TREX/qmckl

mirror of https://github.com/TREX-CoE/qmckl.git synced 2024-06-30 00:44:52 +02:00

vijay gopal chilkuri 48436607d6 Activated header. #22

2021-07-07 19:42:07 +05:30

196 KiB

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Jastrow Factor

Context
Computation

Functions for the calculation of the Jastrow factor \(f_{ee}, f_{en}, f_{een}\). These are stored in the factor_ee, factor_en, and factor_een variables. The jastrow structure contains all the information required to build these factors along with their derivatives.

Context

The following data stored in the context:

`int32_t`	`uninitialized`	in	Keeps bit set for uninitialized data
`int64_t`	`aord_num`	in	The number of a coeffecients
`int64_t`	`bord_num`	in	The number of b coeffecients
`int64_t`	`cord_num`	in	The number of c coeffecients
`int64_t`	`type_nucl_num`	in	Number of Nucleii types
`int64_t`	`type_nucl_vector[nucl_num]`	in	IDs of types of Nucleii
`double`	`aord_vector[aord_num + 1][type_nucl_num]`	in	Order of a polynomial coefficients
`double`	`bord_vector[bord_num + 1]`	in	Order of b polynomial coefficients
`double`	`cord_vector[cord_num][type_nucl_num]`	in	Order of c polynomial coefficients
`double`	`factor_ee[walk_num]`	out	Jastrow factor: electron-electron part
`int64_t`	`factor_ee_date`	out	Jastrow factor: electron-electron part
`double`	`factor_en[walk_num]`	out	Jastrow factor: electron-nucleus part
`int64_t`	`factor_en_date`	out	Jastrow factor: electron-nucleus part
`double`	`factor_een[walk_num]`	out	Jastrow factor: electron-electron-nucleus part
`int64_t`	`factor_een_date`	out	Jastrow factor: electron-electron-nucleus part
`double`	`factor_ee_deriv_e[4][nelec][walk_num]`	out	Derivative of the Jastrow factor: electron-electron-nucleus part
`int64_t`	`factor_ee_deriv_e_date`	out	Keep track of the date for the derivative
`double`	`factor_en_deriv_e[4][nelec][walk_num]`	out	Derivative of the Jastrow factor: electron-electron-nucleus part
`int64_t`	`factor_en_deriv_e_date`	out	Keep track of the date for the en derivative
`double`	`factor_een_deriv_e[4][nelec][walk_num]`	out	Derivative of the Jastrow factor: electron-electron-nucleus part
`int64_t`	`factor_een_deriv_e_date`	out	Keep track of the date for the een derivative

computed data:

`int64_t`	`dim_cord_vect`	Number of unique C coefficients
`int64_t`	`dim_cord_vect_date`	Number of unique C coefficients
`double`	`asymp_jasb[2]`	Asymptotic component
`int64_t`	`asymp_jasb_date`	Asymptotic component
`double`	`cord_vect_full[dim_cord_vect][nucl_num]`	vector of non-zero coefficients
`int64_t`	`cord_vect_full_date`	Keep track of changes here
`int64_t`	`lkpm_combined_index[4][dim_cord_vect]`	Transform l,k,p, and m into consecutive indices
`int64_t`	`lkpm_combined_index_date`	Transform l,k,p, and m into consecutive indices
`double`	`tmp_c[elec_num][nucl_num][ncord + 1][ncord][walk_num]`	vector of non-zero coefficients
`double`	`dtmp_c[elec_num][4][nucl_num][ncord + 1][ncord][walk_num]`	vector of non-zero coefficients
`double`	`een_rescaled_e[walk_num][elec_num][elec_num][0:cord_num]`	The electron-electron rescaled distances raised to the powers defined by cord
`int64_t`	`een_rescaled_e_date`	Keep track of the date of creation
`double`	`een_rescaled_n[walk_num][elec_num][nucl_num][0:cord_num]`	The electron-electron rescaled distances raised to the powers defined by cord
`int64_t`	`een_rescaled_n_date`	Keep track of the date of creation
`double`	`een_rescaled_e_deriv_e[walk_num][elec_num][4][elec_num][0:cord_num]`	The electron-electron rescaled distances raised to the powers defined by cord derivatives wrt electrons
`int64_t`	`een_rescaled_e_deriv_e_date`	Keep track of the date of creation
`double`	`een_rescaled_n_deriv_e[walk_num][elec_num][4][nucl_num][0:cord_num]`	The electron-electron rescaled distances raised to the powers defined by cord derivatives wrt electrons
`int64_t`	`een_rescaled_n_deriv_e_date`	Keep track of the date of creation

