qmckl/org/qmckl_determinant.org

#+TITLE: Slater Determinant
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org

The slater deteminant is required for the calculation of the
wavefunction, gradient, and derivatives. These quantities will be used
to calculate the local Energy (\[E_L\]).

ψ(x) = det|ϕ₁(x₁)...ϕᵢ(yᵢ)...ϕₙ(xₙ)|

The above slater-matrix is also required and is denoted by Dᵢⱼ(x) such that:

ψ(x) = det|Dᵢⱼ(x)|

We also require the inverse of the slater-matrix which is denoted by D⁻¹ᵢⱼ(x).
Using this notation, the acceptance probability which is proportional to
ψ(y)/ψ(x) can be calculated as follows:

ψ(yᵢ)/ψ(xᵢ) = ∑ⱼDᵢⱼ(y)D⁻¹ⱼᵢ(x)

Concerning the gradient and laplacian, in fact what is actually
calculated is the ratio of the gradient/laplacian and the determinant
of the slater matrix:

∇ψ(x)/ψ(x)

and

∇²ψ(x)/ψ(x)

This avoids the unnecessary multiplication and division of by the
determinant ψ(x).


* 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_DETERMINANT_HPT
#define QMCKL_DETERMINANT_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"
#include "qmckl_determinant_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"
#include "qmckl_determinant_private_type.h"
#include "qmckl_determinant_private_func.h"
  #+end_src

* Context

  The following arrays are stored in the context:

  |------------------+------------------------------------------------+------------------------------------|
  | ~type~           | ~char~                                         | α (~'A'~) or β (~'B'~) determinant |
  | ~walk_num~       | ~int64_t~                                      | Number of walkers                  |
  | ~det_num_alpha~  | ~int64_t~                                      | Number of determinants per walker  |
  | ~det_num_beta~   | ~int64_t~                                      | Number of determinants per walker  |
  | ~mo_index_alpha~ | ~mo_index[det_num_alpha][walk_num][alpha_num]~ | Index of MOs for each walker       |
  | ~mo_index_beta~  | ~mo_index[det_num_beta][walk_num][beta_num]~   | Index of MOs for each walker       |

  Computed data:

  |-----------------------------+------------------------------------------------------+-------------------------------------------------------------------------------------------|
  | ~up_num~                    | ~int64_t~                                            | Number of number of α electrons                                                           |
  | ~donwn_num~                 | ~int64_t~                                            | Number of number of β electrons                                                           |
  | ~det_value_alpha~           | ~[det_num_alpha][walk_num]~                          | The α slater matrix for each determinant of each walker.                                  |
  | ~det_value_alpha_date~      | ~int64_t~                                            | Date of The α slater matrix for each determinant of each walker.                          |
  | ~det_value_beta~            | ~[det_num_beta][walk_num]~                           | The β slater matrix for each determinant of each walker.                                  |
  | ~det_value_beta_date~       | ~int64_t~                                            | Date of The β slater matrix for each determinant of each walker.                          |
  | ~det_adj_matrix_alpha~      | ~[det_num_alpha][walk_num][alpha_num][alpha_num]~    | Adjoint of the α slater matrix for each determinant of each walker.                       |
  | ~det_adj_matrix_alpha_date~ | ~int64_t~                                            | Date of the Adjoint of the α slater matrix for each determinant of each walker.           |
  | ~det_adj_matrix_beta~       | ~[det_num_beta][walk_num][beta_num][beta_num]~       | Adjoint of the β slater matrix for each determinant of each walker.                       |
  | ~det_adj_matrix_beta_date~  | ~int64_t~                                            | Date of the Adjoint of the β slater matrix for each determinant of each walker.           |
  |-----------------------------+------------------------------------------------------+-------------------------------------------------------------------------------------------|
  | ~det_vgl_alpha~             | ~[5][det_num_alpha][walk_num][alpha_num][alpha_num]~ | Value, gradients, Laplacian of Dᵅᵢⱼ(x) at electron positions                              |
  | ~det_vgl_alpha_date~        | ~int64_t~                                            | Late modification date of Value, gradients, Laplacian of the MOs at electron positions    |
  | ~det_vgl_beta~              | ~[5][det_num_beta][walk_num][beta_num][beta_num]~    | Value, gradients, Laplacian of Dᵝᵢⱼ(x) at electron positions                              |
  | ~det_vgl_beta_date~         | ~int64_t~                                            | Late modification date of Value, gradients, Laplacian of the MOs at electron positions    |
  | ~det_inv_matrix_alpha~      | ~[det_num_alpha][walk_num][alpha_num][alpha_num]~    | Inverse of the α electron slater matrix for each determinant of each walker.              |
  | ~det_inv_matrix_alpha_date~ | ~int64_t~                                            | Date for the Inverse of the α electron slater matrix for each determinant of each walker. |
  | ~det_inv_matrix_beta~       | ~[det_num_beta][walk_num][beta_num][beta_num]~       | Inverse of the β electron slater matrix for each determinant of each walker.              |
  | ~det_inv_matrix_beta_date~  | ~int64_t~                                            | Date for the Inverse of the β electron slater matrix for each determinant of each walker. |
  |-----------------------------+------------------------------------------------------+-------------------------------------------------------------------------------------------|

