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Implemented MOs. Needs testing. #32
2021-09-15 18:30:41 +02:00
#+TITLE: Molecular Orbitals
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
The molecular orbitals (MOs) are defined in the basis of AOs along with a AO to MO
coefficient matrix \[C\]. Using these coefficients (e.g. from Hartree Fock SCF method)
the MOs are defined as follows:
\[
\phi_i(\mathbf{r}) = C_i * \chi_i (\mathbf{r})
\]
In this section we demonstrate how to use the QMCkl specific DGEMM
function to calculate the MOs.
* Headers :noexport:
#+begin_src elisp :noexport :results none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
#+begin_src c :tangle (eval h_private_type)
#ifndef QMCKL_MO_HPT
#define QMCKL_MO_HPT
#include <stdbool.h>
#+end_src
#+begin_src c :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "assert.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <stdio.h>
#include <math.h>
#include "chbrclf.h"
#include "qmckl_ao_private_func.h"
#include "qmckl_mo_private_func.h"
int main() {
qmckl_context context;
context = qmckl_context_create();
qmckl_exit_code rc;
#+end_src
#+begin_src c :tangle (eval c)
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#ifdef HAVE_STDINT_H
#include <stdint.h>
#elif HAVE_INTTYPES_H
#include <inttypes.h>
#endif
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>
#include "qmckl.h"
#include "qmckl_context_private_type.h"
#include "qmckl_memory_private_type.h"
#include "qmckl_memory_private_func.h"
#include "qmckl_ao_private_type.h"
#include "qmckl_ao_private_func.h"
#include "qmckl_mo_private_type.h"
#include "qmckl_mo_private_func.h"
#+end_src
* Context
The following arrays are stored in the context:
|---------------------+--------------------+--------------------------------------------------------------|
| ~type~ | | Gaussian (~'G'~) or Slater (~'S'~) |
| ~nucleus_index~ | ~[nucl_num]~ | Index of the first shell of each nucleus |
| ~nucleus_shell_num~ | ~[nucl_num]~ | Number of shells per nucleus |
| ~ao_num~ | | Number of AOs |
| ~ao_cartesian~ | | If true, use polynomials. Otherwise, use spherical harmonics |
| ~ao_factor~ | ~[ao_num]~ | Normalization factor of the AO |
| ~ao_shell~ | ~[ao_num]~ | For each AO, specify to which shell it belongs |
| ~coefficient~ | ~[mo_num, ao_num]~ | Orbital coefficients |
Computed data:
|---------------+-----------------------------------+----------------------------------------------------------------------------------------|
|---------------+-----------------------------------+----------------------------------------------------------------------------------------|
| ~mo_vgl~ | ~[5][walk_num][elec_num][mo_num]~ | Value, gradients, Laplacian of the MOs at electron positions |
| ~mo_vgl_date~ | ~uint64_t~ | Late modification date of Value, gradients, Laplacian of the MOs at electron positions |
|---------------+-----------------------------------+----------------------------------------------------------------------------------------|
** Data structure
#+begin_src c :comments org :tangle (eval h_private_type)
typedef struct qmckl_mo_basis_struct {
int64_t mo_num;
double * coefficient;
double * mo_vgl;
int64_t mo_vgl_date;
int32_t uninitialized;
bool provided;
char type;
} qmckl_mo_basis_struct;
#+end_src
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.
** Access functions
#+begin_src c :comments org :tangle (eval h_private_func) :exports none
char qmckl_get_mo_basis_type (const qmckl_context context);
int64_t qmckl_get_mo_basis_mo_num (const qmckl_context context);
double* qmckl_get_mo_basis_coefficient (const qmckl_context context);
#+end_src
When all the data for the AOs have been provided, the following
function returns ~true~.
#+begin_src c :comments org :tangle (eval h_func)
bool qmckl_mo_basis_provided (const qmckl_context context);
#+end_src
#+NAME:post
#+begin_src c :exports none
if ( (ctx->mo_basis.uninitialized & mask) != 0) {
return NULL;
}
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
char qmckl_get_mo_basis_type (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return (char) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1;
if ( (ctx->mo_basis.uninitialized & mask) != 0) {
return (char) 0;
}
assert (ctx->mo_basis.type != (char) 0);
return ctx->mo_basis.type;
}
int64_t qmckl_get_mo_basis_mo_num (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return (int64_t) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 1;
if ( (ctx->mo_basis.uninitialized & mask) != 0) {
return (int64_t) 0;
}
assert (ctx->mo_basis.mo_num > (int64_t) 0);
return ctx->mo_basis.mo_num;
}
#+end_src
** Initialization functions
To set the basis set, all the following functions need to be
called.
