Jastrow Factor

1. Introduction
2. Context
3. Computation

1 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 us 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:

\[ J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{i=1}^{N_\text{elec}} \sum_{\alpha=1}^{N_\text{nucl}} \frac{a_1\, f(R_{i\alpha})}{1+a_2\, f(R_{i\alpha})} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1}\, [f(R_{i\alpha})]^p - J_{eN}^\infty \]

\(J_{\text{ee}}\) contains electron-electron terms: \[ J_{\text{ee}}(\mathbf{r}) = \sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{b_1\, f(r_{ij})}{1+b_2\, f(r_{ij})} + \sum_{p=2}^{N_\text{ord}^b} a_{p+1}\, [f(r_{ij})]^p - J_{ee}^\infty \]

and \(J_{\text{eeN}}\) contains electron-electron-Nucleus terms:

\[ J_{\text{eeN}}(\mathbf{r},\mathbf{R}) = \sum_{\alpha=1}^{N_{\text{nucl}}} \sum_{i=1}^{N_{\text{elec}}} \sum_{j=1}^{i-1} \sum_{p=2}^{N_{\text{ord}}} \sum_{k=0}^{p-1} \sum_{l=0}^{p-k-2\delta_{k,0}} c_{lkp\alpha} \left[ g({r}_{ij}) \right]^k \left[ \left[ g({R}_{i\alpha}) \right]^l + \left[ g({R}_{j\alpha}) \right]^l \right] \left[ g({R}_{i\,\alpha}) \, g({R}_{j\alpha}) \right]^{(p-k-l)/2} \]

\(c_{lkp\alpha}\) are non-zero only when \(p-k-l\) is even.

\(f\) and \(g\) are scaling function defined as

\[ f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and } g(r) = e^{-\kappa\, r}. \]

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.

2 Context

The following data stored in the context:

Variable	Type	In/Out	Description
`uninitialized`	`int32_t`	in	Keeps bits set for uninitialized data
`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 Nucleii types
`type_nucl_vector`	`int64_t[nucl_num]`	in	IDs of types of Nucleii
`aord_vector`	`double[aord_num + 1][type_nucl_num]`	in	Order of a polynomial coefficients
`bord_vector`	`double[bord_num + 1]`	in	Order of b polynomial coefficients
`cord_vector`	`double[cord_num][type_nucl_num]`	in	Order of c polynomial coefficients
`factor_ee`	`double[walk_num]`	out	Jastrow factor: electron-electron part
`factor_ee_date`	`uint64_t`	out	Jastrow factor: electron-electron part
`factor_en`	`double[walk_num]`	out	Jastrow factor: electron-nucleus part
`factor_en_date`	`uint64_t`	out	Jastrow factor: electron-nucleus part
`factor_een`	`double[walk_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][walk_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][walk_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][walk_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_cord_vect`	`int64_t`	Number of unique C coefficients
`dim_cord_vect_date`	`uint64_t`	Number of unique C coefficients
`asymp_jasb`	`double[2]`	Asymptotic component
`asymp_jasb_date`	`uint64_t`	Asymptotic component
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	vector of non-zero coefficients
`cord_vect_full_date`	`uint64_t`	Keep track of changes here
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	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[walk_num][cord_num][cord_num+1][nucl_num][elec_num]`	vector of non-zero coefficients
`dtmp_c`	`double[walk_num][elec_num][4][nucl_num][cord_num+1][cord_num]`	vector of non-zero coefficients

`een_rescaled_n`	`double[walk_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[walk_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[walk_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

2.1 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_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;
  int64_t* type_nucl_vector;
  double * aord_vector;
  double * bord_vector;
  double * cord_vector;
  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_cord_vect;
  uint64_t  dim_cord_vect_date;
  double * cord_vect_full;
  uint64_t  cord_vect_full_date;
  int64_t* lkpm_combined_index;
  uint64_t  lkpm_combined_index_date;
  double * tmp_c;
  double * dtmp_c;
  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;

  #ifdef HAVE_HPC
  bool     gpu_offload;
  #endif
} 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 << 5) - 1;