** Data structure

   #+begin_src c :comments org :tangle (eval h_private_type)
typedef struct qmckl_determinant_struct {
  char      type;
  int64_t  walk_num;
  int64_t  det_num_alpha;
  int64_t  det_num_beta ;
  int64_t  up_num;
  int64_t  down_num;
  int64_t* mo_index_alpha;
  int64_t* mo_index_beta;

  double  * det_value_alpha;
  double  * det_value_beta;
  double  * det_vgl_alpha;
  double  * det_adj_matrix_alpha;
  double  * det_inv_matrix_alpha;
  double  * det_vgl_beta;
  double  * det_adj_matrix_beta;
  double  * det_inv_matrix_beta;
  int64_t   det_value_alpha_date;
  int64_t   det_vgl_alpha_date;
  int64_t   det_adj_matrix_alpha_date;
  int64_t   det_inv_matrix_alpha_date;
  int64_t   det_value_beta_date;
  int64_t   det_vgl_beta_date;
  int64_t   det_adj_matrix_beta_date;
  int64_t   det_inv_matrix_beta_date;

  int32_t   uninitialized;
  bool      provided;
} qmckl_determinant_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.

   #+begin_src c :comments org :tangle (eval h_private_func)
qmckl_exit_code qmckl_init_determinant(qmckl_context context);
   #+end_src

   #+begin_src c :comments org :tangle (eval c)
qmckl_exit_code qmckl_init_determinant(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->det.uninitialized = (1 << 6) - 1;

  return QMCKL_SUCCESS;
}
   #+end_src

** Access functions

   #+begin_src c :comments org :tangle (eval h_private_func) :exports none
char      qmckl_get_determinant_type             (const qmckl_context context);
int64_t   qmckl_get_determinant_walk_num         (const qmckl_context context);
int64_t   qmckl_get_determinant_det_num_alpha    (const qmckl_context context);
int64_t   qmckl_get_determinant_det_num_beta     (const qmckl_context context);
int64_t*   qmckl_get_determinant_mo_index_alpha  (const qmckl_context context);
int64_t*   qmckl_get_determinant_mo_index_beta   (const qmckl_context context);
   #+end_src

   When all the data for the slater determinants have been provided, the following
   function returns ~true~.

