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Rewrote Jastrow ee

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Anthony Scemama 2023-05-23 13:49:26 +02:00
parent cfda515885
commit 19a0a4a675
1 changed files with 141 additions and 116 deletions
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@ -2550,12 +2550,17 @@ assert(fabs(factor_ee[0]+4.282760865958113) < 1.e-12);
There are four components, the gradient which has 3 components in the \(x, y, z\)
directions and the laplacian as the last component.
\[ \nabla_i f_\text{ee} = \frac{1}{2}\sum_{j}
\[ \nabla_i f_\text{ee} = \sum_{j\ne i}
\left[\frac{\delta_{ij}^{\uparrow\downarrow} B_0\, \nabla_i
C_{ij}}{(1 - B_1\, C_{ij})^2} + \sum^{n_\text{ord}}_{k=2}
C_{ij}}{(1 + B_1\, C_{ij})^2} + \sum^{n_\text{ord}}_{k=2}
B_k\, k\, C_{ij}^{k-1} \nabla C_{ij} \right] \]
# TODO Formula for Laplacian
\[ \Delta_i f_\text{ee} = \sum_{j \ne i}
\left[ \delta_{ij}^{\uparrow\downarrow} B_0
\left(\frac{ \Delta_i C_{ij}}{(1 + B_1\, C_{ij})^2} -\frac{2\,B_1
\left(\nabla_i C_{ij}\right)^2 }{(1 + B_1\, C_{ij})^3} \right) + \sum^{n_\text{ord}}_{k=2}
B_k\, k\, \left((k-1)\, C_{ij}^{k-2} \left(\nabla_i C_{ij}\right)^2 + C_{ij}^{k-1} \Delta_i C_{ij} \right) \right] \]
**** Get
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code
@ -2734,12 +2739,11 @@ integer function qmckl_compute_jastrow_champ_factor_ee_deriv_e_doc_f( &
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
integer*8 :: i, j, k, nw, ii
double precision :: x, x1, kf
double precision :: denom, invdenom, invdenom2, f
double precision :: grad_c2
double precision :: dx(4)
info = QMCKL_SUCCESS
@ -2763,60 +2767,56 @@ integer function qmckl_compute_jastrow_champ_factor_ee_deriv_e_doc_f( &
return
endif
factor_ee_deriv_e = 0.0d0
third = 1.0d0 / 3.0d0
do nw =1, walk_num
do j = 1, elec_num
factor_ee_deriv_e(:,:,nw) = 0.0d0
do i = 1, elec_num
x = ee_distance_rescaled(i,j,nw)
if(abs(x) < 1.0d-18) cycle
pow_ser_g = 0.0d0
spin_fact = 1.0d0
den = 1.0d0 + b_vector(2) * x
invden = 1.0d0 / den
invden2 = invden * invden
invden3 = invden2 * invden
xinv = 1.0d0 / (x + 1.0d-18)
do j = 1, elec_num
if (j==i) cycle
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)
x = ee_distance_rescaled(j,i,nw)
if((i <= up_num .and. j <= up_num ) .OR. &
(i > up_num .and. j > up_num)) then
spin_fact = 0.5d0
endif
denom = 1.0d0 + b_vector(2) * x
invdenom = 1.0d0 / denom
invdenom2 = invdenom * invdenom
lap1 = 0.0d0
lap2 = 0.0d0
lap3 = 0.0d0
do ii = 1, 3
x = ee_distance_rescaled(i, j, nw)
if(abs(x) < 1.0d-18) cycle
do p = 2, bord_num
y = p * b_vector(p + 1) * x
pow_ser_g(ii) = pow_ser_g(ii) + y * dx(ii)
lap1 = lap1 + (p - 1) * y * xinv * dx(ii) * dx(ii)
lap2 = lap2 + y
x = x * ee_distance_rescaled(i, j, nw)
end do
dx(1) = ee_distance_rescaled_deriv_e(1, j, i, nw)
dx(2) = ee_distance_rescaled_deriv_e(2, j, i, nw)
dx(3) = ee_distance_rescaled_deriv_e(3, j, i, nw)
dx(4) = ee_distance_rescaled_deriv_e(4, j, i, nw)
lap3 = lap3 - 2.0d0 * b_vector(2) * dx(ii) * dx(ii)
grad_c2 = dx(1)*dx(1) + dx(2)*dx(2) + dx(3)*dx(3)
if((i <= up_num .and. j <= up_num ) .or. (i > up_num .and. j > up_num)) then
f = 0.5d0 * b_vector(1) * invdenom2
else
f = b_vector(1) * invdenom2
end if