  /* Default values */

  return QMCKL_SUCCESS;
}

2.2 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);

2.3 Initialization functions

To prepare for the Jastrow and its derivative, all the following functions need to be called.

qmckl_exit_code  qmckl_set_jastrow_ord_num           (qmckl_context context, const int64_t aord_num, const int64_t bord_num, 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_aord_vector       (qmckl_context context, const double * aord_vector, const int64_t size_max);
qmckl_exit_code  qmckl_set_jastrow_bord_vector       (qmckl_context context, const double * bord_vector, const int64_t size_max);
qmckl_exit_code  qmckl_set_jastrow_cord_vector       (qmckl_context context, const double * cord_vector, const int64_t size_max);

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 for an optimal flop count.

2.4 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;
double  rescale_factor_kappa_ee   = 1.0;
double  rescale_factor_kappa_en   = 1.0;
double  nucl_rescale_factor_kappa = 1.0;
double* elec_coord    = &(n2_elec_coord[0][0][0]);

const double*   nucl_charge   = n2_charge;
int64_t  nucl_num      = n2_nucl_num;
double*  nucl_coord    = &(n2_nucl_coord[0][0]);
int64_t size_max;

/* Provide Electron data */

qmckl_exit_code rc;

assert(!qmckl_electron_provided(context));

int64_t n;
rc = qmckl_get_electron_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_get_electron_up_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_get_electron_down_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);


rc = qmckl_set_electron_num (context, elec_up_num, elec_dn_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_electron_provided(context));

rc = qmckl_get_electron_up_num (context, &n);
assert(rc == QMCKL_SUCCESS);
assert(n == elec_up_num);

rc = qmckl_get_electron_down_num (context, &n);
assert(rc == QMCKL_SUCCESS);
assert(n == elec_dn_num);

rc = qmckl_get_electron_num (context, &n);
assert(rc == QMCKL_SUCCESS);
assert(n == elec_num);

double k_ee = 0.;
double k_en = 0.;
rc = qmckl_get_electron_rescale_factor_ee (context, &k_ee);
assert(rc == QMCKL_SUCCESS);
assert(k_ee == 1.0);

rc = qmckl_get_electron_rescale_factor_en (context, &k_en);
assert(rc == QMCKL_SUCCESS);
assert(k_en == 1.0);

rc = qmckl_set_electron_rescale_factor_en(context, rescale_factor_kappa_en);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_electron_rescale_factor_ee(context, rescale_factor_kappa_ee);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_electron_rescale_factor_ee (context, &k_ee);
assert(rc == QMCKL_SUCCESS);
assert(k_ee == rescale_factor_kappa_ee);

rc = qmckl_get_electron_rescale_factor_en (context, &k_en);
assert(rc == QMCKL_SUCCESS);
assert(k_en == rescale_factor_kappa_en);


int64_t w;
rc = qmckl_get_electron_walk_num (context, &w);
assert(rc == QMCKL_NOT_PROVIDED);


rc = qmckl_set_electron_walk_num (context, walk_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_electron_walk_num (context, &w);
assert(rc == QMCKL_SUCCESS);
assert(w == walk_num);

assert(qmckl_electron_provided(context));

rc = qmckl_set_electron_coord (context, 'N', elec_coord, walk_num*3*elec_num);
assert(rc == QMCKL_SUCCESS);

double elec_coord2[walk_num*3*elec_num];

rc = 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_get_nucleus_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);


rc = qmckl_set_nucleus_num (context, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_nucleus_provided(context));

rc = qmckl_get_nucleus_num (context, &n);
assert(rc == QMCKL_SUCCESS);
assert(n == nucl_num);

double k;
rc = qmckl_get_nucleus_rescale_factor (context, &k);
assert(rc == QMCKL_SUCCESS);
assert(k == 1.0);


rc = qmckl_set_nucleus_rescale_factor (context, nucl_rescale_factor_kappa);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_nucleus_rescale_factor (context, &k);
assert(rc == QMCKL_SUCCESS);
assert(k == nucl_rescale_factor_kappa);

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_set_nucleus_coord (context, 'T', &(nucl_coord[0]), 3*nucl_num);
assert(rc == QMCKL_SUCCESS);

assert(!qmckl_nucleus_provided(context));

rc = 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_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_set_nucleus_charge(context, nucl_charge, nucl_num);
assert(rc == QMCKL_SUCCESS);

rc = 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));

3 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.