   #+begin_src c :comments org :tangle (eval h_func)
bool      qmckl_determinant_provided           (const qmckl_context context);
   #+end_src

      #+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
bool qmckl_determinant_provided(const 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);

  return ctx->det.provided;
}
      #+end_src

   #+NAME:post
   #+begin_src c :exports none
if ( (ctx->det.uninitialized & mask) != 0) {
  return NULL;
}
   #+end_src


   #+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
char qmckl_get_determinant_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->det.uninitialized & mask) != 0) {
    return (char) 0;
  }

  assert (ctx->det.type != (char) 0);
  return ctx->det.type;
}

int64_t qmckl_get_determinant_walk_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->det.uninitialized & mask) != 0) {
    return (int64_t) 0;
  }

  assert (ctx->det.walk_num > (int64_t) 0);
  return ctx->det.walk_num;
}

int64_t qmckl_get_determinant_det_num_alpha (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 << 2;

  if ( (ctx->det.uninitialized & mask) != 0) {
    return (int64_t) 0;
  }

  assert (ctx->det.det_num_alpha > (int64_t) 0);
  return ctx->det.det_num_alpha;
}

int64_t qmckl_get_determinant_det_num_beta (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 << 3;

  if ( (ctx->det.uninitialized & mask) != 0) {
    return (int64_t) 0;
  }

  assert (ctx->det.det_num_beta > (int64_t) 0);
  return ctx->det.det_num_beta;
}

int64_t* qmckl_get_determinant_mo_index_alpha (const qmckl_context context) {
  if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
    return NULL;
  }

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

  int32_t mask = 1 << 4;

  if ( (ctx->det.uninitialized & mask) != 0) {
    return (int64_t) 0;
  }

  assert (ctx->det.mo_index_alpha != NULL);
  return ctx->det.mo_index_alpha;
}

int64_t* qmckl_get_determinant_mo_index_beta (const qmckl_context context) {
  if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
    return NULL;
  }

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

  int32_t mask = 1 << 5;

  if ( (ctx->det.uninitialized & mask) != 0) {
    return NULL;
  }

  assert (ctx->det.mo_index_beta != NULL);
  return ctx->det.mo_index_beta;
}

   #+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_determinant_type             (const qmckl_context context, const char t);
qmckl_exit_code  qmckl_set_determinant_walk_num         (const qmckl_context context, const int64_t walk_num);
qmckl_exit_code  qmckl_set_determinant_det_num_alpha    (const qmckl_context context, const int64_t det_num_alpha);
qmckl_exit_code  qmckl_set_determinant_det_num_beta     (const qmckl_context context, const int64_t det_num_beta);
qmckl_exit_code  qmckl_set_determinant_mo_index_alpha   (const qmckl_context context, const int64_t* mo_index_alpha);
qmckl_exit_code  qmckl_set_determinant_mo_index_beta    (const qmckl_context context, const int64_t* mo_index_beta);
   #+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->det.uninitialized &= ~mask;
ctx->det.provided = (ctx->det.uninitialized == 0);
if (ctx->det.provided) {
  qmckl_exit_code rc_ = qmckl_finalize_determinant(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_determinant_type(qmckl_context context, const char t) {
  <<pre2>>

  if (t != 'G' && t != 'S') {
    return qmckl_failwith( context,
                           QMCKL_INVALID_ARG_2,
                           "qmckl_set_determinant_type",
                           NULL);
  }

  int32_t mask = 1;
  ctx->det.type = t;

  <<post2>>
}

qmckl_exit_code qmckl_set_determinant_walk_num(qmckl_context context, const int64_t walk_num) {
  <<pre2>>

  if (walk_num <= 0) {
    return qmckl_failwith( context,
                           QMCKL_INVALID_ARG_2,
                           "qmckl_set_determinant_walk_num",
                           "walk_num <= 0");
  }

  int32_t mask = 1 << 1;
  ctx->det.walk_num = walk_num;

  <<post2>>
}

qmckl_exit_code qmckl_set_determinant_det_num_alpha(qmckl_context context, const int64_t det_num_alpha) {
  <<pre2>>

  if (det_num_alpha <= 0) {
    return qmckl_failwith( context,
                           QMCKL_INVALID_ARG_2,
                           "qmckl_set_determinant_det_num_alpha",
                           "det_num_alpha <= 0");
  }

  int32_t mask = 1 << 2;
  ctx->det.det_num_alpha = det_num_alpha;