#+begin_src c :comments org :tangle (eval h_func)
qmckl_exit_code qmckl_set_mo_basis_type (qmckl_context context, const char t);
qmckl_exit_code qmckl_set_mo_basis_mo_num (qmckl_context context, const int64_t mo_num);
qmckl_exit_code qmckl_set_mo_basis_coefficient (qmckl_context context, const double * coefficient);
#+end_src
#+NAME:pre2
#+begin_src c :exports none
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
#+end_src
#+NAME:post2
#+begin_src c :exports none
ctx->mo_basis.uninitialized &= ~mask;
ctx->mo_basis.provided = (ctx->mo_basis.uninitialized == 0);
if (ctx->mo_basis.provided) {
qmckl_exit_code rc_ = qmckl_finalize_basis(context);
if (rc_ != QMCKL_SUCCESS) return rc_;
}
return QMCKL_SUCCESS;
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_set_mo_basis_type(qmckl_context context, const char t) {
<<pre2>>
if (t != 'G' && t != 'S') {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_mo_basis_type",
NULL);
}
int32_t mask = 1;
ctx->mo_basis.type = t;
<<post2>>
}
qmckl_exit_code qmckl_set_mo_basis_mo_num(qmckl_context context, const int64_t mo_num) {
<<pre2>>
if (mo_num <= 0) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_mo_basis_mo_num",
"mo_num <= 0");
}
int32_t mask = 1 << 1;
ctx->mo_basis.mo_num = mo_num;
<<post2>>
}
qmckl_exit_code qmckl_set_mo_basis_coefficient(qmckl_context context, const double* coefficient) {
<<pre2>>
int32_t mask = 1 << 2;
if (ctx->mo_basis.coefficient != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->mo_basis.coefficient);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_mo_basis_coefficient",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ctx->ao_basis.ao_num * ctx->mo_basis.mo_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_mo_basis_coefficient",
NULL);
}
memcpy(new_array, coefficient, mem_info.size);
ctx->mo_basis.coefficient = new_array;
<<post2>>
}
#+end_src
When the basis set is completely entered, other data structures are
computed to accelerate the calculations.
* Computation
** Computation of MOs
*** Get
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code qmckl_get_mo_basis_vgl(qmckl_context context, double* const mo_vgl);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_get_mo_basis_vgl(qmckl_context context, double* const mo_vgl) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_exit_code rc;
rc = qmckl_provide_ao_vgl(context);
if (rc != QMCKL_SUCCESS) return rc;
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
size_t sze = 5 * ctx->electron.num * ctx->mo_basis.mo_num * ctx->electron.walk_num;
memcpy(mo_vgl, ctx->mo_basis.mo_vgl, sze * sizeof(double));
return QMCKL_SUCCESS;
}
#+end_src
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_get_mo_basis_vgl (context, mo_vgl) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
double precision, intent(out) :: mo_vgl(*)
end function
end interface
#+end_src
*** Provide
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_mo_basis_vgl(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_provide_mo_basis_vgl(qmckl_context context)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
if (!ctx->ao_basis.provided) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_ao_basis",
NULL);
}
if(!(ctx->electron.provided)) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_electron",
NULL);
}
/* Compute if necessary */
if (ctx->electron.coord_new_date > ctx->mo_basis.mo_vgl_date) {
/* Allocate array */
if (ctx->mo_basis.mo_vgl == NULL) {
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = 5 * ctx->electron.num * ctx->mo_basis.mo_num *
ctx->electron.walk_num * sizeof(double);
double* mo_vgl = (double*) qmckl_malloc(context, mem_info);
if (mo_vgl == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_mo_basis_vgl",
NULL);
}
ctx->mo_basis.mo_vgl = mo_vgl;
}
qmckl_exit_code rc;
if (ctx->mo_basis.type == 'G') {
rc = qmckl_compute_mo_basis_gaussian_vgl(context,
ctx->ao_basis.ao_num,
ctx->mo_basis.mo_num,
ctx->electron.num,
ctx->electron.walk_num,
ctx->mo_basis.coefficient,
ctx->ao_basis.ao_vgl,
ctx->mo_basis.mo_vgl);
} else {
return qmckl_failwith( context,
QMCKL_FAILURE,
"compute_mo_basis_vgl",
"Not yet implemented");
}
if (rc != QMCKL_SUCCESS) {
return rc;
}
ctx->mo_basis.mo_vgl_date = ctx->date;
}
return QMCKL_SUCCESS;
}
#+end_src
*** Compute
:PROPERTIES:
:Name: qmckl_compute_mo_basis_gaussian_vgl
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
#+NAME: qmckl_mo_basis_gaussian_vgl_args
| ~qmckl_context~ | ~context~ | in | Global state |
| ~int64_t~ | ~ao_num~ | in | Number of AOs |
| ~int64_t~ | ~mo_num~ | in | Number of MOs |
| ~int64_t~ | ~elec_num~ | in | Number of electrons |
| ~int64_t~ | ~walk_num~ | in | Number of walkers |
| ~double~ | ~coef_normalized[mo_num][ao_num]~ | in | AO to MO transformation matrix |
| ~double~ | ~ao_vgl[5][walk_num][elec_num][mo_num]~ | in | Value, gradients and Laplacian of the AOs |
| ~double~ | ~mo_vgl[5][walk_num][elec_num][mo_num]~ | out | Value, gradients and Laplacian of the MOs |
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_mo_basis_gaussian_vgl_f(context, &
ao_num, mo_num, elec_num, walk_num, &
coef_normalized, ao_vgl, mo_vgl) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: ao_num, mo_num
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: ao_vgl(ao_num,elec_num,walk_num,5)
double precision , intent(in) :: coef_normalized(mo_num,ao_num)
double precision , intent(out) :: mo_vgl(mo_num,elec_num,walk_num,5)
logical :: TransA, TransB
double precision :: alpha, beta
integer :: info_qmckl_dgemm_value
integer :: info_qmckl_dgemm_Gx
integer :: info_qmckl_dgemm_Gy
integer :: info_qmckl_dgemm_Gz
integer :: info_qmckl_dgemm_lap
integer*8 :: M, N, K, LDA, LDB, LDC
integer*8 :: inucl, iprim, iwalk, ielec, ishell
double precision :: x, y, z, two_a, ar2, r2, v, cutoff
TransA = .False.
