] |
out | Electron-nucleus distance derivatives |
integer function qmckl_compute_en_distance_rescaled_deriv_e_f(context, elec_num, nucl_num, &
type_nucl_num, type_nucl_vector, rescale_factor_en, walk_num, elec_coord, &
nucl_coord, en_distance_rescaled_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
double precision , intent(in) :: rescale_factor_en(nucl_num)
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: elec_coord(elec_num,walk_num,3)
double precision , intent(in) :: nucl_coord(nucl_num,3)
double precision , intent(out) :: en_distance_rescaled_deriv_e(4,elec_num,nucl_num,walk_num)
integer*8 :: i, k
double precision :: coord(3)
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_5
return
endif
do i=1, nucl_num
coord(1:3) = nucl_coord(i,1:3)
do k=1,walk_num
info = qmckl_distance_rescaled_deriv_e(context, 'T', 'T', elec_num, 1_8, &
elec_coord(1,k,1), elec_num*walk_num, coord, 1_8, &
en_distance_rescaled_deriv_e(1,1,i,k), elec_num, rescale_factor_en(type_nucl_vector(i)))
if (info /= QMCKL_SUCCESS) then
return
endif
end do
end do
end function qmckl_compute_en_distance_rescaled_deriv_e_f
Test
assert(qmckl_electron_provided(context));
assert(qmckl_nucleus_provided(context));
double en_distance_rescaled_deriv_e[walk_num][4][nucl_num][elec_num];
rc = qmckl_check(context,
qmckl_get_electron_en_distance_rescaled_deriv_e(context, &(en_distance_rescaled_deriv_e[0][0][0][0]))
);
assert (rc == QMCKL_SUCCESS);
// TODO: check exact values
//// (e,n,w) in Fortran notation
//// (1,1,1)
//assert(fabs(en_distance_rescaled[0][0][0] - 7.546738741619978) < 1.e-12);
//
//// (1,2,1)
//assert(fabs(en_distance_rescaled[0][1][0] - 8.77102435246984) < 1.e-12);
//
//// (2,1,1)
//assert(fabs(en_distance_rescaled[0][0][1] - 3.698922010513608) < 1.e-12);
//
//// (1,1,2)
//assert(fabs(en_distance_rescaled[1][0][0] - 5.824059436060509) < 1.e-12);
//
//// (1,2,2)
//assert(fabs(en_distance_rescaled[1][1][0] - 7.080482110317645) < 1.e-12);
//
//// (2,1,2)
//assert(fabs(en_distance_rescaled[1][0][1] - 3.1804527583077356) < 1.e-12);
Electron-electron-nucleus component
Electron-electron rescaled distances in $J_\text{eeN}$
een_rescaled_e
stores the table of the rescaled distances between all
pairs of electrons and raised to the power \(p\) defined by cord_num
:
\[ C_{ij,p} = \left[ \exp\left(-\kappa_\text{e}\, r_{ij}\right) \right]^p \]
where \(r_{ij}\) is the matrix of electron-electron distances.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_een_rescaled_e(qmckl_context context,
double* const distance_rescaled,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
cord_num |
int64_t |
in | Order of polynomials |
rescale_factor_ee |
double |
in | Factor to rescale ee distances |
ee_distance |
double[walk_num][elec_num][elec_num] |
in | Electron-electron distances for each walker |
een_rescaled_e |
double[walk_num][0:cord_num][elec_num][elec_num] |
out | Electron-electron rescaled distances for each walker |
integer function qmckl_compute_een_rescaled_e_doc_f( &
context, walk_num, elec_num, cord_num, rescale_factor_ee, &
ee_distance, een_rescaled_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: cord_num
double precision , intent(in) :: rescale_factor_ee
double precision , intent(in) :: ee_distance(elec_num,elec_num,walk_num)
double precision , intent(out) :: een_rescaled_e(elec_num,elec_num,0:cord_num,walk_num)
double precision,dimension(:,:),allocatable :: een_rescaled_e_ij
double precision :: x
integer*8 :: i, j, k, l, nw
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_4
return
endif
allocate(een_rescaled_e_ij(elec_num * (elec_num - 1) / 2, cord_num + 1))
! Prepare table of exponentiated distances raised to appropriate power
een_rescaled_e = 0.0d0
do nw = 1, walk_num
een_rescaled_e_ij = 0.0d0
een_rescaled_e_ij(:, 1) = 1.0d0
k = 0
do j = 1, elec_num
do i = 1, j - 1
k = k + 1
een_rescaled_e_ij(k, 2) = dexp(-rescale_factor_ee * ee_distance(i, j, nw))
end do
end do
do l = 2, cord_num
do k = 1, elec_num * (elec_num - 1)/2
een_rescaled_e_ij(k, l + 1) = een_rescaled_e_ij(k, l) * een_rescaled_e_ij(k, 2)
end do
end do
! prepare the actual een table
een_rescaled_e(:, :, 0, nw) = 1.0d0
do l = 1, cord_num
k = 0
do j = 1, elec_num
do i = 1, j - 1
k = k + 1
x = een_rescaled_e_ij(k, l + 1)
een_rescaled_e(i, j, l, nw) = x
een_rescaled_e(j, i, l, nw) = x
end do
end do
end do
do l = 0, cord_num
do j = 1, elec_num
een_rescaled_e(j, j, l, nw) = 0.0d0
end do
end do
end do
end function qmckl_compute_een_rescaled_e_doc_f
qmckl_exit_code qmckl_compute_een_rescaled_e_hpc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t cord_num,
const double rescale_factor_ee,
const double* ee_distance,
double* const een_rescaled_e ) {
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (walk_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (elec_num <= 0) {
return QMCKL_INVALID_ARG_3;
}
if (cord_num < 0) {
return QMCKL_INVALID_ARG_4;
}
// Prepare table of exponentiated distances raised to appropriate power
// init
for (int kk = 0; kk < walk_num*(cord_num+1)*elec_num*elec_num; ++kk) {
een_rescaled_e[kk]= 0.0;
}
double x;
const int64_t elec_pairs = (elec_num * (elec_num - 1)) / 2;
const int64_t len_een_ij = elec_pairs * (cord_num + 1);
// number of elements for the een_rescaled_e_ij[N_e*(N_e-1)/2][cord+1]
// probably in C is better [cord+1, Ne*(Ne-1)/2]
// elec_pairs = (elec_num * (elec_num - 1)) / 2;
// len_een_ij = elec_pairs * (cord_num + 1);
double* een_rescaled_e_ij = (double *) malloc (len_een_ij * sizeof(double));
if (een_rescaled_e_ij == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_compute_een_rescaled_e_hpc",
NULL);
}
/*
for (int nw = 0; nw < walk_num; ++nw) {
for (int l = 0; l < (cord_num + 1); ++l) {
for (int i = 0; i < elec_num; ++i) {
for (int j = 0; j < elec_num; ++j) {
een_rescaled_e[j + i*elec_num + l*elec_num*elec_num + nw*(cord_num+1)*elec_num*elec_num]= 0.0;
}
}
}
}
*/
for (int nw = 0; nw < walk_num; ++nw) {
for (int kk = 0; kk < len_een_ij; ++kk) {
// this array initialized at 0 except een_rescaled_e_ij(:, 1) = 1.0d0
// and the arrangement of indices is [cord_num+1, ne*(ne-1)/2]
een_rescaled_e_ij[kk]= ( kk < (elec_pairs) ? 1.0 : 0.0 );
}
int64_t kk = 0;
for (int i = 0; i < elec_num; ++i) {
for (int j = 0; j < i; ++j) {
// een_rescaled_e_ij(kk, 2) = dexp(-rescale_factor_ee * ee_distance(i, j, nw));
een_rescaled_e_ij[kk + elec_pairs] = exp(-rescale_factor_ee * \
ee_distance[j + i*elec_num + nw*(elec_num*elec_num)]);
kk += 1;
}
}
for (int l = 2; l < (cord_num+1); ++l) {
for (int k = 0; k < elec_pairs; ++k) {
// een_rescaled_e_ij(k, l + 1) = een_rescaled_e_ij(k, l + 1 - 1) * een_rescaled_e_ij(k, 2)
een_rescaled_e_ij[k+l*elec_pairs] = een_rescaled_e_ij[k + (l - 1)*elec_pairs] * \
een_rescaled_e_ij[k + elec_pairs];
}
}
// prepare the actual een table
for (int i = 0; i < elec_num; ++i){
for (int j = 0; j < elec_num; ++j) {
een_rescaled_e[j + i*elec_num + 0 + nw*(cord_num+1)*elec_num*elec_num] = 1.0;
}
}
// Up to here it should work.