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

Calculate the asymptotic component asymp_jasb to be substracted from the final electron-electron jastrow factor \(J_{\text{ee}}\). The asymptotic component is calculated via the bord_vector and the electron-electron rescale factor rescale_factor_kappa.

\[ J_{\text{ee}}^{\infty} = \frac{b_1 \kappa^{-1}}{1 + b_2 \kappa^{-1}} \]

3.1.1 Get

qmckl_exit_code
qmckl_get_jastrow_asymp_jasb(qmckl_context context,
                             double* const asymp_jasb,
                             const int64_t size_max);

3.1.2 Compute

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`bord_num`	`int64_t`	in	Order of the polynomial
`bord_vector`	`double[bord_num+1]`	in	Values of b
`rescale_factor_kappa_ee`	`double`	in	Electron coordinates
`asymp_jasb`	`double[2]`	out	Asymptotic value

integer function qmckl_compute_asymp_jasb_f(context, bord_num, bord_vector, rescale_factor_kappa_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)  :: bord_vector(bord_num + 1)
  double precision      , intent(in)  :: rescale_factor_kappa_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_kappa_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 = bord_vector(1) * kappa_inv / (1.0d0 + bord_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) + bord_vector(p + 1) * x
     end do
  end do

end function qmckl_compute_asymp_jasb_f

qmckl_exit_code qmckl_compute_asymp_jasb (
          const qmckl_context context,
          const int64_t bord_num,
          const double* bord_vector,
          const double rescale_factor_kappa_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_kappa_ee;
    const double asym_one = bord_vector[0] * kappa_inv / (1.0 + bord_vector[1] * kappa_inv);
    asymp_jasb[0] = asym_one;
    asymp_jasb[1] = 0.5 * asym_one;

    for (int i = 0 ; i <= 1; ++i) {
      double x = kappa_inv;
      for (int p = 1; p < bord_num; ++p){
        x *= kappa_inv;
        asymp_jasb[i] = asymp_jasb[i] + bord_vector[p + 1] * x;
      }
    }

  return QMCKL_SUCCESS;
}

3.1.3 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* aord_vector = &(n2_aord_vector[0][0]);
double* bord_vector = &(n2_bord_vector[0]);
double* cord_vector = &(n2_cord_vector[0][0]);
int64_t dim_cord_vect=0;

/* Initialize the Jastrow data */
rc = qmckl_init_jastrow(context);
assert(!qmckl_jastrow_provided(context));

/* Set the data */
rc = qmckl_set_jastrow_ord_num(context, aord_num, bord_num, cord_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_jastrow_type_nucl_num(context, type_nucl_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_jastrow_type_nucl_vector(context, type_nucl_vector, nucl_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_jastrow_aord_vector(context, aord_vector,(aord_num+1)*type_nucl_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_jastrow_bord_vector(context, bord_vector,(bord_num+1));
assert(rc == QMCKL_SUCCESS);
rc = qmckl_get_jastrow_dim_cord_vect(context, &dim_cord_vect);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_jastrow_cord_vector(context, cord_vector,dim_cord_vect*type_nucl_num);
assert(rc == QMCKL_SUCCESS);

/* 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);

3.2 Electron-electron component \(f_{ee}\)

Calculate the electron-electron jastrow component factor_ee using the asymp_jasb componenet and the electron-electron rescaled distances ee_distance_rescaled.

\[ f_{ee} = \sum_{i,j

3.2.1 Get

qmckl_exit_code
qmckl_get_jastrow_factor_ee(qmckl_context context,
                            double* const factor_ee,
                            const int64_t size_max);