TransB = .False.
alpha = 1.0d0
beta = 0.0d0
info = QMCKL_SUCCESS
! Don't compute exponentials when the result will be almost zero.
! TODO : Use numerical precision here
cutoff = -dlog(1.d-15)
M = mo_num * 1_8
N = ao_num * 1_8
K = 1_8
do iwalk = 1, walk_num
do ielec = 1, elec_num
! Value
info_qmckl_dgemm_value = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, iwalk, 1), size(ao_vgl,1) * 1_8, &
coef_normalized,size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,iwalk,1),size(mo_vgl,1) * 1_8)
! Grad_x
info_qmckl_dgemm_Gx = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, iwalk, 2), size(ao_vgl,1) * 1_8, &
coef_normalized,size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,iwalk,2),size(mo_vgl,1) * 1_8)
! Grad_y
info_qmckl_dgemm_Gy = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, iwalk, 3), size(ao_vgl,1) * 1_8, &
coef_normalized,size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,iwalk,3),size(mo_vgl,1) * 1_8)
! Grad_z
info_qmckl_dgemm_Gz = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, iwalk, 4), size(ao_vgl,1) * 1_8, &
coef_normalized,size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,iwalk,4),size(mo_vgl,1) * 1_8)
! Lapl_z
info_qmckl_dgemm_lap = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, iwalk, 5), size(ao_vgl,1) * 1_8, &
coef_normalized,size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,iwalk,5),size(mo_vgl,1) * 1_8)
end do
end do
if(info_qmckl_dgemm_value .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gx .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gy .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gz .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_lap .eq. QMCKL_SUCCESS ) then
info = QMCKL_SUCCESS
else
info = QMCKL_FAILURE
end if
end function qmckl_compute_mo_basis_gaussian_vgl_f
#+end_src
#+CALL: generate_c_header(table=qmckl_mo_basis_gaussian_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_gaussian_vgl"))
#+RESULTS:
#+BEGIN_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_compute_mo_basis_gaussian_vgl (
const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t elec_num,
const int64_t walk_num,
const double* coef_normalized,
const double* ao_vgl,
double* const mo_vgl );
#+END_src
#+CALL: generate_c_interface(table=qmckl_mo_basis_gaussian_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_gaussian_vgl"))
#+RESULTS:
#+BEGIN_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_compute_mo_basis_gaussian_vgl &
(context, ao_num, mo_num, elec_num, walk_num, coef_normalized, ao_vgl, mo_vgl) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: ao_num
integer (c_int64_t) , intent(in) , value :: mo_num
integer (c_int64_t) , intent(in) , value :: elec_num
integer (c_int64_t) , intent(in) , value :: walk_num
real (c_double ) , intent(in) :: coef_normalized(ao_num,mo_num)
real (c_double ) , intent(in) :: ao_vgl(mo_num,elec_num,walk_num,5)
real (c_double ) , intent(out) :: mo_vgl(mo_num,elec_num,walk_num,5)
integer(c_int32_t), external :: qmckl_compute_mo_basis_gaussian_vgl_f
info = qmckl_compute_mo_basis_gaussian_vgl_f &
(context, ao_num, mo_num, elec_num, walk_num, coef_normalized, ao_vgl, mo_vgl)
end function qmckl_compute_mo_basis_gaussian_vgl
#+END_src
#+begin_src python :results output :exports none
import numpy as np
def f(a,x,y):
return np.sum( [c * np.exp( -b*(np.linalg.norm(x-y))**2) for b,c in a] )
def df(a,x,y,n):
h0 = 1.e-6
if n == 1: h = np.array([h0,0.,0.])
