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Example in C

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Anthony Scemama 2023-08-31 12:05:37 +02:00
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@ -8,6 +8,9 @@ in a [[https://github.com/TREX-CoE/trexio][TREXIO]] file.
* Python * Python
** Check numerically that MOs are orthonormal ** Check numerically that MOs are orthonormal
:PROPERTIES:
:header-args: :tangle mo_ortho.py
:END:
In this example, we will compute numerically the overlap In this example, we will compute numerically the overlap
between the molecular orbitals: between the molecular orbitals:
@ -127,7 +130,7 @@ before = time.time()
mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num) mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
after = time.time() after = time.time()
mo_value = np.reshape( mo_value, (point_num, mo_num) ) mo_value = np.reshape( mo_value, (point_num, mo_num) ).T # Transpose to get mo_num x point_num
print("Number of MOs: ", mo_num) print("Number of MOs: ", mo_num)
print("Number of grid points: ", point_num) print("Number of grid points: ", point_num)
@ -138,14 +141,14 @@ print("Execution time : ", (after - before), "seconds")
#+begin_example #+begin_example
Number of MOs: 201 Number of MOs: 201
Number of grid points: 1728000 Number of grid points: 1728000
Execution time : 3.511528968811035 seconds Execution time : 5.577778577804565 seconds
#+end_example #+end_example
and finally we compute the overlap between all the MOs as and finally we compute the overlap between all the MOs as
$M^\dagger M$. $M.M^\dagger$.
#+begin_src python :exports code #+begin_src python :exports code
overlap = mo_value.T @ mo_value * dr overlap = mo_value @ mo_value.T * dr
print (overlap) print (overlap)
#+end_src #+end_src
@ -167,6 +170,9 @@ print (overlap)
* C * C
** Check numerically that MOs are orthonormal, with cusp fitting ** Check numerically that MOs are orthonormal, with cusp fitting
:PROPERTIES:
:header-args: :tangle mo_ortho.c
:END:
In this example, we will compute numerically the overlap In this example, we will compute numerically the overlap
between the molecular orbitals: between the molecular orbitals:
@ -188,6 +194,9 @@ print (overlap)
#+begin_src c :exports code #+begin_src c :exports code
#include <qmckl.h> #include <qmckl.h>
#include <stdio.h> #include <stdio.h>
#include <string.h>
//#include <time.h>
#include <sys/time.h>
int main(int argc, char** argv) int main(int argc, char** argv)
{ {
@ -201,10 +210,6 @@ int main(int argc, char** argv)
#+begin_src c :exports code #+begin_src c :exports code
qmckl_context context = qmckl_context_create(); qmckl_context context = qmckl_context_create();
if (context == NULL) {
fprintf(stderr, "Error creating context\n");
exit(1);
}
rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename)); rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename));
@ -221,7 +226,7 @@ int main(int argc, char** argv)
To identify which atom is an oxygen and which are hydrogens, we To identify which atom is an oxygen and which are hydrogens, we
fetch the nuclear charges from the context. fetch the nuclear charges from the context.
#+begin_src python :exports code #+begin_src c :exports code
int64_t nucl_num; int64_t nucl_num;
rc = qmckl_get_nucleus_num(context, &nucl_num); rc = qmckl_get_nucleus_num(context, &nucl_num);
@ -234,7 +239,7 @@ int main(int argc, char** argv)
double nucl_charge[nucl_num]; double nucl_charge[nucl_num];
rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0])); rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0]), nucl_num);
if (rc != QMCKL_SUCCESS) { if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting nucl_charge:\n%s\n", qmckl_string_of_error(rc)); fprintf(stderr, "Error getting nucl_charge:\n%s\n", qmckl_string_of_error(rc));
@ -242,28 +247,43 @@ int main(int argc, char** argv)
} }
double r_c[nucl_num]; double r_cusp[nucl_num];
for (size_t i=0 ; i<nucl_num ; ++i) { for (size_t i=0 ; i<nucl_num ; ++i) {
switch ((int) nucl_charge[i]) { switch ((int) nucl_charge[i]) {
case 1:
nucl_charge[i] = 0.5; case 1:
break; r_cusp[i] = 0.5;
break;
case 8:
nucl_charge[i] = 0.1; case 8:
break; r_cusp[i] = 0.1;
} break;
}
} }
rc = qmckl_set_mo_basis_r_cusp(context, &(r_cusp[0]), nucl_num);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error setting r_cusp:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}
#+end_src #+end_src
#+begin_src python :exports code
We now define the grid points $\mathbf{r}_k$ as a regular grid around the
molecule.