3.2.2 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
`bord_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_f(context, walk_num, elec_num, up_num, bord_num,            &
                                           bord_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)  :: bord_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 + bord_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 * bord_vector(1)  * &
                                ee_distance_rescaled(i,j,nw) / &
                                (1.0d0 + bord_vector(2) *   &
                                ee_distance_rescaled(i,j,nw))  &
                               -asymp_jasb(ipar) + power_ser

     end do
  end do
  end do

end function qmckl_compute_factor_ee_f

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* bord_vector,
      const double* ee_distance_rescaled,
      const double* asymp_jasb,
      double* const factor_ee ) {

  int ipar; // can we use a smaller integer?
  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.
    for (int i = 0; i < elec_num; ++i ) {
      for (int j = 0; j < i; ++j) {
        //x = ee_distance_rescaled[j * (walk_num * elec_num) + i * (walk_num) + nw];
        x = ee_distance_rescaled[j + i * elec_num + nw*(elec_num * elec_num)];
        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 = power_ser + bord_vector[p + 1] * x;
        }

        if(i < up_num || j >= up_num) {
          spin_fact = 0.5;
          ipar = 1;
        }

        factor_ee[nw] = factor_ee[nw] + spin_fact * bord_vector[0]  * \
                                x1 /  \
                                (1.0 + bord_vector[1] *               \
                                x1)   \
                               -asymp_jasb[ipar] + power_ser;

      }
    }
  }

  return QMCKL_SUCCESS;
}

3.2.3 Test

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

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

// calculate factor_ee
assert(fabs(factor_ee[0]+4.282760865958113) < 1.e-12);

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

Calculate the derivative of the factor_ee 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.

TODO: Add equation

3.3.1 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);

3.3.2 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
`bord_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, &
     bord_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)  :: bord_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 + bord_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 .LE. up_num .AND. j .LE. up_num ) .OR.  &
           (i .GT. up_num .AND. j .GT. 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 * bord_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 * bord_vector(2) * dx(ii) * dx(ii)

          factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) + spin_fact * bord_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 * bord_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* bord_vector,
      const double* ee_distance_rescaled,
      const double* ee_distance_rescaled_deriv_e,
      double* const factor_ee_deriv_e ) {

  int64_t ii;
  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 + bord_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 * bord_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 * bord_vector[1] * dx[ii] * dx[ii];

          factor_ee_deriv_e[i  + ii * elec_num  + nw * elec_num * 4 ] +=              \
                                       + spin_fact * bord_vector[0] * dx[ii] * invden2 \
                                       + pow_ser_g[ii] ;
        }

        ii = 3;
        lap2 = lap2 * dx[ii] * third;
        lap3 = lap3 + den * dx[ii];
        lap3 = lap3 * (spin_fact * bord_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* bord_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* bord_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* bord_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, bord_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, bord_vector, ee_distance_rescaled, ee_distance_rescaled_deriv_e, factor_ee_deriv_e ); 
      #endif
}

3.3.3 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);

3.4 Electron-nucleus component \(f_{en}\)

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

\[ f_{en} = \sum_{i,j

3.4.1 Get

qmckl_exit_code
qmckl_get_jastrow_factor_en(qmckl_context context,
                            double* const factor_en,
                            const int64_t size_max);

3.4.2 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
`aord_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
`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, aord_vector, &
     en_distance_rescaled, 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)  :: aord_vector(aord_num + 1, type_nucl_num)
  double precision      , intent(in)  :: en_distance_rescaled(elec_num, nucl_num, walk_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

  factor_en = 0.0d0

  do nw =1, walk_num
  do a = 1, nucl_num
     do i = 1, elec_num
        x = en_distance_rescaled(i, a, nw)
        power_ser = 0.0d0

        do p = 2, aord_num
          x = x * en_distance_rescaled(i, a, nw)
          power_ser = power_ser + aord_vector(p + 1, type_nucl_vector(a)) * x
        end do

        factor_en(nw) = factor_en(nw) + aord_vector(1, type_nucl_vector(a)) *  &
                                en_distance_rescaled(i, a, nw) /               &
                                (1.0d0 + aord_vector(2, type_nucl_vector(a)) * &
                                en_distance_rescaled(i, a, nw))                &
                                + power_ser

