qmckl/org/qmckl_examples.org

#+TITLE: Code examples
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org

In this section, we provide hands-on examples to demonstrate the capabilities
of the QMCkl library.  We furnish code samples in C, Fortran, and Python,
serving as exhaustive tutorials for effectively leveraging QMCkl.
For simplicity, we assume that the wave function parameters are stored in a
[[https://github.com/TREX-CoE/trexio][TREXIO]] file.

* Overlap matrix in the MO basis

The focal point of this example is the numerical evaluation of the overlap
matrix in the MO basis. Utilizing QMCkl, we approximate the MOs at
discrete grid points to compute the overlap matrix \( S_{ij} \) as follows:
\[
S_{ij} = \int \phi_i(\mathbf{r})\, \phi_j(\mathbf{r}) \text{d}\mathbf{r} \approx
         \sum_k \phi_i(\mathbf{r}_k)\, \phi_j(\mathbf{r}_k) \delta\mathbf{r}
\]


The code starts by reading a wave function from a TREXIO file.  This is
accomplished using the ~qmckl_trexio_read~ function, which populates a
~qmckl_context~ with the necessary wave function parameters.  The context
serves as the primary interface for interacting with the QMCkl library,
encapsulating the state and configurations of the system.
Subsequently, the code retrieves various attributes such as the number of
nuclei ~nucl_num~ and coordinates ~nucl_coord~.
These attributes are essential for setting up the integration grid.

The core of the example lies in the numerical computation of the overlap
matrix. To achieve this, the code employs a regular grid in three-dimensional
space, and the grid points are then populated into the ~qmckl_context~ using
the ~qmckl_set_point~ function.

The MO values at these grid points are computed using the
~qmckl_get_mo_basis_mo_value~ function.  These values are then used to
calculate the overlap matrix through a matrix multiplication operation
facilitated by the ~qmckl_dgemm~ function.

The code is also instrumented to measure the execution time for the MO
value computation, providing an empirical assessment of the computational
efficiency. Error handling is robustly implemented at each stage to ensure the
reliability of the simulation.

In summary, this example serves as a holistic guide for leveraging the QMCkl
library, demonstrating its ease of use. It provides a concrete starting point
for researchers and developers interested in integrating QMCkl into their QMC
code.

** Python
   :PROPERTIES:
   :header-args: :tangle mo_ortho.py
   :END:

   In this example, we will compute numerically the overlap
   between the molecular orbitals:

   \[
      S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
   \text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
   \phi_j(\mathbf{r}_k) \delta \mathbf{r}
   \]
   \[
      S_{ij} = \langle \phi_i | \phi_j \rangle
   \sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
   \langle \mathbf{r}_k | \phi_j \rangle
   \]


   #+begin_src python :exports code
import numpy as np
import qmckl
   #+end_src

   #+RESULTS:

   First, we create a context for the QMCkl calculation, and load the
   wave function stored in =h2o_5z.h5= inside it. It is a Hartree-Fock
   determinant for the water molecule in the cc-pV5Z basis set.

   #+begin_src python :exports code
trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5"

context = qmckl.context_create()
qmckl.trexio_read(context, trexio_filename)
   #+end_src

   #+RESULTS:
   : None

   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 python :exports code
nucl_num = qmckl.get_nucleus_num(context)

nucl_charge = qmckl.get_nucleus_charge(context, nucl_num)

nucl_coord = qmckl.get_nucleus_coord(context, 'N', nucl_num*3)
nucl_coord = np.reshape(nucl_coord, (3, nucl_num))

for i in range(nucl_num):
    print("%d  %+f %+f %+f"%(int(nucl_charge[i]),
                             nucl_coord[i,0],
                             nucl_coord[i,1],
                             nucl_coord[i,2]) )
   #+end_src

   #+begin_example
8  +0.000000 +0.000000 +0.000000
1  -1.430429 +0.000000 -1.107157
1  +1.430429 +0.000000 -1.107157
   #+end_example

   and compute the coordinates of the grid points:

   #+begin_src python :exports code
nx = ( 120, 120, 120 )
shift = np.array([5.,5.,5.])
point_num = nx[0] * nx[1] * nx[2]

rmin  = np.array( list([ np.min(nucl_coord[:,a]) for a in range(3) ]) )
rmax  = np.array( list([ np.max(nucl_coord[:,a]) for a in range(3) ]) )


linspace = [ None for i in range(3) ]
step     = [ None for i in range(3) ]
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]
   #+end_src

   #+RESULTS:

   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
   transfer them to the QMCkl context:

   #+begin_src python :exports code
point = []
for x in linspace[0]:
    for y in linspace[1]:
        for z in linspace[2]:
            point += [ [x, y, z] ]

point = np.array(point)
point_num = len(point)
qmckl.set_point(context, 'N', point_num, np.reshape(point, (point_num*3)))
   #+end_src

   #+RESULTS:
   : None

   Then, we evaluate all the MOs at the grid points (and time the execution),
   and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle =
   \phi_i(\mathbf{r}_k)$.