for ( int l = 1; l < (cord_num+1); ++l) {
int k = 0;
for (int i = 0; i < elec_num; ++i) {
for (int j = 0; j < i; ++j) {
x = een_rescaled_e_ij[k + l*elec_pairs];
een_rescaled_e[j + i*elec_num + l*elec_num*elec_num + nw*elec_num*elec_num*(cord_num+1)] = x;
een_rescaled_e[i + j*elec_num + l*elec_num*elec_num + nw*elec_num*elec_num*(cord_num+1)] = x;
k = k + 1;
}
}
}
for (int l = 0; l < (cord_num + 1); ++l) {
for (int j = 0; j < elec_num; ++j) {
een_rescaled_e[j + j*elec_num + l*elec_num*elec_num + nw*elec_num*elec_num*(cord_num+1)] = 0.0;
}
}
}
free(een_rescaled_e_ij);
return QMCKL_SUCCESS;
}
qmckl_exit_code qmckl_compute_een_rescaled_e_doc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t cord_num,
const double rescale_factor_ee,
const double* ee_distance,
double* const een_rescaled_e );
qmckl_exit_code qmckl_compute_een_rescaled_e_hpc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t cord_num,
const double rescale_factor_ee,
const double* ee_distance,
double* const een_rescaled_e );
qmckl_exit_code qmckl_compute_een_rescaled_e (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t cord_num,
const double rescale_factor_ee,
const double* ee_distance,
double* const een_rescaled_e ) {
#ifdef HAVE_HPC
return qmckl_compute_een_rescaled_e_hpc(context, walk_num, elec_num, cord_num, rescale_factor_ee, ee_distance, een_rescaled_e);
#else
return qmckl_compute_een_rescaled_e_doc(context, walk_num, elec_num, cord_num, rescale_factor_ee, ee_distance, een_rescaled_e);
#endif
}
Test
assert(qmckl_electron_provided(context));
double een_rescaled_e[walk_num][(cord_num + 1)][elec_num][elec_num];
rc = qmckl_get_jastrow_champ_een_rescaled_e(context, &(een_rescaled_e[0][0][0][0]),elec_num*elec_num*(cord_num+1)*walk_num);
// value of (0,2,1)
assert(fabs(een_rescaled_e[0][1][0][2]-0.08084493981483197) < 1.e-12);
assert(fabs(een_rescaled_e[0][1][0][3]-0.1066745707571846) < 1.e-12);
assert(fabs(een_rescaled_e[0][1][0][4]-0.01754273169464735) < 1.e-12);
assert(fabs(een_rescaled_e[0][2][1][3]-0.02214680362033448) < 1.e-12);
assert(fabs(een_rescaled_e[0][2][1][4]-0.0005700154999202759) < 1.e-12);
assert(fabs(een_rescaled_e[0][2][1][5]-0.3424402276009091) < 1.e-12);
Electron-electron rescaled distances derivatives in $J_\text{eeN}$
een_rescaled_e_deriv_e
stores the table of the derivatives of the
rescaled distances between all pairs of electrons and raised to the
power $p$ defined by cord_num
. Here we take its derivatives
required for the een jastrow_champ.
\[ \frac{\partial}{\partial x} \left[ {g_\text{e}(r)}\right]^p = -\frac{x}{r} \kappa_\text{e}\, p\,\left[ {g_\text{e}(r)}\right]^p \] \[ \Delta \left[ {g_\text{e}(r)}\right]^p = \frac{2}{r} \kappa_\text{e}\, p\,\left[ {g_\text{e}(r)}\right]^p \right] + \left(\frac{\partial}{\partial x}\left[ {g_\text{e}(r)}\right]^p \right)^2 + \left(\frac{\partial}{\partial y}\left[ {g_\text{e}(r)}\right]^p \right)^2 + \left(\frac{\partial}{\partial z}\left[ {g_\text{e}(r)}\right]^p \right)^2 \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_een_rescaled_e_deriv_e(qmckl_context context,
double* const distance_rescaled,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
cord_num |
int64_t |
in | Order of polynomials |
rescale_factor_ee |
double |
in | Factor to rescale ee distances |
coord_ee |
double[walk_num][3][elec_num] |
in | Electron coordinates |
ee_distance |
double[walk_num][elec_num][elec_num] |
in | Electron-electron distances |
een_rescaled_e |
double[walk_num][0:cord_num][elec_num][elec_num] |
in | Electron-electron distances |
een_rescaled_e_deriv_e |
double[walk_num][0:cord_num][elec_num][4][elec_num] |
out | Electron-electron rescaled distances |
integer function qmckl_compute_factor_een_rescaled_e_deriv_e_f( &
context, walk_num, elec_num, cord_num, rescale_factor_ee, &
coord_ee, ee_distance, een_rescaled_e, een_rescaled_e_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: cord_num
double precision , intent(in) :: rescale_factor_ee
double precision , intent(in) :: coord_ee(elec_num,3,walk_num)
double precision , intent(in) :: ee_distance(elec_num,elec_num,walk_num)
double precision , intent(in) :: een_rescaled_e(elec_num,elec_num,0:cord_num,walk_num)
double precision , intent(out) :: een_rescaled_e_deriv_e(elec_num,4,elec_num,0:cord_num,walk_num)
double precision,dimension(:,:,:),allocatable :: elec_dist_deriv_e
double precision :: x, rij_inv, kappa_l
integer*8 :: i, j, k, l, nw, ii
allocate(elec_dist_deriv_e(4,elec_num,elec_num))
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_4
return
endif
! Prepare table of exponentiated distances raised to appropriate power
een_rescaled_e_deriv_e = 0.0d0
do nw = 1, walk_num
do j = 1, elec_num
do i = 1, elec_num
rij_inv = 1.0d0 / ee_distance(i, j, nw)
do ii = 1, 3
elec_dist_deriv_e(ii, i, j) = (coord_ee(i, ii, nw) - coord_ee(j, ii, nw)) * rij_inv
end do
elec_dist_deriv_e(4, i, j) = 2.0d0 * rij_inv
end do
elec_dist_deriv_e(:, j, j) = 0.0d0
end do
! prepare the actual een table
do l = 1, cord_num
kappa_l = - dble(l) * rescale_factor_ee
do j = 1, elec_num
do i = 1, elec_num
een_rescaled_e_deriv_e(i, 1, j, l, nw) = kappa_l * elec_dist_deriv_e(1, i, j)
een_rescaled_e_deriv_e(i, 2, j, l, nw) = kappa_l * elec_dist_deriv_e(2, i, j)
een_rescaled_e_deriv_e(i, 3, j, l, nw) = kappa_l * elec_dist_deriv_e(3, i, j)
een_rescaled_e_deriv_e(i, 4, j, l, nw) = kappa_l * elec_dist_deriv_e(4, i, j)
een_rescaled_e_deriv_e(i, 4, j, l, nw) = een_rescaled_e_deriv_e(i, 4, j, l, nw) &
+ een_rescaled_e_deriv_e(i, 1, j, l, nw) * een_rescaled_e_deriv_e(i, 1, j, l, nw) &
+ een_rescaled_e_deriv_e(i, 2, j, l, nw) * een_rescaled_e_deriv_e(i, 2, j, l, nw) &
+ een_rescaled_e_deriv_e(i, 3, j, l, nw) * een_rescaled_e_deriv_e(i, 3, j, l, nw)
een_rescaled_e_deriv_e(i, 1, j, l, nw) = een_rescaled_e_deriv_e(i, 1, j, l, nw) * &
een_rescaled_e(i, j, l, nw)