     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* aord_vector,
      const double* en_distance_rescaled,
      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 (aord_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 = ee_distance_rescaled[j * (walk_num * elec_num) + i * (walk_num) + nw];
        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 + aord_vector[(p+1)-1 + (type_nucl_vector[a]-1) * aord_num] * x;
        }

        factor_en[nw] = factor_en[nw] + aord_vector[0 + (type_nucl_vector[a]-1)*aord_num] * x1 / \
                        (1.0 + aord_vector[1 + (type_nucl_vector[a]-1) * aord_num] * x1) + \
                        power_ser;

      }
    }
  }

  return QMCKL_SUCCESS;
}

3.4.3 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(factor_en[0]+5.865822569188727) < 1.e-12);

3.5 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.

3.5.1 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);

3.5.2 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
`aord_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, aord_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)  :: aord_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 + aord_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 * aord_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 * aord_vector(2, type_nucl_vector(a)) * dx(ii) * dx(ii)

          factor_en_deriv_e(i, ii, nw) = factor_en_deriv_e(i, ii, nw) + aord_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 * aord_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

3.5.3 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);

3.6 Electron-electron 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.

3.6.1 Get

qmckl_exit_code
qmckl_get_jastrow_een_rescaled_e(qmckl_context context,
                                 double* const distance_rescaled,
                                 const int64_t size_max);

3.6.2 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_kappa_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_kappa_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_kappa_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

  allocate(een_rescaled_e_ij(elec_num * (elec_num - 1) / 2, cord_num + 1))

  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             = 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_kappa_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_kappa_ee,
          const double* ee_distance,
          double* const een_rescaled_e ) {

  double   *een_rescaled_e_ij;
  double   x;
  const int64_t   elec_pairs = (elec_num * (elec_num - 1)) / 2;
  const int64_t   len_een_ij = elec_pairs * (cord_num + 1);
  int64_t   k;

  // number of element 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);
  een_rescaled_e_ij = (double *) malloc (len_een_ij * sizeof(double));

  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;
  }

  /*
  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 );
    }

    k = 0;
    for (int i = 0; i < elec_num; ++i) {
      for (int j = 0; j < i; ++j) {
        // een_rescaled_e_ij(k, 2) = dexp(-rescale_factor_kappa_ee * ee_distance(i, j, nw));
        een_rescaled_e_ij[k + elec_pairs] = exp(-rescale_factor_kappa_ee * \
                                    ee_distance[j + i*elec_num + nw*(elec_num*elec_num)]);
        k = k + 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) {
    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_kappa_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_kappa_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_kappa_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_kappa_ee, ee_distance, een_rescaled_e);
#else
return qmckl_compute_een_rescaled_e_doc(context, walk_num, elec_num, cord_num, rescale_factor_kappa_ee, ee_distance, een_rescaled_e);
#endif
}

3.6.3 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);

3.7 Electron-electron 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

3.7.1 Get

qmckl_exit_code
qmckl_get_jastrow_een_rescaled_e_deriv_e(qmckl_context context,
                                         double* const distance_rescaled,
                                         const int64_t size_max);

3.7.2 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_kappa_ee`	`double`	in	Factor to rescale ee distances
`coord_new`	`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_kappa_ee,  &
     coord_new, 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_kappa_ee
  double precision      , intent(in)  :: coord_new(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_new(i, ii, nw) - coord_new(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_kappa_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

3.7.3 Test

//assert(qmckl_electron_provided(context));
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);

3.8 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.

3.8.1 Get

qmckl_exit_code
qmckl_get_jastrow_een_rescaled_n(qmckl_context context,
                                 double* const distance_rescaled,
                                 const int64_t size_max);