For H2O we have the following data:

import numpy as np

elec_num     = 10
nucl_num     = 2
up_num       = 5
down_num     = 5
nucl_coord = np.array([ [0.000000,  0.000000 ],
[0.000000,  0.000000 ],
[0.000000,  2.059801 ] ])

elec_coord =    [[[-0.250655104764153      ,  0.503070975550133      ,  -0.166554344502303],
  [-0.587812193472177      , -0.128751981129274      ,   0.187773606533075], 
  [ 1.61335569047166       , -0.615556732874863      ,  -1.43165470979934 ],
  [-4.901239896295210E-003 , -1.120440036458986E-002 ,   1.99761909330422 ],
  [ 0.766647499681200      , -0.293515395797937      ,   3.66454589201239 ],
  [-0.127732483187947      , -0.138975497694196      ,  -8.669850480215846E-002],
  [-0.232271834949124      , -1.059321673434182E-002 ,  -0.504862241464867],
  [ 1.09360863531826       , -2.036103063808752E-003 ,  -2.702796910818986E-002],
  [-0.108090166832043      ,  0.189161729653261      ,   2.15398313919894],
  [ 0.397978144318712      , -0.254277292595981      ,   2.54553335476344]]];

ee_distance_rescaled = [
[ 0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.550227800352402      ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.919155060185168      ,0.937695909123175      ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.893325429242815      ,0.851181978173561      ,0.978501685226877     ,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.982457268305353      ,0.976125002619471      ,0.994349933143149     ,
0.844077311588328      ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.482407528408731      ,0.414816073699124      ,0.894716035479343     ,
0.876540187084407      ,0.978921170036895      ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.459541909660400      ,0.545007215761510      ,0.883752955884551     ,
0.918958134888791      ,0.986386936267237      ,0.362209822236419     ,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.763732576854455      ,0.817282762358449      ,0.801802919535959     ,
0.900089095449775      ,0.975704636491453      ,0.707836537586060     ,
0.755705808346586      ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.904249454052971      ,0.871097965261373      ,0.982717262706270     ,
0.239901207363622      ,0.836519456769083      ,0.896135326270534     ,
0.930694340243023      ,0.917708540815567      ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.944400908070716      ,0.922589018494961      ,0.984615718580670     ,
0.514328661540623      ,0.692362267147064      ,0.931894098453677     ,
0.956034127544344      ,0.931221472309472      ,0.540903688625053     ,
0.000000000000000E+000]]

en_distance_rescaled = np.transpose(np.array([
[ 0.443570948411811  ,    0.467602196999105    ,  0.893870160799932 ,   
0.864347190364447  ,    0.976608182392358    ,  0.187563183468210 ,   
0.426404699872689  ,    0.665107090128166    ,  0.885246991424583 ,   
0.924902909715270     ],
[ 0.899360150637444     , 0.860035135365386   ,   0.979659405613798 ,   
6.140678415933776E-002, 0.835118398056681   ,   0.884071658981068 ,   
0.923860000907362     , 0.905203414522289   ,   0.211286300932359 ,   
0.492104840907350 ]]))

# symmetrize it
for i in range(elec_num):
for j in range(elec_num):
 ee_distance_rescaled[i][j] = ee_distance_rescaled[j][i]

type_nucl_num = 1
aord_num     = 5
bord_num     = 5
cord_num     = 23
dim_cord_vect= 23
type_nucl_vector = [ 1, 1]
aord_vector = [ 
[0.000000000000000E+000],
[0.000000000000000E+000],
[-0.380512000000000E+000],
[-0.157996000000000E+000],
[-3.155800000000000E-002],
[2.151200000000000E-002]]

bord_vector = [ 0.500000000000000E-000,  0.153660000000000E-000,  6.722620000000000E-002,
2.157000000000000E-002,  7.309600000000000E-003,  2.866000000000000E-003]
cord_vector = [ 0.571702000000000E-000, -0.514253000000000E-000, -0.513043000000000E-000, 
9.486000000000000E-003, -4.205000000000000E-003,  0.426325800000000E-000,
8.288150000000000E-002,  5.118600000000000E-003, -2.997800000000000E-003,
-5.270400000000000E-003, -7.499999999999999E-005, -8.301649999999999E-002,
1.454340000000000E-002,  5.143510000000000E-002,  9.250000000000000E-004,
-4.099100000000000E-003,  4.327600000000000E-003, -1.654470000000000E-003,
2.614000000000000E-003, -1.477000000000000E-003, -1.137000000000000E-003,
-4.010475000000000E-002,  6.106710000000000E-003 ]
cord_vector_full = [
[ 0.571702000000000E-000, -0.514253000000000E-000, -0.513043000000000E-000, 
9.486000000000000E-003, -4.205000000000000E-003,  0.426325800000000E-000,
8.288150000000000E-002,  5.118600000000000E-003, -2.997800000000000E-003,
-5.270400000000000E-003, -7.499999999999999E-005, -8.301649999999999E-002,
1.454340000000000E-002,  5.143510000000000E-002,  9.250000000000000E-004,
-4.099100000000000E-003,  4.327600000000000E-003, -1.654470000000000E-003,
2.614000000000000E-003, -1.477000000000000E-003, -1.137000000000000E-003,
-4.010475000000000E-002,  6.106710000000000E-003 ],
[ 0.571702000000000E-000, -0.514253000000000E-000, -0.513043000000000E-000, 
9.486000000000000E-003, -4.205000000000000E-003,  0.426325800000000E-000,
8.288150000000000E-002,  5.118600000000000E-003, -2.997800000000000E-003,
-5.270400000000000E-003, -7.499999999999999E-005, -8.301649999999999E-002,
1.454340000000000E-002,  5.143510000000000E-002,  9.250000000000000E-004,
-4.099100000000000E-003,  4.327600000000000E-003, -1.654470000000000E-003,
2.614000000000000E-003, -1.477000000000000E-003, -1.137000000000000E-003,
-4.010475000000000E-002,  6.106710000000000E-003 ],
]
lkpm_combined_index = [[1 , 1 , 2 , 0], 
       [0 , 0 , 2 , 1],
       [1 , 2 , 3 , 0],
       [2 , 1 , 3 , 0],
       [0 , 1 , 3 , 1],
       [1 , 0 , 3 , 1],
       [1 , 3 , 4 , 0],
       [2 , 2 , 4 , 0],
       [0 , 2 , 4 , 1],
       [3 , 1 , 4 , 0],
       [1 , 1 , 4 , 1],
       [2 , 0 , 4 , 1],
       [0 , 0 , 4 , 2],
       [1 , 4 , 5 , 0],
       [2 , 3 , 5 , 0],
       [0 , 3 , 5 , 1],
       [3 , 2 , 5 , 0],
       [1 , 2 , 5 , 1],
       [4 , 1 , 5 , 0],
       [2 , 1 , 5 , 1],
       [0 , 1 , 5 , 2],
       [3 , 0 , 5 , 1],
       [1 , 0 , 5 , 2]]