factor_ee_deriv_e(i,1,nw) = factor_ee_deriv_e(i,1,nw) + f * dx(1)
factor_ee_deriv_e(i,2,nw) = factor_ee_deriv_e(i,2,nw) + f * dx(2)
factor_ee_deriv_e(i,3,nw) = factor_ee_deriv_e(i,3,nw) + f * dx(3)
factor_ee_deriv_e(i,4,nw) = factor_ee_deriv_e(i,4,nw) &
+ f * (dx(4) - 2.d0 * b_vector(2) * grad_c2 * invdenom)
kf = 2.d0
x1 = x
x = 1.d0
do k=2, bord_num
f = b_vector(k+1) * kf * x
factor_ee_deriv_e(i,1,nw) = factor_ee_deriv_e(i,1,nw) + f * x1 * dx(1)
factor_ee_deriv_e(i,2,nw) = factor_ee_deriv_e(i,2,nw) + f * x1 * dx(2)
factor_ee_deriv_e(i,3,nw) = factor_ee_deriv_e(i,3,nw) + f * x1 * dx(3)
factor_ee_deriv_e(i,4,nw) = factor_ee_deriv_e(i,4,nw) &
+ f * (x1 * dx(4) + (kf-1.d0) * grad_c2)
x = x*x1
kf = kf + 1.d0
end do
factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) &
+ spin_fact * b_vector(1) * dx(ii) * invden2 + pow_ser_g(ii)
end do
ii = 4
lap2 = lap2 * dx(ii) * third
lap3 = lap3 + den * dx(ii)
lap3 = lap3 * (spin_fact * b_vector(1) * invden3)
factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) + lap1 + lap2 + lap3
end do
end do
end do
end function qmckl_compute_jastrow_champ_factor_ee_deriv_e_doc_f
@ -3036,7 +3036,6 @@ integer(c_int32_t) function qmckl_compute_jastrow_champ_factor_ee_deriv_e_doc &
}
#+end_src
**** Test
#+begin_src python :results output :exports none :noweb yes
import numpy as np
@ -3046,84 +3045,103 @@ import numpy as np
<<asymp_jasb>>
kappa = 1.0
dx = 1.e-3
elec_coord = np.array(elec_coord)[0]
elec_dist = np.zeros(shape=(elec_num, elec_num),dtype=float)
for i in range(elec_num):
for j in range(elec_num):
elec_dist[i, j] = np.linalg.norm(elec_coord[i] - elec_coord[j])
elec_dist_deriv_e = np.zeros(shape=(4,elec_num, elec_num),dtype=float)
for j in range(elec_num):
for i in range(elec_num):
rij_inv = 1.0 / elec_dist[i, j]
for ii in range(3):
elec_dist_deriv_e[ii, i, j] = (elec_coord[j][ii] - elec_coord[i][ii]) * rij_inv
elec_dist_deriv_e[3, i, j] = 2.0 * rij_inv
elec_dist_deriv_e[:, j, j] = 0.0
def make_dist(elec_coord):
ee_distance_rescaled_deriv_e = np.zeros(shape=(4,elec_num,elec_num),dtype=float)
for j in range(elec_num):
for i in range(elec_num):
f = 1.0 - kappa * ee_distance_rescaled[i][j]
for ii in range(4):
ee_distance_rescaled_deriv_e[ii][i][j] = elec_dist_deriv_e[ii][i][j]
ee_distance_rescaled_deriv_e[3][i][j] = ee_distance_rescaled_deriv_e[3][i][j] + \
(-kappa * ee_distance_rescaled_deriv_e[0][i][j] * ee_distance_rescaled_deriv_e[0][i][j]) + \
(-kappa * ee_distance_rescaled_deriv_e[1][i][j] * ee_distance_rescaled_deriv_e[1][i][j]) + \
(-kappa * ee_distance_rescaled_deriv_e[2][i][j] * ee_distance_rescaled_deriv_e[2][i][j])
for ii in range(4):
ee_distance_rescaled_deriv_e[ii][i][j] = ee_distance_rescaled_deriv_e[ii][i][j] * f
elec_dist = np.zeros(shape=(elec_num, elec_num),dtype=float)
for i in range(elec_num):
for j in range(elec_num):
elec_dist[i, j] = np.linalg.norm(elec_coord[i] - elec_coord[j])
return elec_dist
def make_dist_deriv(elec_coord):
elec_dist_d = np.zeros(shape=(4, elec_num, elec_num),dtype=float)
for i in range(elec_num):
for j in range(elec_num):
rij = np.linalg.norm(elec_coord[i] - elec_coord[j])
rijm = np.linalg.norm(elec_coord[i] - elec_coord[j]+np.array((dx,0.,0.)))