een_rescaled_e_deriv_e(i, 3, j, l, nw) = een_rescaled_e_deriv_e(i, 2, j, l, nw) * &
een_rescaled_e(i, j, l, nw)
een_rescaled_e_deriv_e(i, 3, j, l, nw) = een_rescaled_e_deriv_e(i, 3, j, l, nw) * &
een_rescaled_e(i, j, l, nw)
een_rescaled_e_deriv_e(i, 4, j, l, nw) = een_rescaled_e_deriv_e(i, 4, j, l, nw) * &
een_rescaled_e(i, j, l, nw)
end do
end do
end do
end do
end function qmckl_compute_factor_een_rescaled_e_deriv_e_f
Test
double een_rescaled_e_deriv_e[walk_num][(cord_num + 1)][elec_num][4][elec_num];
size_max=walk_num*(cord_num + 1)*elec_num*4*elec_num;
rc = qmckl_get_jastrow_champ_een_rescaled_e_deriv_e(context,
&(een_rescaled_e_deriv_e[0][0][0][0][0]),size_max);
// value of (0,0,0,2,1)
assert(fabs(een_rescaled_e_deriv_e[0][1][0][0][2] + 0.05991352796887283 ) < 1.e-12);
assert(fabs(een_rescaled_e_deriv_e[0][1][0][0][3] + 0.011714035071545248 ) < 1.e-12);
assert(fabs(een_rescaled_e_deriv_e[0][1][0][0][4] + 0.00441398875758468 ) < 1.e-12);
assert(fabs(een_rescaled_e_deriv_e[0][2][1][0][3] + 0.013553180060167595 ) < 1.e-12);
assert(fabs(een_rescaled_e_deriv_e[0][2][1][0][4] + 0.00041342909359870457) < 1.e-12);
assert(fabs(een_rescaled_e_deriv_e[0][2][1][0][5] + 0.5880599146214673 ) < 1.e-12);
Electron-nucleus rescaled distances in $J_\text{eeN}$
een_rescaled_n
stores the table of the rescaled distances between
electrons and nuclei raised to the power \(p\) defined by cord_num
:
\[ C_{i\alpha,p} = \left[ \exp\left(-\kappa_\alpha\, R_{i\alpha}\right) \right]^p \]
where \(R_{i\alpha}\) is the matrix of electron-nucleus distances.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_een_rescaled_n(qmckl_context context,
double* const distance_rescaled,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of atoms |
type_nucl_num |
int64_t |
in | Number of atom types |
type_nucl_vector |
int64_t[nucl_num] |
in | Types of atoms |
cord_num |
int64_t |
in | Order of polynomials |
rescale_factor_en |
double[nucl_num] |
in | Factor to rescale ee distances |
en_distance |
double[walk_num][elec_num][nucl_num] |
in | Electron-nucleus distances |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
out | Electron-nucleus rescaled distances |
integer function qmckl_compute_een_rescaled_n_f( &
context, walk_num, elec_num, nucl_num, &
type_nucl_num, type_nucl_vector, cord_num, rescale_factor_en, &
en_distance, een_rescaled_n) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
integer*8 , intent(in) :: cord_num
double precision , intent(in) :: rescale_factor_en(type_nucl_num)
double precision , intent(in) :: en_distance(nucl_num,elec_num,walk_num)
double precision , intent(out) :: een_rescaled_n(elec_num,nucl_num,0:cord_num,walk_num)
double precision :: x
integer*8 :: i, a, k, l, nw
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
! Prepare table of exponentiated distances raised to appropriate power
een_rescaled_n = 0.0d0
do nw = 1, walk_num
! prepare the actual een table
een_rescaled_n(:, :, 0, nw) = 1.0d0
do a = 1, nucl_num
do i = 1, elec_num
een_rescaled_n(i, a, 1, nw) = dexp(-rescale_factor_en(type_nucl_vector(a)) * en_distance(a, i, nw))
end do
end do
do l = 2, cord_num
do a = 1, nucl_num
do i = 1, elec_num
een_rescaled_n(i, a, l, nw) = een_rescaled_n(i, a, l - 1, nw) * een_rescaled_n(i, a, 1, nw)
end do
end do
end do
end do
end function qmckl_compute_een_rescaled_n_f
/*
qmckl_exit_code qmckl_compute_een_rescaled_n (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
int64_t* const type_nucl_vector,
const int64_t cord_num,
const double* rescale_factor_en,
const double* en_distance,
double* const een_rescaled_n ) {
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (walk_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (elec_num <= 0) {
return QMCKL_INVALID_ARG_3;
}
if (nucl_num <= 0) {
return QMCKL_INVALID_ARG_4;
}
if (cord_num < 0) {
return QMCKL_INVALID_ARG_5;
}
// Prepare table of exponentiated distances raised to appropriate power
for (int i = 0; i < (walk_num*(cord_num+1)*nucl_num*elec_num); ++i) {
een_rescaled_n[i] = 1.0;
}
for (int nw = 0; nw < walk_num; ++nw) {
for (int a = 0; a < nucl_num; ++a) {
for (int i = 0; i < elec_num; ++i) {
een_rescaled_n[i + a*elec_num + nw * elec_num*nucl_num*(cord_num+1)] = 1.0;
een_rescaled_n[i + a*elec_num + elec_num*nucl_num + nw*elec_num*nucl_num*(cord_num+1)] =
exp(-rescale_factor_en[type_nucl_vector[a]] * en_distance[a + i*nucl_num + nw*elec_num*nucl_num]);
}
}
for (int l = 2; l < (cord_num+1); ++l){
for (int a = 0; a < nucl_num; ++a) {
for (int i = 0; i < elec_num; ++i) {
een_rescaled_n[i + a*elec_num + l*elec_num*nucl_num + nw*elec_num*nucl_num*(cord_num+1)] =
een_rescaled_n[i + a*elec_num + (l-1)*elec_num*nucl_num + nw*elec_num*nucl_num*(cord_num+1)] *
een_rescaled_n[i + a*elec_num + elec_num*nucl_num + nw*elec_num*nucl_num*(cord_num+1)];
}
}
}
}
return QMCKL_SUCCESS;
}
*/
Test
assert(qmckl_electron_provided(context));
double een_rescaled_n[walk_num][(cord_num + 1)][nucl_num][elec_num];
size_max=walk_num*(cord_num + 1)*nucl_num*elec_num;
rc = qmckl_get_jastrow_champ_een_rescaled_n(context, &(een_rescaled_n[0][0][0][0]),size_max);
// value of (0,2,1)
assert(fabs(een_rescaled_n[0][1][0][2]-0.10612983920006765) < 1.e-12);
assert(fabs(een_rescaled_n[0][1][0][3]-0.135652809635553) < 1.e-12);
assert(fabs(een_rescaled_n[0][1][0][4]-0.023391817607642338) < 1.e-12);
assert(fabs(een_rescaled_n[0][2][1][3]-0.880957224822116) < 1.e-12);
assert(fabs(een_rescaled_n[0][2][1][4]-0.027185942659395074) < 1.e-12);
assert(fabs(een_rescaled_n[0][2][1][5]-0.01343938025140174) < 1.e-12);
Electron-nucleus rescaled distances derivatives in $J_\text{eeN}$
een_rescaled_n_deriv_e
stores the table of the derivatives of the
rescaled distances between all electron-nucleus pairs and raised to the
power $p$ defined by cord_num
. Here we take its derivatives
required for the een jastrow_champ.