We fetch the nuclear coordinates from the context,
#+begin_src c :exports code
double nucl_coord[nucl_num][3]; double nucl_coord[nucl_num][3];
rc = qmckl_get_nucleus_coord(context, 'N', &(nucl_coord[0][0]), nucl_num*3) rc = qmckl_get_nucleus_coord(context, 'N', &(nucl_coord[0][0]), nucl_num*3);
if (rc != QMCKL_SUCCESS) { if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting nucl_coord:\n%s\n", qmckl_string_of_error(rc)); fprintf(stderr, "Error getting nucl_coord:\n%s\n", qmckl_string_of_error(rc));
@ -271,10 +291,12 @@ int main(int argc, char** argv)
} }
for (size_t i=0 ; i<nucl_num ; ++i) { for (size_t i=0 ; i<nucl_num ; ++i) {
printf("%d %+f %+f %+f\n", (int32_t) nucl_charge[i], printf("%d %+f %+f %+f\n",
nucl_coord[i][0], (int32_t) nucl_charge[i],
nucl_coord[i][1], nucl_coord[i][0],
nucl_coord[i][2]) ); nucl_coord[i][1],
nucl_coord[i][2]);
}
#+end_src #+end_src
#+begin_example #+begin_example
@ -283,103 +305,157 @@ int main(int argc, char** argv)
1 +1.430429 +0.000000 -1.107157 1 +1.430429 +0.000000 -1.107157
#+end_example #+end_example
We now define the grid points $\mathbf{r}_k$ as a regular grid around the
molecule.
We fetch the nuclear coordinates from the context,
and compute the coordinates of the grid points: and compute the coordinates of the grid points:
#+begin_src python :exports code #+begin_src c :exports code
nx = ( 120, 120, 120 ) size_t nx[3] = { 120, 120, 120 };
shift = np.array([5.,5.,5.]) double shift[3] = {5.,5.,5.};
point_num = nx[0] * nx[1] * nx[2] int64_t point_num = nx[0] * nx[1] * nx[2];
rmin = np.array( list([ np.min(nucl_coord[:,a]) for a in range(3) ]) ) double rmin[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
rmax = np.array( list([ np.max(nucl_coord[:,a]) for a in range(3) ]) ) double rmax[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
for (size_t i=0 ; i<nucl_num ; ++i) {
for (int j=0 ; j<3 ; ++j) {
rmin[j] = nucl_coord[i][j] < rmin[j] ? nucl_coord[i][j] : rmin[j];
rmax[j] = nucl_coord[i][j] > rmax[j] ? nucl_coord[i][j] : rmax[j];
}
}
linspace = [ None for i in range(3) ] rmin[0] -= shift[0]; rmin[1] -= shift[1]; rmin[2] -= shift[2];
step = [ None for i in range(3) ] rmax[0] += shift[0]; rmax[1] += shift[1]; rmax[2] += shift[2];
for a in range(3):
linspace[a], step[a] = np.linspace(rmin[a]-shift[a],
rmax[a]+shift[a],
num=nx[a],
retstep=True)
dr = step[0] * step[1] * step[2] double step[3];
double* linspace[3];
for (int i=0 ; i<3 ; ++i) {
linspace[i] = (double*) calloc( sizeof(double), nx[i] );
if (linspace[i] == NULL) {
fprintf(stderr, "Allocation failed (linspace)\n");
exit(1);
}
step[i] = (rmax[i] - rmin[i]) / ((double) (nx[i]-1));
for (size_t j=0 ; j<nx[i] ; ++j) {
linspace[i][j] = rmin[i] + j*step[i];
}
}
double dr = step[0] * step[1] * step[2];
#+end_src #+end_src
#+RESULTS:
Now the grid is ready, we can create the list of grid points Now the grid is ready, we can create the list of grid points