  <<post2>>
}

qmckl_exit_code qmckl_set_determinant_det_num_beta(qmckl_context context, const int64_t det_num_beta) {
  <<pre2>>

  if (det_num_beta <= 0) {
    return qmckl_failwith( context,
                           QMCKL_INVALID_ARG_2,
                           "qmckl_set_determinant_det_num_beta",
                           "det_num_beta <= 0");
  }

  int32_t mask = 1 << 3;
  ctx->det.det_num_beta = det_num_beta;

  <<post2>>
}

qmckl_exit_code  qmckl_set_determinant_mo_index_alpha(qmckl_context context, const int64_t* mo_index_alpha) {
  <<pre2>>

  int32_t mask = 1 << 4;

  if (ctx->det.mo_index_alpha != NULL) {
    qmckl_exit_code rc = qmckl_free(context, ctx->det.mo_index_alpha);
    if (rc != QMCKL_SUCCESS) {
      return qmckl_failwith( context, rc,
                             "qmckl_set_determinant_mo_index_alpha",
                             NULL);
    }
  }

  qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
  mem_info.size = ctx->det.walk_num * ctx->det.det_num_alpha *
                  ctx->electron.up_num * sizeof(int64_t);
  int64_t* new_array = (int64_t*) qmckl_malloc(context, mem_info);
  if (new_array == NULL) {
    return qmckl_failwith( context,
                           QMCKL_ALLOCATION_FAILED,
                           "qmckl_set_determinant_mo_index_alpha",
                           NULL);
  }

  memcpy(new_array, mo_index_alpha, mem_info.size);

  ctx->det.mo_index_alpha = new_array;

  <<post2>>
}

qmckl_exit_code  qmckl_set_determinant_mo_index_beta(qmckl_context context, const int64_t* mo_index_beta) {
  <<pre2>>

  int32_t mask = 1 << 5;

  if (ctx->det.mo_index_beta != NULL) {
    qmckl_exit_code rc = qmckl_free(context, ctx->det.mo_index_beta);
    if (rc != QMCKL_SUCCESS) {
      return qmckl_failwith( context, rc,
                             "qmckl_set_determinant_mo_index_beta",
                             NULL);
    }
  }

  qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
  mem_info.size = ctx->det.walk_num * ctx->det.det_num_beta *
                  ctx->electron.down_num * sizeof(int64_t);
  int64_t* new_array = (int64_t*) qmckl_malloc(context, mem_info);
  if (new_array == NULL) {
    return qmckl_failwith( context,
                           QMCKL_ALLOCATION_FAILED,
                           "qmckl_set_determinant_mo_index_beta",
                           NULL);
  }

  memcpy(new_array, mo_index_beta, mem_info.size);

  ctx->det.mo_index_beta = new_array;

  <<post2>>
}

   #+end_src

 When the basis set is completely entered, other data structures are
 computed to accelerate the calculations.

   #+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_determinant(qmckl_context context);
   #+end_src

   #+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_determinant(qmckl_context context) {
  if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
    return qmckl_failwith( context,
                           QMCKL_INVALID_CONTEXT,
                           "qmckl_finalize_determinant",
                           NULL);
  }

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

  qmckl_exit_code rc;
  rc = qmckl_provide_det_vgl_alpha(context);
  if (rc != QMCKL_SUCCESS) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_finalize_determinant",
                            NULL);
  }
  rc = qmckl_provide_det_vgl_beta(context);
  if (rc != QMCKL_SUCCESS) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_finalize_determinant",
                            NULL);
  }
  rc = qmckl_provide_det_inv_matrix_alpha(context);
  if (rc != QMCKL_SUCCESS) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_finalize_determinant",
                            NULL);
  }
  rc = qmckl_provide_det_inv_matrix_beta(context);
  if (rc != QMCKL_SUCCESS) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_finalize_determinant",
                            NULL);
  }
  return rc;
}
   #+end_src