kappa     = 1.0
kappa_inv = 1.0/kappa

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;
int64_t  asymp_jasb_date;
int64_t  tmp_c_date;
int64_t  dtmp_c_date;
int64_t  factor_ee_date;
int64_t  factor_en_date;
int64_t  factor_een_date;
int64_t  factor_ee_deriv_e_date;
int64_t  factor_en_deriv_e_date;
int64_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;
int64_t  dim_cord_vect_date;
double * cord_vect_full;
int64_t  cord_vect_full_date;
int64_t* lkpm_combined_index;
int64_t  lkpm_combined_index_date;
double * tmp_c;
double * dtmp_c;
double * een_rescaled_e;
double * een_rescaled_n;
int64_t  een_rescaled_e_date;
int64_t  een_rescaled_n_date;
double * een_rescaled_e_deriv_e;
double * een_rescaled_n_deriv_e;
int64_t  een_rescaled_e_deriv_e_date;
int64_t  een_rescaled_n_deriv_e_date;
bool     provided;
char *   type;
} qmckl_jastrow_struct;

The uninitialized integer contains one bit set to one for each initialization function which has not been called. It becomes equal to zero after all initialization functions have been called. The struct is then initialized and provided == true. Some values are initialized by default, and are not concerned by this mechanism.

qmckl_exit_code qmckl_init_jastrow(qmckl_context context);

qmckl_exit_code qmckl_init_jastrow(qmckl_context context) {

if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
 return false;
}

qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);

ctx->jastrow.uninitialized = (1 << 6) - 1;

/* Default values */

return QMCKL_SUCCESS;
}

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);

#+NAME:post

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);
qmckl_exit_code  qmckl_set_jastrow_bord_vector       (qmckl_context context, const double * bord_vector);
qmckl_exit_code  qmckl_set_jastrow_cord_vector       (qmckl_context context, const double * cord_vector);
qmckl_exit_code  qmckl_set_jastrow_dependencies      (qmckl_context context);

#+NAME:pre2

#+NAME:post2

When the required information is completely entered, other data structures are computed to accelerate the calculations. The intermediates factors are precontracted using BLAS LEVEL 3 operations for an optimal FLOP count.

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*  charge        = n2_charge;
//double*  nucl_coord    = &(n2_nucl_coord[0][0]);

/* 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);
//assert(rc == QMCKL_SUCCESS);
//
//double elec_coord2[walk_num*3*elec_num];
//
//rc = qmckl_get_electron_coord (context, 'N', elec_coord2);
//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);
//assert(rc == QMCKL_NOT_PROVIDED);
//
//rc = qmckl_set_nucleus_coord (context, 'T', &(nucl_coord[0]));
//assert(rc == QMCKL_SUCCESS);
//
//assert(!qmckl_nucleus_provided(context));
//
//rc = qmckl_get_nucleus_coord (context, 'N', nucl_coord2);
//assert(rc == QMCKL_SUCCESS);
//for (size_t k=0 ; k<3 ; ++k) {
//  for (size_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);
//assert(rc == QMCKL_SUCCESS);
//for (size_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);
//assert(rc == QMCKL_NOT_PROVIDED);
//
//rc = qmckl_set_nucleus_charge(context, nucl_charge);
//assert(rc == QMCKL_SUCCESS);
//
//rc = qmckl_get_nucleus_charge(context, nucl_charge2);
//assert(rc == QMCKL_SUCCESS);
//for (size_t i=0 ; i<nucl_num ; ++i) {
//  assert( nucl_charge[i] == nucl_charge2[i] );
// }
//assert(qmckl_nucleus_provided(context));

Computation

The computed data is stored in the context so that it can be reused by different kernels. To ensure that the data is valid, for each computed data the date of the context is stored when it is computed. To know if some data needs to be recomputed, we check if the date of the dependencies are more recent than the date of the data to compute. If it is the case, then the data is recomputed and the current date is stored.