   #+begin_src python :exports code
import time

mo_num = qmckl.get_mo_basis_mo_num(context)

before   = time.time()
mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
after    = time.time()

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 grid points: ", point_num)
print("Execution time : ", (after - before), "seconds")

   #+end_src

   #+begin_example
Number of MOs:  201
Number of grid points:  1728000
Execution time :  5.577778577804565 seconds
   #+end_example

   and finally we compute the overlap between all the MOs as
   $M.M^\dagger$.

   #+begin_src python :exports code
overlap = mo_value @ mo_value.T * dr
print (overlap)
   #+end_src

   #+begin_example
   [[ 9.88693941e-01  2.34719693e-03 -1.50518232e-08 ...  3.12084178e-09
     -5.81064929e-10  3.70130091e-02]
    [ 2.34719693e-03  9.99509628e-01  3.18930040e-09 ... -2.46888958e-10
     -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

** C
   In this example, electron-nucleus cusp fitting is added.

   :PROPERTIES:
   :header-args: :tangle mo_ortho.c
   :END:

   In this example, we will compute numerically the overlap
   between the molecular orbitals:

   \[
      S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
   \text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
   \phi_j(\mathbf{r}_k) \delta \mathbf{r}
   \]
   \[
      S_{ij} = \langle \phi_i | \phi_j \rangle
   \sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
   \langle \mathbf{r}_k | \phi_j \rangle
   \]

   We apply the cusp fitting procedure, so the MOs might deviate
   slightly from orthonormality.

   #+begin_src c :exports code
#include <qmckl.h>
#include <stdio.h>
#include <string.h>
#include <sys/time.h>

int main(int argc, char** argv)
{
  const char* trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5";
  qmckl_exit_code rc = QMCKL_SUCCESS;
   #+end_src

   First, we create a context for the QMCkl calculation, and load the
   wave function stored in =h2o_5z.h5= inside it. It is a Hartree-Fock
   determinant for the water molecule in the cc-pV5Z basis set.

   #+begin_src c :exports code
  qmckl_context context = qmckl_context_create();

  rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename));

  if (rc != QMCKL_SUCCESS) {
    fprintf(stderr, "Error reading TREXIO file:\n%s\n", qmckl_string_of_error(rc));
    exit(1);
  }

   #+end_src

   We impose the electron-nucleus cusp fitting to occur when the
   electrons are close to the nuclei. The critical distance
   is 0.5 atomic units for hydrogens and 0.1 for the oxygen.
   To identify which atom is an oxygen and which are hydrogens, we
   fetch the nuclear charges from the context.

   #+begin_src c :exports code
  int64_t nucl_num;

  rc = qmckl_get_nucleus_num(context, &nucl_num);

  if (rc != QMCKL_SUCCESS) {
    fprintf(stderr, "Error getting nucl_num:\n%s\n", qmckl_string_of_error(rc));
    exit(1);
  }


  double nucl_charge[nucl_num];

  rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0]), nucl_num);

  if (rc != QMCKL_SUCCESS) {
    fprintf(stderr, "Error getting nucl_charge:\n%s\n", qmckl_string_of_error(rc));
    exit(1);
  }


  double r_cusp[nucl_num];

  for (size_t i=0 ; i<nucl_num ; ++i) {

    switch ((int) nucl_charge[i]) {

    case 1:
      r_cusp[i] = 0.5;
      break;

    case 8:
      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


   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];

  rc = qmckl_get_nucleus_coord(context, 'N', &(nucl_coord[0][0]), nucl_num*3);

  if (rc != QMCKL_SUCCESS) {
    fprintf(stderr, "Error getting nucl_coord:\n%s\n", qmckl_string_of_error(rc));
    exit(1);
  }

  for (size_t i=0 ; i<nucl_num ; ++i) {
    printf("%d  %+f %+f %+f\n",
           (int32_t) nucl_charge[i],
           nucl_coord[i][0],
           nucl_coord[i][1],
           nucl_coord[i][2]);
  }
   #+end_src