elif n == 2: h = np.array([0.,h0,0.])
elif n == 3: h = np.array([0.,0.,h0])
return ( f(a,x+h,y) - f(a,x-h,y) ) / (2.*h0)
def d2f(a,x,y,n):
h0 = 1.e-6
if n == 1: h = np.array([h0,0.,0.])
elif n == 2: h = np.array([0.,h0,0.])
elif n == 3: h = np.array([0.,0.,h0])
return ( f(a,x+h,y) - 2.*f(a,x,y) + f(a,x-h,y) ) / h0**2
def lf(a,x,y):
return d2f(a,x,y,1) + d2f(a,x,y,2) + d2f(a,x,y,3)
elec_26_w1 = np.array( [ 1.49050402641, 2.90106987953, -1.05920815468 ] )
elec_15_w2 = np.array( [ -2.20180344582,-1.9113150239, 2.2193744778600002 ] )
nucl_1 = np.array( [ 1.096243353458458e+00, 8.907054016973815e-01, 7.777092280258892e-01 ] )
nucl_2 = np.array( [ 1.168459237342663e+00, 1.125660720053393e+00, 2.833370314829343e+00 ] )
#double prim_vgl[prim_num][5][walk_num][elec_num];
x = elec_26_w1 ; y = nucl_1
a = [( 8.236000E+03, -1.130000E-04 * 6.1616545431994848e+02 ),
( 1.235000E+03, -8.780000E-04 * 1.4847738511079908e+02 ),
( 2.808000E+02, -4.540000E-03 * 4.8888635917437597e+01 ),
( 7.927000E+01, -1.813300E-02 * 1.8933972232608955e+01 ),
( 2.559000E+01, -5.576000E-02 * 8.1089160941724145e+00 ),
( 8.997000E+00, -1.268950E-01 * 3.7024003863155635e+00 ),
( 3.319000E+00, -1.703520E-01 * 1.7525302846177560e+00 ),
( 9.059000E-01, 1.403820E-01 * 6.6179013183966806e-01 ),
( 3.643000E-01, 5.986840E-01 * 3.3419848027174592e-01 ),
( 1.285000E-01, 3.953890E-01 * 1.5296336817449557e-01 )]
print ( "[1][0][0][26] : %25.15e"% f(a,x,y))
print ( "[1][1][0][26] : %25.15e"% df(a,x,y,1))
print ( "[1][2][0][26] : %25.15e"% df(a,x,y,2))
print ( "[1][3][0][26] : %25.15e"% df(a,x,y,3))
print ( "[1][4][0][26] : %25.15e"% lf(a,x,y))
x = elec_15_w2 ; y = nucl_2
a = [(3.387000E+01, 6.068000E-03 *1.0006253235944540e+01),
(5.095000E+00, 4.530800E-02 *2.4169531573445120e+00),
(1.159000E+00, 2.028220E-01 *7.9610924849766440e-01),
(3.258000E-01, 5.039030E-01 *3.0734305383061117e-01),
(1.027000E-01, 3.834210E-01 *1.2929684417481876e-01)]
print ( "[0][1][15][14] : %25.15e"% f(a,x,y))
print ( "[1][1][15][14] : %25.15e"% df(a,x,y,1))
print ( "[2][1][15][14] : %25.15e"% df(a,x,y,2))
print ( "[3][1][15][14] : %25.15e"% df(a,x,y,3))
print ( "[4][1][15][14] : %25.15e"% lf(a,x,y))
#+end_src
*** Test
#+begin_src c :tangle (eval c_test) :exports none
#+end_src
* End of files :noexport:
#+begin_src c :tangle (eval h_private_type)
#endif
#+end_src
*** Test
#+begin_src c :tangle (eval c_test)
rc = qmckl_context_destroy(context);
assert (rc == QMCKL_SUCCESS);
return 0;
}
#+end_src
*** Compute file names
#+begin_src emacs-lisp
; The following is required to compute the file names
(setq pwd (file-name-directory buffer-file-name))
(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
(setq f (concat pwd name "_f.f90"))
(setq fh (concat pwd name "_fh.f90"))
(setq c (concat pwd name ".c"))
(setq h (concat name ".h"))
(setq h_private (concat name "_private.h"))
(setq c_test (concat pwd "test_" name ".c"))
(setq f_test (concat pwd "test_" name "_f.f90"))
; Minted
(require 'ox-latex)
(setq org-latex-listings 'minted)
(add-to-list 'org-latex-packages-alist '("" "listings"))
(add-to-list 'org-latex-packages-alist '("" "color"))
#+end_src
# -*- mode: org -*-
# vim: syntax=c
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