qmckl/org/qmckl_jastrow.org

Jastrow Factor

• Introduction
• Context
  • Data structure
  • Initialization functions
    • Fortran interface
  • Access functions
    • Fortran interface
  • Test
• Computation
  • Asymptotic component for \(J_\text{ee}\)
    • Get
      • Fortran interface
    • Compute
    • Test
  • Electron-electron component \(f_\text{ee}\)
    • Get
      • Fortran interface
    • Compute
    • Test
  • Electron-electron component derivative \(f'_{ee}\)
    • Get
    • Compute
    • Test
  • Asymptotic component for \(J_{eN}\)
    • Get
      • Fortran interface
    • Compute
    • Test
  • Electron-nucleus component \(f_{en}\)
    • Get
      • Fortran interface
    • Compute
    • Test
  • Electron-nucleus component derivative \(f'_{en}\)
    • Get
    • Compute
    • Test
  • Electron-electron rescaled distances
    • Get
    • Compute
    • Test
  • Electron-electron rescaled distance gradients and Laplacian with respect to electron coords
    • Get
    • Compute
    • Test
  • Electron-electron-nucleus rescaled distances for each order
    • Get
    • Compute
    • Test
  • Electron-electron-nucleus rescaled distances for each order and derivatives
    • Get
    • Compute
    • Test
  • Electron-nucleus rescaled distances
    • Get
    • Compute
    • Test
  • Electron-electron-nucleus rescaled distance gradients and laplacian with respect to electron coords
    • Get
    • Compute
    • Test
  • Electron-electron-nucleus rescaled distances for each order
    • Get
    • Compute
    • Test
  • Electron-nucleus rescaled distances for each order and derivatives
    • Get
    • Compute
    • Test
  • Prepare for electron-electron-nucleus Jastrow \(f_{een}\)
    • Get
    • Compute dim_c_vector
    • Compute c_vector_full
    • Compute lkpm_combined_index
    • Compute tmp_c
    • Compute dtmp_c
    • Test
  • Electron-electron-nucleus Jastrow \(f_{een}\)
    • Get
      • Fortran interface
    • Compute naive
    • Compute
    • Test
  • Electron-electron-nucleus Jastrow \(f_{een}\) derivative
    • Get
    • Compute Naive
    • Compute
    • Test
  • Jastrow VGL functions

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:

\[ J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{\alpha=1}^{N_\text{nucl}} \sum_{i=1}^{N_\text{elec}} \frac{a_{1\,\alpha}\, f_\alpha(R_{i\,\alpha})}{1+a_{2\,\alpha}\, f_\alpha(R_{i\alpha})} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1\,\alpha}\, [f_\alpha(R_{i\alpha})]^p - J_{eN}^{\infty \alpha} \]

$J_{\text{ee}}$ 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

\[ f_\alpha(r) = \frac{1-e^{-\kappa_\alpha\, r}}{\kappa_\alpha} \text{ and } g_\alpha(r) = e^{-\kappa_\alpha\, r}. \]

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

Data structure

typedef struct qmckl_jastrow_struct{
int32_t   uninitialized;
int64_t   aord_num;
int64_t   bord_num;
int64_t   cord_num;
int64_t   type_nucl_num;
uint64_t  asymp_jasa_date;
uint64_t  asymp_jasb_date;
uint64_t  tmp_c_date;
uint64_t  dtmp_c_date;
uint64_t  factor_ee_date;
uint64_t  factor_en_date;
uint64_t  factor_een_date;
uint64_t  factor_ee_deriv_e_date;
uint64_t  factor_en_deriv_e_date;
uint64_t  factor_een_deriv_e_date;
double    rescale_factor_ee;
double*   rescale_factor_en;
int64_t*  type_nucl_vector;
double *  a_vector;
double *  b_vector;
double *  c_vector;
double *  asymp_jasa;
double *  asymp_jasb;
double *  factor_ee;
double *  factor_en;
double *  factor_een;
double *  factor_ee_deriv_e;
double *  factor_en_deriv_e;
double *  factor_een_deriv_e;
int64_t   dim_c_vector;
uint64_t  dim_c_vector_date;
double *  c_vector_full;
uint64_t  c_vector_full_date;
int64_t*  lkpm_combined_index;
uint64_t  lkpm_combined_index_date;
double *  tmp_c;
double *  dtmp_c;
uint64_t  ee_distance_rescaled_date;
uint64_t  ee_distance_rescaled_deriv_e_date;
uint64_t  en_distance_rescaled_date;
uint64_t  en_distance_rescaled_deriv_e_date;
double*   ee_distance_rescaled;
double*   ee_distance_rescaled_deriv_e;
double*   en_distance_rescaled;
double*   en_distance_rescaled_deriv_e;
double *  een_rescaled_e;
double *  een_rescaled_n;
uint64_t  een_rescaled_e_date;
uint64_t  een_rescaled_n_date;
double *  een_rescaled_e_deriv_e;
double *  een_rescaled_n_deriv_e;
uint64_t  een_rescaled_e_deriv_e_date;
uint64_t  een_rescaled_n_deriv_e_date;
bool      provided;
char *    type;