rijp = np.linalg.norm(elec_coord[i] - elec_coord[j]-np.array((dx,0.,0.)))
elec_dist_d[0, i, j] = (rijp-rijm)/(2.*dx)
elec_dist_d[3, i, j] = (rijp+rijm-2.*rij)/(dx**2)
rijm = np.linalg.norm(elec_coord[i] - elec_coord[j]+np.array((0.,dx,0.)))
rijp = np.linalg.norm(elec_coord[i] - elec_coord[j]-np.array((0.,dx,0.)))
elec_dist_d[1, i, j] = (rijp-rijm)/(2.*dx)
elec_dist_d[3, i, j] += (rijp+rijm-2.*rij)/(dx**2)
rijm = np.linalg.norm(elec_coord[i] - elec_coord[j]+np.array((0.,0.,dx)))
rijp = np.linalg.norm(elec_coord[i] - elec_coord[j]-np.array((0.,0.,dx)))
elec_dist_d[2, i, j] = (rijp-rijm)/(2.*dx)
elec_dist_d[3, i, j] += (rijp+rijm-2.*rij)/(dx**2)
return elec_dist_d
def func(elec_coord):
elec_dist = make_dist(elec_coord)
elec_dist_deriv_e = np.zeros(shape=(4,elec_num, elec_num),dtype=float)
for j in range(elec_num):
for i in range(elec_num):
rij_inv = 1.0 / elec_dist[i, j]
for ii in range(3):
elec_dist_deriv_e[ii, i, j] = (elec_coord[j][ii] - elec_coord[i][ii]) * rij_inv
elec_dist_deriv_e[3, i, j] = 2.0 * rij_inv
elec_dist_deriv_e[:, j, j] = 6.0
ee_distance_rescaled_deriv_e = np.zeros(shape=(4,elec_num,elec_num),dtype=float)
for j in range(elec_num):
for i in range(elec_num):
f = 1.0 - kappa * ee_distance_rescaled[i][j]
for ii in range(4):
ee_distance_rescaled_deriv_e[ii][i][j] = elec_dist_deriv_e[ii][i][j]
ee_distance_rescaled_deriv_e[3][i][j] = ee_distance_rescaled_deriv_e[3][i][j] + \
(-kappa * ee_distance_rescaled_deriv_e[0][i][j] * ee_distance_rescaled_deriv_e[0][i][j]) + \
(-kappa * ee_distance_rescaled_deriv_e[1][i][j] * ee_distance_rescaled_deriv_e[1][i][j]) + \
(-kappa * ee_distance_rescaled_deriv_e[2][i][j] * ee_distance_rescaled_deriv_e[2][i][j])
for ii in range(4):
ee_distance_rescaled_deriv_e[ii][i][j] = ee_distance_rescaled_deriv_e[ii][i][j] * f
return ee_distance_rescaled_deriv_e, elec_dist_deriv_e
ee_distance_rescaled_deriv_e, elec_dist_deriv_e = func(elec_coord)
#print(elec_dist_deriv_e[3,:,:])
#print(make_dist_deriv(elec_coord)[3,:,:])
third = 1.0 / 3.0
factor_ee_deriv_e = np.zeros(shape=(4,elec_num),dtype=float)
dx = np.zeros(shape=(4),dtype=float)
pow_ser_g = np.zeros(shape=(4),dtype=float)
for j in range(elec_num):
for i in range(elec_num):
x = ee_distance_rescaled[j][i]
if abs(x) < 1e-18:
continue
pow_ser_g = np.zeros(shape=(4),dtype=float)
spin_fact = 1.0
den = 1.0 + b_vector[1] * ee_distance_rescaled[j][i]
if i == j: continue
x = ee_distance_rescaled[j,i]
den = 1.0 + b_vector[1] * x
invden = 1.0 / den
invden2 = invden * invden
invden3 = invden2 * invden
xinv = 1.0 / (ee_distance_rescaled[j][i] + 1.0E-18)
xinv = 1.0 / x
ipar = 1
for ii in range(4):
dx[ii] = ee_distance_rescaled_deriv_e[ii][j][i]