3.8.2 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
`cord_num`	`int64_t`	in	Order of polynomials
`rescale_factor_kappa_en`	`double`	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, cord_num, rescale_factor_kappa_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)  :: cord_num
  double precision      , intent(in)  :: rescale_factor_kappa_en
  double precision      , intent(in)  :: en_distance(elec_num,nucl_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_kappa_en * en_distance(i, a, 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 cord_num,
      const double rescale_factor_kappa_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] = 17.0;
  }

  for (int nw = 0; nw < walk_num; ++nw) {
    for (int a = 0; a < nucl_num; ++a) {
      for (int i = 0; i < elec_num; ++i) {
        // prepare the actual een table
        //een_rescaled_n(:, :, 0, nw) = 1.0d0
        een_rescaled_n[i + a * elec_num + 0 + nw * elec_num*nucl_num*(cord_num+1)] = 1.0;
        //een_rescaled_n(i, a, 1, nw) = dexp(-rescale_factor_kappa_en * en_distance(i, a, nw))
        een_rescaled_n[i + a*elec_num + elec_num*nucl_num + nw*elec_num*nucl_num*(cord_num+1)] = exp(-rescale_factor_kappa_en * \
                                                                              en_distance[i + a*elec_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;
}

3.8.3 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);

3.9 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:

3.9.1 Get

qmckl_exit_code
qmckl_get_jastrow_een_rescaled_n_deriv_e(qmckl_context context,
                                         double* const distance_rescaled,
                                         const int64_t size_max);

3.9.2 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
`cord_num`	`int64_t`	in	Order of polynomials
`rescale_factor_kappa_en`	`double`	in	Factor to rescale ee distances
`coord_new`	`double[walk_num][3][elec_num]`	in	Electron coordinates
`coord`	`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, &
     cord_num, rescale_factor_kappa_en, &
     coord_new, coord, 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)  :: cord_num
  double precision      , intent(in)  :: rescale_factor_kappa_en
  double precision      , intent(in)  :: coord_new(elec_num,3,walk_num)
  double precision      , intent(in)  :: coord(nucl_num,3)
  double precision      , intent(in)  :: en_distance(elec_num,nucl_num,walk_num)
  double precision      , intent(in)  :: een_rescaled_n(elec_num,nucl_num,0:cord_num,walk_num)
  double precision      , intent(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(i, a, nw)
      do ii = 1, 3
        elnuc_dist_deriv_e(ii, i, a) = (coord_new(i, ii, nw) - coord(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
    kappa_l = - dble(l) * rescale_factor_kappa_en
    do a = 1, nucl_num
      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

3.9.3 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);

3.10 Prepare for electron-electron-nucleus Jastrow \(f_{een}\)

Prepare cord_vect_full and lkpm_combined_index tables required for the calculation of the three-body jastrow factor_een and its derivative factor_een_deriv_e.

3.10.1 Get

qmckl_exit_code qmckl_get_jastrow_dim_cord_vect(qmckl_context context, int64_t* const dim_cord_vect);
qmckl_exit_code qmckl_get_jastrow_cord_vect_full(qmckl_context context, double* const cord_vect_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);

3.10.2 Compute dim_cord_vect

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`cord_num`	`int64_t`	in	Order of polynomials
`dim_cord_vect`	`int64_t`	out	dimension of cord_vect_full table

integer function qmckl_compute_dim_cord_vect_f( &
     context, cord_num, dim_cord_vect) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: cord_num
  integer*8             , intent(out) :: dim_cord_vect
  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_cord_vect = 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_cord_vect = dim_cord_vect + 1
      end do
    end do
  end do

end function qmckl_compute_dim_cord_vect_f

qmckl_exit_code qmckl_compute_dim_cord_vect (
      const qmckl_context context,
      const int64_t cord_num,
      int64_t* const dim_cord_vect){

  int         lmax;


  if (context == QMCKL_NULL_CONTEXT) {
    return QMCKL_INVALID_CONTEXT;
  }

  if (cord_num <= 0) {
    return QMCKL_INVALID_ARG_2;
  }

  *dim_cord_vect = 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_cord_vect=*dim_cord_vect+1;
      }
    }
  }

  return QMCKL_SUCCESS;
}

3.10.3 Compute cord_vect_full

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`nucl_num`	`int64_t`	in	Number of atoms
`dim_cord_vect`	`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
`cord_vector`	`double[dim_cord_vect][type_nucl_num]`	in	dimension of cord full table
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	out	Full list of coefficients