} qmckl_jastrow_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(qmckl_context context);

qmckl_exit_code qmckl_init_jastrow(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.uninitialized = (1 << 10) - 1;

/* Default values */
ctx->jastrow.aord_num = -1;
ctx->jastrow.bord_num = -1;
ctx->jastrow.cord_num = -1;
ctx->jastrow.type_nucl_num = -1;
ctx->jastrow.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_rescale_factor_ee (qmckl_context context, const double  kappa_ee);
qmckl_exit_code  qmckl_set_jastrow_rescale_factor_en (qmckl_context context, const double* kappa_en, const int64_t size_max);
qmckl_exit_code  qmckl_set_jastrow_aord_num          (qmckl_context context, const int64_t aord_num);
qmckl_exit_code  qmckl_set_jastrow_bord_num          (qmckl_context context, const int64_t bord_num);
qmckl_exit_code  qmckl_set_jastrow_cord_num          (qmckl_context context, const int64_t cord_num);
qmckl_exit_code  qmckl_set_jastrow_type_nucl_num     (qmckl_context context, const int64_t type_nucl_num);
qmckl_exit_code  qmckl_set_jastrow_type_nucl_vector  (qmckl_context context, const int64_t* type_nucl_vector, const int64_t nucl_num);
qmckl_exit_code  qmckl_set_jastrow_a_vector          (qmckl_context context, const double * a_vector, const int64_t size_max);
qmckl_exit_code  qmckl_set_jastrow_b_vector          (qmckl_context context, const double * b_vector, const int64_t size_max);
qmckl_exit_code  qmckl_set_jastrow_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_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_rescale_factor_ee

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_rescale_factor_en

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_aord_num

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_bord_num

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_cord_num

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_type_nucl_num

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_type_nucl_vector

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_a_vector

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_b_vector

   integer(qmckl_exit_code) function qmckl_set_jastrow_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_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_provided           (const qmckl_context context);

Fortran interface

interface
   integer(qmckl_exit_code) function qmckl_get_jastrow_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_rescale_factor_ee

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_rescale_factor_en

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_aord_num

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_bord_num

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_cord_num

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_type_nucl_num

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_type_nucl_vector

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_a_vector

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_b_vector

   integer(qmckl_exit_code) function qmckl_get_jastrow_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_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.

Asymptotic component for \(J_\text{ee}\)

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_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_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_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_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_asymp_jasb_doc_f

qmckl_exit_code
qmckl_compute_jastrow_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_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_asymp_jasb_hpc (context,
	  bord_num, b_vector, rescale_factor_ee, asymp_jasb);
#else
  return qmckl_compute_jastrow_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_provided(context));

/* Set the data */
rc = qmckl_check(context,
            qmckl_set_jastrow_aord_num(context, aord_num)
            );
rc = qmckl_check(context,
            qmckl_set_jastrow_bord_num(context, bord_num)
            );
rc = qmckl_check(context,
            qmckl_set_jastrow_cord_num(context, cord_num)
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_set_jastrow_type_nucl_num(context, type_nucl_num)
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_set_jastrow_type_nucl_vector(context, type_nucl_vector, nucl_num)
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_set_jastrow_a_vector(context, a_vector,(aord_num+1)*type_nucl_num)
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_set_jastrow_b_vector(context, b_vector,(bord_num+1))
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_get_jastrow_dim_c_vector(context, &dim_c_vector)
            );
assert(rc == QMCKL_SUCCESS);
rc = qmckl_check(context,
            qmckl_set_jastrow_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_rescale_factor_en(context, rescale_factor_en, type_nucl_num)
            );
assert(rc == QMCKL_SUCCESS);

rc = qmckl_check(context,
            qmckl_set_jastrow_rescale_factor_ee(context, rescale_factor_ee)
            );
assert(rc == QMCKL_SUCCESS);

rc = qmckl_check(context,
            qmckl_get_jastrow_rescale_factor_ee (context, &k_ee)
            );
assert(rc == QMCKL_SUCCESS);
assert(k_ee == rescale_factor_ee);

rc = qmckl_check(context,
            qmckl_get_jastrow_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_provided(context));

double asymp_jasb[2];
rc = qmckl_get_jastrow_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 \(f_\text{ee}\)

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 scaled distances.

Get

qmckl_exit_code
qmckl_get_jastrow_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_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_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	Electron-electron distances
factor_ee	double[walk_num]	out	Electron-electron distances

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_provided(context));

double factor_ee[walk_num];
rc = qmckl_check(context,
            qmckl_get_jastrow_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);

Electron-electron component derivative \(f'_{ee}\)

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_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_provided(context));

// calculate factor_ee_deriv_e
double factor_ee_deriv_e[walk_num][4][elec_num];
rc = qmckl_get_jastrow_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);

Asymptotic component for \(J_{eN}\)

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_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_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_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_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_asymp_jasa_f

/*
qmckl_exit_code qmckl_compute_jastrow_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_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_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 \(f_{en}\)

Calculate the electron-electron jastrow component factor_en using the a_vector coeffecients and the electron-nucleus rescaled distances en_distance_rescaled.