\[ \frac{\partial}{\partial x} \left[ {g_\alpha(R_{i\alpha})}\right]^p = -\frac{x}{R_{i\alpha}} \kappa_\alpha\, p\,\left[ {g_\alpha(R_{i\alpha})}\right]^p \] \[ \Delta \left[ {g_\alpha(R_{i\alpha})}\right]^p = \frac{2}{R_{i\alpha}} \kappa_\alpha\, p\,\left[ {g_\alpha(R_{i\alpha})}\right]^p \right] + \left(\frac{\partial}{\partial x}\left[ {g_\alpha(R_{i\alpha})}\right]^p \right)^2 + \left(\frac{\partial}{\partial y}\left[ {g_\alpha(R_{i\alpha})}\right]^p \right)^2 + \left(\frac{\partial}{\partial z}\left[ {g_\alpha(R_{i\alpha})}\right]^p \right)^2 \]
Get
qmckl_exit_code
qmckl_get_jastrow_champ_een_rescaled_n_deriv_e(qmckl_context context,
double* const distance_rescaled,
const int64_t size_max);
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of atoms |
type_nucl_num |
int64_t |
in | Number of atom types |
type_nucl_vector |
int64_t[nucl_num] |
in | Types of atoms |
cord_num |
int64_t |
in | Order of polynomials |
rescale_factor_en |
double[nucl_num] |
in | Factor to rescale ee distances |
coord_ee |
double[walk_num][3][elec_num] |
in | Electron coordinates |
coord_en |
double[3][nucl_num] |
in | Nuclear coordinates |
en_distance |
double[walk_num][elec_num][nucl_num] |
in | Electron-nucleus distances |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus distances |
een_rescaled_n_deriv_e |
double[walk_num][0:cord_num][nucl_num][4][elec_num] |
out | Electron-nucleus rescaled distances |
integer function qmckl_compute_factor_een_rescaled_n_deriv_e_f( &
context, walk_num, elec_num, nucl_num, type_nucl_num, type_nucl_vector, &
cord_num, rescale_factor_en, &
coord_ee, coord_en, en_distance, een_rescaled_n, een_rescaled_n_deriv_e) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
integer*8 , intent(in) :: cord_num
double precision , intent(in) :: rescale_factor_en(type_nucl_num)
double precision , intent(in) :: coord_ee(elec_num,3,walk_num)
double precision , intent(in) :: coord_en(nucl_num,3)
double precision , intent(in) :: en_distance(nucl_num,elec_num,walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num,nucl_num,0:cord_num,walk_num)
double precision , intent(out) :: een_rescaled_n_deriv_e(elec_num,4,nucl_num,0:cord_num,walk_num)
double precision,dimension(:,:,:),allocatable :: elnuc_dist_deriv_e
double precision :: x, ria_inv, kappa_l
integer*8 :: i, a, k, l, nw, ii
allocate(elnuc_dist_deriv_e(4, elec_num, nucl_num))
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
! Prepare table of exponentiated distances raised to appropriate power
een_rescaled_n_deriv_e = 0.0d0
do nw = 1, walk_num
! prepare the actual een table
do a = 1, nucl_num
do i = 1, elec_num
ria_inv = 1.0d0 / en_distance(a, i, nw)
do ii = 1, 3
elnuc_dist_deriv_e(ii, i, a) = (coord_ee(i, ii, nw) - coord_en(a, ii)) * ria_inv
end do
elnuc_dist_deriv_e(4, i, a) = 2.0d0 * ria_inv
end do
end do
do l = 0, cord_num
do a = 1, nucl_num
kappa_l = - dble(l) * rescale_factor_en(type_nucl_vector(a))
do i = 1, elec_num
een_rescaled_n_deriv_e(i, 1, a, l, nw) = kappa_l * elnuc_dist_deriv_e(1, i, a)
een_rescaled_n_deriv_e(i, 2, a, l, nw) = kappa_l * elnuc_dist_deriv_e(2, i, a)
een_rescaled_n_deriv_e(i, 3, a, l, nw) = kappa_l * elnuc_dist_deriv_e(3, i, a)
een_rescaled_n_deriv_e(i, 4, a, l, nw) = kappa_l * elnuc_dist_deriv_e(4, i, a)
een_rescaled_n_deriv_e(i, 4, a, l, nw) = een_rescaled_n_deriv_e(i, 4, a, l, nw) &
+ een_rescaled_n_deriv_e(i, 1, a, l, nw) * een_rescaled_n_deriv_e(i, 1, a, l, nw) &
+ een_rescaled_n_deriv_e(i, 2, a, l, nw) * een_rescaled_n_deriv_e(i, 2, a, l, nw) &
+ een_rescaled_n_deriv_e(i, 3, a, l, nw) * een_rescaled_n_deriv_e(i, 3, a, l, nw)
een_rescaled_n_deriv_e(i, 1, a, l, nw) = een_rescaled_n_deriv_e(i, 1, a, l, nw) * &
een_rescaled_n(i, a, l, nw)
een_rescaled_n_deriv_e(i, 2, a, l, nw) = een_rescaled_n_deriv_e(i, 2, a, l, nw) * &
een_rescaled_n(i, a, l, nw)
een_rescaled_n_deriv_e(i, 3, a, l, nw) = een_rescaled_n_deriv_e(i, 3, a, l, nw) * &
een_rescaled_n(i, a, l, nw)
een_rescaled_n_deriv_e(i, 4, a, l, nw) = een_rescaled_n_deriv_e(i, 4, a, l, nw) * &
een_rescaled_n(i, a, l, nw)
end do
end do
end do
end do
end function qmckl_compute_factor_een_rescaled_n_deriv_e_f
Test
assert(qmckl_electron_provided(context));
double een_rescaled_n_deriv_e[walk_num][(cord_num + 1)][nucl_num][4][elec_num];
size_max=walk_num*(cord_num + 1)*nucl_num*4*elec_num;
rc = qmckl_get_jastrow_champ_een_rescaled_n_deriv_e(context, &(een_rescaled_n_deriv_e[0][0][0][0][0]),size_max);
// value of (0,2,1)
assert(fabs(een_rescaled_n_deriv_e[0][1][0][0][2]+0.07633444246999128 ) < 1.e-12);
assert(fabs(een_rescaled_n_deriv_e[0][1][0][0][3]-0.00033282346259738276) < 1.e-12);
assert(fabs(een_rescaled_n_deriv_e[0][1][0][0][4]+0.004775370547333061 ) < 1.e-12);
assert(fabs(een_rescaled_n_deriv_e[0][2][1][0][3]-0.1362654644223866 ) < 1.e-12);
assert(fabs(een_rescaled_n_deriv_e[0][2][1][0][4]+0.0231253431662794 ) < 1.e-12);
assert(fabs(een_rescaled_n_deriv_e[0][2][1][0][5]-0.001593334817691633 ) < 1.e-12);
Temporary arrays for electron-electron-nucleus Jastrow $f_{een}$
Prepare c_vector_full
and lkpm_combined_index
tables required for the
calculation of the three-body jastrow factor_een
and its derivative
factor_een_deriv_e
.