integer function qmckl_compute_cord_vect_full_doc_f( &
     context, nucl_num, dim_cord_vect, type_nucl_num,  &
     type_nucl_vector, cord_vector, cord_vect_full) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: nucl_num
  integer*8             , intent(in)  :: dim_cord_vect
  integer*8             , intent(in)  :: type_nucl_num
  integer*8             , intent(in)  :: type_nucl_vector(nucl_num)
  double precision      , intent(in)  :: cord_vector(type_nucl_num, dim_cord_vect)
  double precision      , intent(out) :: cord_vect_full(nucl_num,dim_cord_vect)
  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_cord_vect <= 0) then
     info = QMCKL_INVALID_ARG_5
     return
  endif


  do a = 1, nucl_num
    cord_vect_full(a,1:dim_cord_vect) = cord_vector(type_nucl_vector(a),1:dim_cord_vect)
  end do

end function qmckl_compute_cord_vect_full_doc_f

qmckl_exit_code qmckl_compute_cord_vect_full_hpc (
          const qmckl_context context,
          const int64_t nucl_num,
          const int64_t dim_cord_vect,
          const int64_t type_nucl_num,
          const int64_t* type_nucl_vector,
          const double* cord_vector,
          double* const cord_vect_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_cord_vect <= 0) {
     return QMCKL_INVALID_ARG_5;
  }

  for (int i=0; i < dim_cord_vect; ++i) {
    for (int a=0; a < nucl_num; ++a){
      cord_vect_full[a + i*nucl_num] = cord_vector[(type_nucl_vector[a]-1)+i*type_nucl_num];
    }
  }

  return QMCKL_SUCCESS;
  }

qmckl_exit_code qmckl_compute_cord_vect_full_doc (
      const qmckl_context context,
      const int64_t nucl_num,
      const int64_t dim_cord_vect,
      const int64_t type_nucl_num,
      const int64_t* type_nucl_vector,
      const double* cord_vector,
      double* const cord_vect_full );

qmckl_exit_code qmckl_compute_cord_vect_full_hpc (
      const qmckl_context context,
      const int64_t nucl_num,
      const int64_t dim_cord_vect,
      const int64_t type_nucl_num,
      const int64_t* type_nucl_vector,
      const double* cord_vector,
      double* const cord_vect_full );

qmckl_exit_code qmckl_compute_cord_vect_full (
          const qmckl_context context,
          const int64_t nucl_num,
          const int64_t dim_cord_vect,
          const int64_t type_nucl_num,
          const int64_t* type_nucl_vector,
          const double* cord_vector,
          double* const cord_vect_full ) {

    #ifdef HAVE_HPC
      return qmckl_compute_cord_vect_full_hpc(context, nucl_num, dim_cord_vect, type_nucl_num, type_nucl_vector, cord_vector, cord_vect_full);
    #else
      return qmckl_compute_cord_vect_full_doc(context, nucl_num, dim_cord_vect, type_nucl_num, type_nucl_vector, cord_vector, cord_vect_full);
    #endif
    }

3.10.4 Compute lkpm_combined_index

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`cord_num`	`int64_t`	in	Order of polynomials
`dim_cord_vect`	`int64_t`	in	dimension of cord full table
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	out	Full list of combined indices

integer function qmckl_compute_lkpm_combined_index_f( &
     context, cord_num, dim_cord_vect,  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_cord_vect
  integer*8             , intent(out) :: lkpm_combined_index(dim_cord_vect, 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_cord_vect <= 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_cord_vect,
      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_cord_vect <= 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_cord_vect] = k;
        lkpm_combined_index[kk + 2*dim_cord_vect] = p;
        lkpm_combined_index[kk + 3*dim_cord_vect] = m;
        kk = kk + 1;
      }
    }
  }

  return QMCKL_SUCCESS;
}

3.10.5 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 );

3.10.6 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

3.10.7 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", tmp_c[0][1][0][0][0],0.237440520852232);
assert(fabs(dtmp_c[0][1][0][0][0][0] - 0.237440520852232) < 1e-12);
return QMCKL_SUCCESS;

3.11 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.