   #+begin_example
8  +0.000000 +0.000000 +0.000000
1  -1.430429 +0.000000 -1.107157
1  +1.430429 +0.000000 -1.107157
   #+end_example

   and compute the coordinates of the grid points:

   #+begin_src c :exports code
  size_t nx[3] = { 120, 120, 120 };
  double shift[3] = {5.,5.,5.};
  int64_t point_num = nx[0] * nx[1] * nx[2];

  double rmin[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
  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];
    }
  }

  rmin[0] -= shift[0]; rmin[1] -= shift[1]; rmin[2] -= shift[2];
  rmax[0] += shift[0]; rmax[1] += shift[1]; rmax[2] += shift[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

   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
   transfer them to the QMCkl context:

   #+begin_src c :exports code
  double* point = (double*) calloc(sizeof(double), 3*point_num);

  if (point == NULL) {
    fprintf(stderr, "Allocation failed (point)\n");
    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

   #+RESULTS:
   : None

   Then, we evaluate all the MOs at the grid points (and time the execution),
   and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i
   \rangle = \phi_i(\mathbf{r}_k)$.

   #+begin_src c :exports code

  int64_t mo_num;
  rc = qmckl_get_mo_basis_mo_num(context, &mo_num);

  long before, after;
  struct timeval timecheck;

  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;

  rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num*mo_num);
  if (rc != QMCKL_SUCCESS) {
    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

   #+begin_example
Number of MOs:  201
Number of grid points:  1728000
Execution time :  5.608000 seconds
   #+end_example

   and finally we compute the overlap between all the MOs as
   $M.M^\dagger$.

   #+begin_src c :exports code
  double* overlap = (double*) malloc (mo_num*mo_num*sizeof(double));

  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");
  }

  // Clean-up and exit
  free(mo_value);
  free(overlap);

  rc = qmckl_context_destroy(context);
  if (rc != QMCKL_SUCCESS) {
    fprintf(stderr, "Error destroying context)\n");
    exit(1);
  }

  return 0;
}
   #+end_src

   #+begin_example
   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
   ...
 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
   #+end_example

   
** Fortran
   Here is the same piece of code translated in Fortran
   #+begin_src f90
#include <qmckl_f.F90>

program main
  use iso_c_binding
  use qmckl
  implicit none

  ! Declare variables
  integer :: argc
  character(128) :: trexio_filename, err_msg
  integer(qmckl_exit_code) :: rc
  integer(qmckl_context) :: context
  integer*8 :: nucl_num, mo_num, point_num
  double precision, allocatable :: nucl_coord(:,:)
  integer*8  :: nx(3)
  double precision, dimension(3) :: shift, step, rmin, rmax
  double precision, allocatable :: mo_value(:,:), overlap(:,:), point(:), linspace(:,:)
  double precision :: before, after, dr
  integer*8 :: i,j,k,m

  ! Initialize variables
  err_msg = ' ' 
  argc = command_argument_count()
  if (argc /= 1) then
    print *, "Usage: ./program <TREXIO filename>"
    stop -1
  end if
  call get_command_argument(1, trexio_filename)
  rc = QMCKL_SUCCESS

  ! Create a QMCkl context
  context = qmckl_context_create()

  ! Read the TREXIO file into the context
  rc = qmckl_trexio_read(context, trim(trexio_filename), len(trexio_filename)*1_8)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error reading TREXIO file:", err_msg
    stop -1
  end if

  ! Retrieve the number of nuclei
  rc = qmckl_get_nucleus_num(context, nucl_num)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error getting nucl_num:", err_msg
    stop -1
  end if

  ! Retrieve the nuclear coordinates
  allocate(nucl_coord(3, nucl_num))
  rc = qmckl_get_nucleus_coord(context, 'N', nucl_coord, nucl_num * 3_8)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error getting nucl_coord:", err_msg
    stop -1
  end if

  ! Retrieve the number of MOs
  rc = qmckl_get_mo_basis_mo_num(context, mo_num)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error getting mo_num:", err_msg
    stop -1
  end if

  ! Initialize grid points for the calculation
  nx = (/ 120, 120, 120 /)
  shift = (/ 5.d0, 5.d0, 5.d0 /)
  point_num = nx(1) * nx(2) * nx(3)

  ! Initialize rmin and rmax
  rmin = nucl_coord(:,1)
  rmax = nucl_coord(:,1)

  ! Update rmin and rmax based on nucl_coord
  do i = 1, 3
    do j = 1, nucl_num
      rmin(i) = min(nucl_coord(i,j), rmin(i))
      rmax(i) = max(nucl_coord(i,j), rmax(i))
    end do
  end do