Get
qmckl_exit_code qmckl_get_jastrow_champ_tmp_c(qmckl_context context, double* const tmp_c);
qmckl_exit_code qmckl_get_jastrow_champ_dtmp_c(qmckl_context context, double* const dtmp_c);
Compute dim_c_vector
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
cord_num |
int64_t |
in | Order of polynomials |
dim_c_vector |
int64_t |
out | dimension of c_vector_full table |
integer function qmckl_compute_dim_c_vector_f( &
context, cord_num, dim_c_vector) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: cord_num
integer*8 , intent(out) :: dim_c_vector
double precision :: x
integer*8 :: i, a, k, l, p, lmax
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
dim_c_vector = 0
do p = 2, cord_num
do k = p - 1, 0, -1
if (k .ne. 0) then
lmax = p - k
else
lmax = p - k - 2
endif
do l = lmax, 0, -1
if (iand(p - k - l, 1_8) == 1) cycle
dim_c_vector = dim_c_vector + 1
end do
end do
end do
end function qmckl_compute_dim_c_vector_f
qmckl_exit_code qmckl_compute_dim_c_vector (
const qmckl_context context,
const int64_t cord_num,
int64_t* const dim_c_vector){
int lmax;
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (cord_num < 0) {
return QMCKL_INVALID_ARG_2;
}
*dim_c_vector = 0;
for (int p=2; p <= cord_num; ++p){
for (int k=p-1; k >= 0; --k) {
if (k != 0) {
lmax = p - k;
} else {
lmax = p - k - 2;
}
for (int l = lmax; l >= 0; --l) {
if ( ((p - k - l) & 1)==1) continue;
*dim_c_vector=*dim_c_vector+1;
}
}
}
return QMCKL_SUCCESS;
}
Compute c_vector_full
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
nucl_num |
int64_t |
in | Number of atoms |
dim_c_vector |
int64_t |
in | dimension of cord full table |
type_nucl_num |
int64_t |
in | dimension of cord full table |
type_nucl_vector |
int64_t[nucl_num] |
in | dimension of cord full table |
c_vector |
double[dim_c_vector][type_nucl_num] |
in | dimension of cord full table |
c_vector_full |
double[dim_c_vector][nucl_num] |
out | Full list of coefficients |
integer function qmckl_compute_c_vector_full_doc_f( &
context, nucl_num, dim_c_vector, type_nucl_num, &
type_nucl_vector, c_vector, c_vector_full) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: dim_c_vector
integer*8 , intent(in) :: type_nucl_num
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
double precision , intent(in) :: c_vector(type_nucl_num, dim_c_vector)
double precision , intent(out) :: c_vector_full(nucl_num,dim_c_vector)
double precision :: x
integer*8 :: i, a, k, l, nw
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (type_nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (dim_c_vector < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
do a = 1, nucl_num
c_vector_full(a,1:dim_c_vector) = c_vector(type_nucl_vector(a),1:dim_c_vector)
end do
end function qmckl_compute_c_vector_full_doc_f
qmckl_exit_code qmckl_compute_c_vector_full_hpc (
const qmckl_context context,
const int64_t nucl_num,
const int64_t dim_c_vector,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const double* c_vector,
double* const c_vector_full ) {
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (nucl_num <= 0) {
return QMCKL_INVALID_ARG_2;
}
if (type_nucl_num <= 0) {
return QMCKL_INVALID_ARG_4;
}
if (dim_c_vector < 0) {
return QMCKL_INVALID_ARG_5;
}
for (int i=0; i < dim_c_vector; ++i) {
for (int a=0; a < nucl_num; ++a){
c_vector_full[a + i*nucl_num] = c_vector[(type_nucl_vector[a]-1)+i*type_nucl_num];
}
}
return QMCKL_SUCCESS;
}
qmckl_exit_code qmckl_compute_c_vector_full_doc (
const qmckl_context context,
const int64_t nucl_num,
const int64_t dim_c_vector,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const double* c_vector,
double* const c_vector_full );
qmckl_exit_code qmckl_compute_c_vector_full_hpc (
const qmckl_context context,
const int64_t nucl_num,
const int64_t dim_c_vector,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const double* c_vector,
double* const c_vector_full );
qmckl_exit_code qmckl_compute_c_vector_full (
const qmckl_context context,
const int64_t nucl_num,
const int64_t dim_c_vector,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const double* c_vector,
double* const c_vector_full ) {
#ifdef HAVE_HPC
return qmckl_compute_c_vector_full_hpc(context, nucl_num, dim_c_vector, type_nucl_num, type_nucl_vector, c_vector, c_vector_full);
#else
return qmckl_compute_c_vector_full_doc(context, nucl_num, dim_c_vector, type_nucl_num, type_nucl_vector, c_vector, c_vector_full);
#endif
}
Compute lkpm_combined_index
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
cord_num |
int64_t |
in | Order of polynomials |
dim_c_vector |
int64_t |
in | dimension of cord full table |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
out | Full list of combined indices |
integer function qmckl_compute_lkpm_combined_index_f( &
context, cord_num, dim_c_vector, lkpm_combined_index) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: cord_num
integer*8 , intent(in) :: dim_c_vector
integer*8 , intent(out) :: lkpm_combined_index(dim_c_vector, 4)
double precision :: x
integer*8 :: i, a, k, l, kk, p, lmax, m
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (dim_c_vector < 0) then
info = QMCKL_INVALID_ARG_3
return
endif
kk = 0
do p = 2, cord_num
do k = p - 1, 0, -1
if (k .ne. 0) then
lmax = p - k
else
lmax = p - k - 2
end if
do l = lmax, 0, -1
if (iand(p - k - l, 1_8) .eq. 1) cycle
m = (p - k - l)/2
kk = kk + 1
lkpm_combined_index(kk, 1) = l
lkpm_combined_index(kk, 2) = k
lkpm_combined_index(kk, 3) = p
lkpm_combined_index(kk, 4) = m
end do
end do
end do
end function qmckl_compute_lkpm_combined_index_f
qmckl_exit_code qmckl_compute_lkpm_combined_index (
const qmckl_context context,
const int64_t cord_num,
const int64_t dim_c_vector,
int64_t* const lkpm_combined_index ) {
int kk, lmax, m;
if (context == QMCKL_NULL_CONTEXT) {
return QMCKL_INVALID_CONTEXT;
}
if (cord_num < 0) {
return QMCKL_INVALID_ARG_2;
}
if (dim_c_vector < 0) {
return QMCKL_INVALID_ARG_3;
}
/*
*/
kk = 0;
for (int p = 2; p <= cord_num; ++p) {
for (int k=(p-1); k >= 0; --k) {
if (k != 0) {
lmax = p - k;
} else {
lmax = p - k - 2;
}
for (int l=lmax; l >= 0; --l) {
if (((p - k - l) & 1) == 1) continue;
m = (p - k - l)/2;
lkpm_combined_index[kk ] = l;
lkpm_combined_index[kk + dim_c_vector] = k;
lkpm_combined_index[kk + 2*dim_c_vector] = p;
lkpm_combined_index[kk + 3*dim_c_vector] = m;
kk = kk + 1;
}
}
}
return QMCKL_SUCCESS;
}
Compute tmp_c
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
cord_num |
int64_t |
in | Order of polynomials |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
walk_num |
int64_t |
in | Number of walkers |
een_rescaled_e |
double[walk_num][0:cord_num][elec_num][elec_num] |
in | Electron-electron rescaled factor |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus rescaled factor |
tmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][elec_num] |
out | vector of non-zero coefficients |
qmckl_exit_code qmckl_compute_tmp_c (const qmckl_context context,
const int64_t cord_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t walk_num,
const double* een_rescaled_e,
const double* een_rescaled_n,
double* const tmp_c )
{
#ifdef HAVE_HPC
return qmckl_compute_tmp_c_hpc(context, cord_num, elec_num, nucl_num, walk_num, een_rescaled_e, een_rescaled_n, tmp_c);
#else
return qmckl_compute_tmp_c_doc(context, cord_num, elec_num, nucl_num, walk_num, een_rescaled_e, een_rescaled_n, tmp_c);
#endif
}
integer function qmckl_compute_tmp_c_doc_f( &
context, cord_num, elec_num, nucl_num, &
walk_num, een_rescaled_e, een_rescaled_n, tmp_c) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: cord_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: een_rescaled_e(elec_num, elec_num, 0:cord_num, walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num, nucl_num, 0:cord_num, walk_num)
double precision , intent(out) :: tmp_c(elec_num, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision :: x
integer*8 :: i, j, a, l, kk, p, lmax, nw
character :: TransA, TransB
double precision :: alpha, beta
integer*8 :: M, N, K, LDA, LDB, LDC
TransA = 'N'
TransB = 'N'
alpha = 1.0d0
beta = 0.0d0
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
M = elec_num
N = nucl_num*(cord_num + 1)
K = elec_num
LDA = size(een_rescaled_e,1)
LDB = size(een_rescaled_n,1)
LDC = size(tmp_c,1)
do nw=1, walk_num
do i=0, cord_num-1