\[ f_{en} = \sum_{i,j<i} \left\{ \frac{ A_0 C_{ij}}{1 - A_1 C_{ij}} + \sum^{nord}_{k}A_k C_{ij}^k \right\} \]

Get

qmckl_exit_code
qmckl_get_jastrow_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_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_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 nucleii
type_nucl_num	int64_t	in	Number of unique nuclei
type_nucl_vector	int64_t[nucl_num]	in	IDs of unique nucleii
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_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_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 );

Test

/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_provided(context));

double factor_en[walk_num];
rc = qmckl_get_jastrow_factor_en(context, factor_en,walk_num);

// calculate factor_en
assert(fabs(5.1052574308112755 - factor_en[0]) < 1.e-12);

Electron-nucleus component derivative \(f'_{en}\)

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_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 nucleii
type_nucl_num	int64_t	in	Number of unique nuclei
type_nucl_vector	int64_t[nucl_num]	in	IDs of unique nucleii
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_provided(context));

// calculate factor_en_deriv_e
double factor_en_deriv_e[walk_num][4][elec_num];
rc = qmckl_get_jastrow_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-electron rescaled distances

ee_distance_rescaled stores the matrix of the rescaled distances between all pairs of electrons:

\[ C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa \]

where \(C_{ij}\) is the matrix of electron-electron distances.

Get

qmckl_exit_code qmckl_get_jastrow_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_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 coords

The rescaled distances which is given as $R = (1 - \exp{-\kappa r})/\kappa$ needs to be perturbed with respect to the electorn coordinates. This data is stored in the ee_distance_rescaled_deriv_e tensor. The The first three elements of this three index tensor [4][num][num] gives the derivatives in the x, y, and z directions $dx, dy, dz$ and the last index gives the Laplacian $\partial x^2 + \partial y^2 + \partial z^2$.

Get

qmckl_exit_code qmckl_get_jastrow_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_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-electron-nucleus rescaled distances for each order

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:

\[ C_{ij,p} = \left( 1 - \exp{-\kappa C_{ij}} \right)^p \]

where \(C_{ij}\) is the matrix of electron-electron distances.

Get

qmckl_exit_code
qmckl_get_jastrow_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
een_rescaled_e	double[walk_num][0:cord_num][elec_num][elec_num]	out	Electron-electron rescaled distances

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 + 1 - 1) * 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_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-nucleus rescaled distances for each order and derivatives

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.

TODO: write formulae

Get

qmckl_exit_code
qmckl_get_jastrow_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_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

en_distance_rescaled stores the matrix of the rescaled distances between electrons and nuclei.

\[ C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa \]

where \(C_{ij}\) 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-nucleus rescaled distance gradients and laplacian with respect to electron coords

The rescaled distances which is given as $R = (1 - \exp{-\kappa r})/\kappa$ needs to be perturbed with respect to the nuclear coordinates. This data is stored in the en_distance_rescaled_deriv_e tensor. The The first three elements of this three index tensor [4][nucl_num][elec_num] gives the derivatives in the x, y, and z directions $dx, dy, dz$ and the last index gives the Laplacian $\partial x^2 + \partial y^2 + \partial z^2$.

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 rescaled distances for each order

een_rescaled_n stores the table of the rescaled distances between electrons and nucleii raised to the power \(p\) defined by cord_num:

\[ C_{ia,p} = \left( 1 - \exp{-\kappa C_{ia}} \right)^p \]

where \(C_{ia}\) is the matrix of electron-nucleus distances.

Get

qmckl_exit_code
qmckl_get_jastrow_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_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 for each order and derivatives

een_rescaled_n_deriv_e stores the table of the rescaled distances between electrons and nucleii raised to the power \(p\) defined by cord_num:

Get

qmckl_exit_code
qmckl_get_jastrow_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_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);

Prepare 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_dim_c_vector(qmckl_context context, int64_t* const dim_c_vector);
qmckl_exit_code qmckl_get_jastrow_c_vector_full(qmckl_context context, double* const c_vector_full);
qmckl_exit_code qmckl_get_jastrow_lkpm_combined_index(qmckl_context context, int64_t* const lkpm_combined_index);
qmckl_exit_code qmckl_get_jastrow_tmp_c(qmckl_context context, double* const tmp_c);
qmckl_exit_code qmckl_get_jastrow_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 nucleii
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 nucleii
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_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_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_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_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_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 nucleii
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 nucleii
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]	vector of non-zero coefficients
een_rescaled_n	double[walk_num][0:cord_num][nucl_num][elec_num]	in	Electron-nucleus rescaled factor
factor_een	double[walk_num]	out	Electron-nucleus jastrow

integer function qmckl_compute_factor_een_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_f

Test

/* Check if Jastrow is properly initialized */
assert(qmckl_jastrow_provided(context));

double factor_een[walk_num];
rc = qmckl_get_jastrow_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_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 nucleii
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 nucleii
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_provided(context));

double factor_een_deriv_e[4][walk_num][elec_num];
rc = qmckl_get_jastrow_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);

TODO Jastrow VGL functions