Asymptotic component for \(f_{ee}\)

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

\[ J_{asymp} = \frac{b_1 \kappa^-1}{1 + b_2 \kappa^-1} \]

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	bord_num	in	Number of electrons
double	bord_vector[bord_num + 1]	in	Number of walkers
double	rescale_factor_kappa_ee	in	Electron coordinates
double	asymp_jasb[2]	out	Electron-electron distances

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)
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 );

Test

asym_one         :  0.43340325572525706
asymp_jasb[0]    :  0.5323750557252571
asymp_jasb[1]    :  0.31567342786262853

//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]);
//
///* 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);
//assert(rc == QMCKL_SUCCESS);
//rc = qmckl_set_jastrow_bord_vector(context, bord_vector);
//assert(rc == QMCKL_SUCCESS);
//rc = qmckl_set_jastrow_cord_vector(context, cord_vector);
//assert(rc == QMCKL_SUCCESS);
//rc = qmckl_set_jastrow_dependencies(context);
//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);
//
//// calculate asymp_jasb
//assert(fabs(asymp_jasb[0]-0.5323750557252571) < 1.e-12);
//assert(fabs(asymp_jasb[1]-0.31567342786262853) < 1.e-12);

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

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

\[ f_{ee} = \sum_{i,j<i} \left\{ \frac{ \eta B_0 C_{ij}}{1 - B_1 C_{ij}} - J_{asymp} + \sum^{nord}_{k}B_k C_{ij}^k \right\} \]

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	up_num	in	Number of alpha electrons
int64_t	bord_num	in	Number of coefficients
double	bord_vector[bord_num + 1]	in	List of coefficients
double	ee_distance_rescaled[walk_num][elec_num][elec_num]	in	Electron-electron distances
double	asymp_jasb[2]	in	Electron-electron distances
double	factor_ee[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)
double precision      , intent(in)  :: ee_distance_rescaled(walk_num, elec_num, elec_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   :: pow_ser, x, spin_fact, 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 (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(nw,i,j)
    power_ser = 0.0d0
    spin_fact = 1.0d0
    ipar = 1

    do p = 2, bord_num
      x = x * ee_distance_rescaled(nw,i,j)
      power_ser = power_ser + bord_vector(p + 1) * x
    end do

    if(j .LE. up_num .OR. i .GT. up_num) then
      spin_fact = 0.5d0
      ipar = 2
    endif
    
    factor_ee(nw) = factor_ee(nw) + spin_fact * bord_vector(1)  * &
                            ee_distance_rescaled(nw,i,j) / &
                            (1.0d0 + bord_vector(2) *   &
                            ee_distance_rescaled(nw,i,j))  &
                           -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 );

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

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

Get

qmckl_exit_code qmckl_get_jastrow_factor_ee_deriv_e(qmckl_context context, double* const factor_ee_deriv_e);

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	up_num	in	Number of alpha electrons
int64_t	bord_num	in	Number of coefficients
double	bord_vector[bord_num + 1]	in	List of coefficients
double	ee_distance_rescaled[walk_num][elec_num][elec_num]	in	Electron-electron distances
double	ee_distance_rescaled_deriv_e[walk_num][4][elec_num][elec_num]	in	Electron-electron distances
double	asymp_jasb[2]	in	Electron-electron distances
double	factor_ee_deriv_e[walk_num][4][elec_num]	out	Electron-electron distances

integer function qmckl_compute_factor_ee_deriv_e_f(context, walk_num, elec_num, up_num, bord_num,            &
                                       bord_vector, ee_distance_rescaled, ee_distance_rescaled_deriv_e,  &
	   asymp_jasb, 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)
double precision      , intent(in)  :: ee_distance_rescaled(walk_num, elec_num, elec_num)
double precision      , intent(in)  :: ee_distance_rescaled_deriv_e(walk_num, 4, elec_num, elec_num)
double precision      , intent(in)  :: asymp_jasb(2)
double precision      , intent(out) :: factor_ee_deriv_e(elec_num,4,walk_num)

integer*8 :: i, j, p, ipar, 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(nw, i, j)
    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)
    ipar        = 1

    do ii = 1, 4
      dx(ii) = ee_distance_rescaled_deriv_e(nw, ii, i, j)
    end do

    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(nw, i, j)
      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(nw, i, j)
      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_f

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,
const double* asymp_jasb,
double* const factor_ee_deriv_e );

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]));
//
//// check factor_ee_deriv_e
//assert(fabs(factor_ee_deriv_e[0][0][0]-0.16364894652107934) < 1.e-12);
//assert(fabs(factor_ee_deriv_e[0][1][0]+0.6927548119830084 ) < 1.e-12);
//assert(fabs(factor_ee_deriv_e[0][2][0]-0.073267755223968  ) < 1.e-12);
//assert(fabs(factor_ee_deriv_e[0][3][0]-1.5111672803213185 ) < 1.e-12);

Electron-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.

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

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of nucleii
int64_t	type_nucl_num	in	Number of unique nuclei
int64_t	type_nucl_vector[type_nucl_num]	in	IDs of unique nucleii
int64_t	aord_num	in	Number of coefficients
double	aord_vector[aord_num + 1][type_nucl_num]	in	List of coefficients
double	en_distance_rescaled[walk_num][nucl_num][elec_num]	in	Electron-nucleus distances
double	factor_en[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(type_nucl_num)
double precision      , intent(in)  :: aord_vector(aord_num, nucl_num)
double precision      , intent(in)  :: en_distance_rescaled(walk_num, elec_num, nucl_num)
double precision      , intent(out) :: factor_en(walk_num)

integer*8 :: i, a, p, ipar, nw
double precision   :: x, spin_fact, 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(nw, i, a)
    power_ser = 0.0d0

    do p = 2, aord_num
      x = x * en_distance_rescaled(nw, i, a)
      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(nw, i, a) /               &
                            (1.0d0 + aord_vector(2, type_nucl_vector(a)) * &
                            en_distance_rescaled(nw, i, a))                &
                            + 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 );

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);
//
//// calculate factor_en
//assert(fabs(factor_en[0]+5.865822569188727) < 1.e-12);

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

Calculate the electron-electron jastrow component factor_en_deriv_e derivative with respect to the electron coordinates using the en_distance_rescaled and en_distance_rescaled_deriv_e which are already calculated previously.