info = qmckl_dgemm(context, TransA, TransB, M, N, K, alpha, &
een_rescaled_e(1,1,i,nw),LDA*1_8, &
een_rescaled_n(1,1,0,nw),LDB*1_8, &
beta, &
tmp_c(1,1,0,i,nw),LDC)
end do
end do
end function qmckl_compute_tmp_c_doc_f
qmckl_exit_code qmckl_compute_tmp_c_doc (
const qmckl_context context,
const int64_t cord_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t walk_num,
const double* een_rescaled_e,
const double* een_rescaled_n,
double* const tmp_c );
Compute dtmp_c
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
cord_num |
int64_t |
in | Order of polynomials |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
walk_num |
int64_t |
in | Number of walkers |
een_rescaled_e_deriv_e |
double[walk_num][0:cord_num][elec_num][4][elec_num] |
in | Electron-electron rescaled factor derivatives |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus rescaled factor |
dtmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][elec_num] |
out | vector of non-zero coefficients |
qmckl_exit_code
qmckl_compute_dtmp_c (const qmckl_context context,
const int64_t cord_num,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t walk_num,
const double* een_rescaled_e_deriv_e,
const double* een_rescaled_n,
double* const dtmp_c )
{
#ifdef HAVE_HPC
return qmckl_compute_dtmp_c_hpc (context, cord_num, elec_num, nucl_num, walk_num, een_rescaled_e_deriv_e,
een_rescaled_n, dtmp_c );
#else
return qmckl_compute_dtmp_c_doc (context, cord_num, elec_num, nucl_num, walk_num, een_rescaled_e_deriv_e,
een_rescaled_n, dtmp_c );
#endif
}
integer function qmckl_compute_dtmp_c_doc_f( &
context, cord_num, elec_num, nucl_num, &
walk_num, een_rescaled_e_deriv_e, een_rescaled_n, dtmp_c) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: cord_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: een_rescaled_e_deriv_e(elec_num, 4, elec_num, 0:cord_num, walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num, nucl_num, 0:cord_num, walk_num)
double precision , intent(out) :: dtmp_c(elec_num, 4, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision :: x
integer*8 :: i, j, a, l, kk, p, lmax, nw, ii
character :: TransA, TransB
double precision :: alpha, beta
integer*8 :: M, N, K, LDA, LDB, LDC
TransA = 'N'
TransB = 'N'
alpha = 1.0d0
beta = 0.0d0
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
M = 4*elec_num
N = nucl_num*(cord_num + 1)
K = elec_num
LDA = 4*size(een_rescaled_e_deriv_e,1)
LDB = size(een_rescaled_n,1)
LDC = 4*size(dtmp_c,1)
do nw=1, walk_num
do i=0, cord_num-1
info = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
een_rescaled_e_deriv_e(1,1,1,i,nw),LDA*1_8, &
een_rescaled_n(1,1,0,nw),LDB*1_8, &
beta, &
dtmp_c(1,1,1,0,i,nw),LDC)
end do
end do
end function qmckl_compute_dtmp_c_doc_f
Test
assert(qmckl_electron_provided(context));
double tmp_c[walk_num][cord_num][cord_num+1][nucl_num][elec_num];
rc = qmckl_get_jastrow_champ_tmp_c(context, &(tmp_c[0][0][0][0][0]));
double dtmp_c[walk_num][cord_num][cord_num+1][nucl_num][4][elec_num];
rc = qmckl_get_jastrow_champ_dtmp_c(context, &(dtmp_c[0][0][0][0][0][0]));
printf("%e\n%e\n", tmp_c[0][0][1][0][0], 2.7083473948352403);
assert(fabs(tmp_c[0][0][1][0][0] - 2.7083473948352403) < 1e-12);
printf("%e\n%e\n", dtmp_c[0][1][0][0][0][0],0.237440520852232);
assert(fabs(dtmp_c[0][1][0][0][0][0] - 0.237440520852232) < 1e-12);
Electron-electron-nucleus Jastrow $f_{een}$
Calculate the electron-electron-nuclear three-body jastrow component factor_een
using the above prepared tables.
TODO: write equations.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_een(qmckl_context context,
double* const factor_een,
const int64_t size_max);
Fortran interface
interface
integer(qmckl_exit_code) function qmckl_get_jastrow_champ_factor_een (context, &
factor_een, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (qmckl_context) , intent(in), value :: context
integer(c_int64_t), intent(in), value :: size_max
double precision, intent(out) :: factor_een(size_max)
end function qmckl_get_jastrow_champ_factor_een
end interface
Compute naive
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
cord_num |
int64_t |
in | order of polynomials |
dim_c_vector |
int64_t |
in | dimension of full coefficient vector |
c_vector_full |
double[dim_c_vector][nucl_num] |
in | full coefficient vector |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
in | combined indices |
een_rescaled_e |
double[walk_num][elec_num][elec_num][0:cord_num] |
in | Electron-nucleus rescaled |
een_rescaled_n |
double[walk_num][elec_num][nucl_num][0:cord_num] |
in | Electron-nucleus rescaled factor |
factor_een |
double[walk_num] |
out | Electron-nucleus jastrow |
integer function qmckl_compute_factor_een_naive_f( &
context, walk_num, elec_num, nucl_num, cord_num,&
dim_c_vector, c_vector_full, lkpm_combined_index, &
een_rescaled_e, een_rescaled_n, factor_een) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, cord_num, nucl_num, dim_c_vector
integer*8 , intent(in) :: lkpm_combined_index(dim_c_vector,4)
double precision , intent(in) :: c_vector_full(nucl_num, dim_c_vector)
double precision , intent(in) :: een_rescaled_e(0:cord_num, elec_num, elec_num, walk_num)
double precision , intent(in) :: een_rescaled_n(0:cord_num, nucl_num, elec_num, walk_num)
double precision , intent(out) :: factor_een(walk_num)
integer*8 :: i, a, j, l, k, p, m, n, nw
double precision :: accu, accu2, cn
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
factor_een = 0.0d0
do nw =1, walk_num
do n = 1, dim_c_vector
l = lkpm_combined_index(n, 1)
k = lkpm_combined_index(n, 2)
p = lkpm_combined_index(n, 3)
m = lkpm_combined_index(n, 4)
do a = 1, nucl_num
accu2 = 0.0d0
cn = c_vector_full(a, n)
do j = 1, elec_num
accu = 0.0d0
do i = 1, elec_num
accu = accu + een_rescaled_e(k,i,j,nw) * &
een_rescaled_n(m,a,i,nw)
!if(nw .eq. 1) then
! print *,l,k,p,m,j,i,een_rescaled_e(k,i,j,nw), een_rescaled_n(m,a,i,nw), accu
!endif
end do
accu2 = accu2 + accu * een_rescaled_n(m + l,a,j,nw)
!print *, l,m,nw,accu, accu2, een_rescaled_n(m + l, a, j, nw), cn, factor_een(nw)
end do
factor_een(nw) = factor_een(nw) + accu2 * cn
end do
end do
end do
end function qmckl_compute_factor_een_naive_f
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
cord_num |
int64_t |
in | order of polynomials |
dim_c_vector |
int64_t |
in | dimension of full coefficient vector |
c_vector_full |
double[dim_c_vector][nucl_num] |
in | full coefficient vector |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
in | combined indices |
tmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][elec_num] |
in | vector of non-zero coefficients |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus rescaled distances |
factor_een |
double[walk_num] |
out | Electron-nucleus jastrow |
integer function qmckl_compute_factor_een_doc_f( &
context, walk_num, elec_num, nucl_num, cord_num, &
dim_c_vector, c_vector_full, lkpm_combined_index, &
tmp_c, een_rescaled_n, factor_een) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, cord_num, nucl_num, dim_c_vector
integer*8 , intent(in) :: lkpm_combined_index(dim_c_vector,4)
double precision , intent(in) :: c_vector_full(nucl_num, dim_c_vector)
double precision , intent(in) :: tmp_c(elec_num, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num, nucl_num, 0:cord_num, walk_num)
double precision , intent(out) :: factor_een(walk_num)
integer*8 :: i, a, j, l, k, p, m, n, nw
double precision :: accu, accu2, cn
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
factor_een = 0.0d0
do nw =1, walk_num
do n = 1, dim_c_vector
l = lkpm_combined_index(n, 1)
k = lkpm_combined_index(n, 2)
p = lkpm_combined_index(n, 3)
m = lkpm_combined_index(n, 4)
do a = 1, nucl_num
cn = c_vector_full(a, n)
if(cn == 0.d0) cycle
accu = 0.0d0
do j = 1, elec_num
accu = accu + een_rescaled_n(j,a,m,nw) * tmp_c(j,a,m+l,k,nw)
end do
factor_een(nw) = factor_een(nw) + accu * cn
end do
end do
end do
end function qmckl_compute_factor_een_doc_f
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
double factor_een[walk_num];
rc = qmckl_get_jastrow_champ_factor_een(context, &(factor_een[0]),walk_num);
assert(fabs(factor_een[0] + 0.37407972141304213) < 1e-12);
Electron-electron-nucleus Jastrow $f_{een}$ derivative
Calculate the electron-electron-nuclear three-body jastrow component factor_een_deriv_e
using the above prepared tables.
TODO: write equations.