  ! Apply shift
  rmin = rmin - shift
  rmax = rmax + shift

  ! Initialize linspace and step
  allocate(linspace(3, maxval(nx)))

  do i = 1, 3
    step(i) = (rmax(i) - rmin(i)) / real(nx(i) - 1, 8)
    do j = 1, nx(i)
      linspace(i, j) = rmin(i) + (j - 1) * step(i)
    end do
  end do

  ! Initialize point array
  allocate(point(3 * point_num))
  m = 1
  do i = 1, nx(1)
    do j = 1, nx(2)
      do k = 1, nx(3)
        point(m) = linspace(1, i); m = m + 1
        point(m) = linspace(2, j); m = m + 1
        point(m) = linspace(3, k); m = m + 1
      end do
    end do
  end do

  deallocate(linspace)


  ! Set points in QMCKL context
  rc = qmckl_set_point(context, 'N', point_num, point, point_num * 3)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error setting point:", err_msg
    stop -1
  end if




  ! Perform the actual calculation and measure the time taken
  call cpu_time(before)
  allocate(mo_value(point_num, mo_num))
  rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num * mo_num)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error getting mo_value:", err_msg
    stop
  end if
  call cpu_time(after)

  write(*,*) "Number of MOs:", mo_num
  write(*,*) "Number of grid points:", point_num
  write(*,*) "Execution time:", (after - before), "seconds"

  ! Compute the overlap matrix
  dr = step(1) * step(2) * step(3)

  allocate(overlap(mo_num, mo_num))
  rc = qmckl_dgemm(context, 'N', 'T', mo_num, mo_num, point_num, dr, &
                   mo_value, mo_num, mo_value, mo_num, 0.d0, overlap, mo_num)

  ! Print the overlap matrix
  do i = 1, mo_num
    write(*,'(i4)', advance='no') i
    do j = 1, mo_num
      write(*,'(f8.4)', advance='no') overlap(i, j)
    end do
    write(*,*)
  end do

  ! Clean-up and exit
  deallocate(mo_value, overlap)
  rc = qmckl_context_destroy(context)
  if (rc /= QMCKL_SUCCESS) then
    call qmckl_string_of_error(rc, err_msg)
    write(*,*) "Error destroying context:", err_msg
    stop -1
  end if

end program main
   #+end_src
* Fortran
** Checking errors

   All QMCkl functions return an error code. A convenient way to handle
   errors is to write an error-checking function that displays the
   error in text format and exits the program.

   #+NAME: qmckl_check_error
   #+begin_src f90
subroutine qmckl_check_error(rc, message)
  use qmckl
  implicit none
  integer(qmckl_exit_code), intent(in) :: rc
  character(len=*)        , intent(in) :: message
  character(len=128)                   :: str_buffer
  if (rc /= QMCKL_SUCCESS) then
     print *, message
     call qmckl_string_of_error(rc, str_buffer)
     print *, str_buffer
     call exit(rc)
  end if
end subroutine qmckl_check_error
   #+end_src

** Computing an atomic orbital on a grid
   :PROPERTIES:
   :header-args: :tangle ao_grid.f90
   :END:

   The following program, in Fortran, computes the values of an atomic
   orbital on a regular 3-dimensional grid. The 100^3 grid points are
   automatically defined, such that the molecule fits in a box with 5
   atomic units in the borders.

   This program uses the ~qmckl_check_error~ function defined above.

   To use this program, run

   #+begin_src bash :tangle no :exports code
$ ao_grid <trexio_file> <AO_id> <point_num>
   #+end_src


   #+begin_src f90  :noweb yes
<<qmckl_check_error>>

program ao_grid
  use qmckl
  implicit none

  integer(qmckl_context)    :: qmckl_ctx  ! QMCkl context
  integer(qmckl_exit_code)  :: rc         ! Exit code of QMCkl functions

  character(len=128)            :: trexio_filename
  character(len=128)            :: str_buffer
  integer                       :: ao_id
  integer                       :: point_num_x

  integer(c_int64_t)            :: nucl_num
  double precision, allocatable :: nucl_coord(:,:)

  integer(c_int64_t)            :: point_num
  integer(c_int64_t)            :: ao_num
  integer(c_int64_t)            :: ipoint, i, j, k
  double precision              :: x, y, z, dr(3)
  double precision              :: rmin(3), rmax(3)
  double precision, allocatable :: points(:,:)
  double precision, allocatable :: ao_vgl(:,:,:)
   #+end_src