TODO: write equations.

Get

qmckl_exit_code qmckl_get_jastrow_factor_en_deriv_e(qmckl_context context, double* const factor_en_deriv_e);

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of nucleii
int64_t	type_nucl_num	in	Number of unique nuclei
int64_t	type_nucl_vector[type_nucl_num]	in	IDs of unique nucleii
int64_t	aord_num	in	Number of coefficients
double	aord_vector[aord_num + 1][type_nucl_num]	in	List of coefficients
double	en_distance_rescaled[walk_num][nucl_num][elec_num]	in	Electron-nucleus distances
double	en_distance_rescaled_deriv_e[walk_num][4][nucl_num][elec_num]	in	Electron-nucleus distance derivatives
double	factor_en_deriv_e[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(type_nucl_num)
double precision      , intent(in)  :: aord_vector(aord_num, nucl_num)
double precision      , intent(in)  :: en_distance_rescaled(walk_num, elec_num, nucl_num)
double precision      , intent(in)  :: en_distance_rescaled_deriv_e(walk_num, 4, elec_num, nucl_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, spin_fact, 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(nw, i, a)
    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(nw, ii, i, a)
    end do

    lap1 = 0.0d0
    lap2 = 0.0d0
    lap3 = 0.0d0
    do ii = 1, 3
      x = en_distance_rescaled(nw, i, a)
      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(nw, i, a)
      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

qmckl_exit_code qmckl_compute_factor_en_deriv_e (
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,
const double* en_distance_rescaled_deriv_e,
double* const factor_en_deriv_e );

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]));
//
//// check factor_en_deriv_e
//assert(fabs(factor_en_deriv_e[0][0][0]-0.11609919541763383) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][1][0]+0.23301394780804574) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][2][0]-0.17548337641865783) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][3][0]+0.9667363412285741 ) < 1.e-12);

Electron-electron rescaled distances for each order

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

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

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

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	cord_num	in	Order of polynomials
double	rescale_factor_kappa_ee	in	Factor to rescale ee distances
double	ee_distance[walk_num][elec_num][elec_num]	in	Electron-electron distances
double	een_rescaled_e[walk_num][elec_num][elec_num][0:cord_num]	out	Electron-electron rescaled distances

integer function qmckl_compute_een_rescaled_e_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(0:cord_num,elec_num,elec_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(l, i, j, nw) = x
    een_rescaled_e(l, j, i, nw) = x
  end do
end do
end do
end do

end function qmckl_compute_een_rescaled_e_f

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 );

Test

//assert(qmckl_electron_provided(context));
//
//
//double een_rescaled_e[walk_num][elec_num][elec_num][(cord_num + 1)];
//rc = qmckl_get_jastrow_een_rescaled_e(context, &(een_rescaled_e[0][0][0][0]));
//
//// value of (0,2,1)
//assert(fabs(een_rescaled_e[0][0][2][1]-0.08084493981483197)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][0][3][1]-0.1066745707571846)    < 1.e-12);
//assert(fabs(een_rescaled_e[0][0][4][1]-0.01754273169464735)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][3][2]-0.02214680362033448)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][4][2]-0.0005700154999202759) < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][5][2]-0.3424402276009091)    < 1.e-12);

Electron-electron rescaled distances for each order and derivatives

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. Here we take its derivatives required for the een jastrow.

TODO: write formulae

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	cord_num	in	Order of polynomials
double	rescale_factor_kappa_ee	in	Factor to rescale ee distances
double	coord_new[walk_num][3][elec_num]	in	Electron coordinates
double	ee_distance[walk_num][elec_num][elec_num]	in	Electron-electron distances
double	een_rescaled_e[walk_num][elec_num][elec_num][0:cord_num]	in	Electron-electron distances
double	een_rescaled_e_deriv_e[walk_num][elec_num][4][elec_num][0:cord_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(0:cord_num,elec_num,elec_num,walk_num)
double precision      , intent(out) :: een_rescaled_e_deriv_e(0:cord_num,elec_num,4,elec_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
      do ii = 1, 4
        een_rescaled_e_deriv_e(l, i, ii, j, nw) = kappa_l * elec_dist_deriv_e(ii, i, j)
      end do

      een_rescaled_e_deriv_e(l, i, 4, j, nw) = een_rescaled_e_deriv_e(l, i, 4, j, nw)              &
                + een_rescaled_e_deriv_e(l, i, 1, j, nw) * een_rescaled_e_deriv_e(l, i, 1, j, nw)  &
                + een_rescaled_e_deriv_e(l, i, 2, j, nw) * een_rescaled_e_deriv_e(l, i, 2, j, nw)  &
                + een_rescaled_e_deriv_e(l, i, 3, j, nw) * een_rescaled_e_deriv_e(l, i, 3, j, nw)

      do ii = 1, 4
        een_rescaled_e_deriv_e(l, i, ii, j, nw) = een_rescaled_e_deriv_e(l, i, ii, j, nw) *   &
                                                  een_rescaled_e(l, i, j, nw)
      end do
    end do
  end do
end do
end do

end function qmckl_compute_factor_een_rescaled_e_deriv_e_f

qmckl_exit_code qmckl_compute_factor_een_rescaled_e_deriv_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* coord_new,
const double* ee_distance,
const double* een_rescaled_e,
double* const een_rescaled_e_deriv_e );