dx[:] = ee_distance_rescaled_deriv_e[:,j,i]
if((i <= (up_num-1) and j <= (up_num-1) ) or \
(i > (up_num-1) and j > (up_num-1))):
if((i < up_num and j < up_num) or (i >= up_num and j >= up_num) ):
spin_fact = 0.5
else:
spin_fact = 1.0
lap1 = 0.0
lap2 = 0.0
lap3 = 0.0
for ii in range(3):
x = ee_distance_rescaled[j][i]
if x < 1e-18:
continue
for p in range(2,bord_num+1):
y = p * b_vector[(p-1) + 1] * x
pow_ser_g[ii] = pow_ser_g[ii] + y * dx[ii]
lap1 = lap1 + (p - 1) * y * xinv * dx[ii] * dx[ii]
lap2 = lap2 + y
x = x * ee_distance_rescaled[j][i]
factor_ee_deriv_e[:,j] += spin_fact * b_vector[0] * dx[:] * invden2
for k in range(2,bord_num+1):
factor_ee_deriv_e[:,j] += b_vector[k]*k*x**(k-1)*dx[:]
lap3 = lap3 - 2.0 * b_vector[1] * dx[ii] * dx[ii]
grad_c2 = np.dot(ee_distance_rescaled_deriv_e[:3,j,i], ee_distance_rescaled_deriv_e[:3,j,i])
factor_ee_deriv_e[3,j] -= spin_fact * b_vector[0] * 2. * b_vector[1] * grad_c2 * invden3
for k in range(2,bord_num+1):
factor_ee_deriv_e[3,j] += b_vector[k]*k*(k-1)*x**(k-2)*grad_c2
factor_ee_deriv_e[ii][j] = factor_ee_deriv_e[ii][j] + spin_fact * b_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 * b_vector[0] * invden3)
factor_ee_deriv_e[ii][j] = factor_ee_deriv_e[ii][j] + lap1 + lap2 + lap3
print("factor_ee_deriv_e[0][0]:",factor_ee_deriv_e[0][0])
print("factor_ee_deriv_e[1][0]:",factor_ee_deriv_e[1][0])
@ -3133,8 +3151,8 @@ print("factor_ee_deriv_e[3][0]:",factor_ee_deriv_e[3][0])
#+RESULTS:
: asym_one : 0.43340325572525706
: asymp_jasb[0] : 0.5323750557252571
: asymp_jasb[1] : 0.31567342786262853
: asymp_jasb[0] : 0.31567342786262853
: asymp_jasb[1] : 0.5323750557252571
: factor_ee_deriv_e[0][0]: 0.16364894652107934
: factor_ee_deriv_e[1][0]: -0.6927548119830084
: factor_ee_deriv_e[2][0]: 0.073267755223968
@ -3150,12 +3168,19 @@ double factor_ee_deriv_e[walk_num][4][elec_num];
rc = qmckl_get_jastrow_champ_factor_ee_deriv_e(context, &(factor_ee_deriv_e[0][0][0]),walk_num*4*elec_num);
// check factor_ee_deriv_e
printf("%f %f\n", factor_ee_deriv_e[0][0][0], 0.16364894652107934);
assert(fabs(factor_ee_deriv_e[0][0][0]-0.16364894652107934) < 1.e-12);
printf("%f %f\n", factor_ee_deriv_e[0][1][0],-0.6927548119830084 );
assert(fabs(factor_ee_deriv_e[0][1][0]+0.6927548119830084 ) < 1.e-12);
printf("%f %f\n", factor_ee_deriv_e[0][2][0], 0.073267755223968 );
assert(fabs(factor_ee_deriv_e[0][2][0]-0.073267755223968 ) < 1.e-12);
printf("%f %f\n", factor_ee_deriv_e[0][3][0], 1.5111672803213185 );
assert(fabs(factor_ee_deriv_e[0][3][0]-1.5111672803213185 ) < 1.e-12);
#+end_src
*** Electron-electron rescaled distances
~ee_distance_rescaled~ stores the matrix of the rescaled distances between all