   Start by fetching the command-line arguments:

   #+begin_src f90
  if (iargc() /= 3) then
     print *, 'Syntax: ao_grid <trexio_file> <AO_id> <point_num>'
     call exit(-1)
  end if
  call getarg(1, trexio_filename)
  call getarg(2, str_buffer)
  read(str_buffer, *) ao_id
  call getarg(3, str_buffer)
  read(str_buffer, *) point_num_x

  if (point_num_x < 0 .or. point_num_x > 300) then
     print *, 'Error: 0 < point_num < 300'
     call exit(-1)
  end if
   #+end_src

   Create the QMCkl context and initialize it with the wave function
   present in the TREXIO file:

   #+begin_src f90
  qmckl_ctx = qmckl_context_create()
  rc  = qmckl_trexio_read(qmckl_ctx, trexio_filename, 1_8*len(trim(trexio_filename)))
  call qmckl_check_error(rc, 'Read TREXIO')
   #+end_src

   We need to check that ~ao_id~ is in the range, so we get the total
   number of AOs from QMCkl:

   #+begin_src f90
  rc = qmckl_get_ao_basis_ao_num(qmckl_ctx, ao_num)
  call qmckl_check_error(rc, 'Getting ao_num')

  if (ao_id < 0 .or. ao_id > ao_num) then
     print *, 'Error: 0 < ao_id < ', ao_num
     call exit(-1)
  end if
   #+end_src

   Now we will compute the limits of the box in which the molecule fits.
   For that, we first need to ask QMCkl the coordinates of nuclei.

   #+begin_src f90
  rc = qmckl_get_nucleus_num(qmckl_ctx, nucl_num)
  call qmckl_check_error(rc, 'Get nucleus num')

  allocate( nucl_coord(3, nucl_num) )
  rc = qmckl_get_nucleus_coord(qmckl_ctx, 'N', nucl_coord, 3_8*nucl_num)
  call qmckl_check_error(rc, 'Get nucleus coord')
   #+end_src

   We now compute the coordinates of opposite points of the box, and
   the distance between points along the 3 directions:

   #+begin_src f90
  rmin(1) = minval( nucl_coord(1,:) ) - 5.d0
  rmin(2) = minval( nucl_coord(2,:) ) - 5.d0
  rmin(3) = minval( nucl_coord(3,:) ) - 5.d0

  rmax(1) = maxval( nucl_coord(1,:) ) + 5.d0
  rmax(2) = maxval( nucl_coord(2,:) ) + 5.d0
  rmax(3) = maxval( nucl_coord(3,:) ) + 5.d0

  dr(1:3) = (rmax(1:3) - rmin(1:3)) / dble(point_num_x-1)
   #+end_src

   We now produce the list of point coordinates where the AO will be
   evaluated:

   #+begin_src f90
  point_num = point_num_x**3
  allocate( points(point_num, 3) )
  ipoint=0
  z = rmin(3)
  do k=1,point_num_x
     y = rmin(2)
     do j=1,point_num_x
        x = rmin(1)
        do i=1,point_num_x
           ipoint = ipoint+1
           points(ipoint,1) = x
           points(ipoint,2) = y
           points(ipoint,3) = z
           x = x + dr(1)
        end do
        y = y + dr(2)
     end do
     z = z + dr(3)
  end do
   #+end_src

   We give the points to QMCkl:

   #+begin_src f90
  rc = qmckl_set_point(qmckl_ctx, 'T', point_num, points, size(points)*1_8 )
  call qmckl_check_error(rc, 'Setting points')
   #+end_src

   We allocate the space required to retrieve the values, gradients and
   Laplacian of all AOs, and ask to retrieve the values of the
   AOs computed at the point positions.

   #+begin_src f90
  allocate( ao_vgl(ao_num, 5, point_num) )
  rc = qmckl_get_ao_basis_ao_vgl(qmckl_ctx, ao_vgl, ao_num*5_8*point_num)
  call qmckl_check_error(rc, 'Setting points')
   #+end_src

   We finally print the value and Laplacian of the AO:

   #+begin_src f90
  do ipoint=1, point_num
     print '(3(F10.6,X),2(E20.10,X))', points(ipoint, 1:3), ao_vgl(ao_id,1,ipoint), ao_vgl(ao_id,5,ipoint)
  end do
   #+end_src

   #+begin_src f90
  deallocate( nucl_coord, points, ao_vgl )
end program ao_grid
   #+end_src