Test

//assert(qmckl_electron_provided(context));
//
//
//double een_rescaled_e[walk_num][elec_num][elec_num][(cord_num + 1)];
//rc = qmckl_get_jastrow_een_rescaled_e(context, &(een_rescaled_e[0][0][0][0]));
//
//// value of (0,2,1)
//assert(fabs(een_rescaled_e[0][0][2][1]-0.08084493981483197)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][0][3][1]-0.1066745707571846)    < 1.e-12);
//assert(fabs(een_rescaled_e[0][0][4][1]-0.01754273169464735)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][3][2]-0.02214680362033448)   < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][4][2]-0.0005700154999202759) < 1.e-12);
//assert(fabs(een_rescaled_e[0][1][5][2]-0.3424402276009091)    < 1.e-12);

Electron-nucleus rescaled distances for each order

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

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

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

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of atoms
int64_t	cord_num	in	Order of polynomials
double	rescale_factor_kappa_en	in	Factor to rescale ee distances
double	en_distance[walk_num][elec_num][nucl_num]	in	Electron-nucleus distances
double	een_rescaled_n[walk_num][elec_num][nucl_num][0:cord_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(0:cord_num,nucl_num,elec_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(1, a, i, 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(l, a, i, nw) = een_rescaled_n(l - 1, a, i, nw) * een_rescaled_n(1, a, i, 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 );

Test

//assert(qmckl_electron_provided(context));
//
//double een_rescaled_n[walk_num][elec_num][nucl_num][(cord_num + 1)];
//rc = qmckl_get_jastrow_een_rescaled_n(context, &(een_rescaled_n[0][0][0][0]));
//
//// value of (0,2,1)
//assert(fabs(een_rescaled_n[0][2][0][1]-0.10612983920006765)  < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][0][1]-0.135652809635553)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][0][1]-0.023391817607642338) < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][1][2]-0.880957224822116)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][1][2]-0.027185942659395074) < 1.e-12);
//assert(fabs(een_rescaled_n[0][5][1][2]-0.01343938025140174)  < 1.e-12);

Electron-nucleus rescaled distances for each order and derivatives

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

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of atoms
int64_t	cord_num	in	Order of polynomials
double	rescale_factor_kappa_en	in	Factor to rescale ee distances
double	coord_new[walk_num][3][elec_num]	in	Electron coordinates
double	coord[3][nucl_num]	in	Nuclear coordinates
double	en_distance[walk_num][elec_num][nucl_num]	in	Electron-nucleus distances
double	een_rescaled_n[walk_num][elec_num][nucl_num][0:cord_num]	in	Electron-nucleus distances
double	een_rescaled_n_deriv_e[walk_num][elec_num][4][nucl_num][0:cord_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(0:cord_num,nucl_num,elec_num,walk_num)
double precision      , intent(out) :: een_rescaled_n_deriv_e(0:cord_num,nucl_num,4,elec_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
    do ii = 1, 4
      een_rescaled_n_deriv_e(l, a, ii, i, nw) = kappa_l * elnuc_dist_deriv_e(ii, i, a)
    end do

    een_rescaled_n_deriv_e(l, a, 4, i, nw) = een_rescaled_n_deriv_e(l, a, 4, i, nw)           &
            + een_rescaled_n_deriv_e(l, a, 1, i, nw) * een_rescaled_n_deriv_e(l, a, 1, i, nw) &
            + een_rescaled_n_deriv_e(l, a, 2, i, nw) * een_rescaled_n_deriv_e(l, a, 2, i, nw) &
            + een_rescaled_n_deriv_e(l, a, 3, i, nw) * een_rescaled_n_deriv_e(l, a, 3, i, nw)

    do ii = 1, 4
      een_rescaled_n_deriv_e(l, a, ii, i, nw) = een_rescaled_n_deriv_e(l, a, ii, i, nw) * &
                                                een_rescaled_n(l, a, i, nw)
    end do
  end do
end do
end do
end do

end function qmckl_compute_factor_een_rescaled_n_deriv_e_f

qmckl_exit_code qmckl_compute_factor_een_rescaled_n_deriv_e (
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* coord_new,
const double* coord,
const double* en_distance,
const double* een_rescaled_n,
double* const een_rescaled_n_deriv_e );

Test

//assert(qmckl_electron_provided(context));
//
//double een_rescaled_n[walk_num][elec_num][nucl_num][(cord_num + 1)];
//rc = qmckl_get_jastrow_een_rescaled_n(context, &(een_rescaled_n[0][0][0][0]));
//
//// value of (0,2,1)
//assert(fabs(een_rescaled_n[0][2][0][1]-0.10612983920006765)  < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][0][1]-0.135652809635553)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][0][1]-0.023391817607642338) < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][1][2]-0.880957224822116)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][1][2]-0.027185942659395074) < 1.e-12);
//assert(fabs(een_rescaled_n[0][5][1][2]-0.01343938025140174)  < 1.e-12);

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.