$\mathbf{r}_k$ on which the MOs $\phi_i$ will be evaluated, and $\mathbf{r}_k$ on which the MOs $\phi_i$ will be evaluated, and
transfer them to the QMCkl context: transfer them to the QMCkl context:
#+begin_src python :exports code #+begin_src c :exports code
point = [] double* point = (double*) calloc(sizeof(double), 3*point_num);
for x in linspace[0]:
for y in linspace[1]:
for z in linspace[2]:
point += [ [x, y, z] ]
point = np.array(point) if (point == NULL) {
point_num = len(point) fprintf(stderr, "Allocation failed (point)\n");
qmckl.set_point(context, 'N', point_num, np.reshape(point, (point_num*3))) exit(1);
}
size_t m = 0;
for (size_t i=0 ; i<nx[0] ; ++i) {
for (size_t j=0 ; j<nx[1] ; ++j) {
for (size_t k=0 ; k<nx[2] ; ++k) {
point[m] = linspace[0][i];
m++;
point[m] = linspace[1][j];
m++;
point[m] = linspace[2][k];
m++;
}
}
}
rc = qmckl_set_point(context, 'N', point_num, point, (point_num*3));
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error setting points:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}
#+end_src #+end_src
#+RESULTS: #+RESULTS:
: None : None
Then, we evaluate all the MOs at the grid points (and time the execution), Then, we evaluate all the MOs at the grid points (and time the execution),
and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle = and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i
\phi_i(\mathbf{r}_k)$. \rangle = \phi_i(\mathbf{r}_k)$.
#+begin_src python :exports code #+begin_src c :exports code
import time
mo_num = qmckl.get_mo_basis_mo_num(context) int64_t mo_num;
rc = qmckl_get_mo_basis_mo_num(context, &mo_num);
before = time.time() long before, after;
mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num) struct timeval timecheck;
after = time.time()
mo_value = np.reshape( mo_value, (point_num, mo_num) ) double* mo_value = (double*) calloc(sizeof(double), point_num*mo_num);
if (mo_value == NULL) {
fprintf(stderr, "Allocation failed (mo_value)\n");
exit(1);
}
gettimeofday(&timecheck, NULL);
before = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
print("Number of MOs: ", mo_num) rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num*mo_num);
print("Number of grid points: ", point_num) if (rc != QMCKL_SUCCESS) {
print("Execution time : ", (after - before), "seconds") fprintf(stderr, "Error getting mo_value)\n");
exit(1);
}
gettimeofday(&timecheck, NULL);
after = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
printf("Number of MOs: %ld\n", mo_num);
printf("Number of grid points: %ld\n", point_num);
printf("Execution time : %f seconds\n", (after - before)*1.e-3);
#+end_src #+end_src
#+begin_example #+begin_example
Number of MOs: 201 Number of MOs: 201
Number of grid points: 1728000 Number of grid points: 1728000
Execution time : 3.511528968811035 seconds Execution time : 5.608000 seconds
#+end_example #+end_example
and finally we compute the overlap between all the MOs as and finally we compute the overlap between all the MOs as
$M^\dagger M$. $M.M^\dagger$.