Get
qmckl_exit_code
qmckl_get_jastrow_champ_factor_een_deriv_e(qmckl_context context,
double* const factor_een_deriv_e,
const int64_t size_max);
Compute Naive
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
cord_num |
int64_t |
in | order of polynomials |
dim_c_vector |
int64_t |
in | dimension of full coefficient vector |
c_vector_full |
double[dim_c_vector][nucl_num] |
in | full coefficient vector |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
in | combined indices |
een_rescaled_e |
double[walk_num][elec_num][elec_num][0:cord_num] |
in | Electron-nucleus rescaled |
een_rescaled_n |
double[walk_num][elec_num][nucl_num][0:cord_num] |
in | Electron-nucleus rescaled factor |
een_rescaled_e_deriv_e |
double[walk_num][elec_num][4][elec_num][0:cord_num] |
in | Electron-nucleus rescaled |
een_rescaled_n_deriv_e |
double[walk_num][elec_num][4][nucl_num][0:cord_num] |
in | Electron-nucleus rescaled factor |
factor_een_deriv_e |
double[walk_num][4][elec_num] |
out | Electron-nucleus jastrow |
integer function qmckl_compute_factor_een_deriv_e_naive_f( &
context, walk_num, elec_num, nucl_num, cord_num, dim_c_vector, &
c_vector_full, lkpm_combined_index, een_rescaled_e, een_rescaled_n, &
een_rescaled_e_deriv_e, een_rescaled_n_deriv_e, factor_een_deriv_e)&
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, cord_num, nucl_num, dim_c_vector
integer*8 , intent(in) :: lkpm_combined_index(dim_c_vector, 4)
double precision , intent(in) :: c_vector_full(nucl_num, dim_c_vector)
double precision , intent(in) :: een_rescaled_e(0:cord_num, elec_num, elec_num, walk_num)
double precision , intent(in) :: een_rescaled_n(0:cord_num, nucl_num, elec_num, walk_num)
double precision , intent(in) :: een_rescaled_e_deriv_e(0:cord_num, elec_num, 4, elec_num, walk_num)
double precision , intent(in) :: een_rescaled_n_deriv_e(0:cord_num, nucl_num, 4, elec_num, walk_num)
double precision , intent(out) :: factor_een_deriv_e(elec_num, 4, walk_num)
integer*8 :: i, a, j, l, k, p, m, n, nw
double precision :: accu, accu2, cn
double precision :: daccu(1:4), daccu2(1:4)
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
factor_een_deriv_e = 0.0d0
do nw =1, walk_num
do n = 1, dim_c_vector
l = lkpm_combined_index(n, 1)
k = lkpm_combined_index(n, 2)
p = lkpm_combined_index(n, 3)
m = lkpm_combined_index(n, 4)
do a = 1, nucl_num
cn = c_vector_full(a, n)
do j = 1, elec_num
accu = 0.0d0
accu2 = 0.0d0
daccu = 0.0d0
daccu2 = 0.0d0
do i = 1, elec_num
accu = accu + een_rescaled_e(k, i, j, nw) * &
een_rescaled_n(m, a, i, nw)
accu2 = accu2 + een_rescaled_e(k, i, j, nw) * &
een_rescaled_n(m + l, a, i, nw)
daccu(1:4) = daccu(1:4) + een_rescaled_e_deriv_e(k, j, 1:4, i, nw) * &
een_rescaled_n(m, a, i, nw)
daccu2(1:4) = daccu2(1:4) + een_rescaled_e_deriv_e(k, j, 1:4, i, nw) * &
een_rescaled_n(m + l, a, i, nw)
end do
factor_een_deriv_e(j, 1:4, nw) = factor_een_deriv_e(j, 1:4, nw) + &
(accu * een_rescaled_n_deriv_e(m + l, a, 1:4, j, nw) &
+ daccu(1:4) * een_rescaled_n(m + l, a, j, nw) &
+ daccu2(1:4) * een_rescaled_n(m, a, j, nw) &
+ accu2 * een_rescaled_n_deriv_e(m, a, 1:4, j, nw)) * cn
factor_een_deriv_e(j, 4, nw) = factor_een_deriv_e(j, 4, nw) + 2.0d0 * ( &
daccu (1) * een_rescaled_n_deriv_e(m + l, a, 1, j, nw) + &
daccu (2) * een_rescaled_n_deriv_e(m + l, a, 2, j, nw) + &
daccu (3) * een_rescaled_n_deriv_e(m + l, a, 3, j, nw) + &
daccu2(1) * een_rescaled_n_deriv_e(m, a, 1, j, nw ) + &
daccu2(2) * een_rescaled_n_deriv_e(m, a, 2, j, nw ) + &
daccu2(3) * een_rescaled_n_deriv_e(m, a, 3, j, nw ) ) * cn
end do
end do
end do
end do
end function qmckl_compute_factor_een_deriv_e_naive_f
Compute
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
nucl_num |
int64_t |
in | Number of nuclei |
cord_num |
int64_t |
in | order of polynomials |
dim_c_vector |
int64_t |
in | dimension of full coefficient vector |
c_vector_full |
double[dim_c_vector][nucl_num] |
in | full coefficient vector |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
in | combined indices |
tmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][elec_num] |
in | Temporary intermediate tensor |
dtmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][4][elec_num] |
in | vector of non-zero coefficients |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus rescaled factor |
een_rescaled_n_deriv_e |
double[walk_num][0:cord_num][nucl_num][4][elec_num] |
in | Derivative of Electron-nucleus rescaled factor |
factor_een_deriv_e |
double[walk_num][4][elec_num] |
out | Derivative of Electron-nucleus jastrow |
integer function qmckl_compute_factor_een_deriv_e_f( &
context, walk_num, elec_num, nucl_num, &
cord_num, dim_c_vector, c_vector_full, lkpm_combined_index, &
tmp_c, dtmp_c, een_rescaled_n, een_rescaled_n_deriv_e, factor_een_deriv_e)&
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, cord_num, nucl_num, dim_c_vector
integer*8 , intent(in) :: lkpm_combined_index(dim_c_vector,4)
double precision , intent(in) :: c_vector_full(nucl_num, dim_c_vector)
double precision , intent(in) :: tmp_c(elec_num, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision , intent(in) :: dtmp_c(elec_num, 4, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num, nucl_num, 0:cord_num, walk_num)
double precision , intent(in) :: een_rescaled_n_deriv_e(elec_num, 4, nucl_num, 0:cord_num, walk_num)
double precision , intent(out) :: factor_een_deriv_e(elec_num,4,walk_num)
integer*8 :: i, a, j, l, k, p, m, n, nw, ii
double precision :: accu, accu2, cn
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (cord_num < 0) then
info = QMCKL_INVALID_ARG_5
return
endif
factor_een_deriv_e = 0.0d0
do nw =1, walk_num
do n = 1, dim_c_vector
l = lkpm_combined_index(n, 1)
k = lkpm_combined_index(n, 2)
p = lkpm_combined_index(n, 3)
m = lkpm_combined_index(n, 4)
do a = 1, nucl_num
cn = c_vector_full(a, n)
if(cn == 0.d0) cycle
do ii = 1, 4
do j = 1, elec_num
factor_een_deriv_e(j,ii,nw) = factor_een_deriv_e(j,ii,nw) + (&
tmp_c(j,a,m,k,nw) * een_rescaled_n_deriv_e(j,ii,a,m+l,nw) + &
(dtmp_c(j,ii,a,m,k,nw)) * een_rescaled_n(j,a,m+l,nw) + &
(dtmp_c(j,ii,a,m+l,k,nw)) * een_rescaled_n(j,a,m ,nw) + &
tmp_c(j,a,m+l,k,nw) * een_rescaled_n_deriv_e(j,ii,a,m,nw) &
) * cn
end do
end do
cn = cn + cn
do j = 1, elec_num
factor_een_deriv_e(j,4,nw) = factor_een_deriv_e(j,4,nw) + (&
(dtmp_c(j,1,a,m ,k,nw)) * een_rescaled_n_deriv_e(j,1,a,m+l,nw) + &
(dtmp_c(j,2,a,m ,k,nw)) * een_rescaled_n_deriv_e(j,2,a,m+l,nw) + &
(dtmp_c(j,3,a,m ,k,nw)) * een_rescaled_n_deriv_e(j,3,a,m+l,nw) + &
(dtmp_c(j,1,a,m+l,k,nw)) * een_rescaled_n_deriv_e(j,1,a,m ,nw) + &
(dtmp_c(j,2,a,m+l,k,nw)) * een_rescaled_n_deriv_e(j,2,a,m ,nw) + &
(dtmp_c(j,3,a,m+l,k,nw)) * een_rescaled_n_deriv_e(j,3,a,m ,nw) &
) * cn
end do
end do
end do
end do
end function qmckl_compute_factor_een_deriv_e_f
Test
/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_champ_provided(context));
double factor_een_deriv_e[4][walk_num][elec_num];
rc = qmckl_get_jastrow_champ_factor_een_deriv_e(context, &(factor_een_deriv_e[0][0][0]),4*walk_num*elec_num);
assert(fabs(factor_een_deriv_e[0][0][0] + 0.0005481671107226865) < 1e-12);
Total Jastrow value
Value of the total Jastrow factor.