3.11.1 Get

qmckl_exit_code
qmckl_get_jastrow_factor_een(qmckl_context context,
                             double* const factor_een,
                             const int64_t size_max);

3.11.2 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_cord_vect`	`int64_t`	in	dimension of full coefficient vector
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	in	full coefficient vector
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	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_cord_vect, cord_vect_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_cord_vect
  integer*8             , intent(in)  :: lkpm_combined_index(dim_cord_vect,4)
  double precision      , intent(in)  :: cord_vect_full(nucl_num, dim_cord_vect)
  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_cord_vect
    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 = cord_vect_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

3.11.3 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_cord_vect`	`int64_t`	in	dimension of full coefficient vector
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	in	full coefficient vector
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	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_cord_vect, cord_vect_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_cord_vect
  integer*8             , intent(in)  :: lkpm_combined_index(dim_cord_vect,4)
  double precision      , intent(in)  :: cord_vect_full(nucl_num, dim_cord_vect)
  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_cord_vect
    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 = cord_vect_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

3.11.4 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);
return QMCKL_SUCCESS;

3.12 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.

3.12.1 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);

3.12.2 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_cord_vect`	`int64_t`	in	dimension of full coefficient vector
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	in	full coefficient vector
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	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_cord_vect, &
     cord_vect_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_cord_vect
  integer*8             , intent(in)  :: lkpm_combined_index(dim_cord_vect, 4)
  double precision      , intent(in)  :: cord_vect_full(nucl_num, dim_cord_vect)
  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_cord_vect
    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 = cord_vect_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

3.12.3 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_cord_vect`	`int64_t`	in	dimension of full coefficient vector
`cord_vect_full`	`double[dim_cord_vect][nucl_num]`	in	full coefficient vector
`lkpm_combined_index`	`int64_t[4][dim_cord_vect]`	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_cord_vect, cord_vect_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_cord_vect
  integer*8             , intent(in)  :: lkpm_combined_index(dim_cord_vect,4)
  double precision      , intent(in)  :: cord_vect_full(nucl_num, dim_cord_vect)
  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_cord_vect
    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 = cord_vect_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

3.12.4 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);

Jastrow Factor

Table of Contents

1 Introduction

2 Context

2.1 Data structure

2.2 Access functions

2.3 Initialization functions

2.4 Test

3 Computation

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

3.1.1 Get

3.1.2 Compute

3.1.3 Test

3.2 Electron-electron component \(f_{ee}\)

3.2.1 Get

3.2.2 Compute

3.2.3 Test

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

3.3.1 Get

3.3.2 Compute

3.3.3 Test

3.4 Electron-nucleus component \(f_{en}\)

3.4.1 Get

3.4.2 Compute

3.4.3 Test

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

3.5.1 Get

3.5.2 Compute

3.5.3 Test

3.6 Electron-electron rescaled distances for each order

3.6.1 Get

3.6.2 Compute

3.6.3 Test

3.7 Electron-electron rescaled distances for each order and derivatives

3.7.1 Get

3.7.2 Compute

3.7.3 Test

3.8 Electron-nucleus rescaled distances for each order

3.8.1 Get

3.8.2 Compute

3.8.3 Test

3.9 Electron-nucleus rescaled distances for each order and derivatives

3.9.1 Get

3.9.2 Compute

3.9.3 Test

3.10 Prepare for electron-electron-nucleus Jastrow \(f_{een}\)

3.10.1 Get

3.10.2 Compute dimcordvect

3.10.3 Compute cordvectfull

3.10.4 Compute lkpmcombinedindex

3.10.5 Compute tmpc

3.10.6 Compute dtmpc

3.10.7 Test

3.11 Electron-electron-nucleus Jastrow \(f_{een}\)

3.11.1 Get

3.11.2 Compute naive

3.11.3 Compute

3.11.4 Test

3.12 Electron-electron-nucleus Jastrow \(f_{een}\) derivative

3.12.1 Get

3.12.2 Compute Naive

3.12.3 Compute

3.12.4 Test

3.10.2 Compute dim_cord_vect

3.10.3 Compute cord_vect_full

3.10.4 Compute lkpm_combined_index

3.10.5 Compute tmp_c

3.10.6 Compute dtmp_c