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);

Compute dim_cord_vect

qmckl_context	context	in	Global state
int64_t	cord_num	in	Order of polynomials
int64_t	dim_cord_vect	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 );

Compute cord_vect_full

qmckl_context	context	in	Global state
int64_t	nucl_num	in	Number of atoms
int64_t	cord_num	in	Order of polynomials
int64_t	dim_cord_vect	in	dimension of cord full table
int64_t	type_nucl_num	in	dimension of cord full table
int64_t	type_nucl_vector[nucl_num]	in	dimension of cord full table
double	cord_vector[cord_num][type_nucl_num]	in	dimension of cord full table
double	cord_vect_full[dim_cord_vect][nucl_num]	out	Full list of coefficients

integer function qmckl_compute_cord_vect_full_f(context, nucl_num, cord_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)  :: cord_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(cord_num, type_nucl_num)
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 (cord_num <= 0) then
 info = QMCKL_INVALID_ARG_3
 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(1:dim_cord_vect,a) = cord_vector(1:dim_cord_vect,type_nucl_vector(a))
end do

end function qmckl_compute_cord_vect_full_f

qmckl_exit_code qmckl_compute_cord_vect_full (
const qmckl_context context,
const int64_t nucl_num,
const int64_t cord_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 );

Compute lkpm_combined_index

qmckl_context	context	in	Global state
int64_t	cord_num	in	Order of polynomials
int64_t	dim_cord_vect	in	dimension of cord full table
int64_t	lpkm_combined_index[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


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 lpkm_combined_index );

Test

//assert(qmckl_electron_provided(context));

//double een_rescaled_n[walk_num][elec_num][nucl_num][(cord_num + 1)];
//rc = qmckl_get_jastrow_een_rescaled_n(context, &(een_rescaled_n[0][0][0][0]));
//
//// value of (0,2,1)
//assert(fabs(een_rescaled_n[0][2][0][1]-0.10612983920006765)  < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][0][1]-0.135652809635553)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][0][1]-0.023391817607642338) < 1.e-12);
//assert(fabs(een_rescaled_n[0][3][1][2]-0.880957224822116)    < 1.e-12);
//assert(fabs(een_rescaled_n[0][4][1][2]-0.027185942659395074) < 1.e-12);
//assert(fabs(een_rescaled_n[0][5][1][2]-0.01343938025140174)  < 1.e-12);

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

Calculate the electron-electron-nuclear three-body jastrow component factor_een using the above prepared tables.

TODO: write equations.

Get

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

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of nucleii
int64_t	cord_num	in	order of polynomials
int64_t	dim_cord_vect	in	dimension of full coefficient vector
double	cord_vect_full[dim_cord_vect][nucl_num]	in	full coefficient vector
int64_t	lkpm_combined_index[4][dim_cord_vect]	in	combined indices
double	een_rescaled_e[walk_num][elec_num][elec_num][0:cord_num]	in	Electron-nucleus rescaled
double	een_rescaled_n[walk_num][elec_num][nucl_num][0:cord_num]	in	Electron-nucleus rescaled factor
double	factor_een[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,                                       &
                                       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(4,dim_cord_vect)
double precision      , intent(in)  :: cord_vect_full(dim_cord_vect, nucl_num)
double precision      , intent(in)  :: een_rescaled_e(walk_num, elec_num, elec_num, 0:cord_num)
double precision      , intent(in)  :: een_rescaled_n(walk_num, elec_num, nucl_num, 0:cord_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(1, n)  
k = lkpm_combined_index(2, n)  
p = lkpm_combined_index(3, n)  
m = lkpm_combined_index(4, n)  

do a = 1, nucl_num
  accu2 = 0.0d0
  cn = cord_vect_full(n, a)
  do j = 1, elec_num
    accu = 0.0d0
    do i = 1, elec_num
      accu = accu + een_rescaled_e(nw, i, j, k) *       &
                    een_rescaled_n(nw, i, a, m)
    end do
    accu2 = accu2 + accu * een_rescaled_n(nw, j, a, m + l)
  end do
  factor_een(nw) = factor_een(nw) + accu2 + cn
end do
end do
end do

end function qmckl_compute_factor_een_f

qmckl_exit_code qmckl_compute_factor_een (
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 int64_t dim_cord_vect,
const double* cord_vect_full,
const int64_t* lkpm_combined_index,
const double* een_rescaled_e,
const double* een_rescaled_n,
double* const factor_een );

Test

/* Check if Jastrow is properly initialized */
//assert(qmckl_jastrow_provided(context));
//
//// calculate factor_en_deriv_e
//double factor_een[walk_num];
//rc = qmckl_get_jastrow_factor_een(context, &(factor_een[0]));

//// check factor_en_deriv_e
//assert(fabs(factor_en_deriv_e[0][0][0]-0.11609919541763383) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][1][0]+0.23301394780804574) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][2][0]-0.17548337641865783) < 1.e-12);
//assert(fabs(factor_en_deriv_e[0][3][0]+0.9667363412285741 ) < 1.e-12);

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

Calculate the electron-electron-nuclear three-body jastrow component factor_een_deriv_e using the above prepared tables.

TODO: write equations.