Reference version
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
walk_num |
int64_t |
in | Number of walkers |
elec_num |
int64_t |
in | Number of electrons |
up_num |
int64_t |
in | Number of $\alpha$ electrons |
nucl_num |
int64_t |
in | Number of nuclei |
type_nucl_num |
int64_t |
in | Number of unique nuclei |
type_nucl_vector |
int64_t[nucl_num] |
in | IDs of unique nuclei |
dim_c_vector |
int64_t |
in | Dimension of full coefficient vector |
aord_num |
int64_t |
in | Number of $a$ coefficients |
bord_num |
int64_t |
in | Number of $b$ coefficients |
cord_num |
int64_t |
in | Order of polynomials |
a_vector |
double[aord_num+1][type_nucl_num] |
in | List of coefficients for $a$ parameters |
b_vector |
double[bord_num+1] |
in | List of coefficients for $b$ parameters |
c_vector_full |
double[dim_c_vector][nucl_num] |
in | Full coefficient vector |
lkpm_combined_index |
int64_t[4][dim_c_vector] |
in | Combined indices |
tmp_c |
double[walk_num][0:cord_num-1][0:cord_num][nucl_num][elec_num] |
in | Vector of non-zero coefficients |
ee_distance_rescaled |
double[walk_num][elec_num][elec_num] |
in | Electron-electron distances |
en_distance_rescaled |
double[walk_num][nucl_num][elec_num] |
in | Electron-nucleus distances |
een_rescaled_n |
double[walk_num][0:cord_num][nucl_num][elec_num] |
in | Electron-nucleus rescaled distances |
asymp_jasa |
double[type_nucl_num] |
in | Type of nuclei |
asymp_jasb |
double[2] |
in | Asymptotic value of the Jastrow |
factor_ee |
double[walk_num] |
out | $f_{ee}$ |
integer function qmckl_compute_jastrow_champ_value_doc_f(context, &
walk_num, elec_num, up_num, nucl_num, type_nucl_num, type_nucl_vector, &
dim_c_vector, aord_num, bord_num, cord_num, a_vector, b_vector, &
c_vector_full, lkpm_combined_index, tmp_c, ee_distance_rescaled, &
en_distance_rescaled, een_rescaled_n, asymp_jasa, asymp_jasb, &
val) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: walk_num, elec_num, up_num, nucl_num
integer*8 , intent(in) :: type_nucl_num, dim_c_vector
integer*8 , intent(in) :: type_nucl_vector(nucl_num)
integer*8 , intent(in) :: aord_num, bord_num, cord_num
double precision , intent(in) :: a_vector(type_nucl_num, aord_num + 1)
double precision , intent(in) :: b_vector(bord_num + 1)
double precision , intent(in) :: c_vector_full(nucl_num, dim_c_vector)
integer*8 , intent(in) :: lkpm_combined_index(dim_c_vector,4)
double precision , intent(in) :: tmp_c(elec_num, nucl_num,0:cord_num, 0:cord_num-1, walk_num)
double precision , intent(in) :: ee_distance_rescaled(elec_num, elec_num, walk_num)
double precision , intent(in) :: en_distance_rescaled(elec_num, nucl_num, walk_num)
double precision , intent(in) :: een_rescaled_n(elec_num, nucl_num, 0:cord_num, walk_num)
double precision , intent(in) :: asymp_jasa(type_nucl_num), asymp_jasb(2)
double precision , intent(out) :: val(walk_num)
integer :: iwalk
double precision, allocatable :: v(:), gl(:,:,:)
integer, external :: qmckl_compute_factor_ee_doc_f
integer, external :: qmckl_compute_factor_en_doc_f
integer, external :: qmckl_compute_factor_een_doc_f
allocate(v(walk_num))
info = qmckl_compute_factor_ee_doc_f(context, walk_num, elec_num, up_num, bord_num, &
b_vector, ee_distance_rescaled, asymp_jasb, val)
if (info /= QMCKL_SUCCESS) return
info = qmckl_compute_factor_en_doc_f(context, walk_num, elec_num, nucl_num, type_nucl_num, &
type_nucl_vector, aord_num, a_vector, en_distance_rescaled, asymp_jasa, v)
if (info /= QMCKL_SUCCESS) return
val(1:walk_num) = val(1:walk_num) + v(1:walk_num)
info = qmckl_compute_factor_een_doc_f(context, walk_num, elec_num, nucl_num, cord_num, &
dim_c_vector, c_vector_full, lkpm_combined_index, tmp_c, een_rescaled_n, v)
if (info /= QMCKL_SUCCESS) return
val(1:walk_num) = val(1:walk_num) + v(1:walk_num)
deallocate(v,gl)
end function qmckl_compute_jastrow_champ_value_doc_f
qmckl_exit_code qmckl_compute_jastrow_champ_value_doc (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t dim_c_vector,
const int64_t aord_num,
const int64_t bord_num,
const int64_t cord_num,
const double* a_vector,
const double* b_vector,
const double* c_vector_full,
const int64_t* lkpm_combined_index,
const double* tmp_c,
const double* ee_distance_rescaled,
const double* en_distance_rescaled,
const double* een_rescaled_n,
const double* asymp_jasa,
const double* asymp_jasb,
double* const factor_ee );
qmckl_exit_code qmckl_compute_jastrow_champ_value (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t dim_c_vector,
const int64_t aord_num,
const int64_t bord_num,
const int64_t cord_num,
const double* a_vector,
const double* b_vector,
const double* c_vector_full,
const int64_t* lkpm_combined_index,
const double* tmp_c,
const double* ee_distance_rescaled,
const double* en_distance_rescaled,
const double* een_rescaled_n,
const double* asymp_jasa,
const double* asymp_jasb,
double* const factor_ee );
qmckl_exit_code qmckl_compute_jastrow_champ_value (
const qmckl_context context,
const int64_t walk_num,
const int64_t elec_num,
const int64_t up_num,
const int64_t nucl_num,
const int64_t type_nucl_num,
const int64_t* type_nucl_vector,
const int64_t dim_c_vector,
const int64_t aord_num,
const int64_t bord_num,
const int64_t cord_num,
const double* a_vector,
const double* b_vector,
const double* c_vector_full,
const int64_t* lkpm_combined_index,
const double* tmp_c,
const double* ee_distance_rescaled,
const double* en_distance_rescaled,
const double* een_rescaled_n,
const double* asymp_jasa,
const double* asymp_jasb,
double* const val)
{
#ifdef HAVE_HPC
return qmckl_compute_jastrow_champ_value_doc (context, walk_num, elec_num, up_num, nucl_num,
type_nucl_num, type_nucl_vector, dim_c_vector, aord_num, bord_num,
cord_num, a_vector, b_vector, c_vector_full, lkpm_combined_index,
tmp_c, ee_distance_rescaled, en_distance_rescaled, een_rescaled_n,
asymp_jasa, asymp_jasb, val);
#else
return qmckl_compute_jastrow_champ_value_doc (context, walk_num, elec_num, up_num, nucl_num,
type_nucl_num, type_nucl_vector, dim_c_vector, aord_num, bord_num,
cord_num, a_vector, b_vector, c_vector_full, lkpm_combined_index,
tmp_c, ee_distance_rescaled, en_distance_rescaled, een_rescaled_n,
asymp_jasa, asymp_jasb, val);
#endif
}