#+begin_src python :exports code #+begin_src c :exports code
overlap = mo_value.T @ mo_value * dr double* overlap = (double*) malloc (mo_num*mo_num*sizeof(double));
print (overlap)
rc = qmckl_dgemm(context, 'N', 'T', mo_num, mo_num, point_num, dr,
mo_value, mo_num, mo_value, mo_num, 0.0,
overlap, mo_num);
for (size_t i=0 ; i<mo_num ; ++i) {
printf("%4ld", i);
for (size_t j=0 ; j<mo_num ; ++j) {
printf(" %f", overlap[i*mo_num+j]);
}
printf("\n");
}
}
#+end_src #+end_src
#+begin_example #+begin_example
[[ 9.88693941e-01 2.34719693e-03 -1.50518232e-08 ... 3.12084178e-09 0 0.988765 0.002336 0.000000 -0.000734 0.000000 0.000530 0.000000 0.000446 0.000000 -0.000000 -0.000511 -0.000000 -0.000267 0.000000 0.000000 0.001007 0.000000 0.000168 -0.000000 -0.000000 -0.000670 -0.000000 0.000000 -0.000251 -0.000261 -0.000000 -0.000000 -0.000000 -0.000397 -0.000000 -0.000810 0.000000 0.000231 -0.000000 -0.000000 0.000000 -0.000000
-5.81064929e-10 3.70130091e-02] ...
[ 2.34719693e-03 9.99509628e-01 3.18930040e-09 ... -2.46888958e-10 200 0.039017 -0.013066 -0.000000 -0.001935 -0.000000 -0.003829 -0.000000 0.000996 -0.000000 0.000000 -0.003733 0.000000 0.000065 -0.000000 -0.000000 -0.002220 -0.000000 -0.001961 0.000000 0.000000 -0.004182 0.000000 -0.000000 -0.000165 -0.002445 0.000000 -0.000000 0.000000 0.001985 0.000000 0.001685 -0.000000 -0.002899 0.000000 0.000000 0.000000 -0.000000 0.002591 0.000000 -0.000000 0.000000 0.002385 0.000000 -0.011086 0.000000 -0.003885 0.000000 -0.000000 0.003602 -0.000000 0.000000 -0.003241 0.000000 0.000000 0.002613 -0.007344 -0.000000 -0.000000 0.000000 0.000017 0.000000 0.000000 0.000000 -0.008719 0.000000 -0.001358 -0.003233 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.003778 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.001190 0.000000 0.000000 -0.000000 0.005578 -0.000000 -0.001502 0.003899 -0.000000 -0.000000 0.000000 -0.003291 -0.001775 -0.000000 -0.002374 0.000000 -0.000000 -0.000000 -0.000000 -0.001290 -0.000000 0.002178 0.000000 0.000000 0.000000 -0.001252 0.000000 -0.000000 -0.000926 0.000000 -0.000000 -0.013130 -0.000000 0.012124 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.025194 0.000343 -0.000000 0.000000 -0.000000 -0.004421 0.000000 0.000000 -0.000599 -0.000000 0.005289 0.000000 -0.000000 0.012826 -0.000000 0.000000 0.006190 0.000000 0.000000 -0.000000 0.000000 -0.000321 0.000000 -0.000000 -0.000000 0.000000 -0.000000 0.001499 -0.006629 0.000000 0.000000 0.000000 -0.000000 0.008737 -0.000000 0.006880 0.000000 -0.001851 -0.000000 -0.000000 0.000000 -0.007464 0.000000 0.010298 -0.000000 -0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.000540 0.000000 -0.006616 -0.000000 0.000000 -0.002927 -0.000000 0.000000 0.010352 0.000000 -0.003103 -0.000000 -0.007640 -0.000000 -0.000000 0.005302 0.000000 0.000000 -0.000000 -0.000000 -0.010181 0.000000 -0.001108 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.000998 -0.009754 0.013562 0.000000 -0.000000 0.887510
-1.06064273e-09 -7.65567973e-03]
[-1.50518232e-08 3.18930040e-09 9.99995073e-01 ... -5.84882580e-06
-1.21598117e-06 4.59036468e-08]
...
[ 3.12084178e-09 -2.46888958e-10 -5.84882580e-06 ... 1.00019107e+00
-2.03342837e-04 -1.36954855e-08]
[-5.81064929e-10 -1.06064273e-09 -1.21598117e-06 ... -2.03342837e-04
9.99262427e-01 1.18264754e-09]
[ 3.70130091e-02 -7.65567973e-03 4.59036468e-08 ... -1.36954855e-08
1.18264754e-09 8.97215950e-01]]
#+end_example #+end_example
* Fortran * Fortran