Get

qmckl_exit_code qmckl_get_jastrow_factor_een_deriv_e(qmckl_context context, double* const factor_een_deriv_e);

Compute

qmckl_context	context	in	Global state
int64_t	walk_num	in	Number of walkers
int64_t	elec_num	in	Number of electrons
int64_t	nucl_num	in	Number of nucleii
int64_t	cord_num	in	order of polynomials
int64_t	dim_cord_vect	in	dimension of full coefficient vector
double	cord_vect_full[dim_cord_vect][nucl_num]	in	full coefficient vector
int64_t	lkpm_combined_index[4][dim_cord_vect]	in	combined indices
double	een_rescaled_e[walk_num][elec_num][elec_num][0:cord_num]	in	Electron-nucleus rescaled
double	een_rescaled_n[walk_num][elec_num][nucl_num][0:cord_num]	in	Electron-nucleus rescaled factor
double	een_rescaled_e_deriv_e[walk_num][elec_num][4][elec_num][0:cord_num]	in	Electron-nucleus rescaled
double	een_rescaled_n_deriv_e[walk_num][elec_num][4][nucl_num][0:cord_num]	in	Electron-nucleus rescaled factor
double	factor_een_deriv_e[walk_num][4][elec_num]	out	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,                                                &
                                       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(4,dim_cord_vect)
double precision      , intent(in)  :: cord_vect_full(dim_cord_vect, nucl_num)
double precision      , intent(in)  :: een_rescaled_e(walk_num, elec_num, elec_num, 0:cord_num)
double precision      , intent(in)  :: een_rescaled_n(walk_num, elec_num, nucl_num, 0:cord_num)
double precision      , intent(in)  :: een_rescaled_e_deriv_e(walk_num, elec_num, 4, elec_num, 0:cord_num)
double precision      , intent(in)  :: een_rescaled_n_deriv_e(walk_num, elec_num, 4, nucl_num, 0:cord_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(1, n)  
k = lkpm_combined_index(2, n)  
p = lkpm_combined_index(3, n)  
m = lkpm_combined_index(4, n)  

do a = 1, nucl_num
  cn = cord_vect_full(n, a)
  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(nw, i, j, k) *         &
                    een_rescaled_n(nw, i, a, m)
      accu2 = accu2 + een_rescaled_e(nw, i, j, k) *       &
                      een_rescaled_n(nw, i, a, m + l)
      daccu(1:4) = daccu(1:4) + een_rescaled_e_deriv_e(nw, j, 1:4, i, k) *         &
                                een_rescaled_n(nw, i, a, m)
      daccu2(1:4) = daccu2(1:4) + een_rescaled_e_deriv_e(nw, j, 1:4, i, k) *       &
                                  een_rescaled_n(nw, i, a, m + l)
    end do
    factor_een_deriv_e(j, 1:4, nw) = factor_een_deriv_e(j, 1:4, nw) +              &
           (accu * een_rescaled_n_deriv_e(nw, j, 1:4, a, m + l)                    &
            + daccu(1:4) * een_rescaled_n(nw, j, a, m + l)                         &
            + daccu2(1:4) * een_rescaled_n(nw, j, a, m)                            &
            + accu2 * een_rescaled_n_deriv_e(nw, j, 1:4, a, m)) * cn

    factor_een_deriv_e(j, 4, nw) = factor_een_deriv_e(j, 4, nw) + 2.0d0 * (        &
        daccu (1) * een_rescaled_n_deriv_e(nw, j, 1, a, m + l) +                    &
        daccu (2) * een_rescaled_n_deriv_e(nw, j, 2, a, m + l) +                    &
        daccu (3) * een_rescaled_n_deriv_e(nw, j, 3, a, m + l) +                    &
        daccu2(1) * een_rescaled_n_deriv_e(nw, j, 1, a, m    ) +                    &
        daccu2(2) * een_rescaled_n_deriv_e(nw, j, 2, a, m    ) +                    &
        daccu2(3) * een_rescaled_n_deriv_e(nw, j, 3, a, m    ) ) * cn
       
  end do
end do
end do
end do

end function qmckl_compute_factor_een_deriv_e_f

qmckl_exit_code qmckl_compute_factor_een_deriv_e (
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 int64_t dim_cord_vect,
const double* cord_vect_full,
const int64_t* lkpm_combined_index,
const double* een_rescaled_e,
const double* een_rescaled_n,
const double* een_rescaled_e_deriv_e,
const double* een_rescaled_n_deriv_e,
double* const factor_een_deriv_e );

Test

/* Check if Jastrow is properly initialized */
//assert(qmckl_jastrow_provided(context));
//
//// calculate factor_en_deriv_e
//double factor_een[walk_num];
//rc = qmckl_get_jastrow_factor_een(context, &(factor_een[0]));

//// 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);

196 KiB Raw Blame History

Jastrow Factor

Context

Data structure

Access functions

Initialization functions

Test

Computation

Asymptotic component for \(f_{ee}\)

Get

Compute

Test

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

Get

Compute

Test

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

Get

Compute

Test

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

Get

Compute

Test

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

Get

Compute

Test

Electron-electron rescaled distances for each order

Get

Compute

Test

Electron-electron rescaled distances for each order and derivatives

Get

Compute

Test

Electron-nucleus rescaled distances for each order

Get

Compute

Test

Electron-nucleus rescaled distances for each order and derivatives

Get

Compute

Test

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

Get

Compute dim_cord_vect

Compute cord_vect_full

Compute lkpm_combined_index

Test

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

Get

Compute

Test

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

Get

Compute

Test

196 KiB

Raw Blame History