** Fortran Interfaces
** Test
* Computation
** Determinant matrix
   :PROPERTIES:
   :Name:     qmckl_compute_det_vgl
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

*** Get

    #+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code qmckl_get_det_vgl_alpha(qmckl_context context, double* const det_vgl_alpha);
qmckl_exit_code qmckl_get_det_vgl_beta(qmckl_context context, double* const det_vgl_beta);
    #+end_src

    #+begin_src c :comments org :tangle (eval c) :noweb yes  :exports none
qmckl_exit_code qmckl_get_det_vgl_alpha(qmckl_context context, double * const det_vgl_alpha) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_alpha(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->det.det_num_alpha * ctx->det.walk_num *
               ctx->electron.up_num * ctx->electron.up_num * sizeof(double);
  memcpy(det_vgl_alpha, ctx->det.det_vgl_alpha, sze);

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_vgl_beta(qmckl_context context, double * const det_vgl_beta) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_beta(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->det.det_num_beta * ctx->det.walk_num *
               ctx->electron.down_num * ctx->electron.down_num * sizeof(double);
  memcpy(det_vgl_beta, ctx->det.det_vgl_beta, sze);

  return QMCKL_SUCCESS;
}
    #+end_src

*** Provide

    #+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_det_vgl_alpha(qmckl_context context);
qmckl_exit_code qmckl_provide_det_vgl_beta(qmckl_context context);
    #+end_src

    #+begin_src c :comments org :tangle (eval c) :noweb yes  :exports none
qmckl_exit_code qmckl_provide_det_vgl_alpha(qmckl_context context) {

  qmckl_exit_code rc;
  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->nucleus.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if(!(ctx->electron.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if (!ctx->ao_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_ao_basis",
                           NULL);
  }

  if (!ctx->mo_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }
  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }


  if (!ctx->det.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_determinant",
                           NULL);
  }

 /* Compute if necessary */
  if (ctx->electron.coord_new_date > ctx->det.det_vgl_alpha_date) {

 /* Allocate array */
    if (ctx->det.det_vgl_alpha == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = 5 * ctx->det.walk_num * ctx->det.det_num_alpha *
                      ctx->electron.up_num * ctx->electron.up_num * sizeof(double);
      double* det_vgl_alpha = (double*) qmckl_malloc(context, mem_info);

      if (det_vgl_alpha == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_vgl_alpha",
                               NULL);
      }
      ctx->det.det_vgl_alpha = det_vgl_alpha;
    }

    if (ctx->det.type == 'G') {
      rc = qmckl_compute_det_vgl_alpha(context,
                                 ctx->det.det_num_alpha,
                                 ctx->det.walk_num,
                                 ctx->electron.up_num,
                                 ctx->electron.down_num,
                                 ctx->electron.num,
                                 ctx->det.mo_index_alpha,
                                 ctx->mo_basis.mo_num,
                                 ctx->mo_basis.mo_vgl,
                                 ctx->det.det_vgl_alpha);
    } else {
      return qmckl_failwith( context,
                             QMCKL_FAILURE,
                             "compute_det_vgl_alpha",
                             "Not yet implemented");
    }
    if (rc != QMCKL_SUCCESS) {
      return rc;
    }

    ctx->det.det_vgl_alpha_date = ctx->date;
  }

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_provide_det_vgl_beta(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->nucleus.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if(!(ctx->electron.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if (!ctx->ao_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_ao_basis",
                           NULL);
  }

  if (!ctx->mo_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

  if (!ctx->det.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

 /* Compute if necessary */
  if (ctx->electron.coord_new_date > ctx->det.det_vgl_beta_date) {

 /* Allocate array */
    if (ctx->det.det_vgl_beta == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = 5 * ctx->det.walk_num * ctx->det.det_num_beta *
                      ctx->electron.down_num * ctx->electron.down_num * sizeof(double);
      double* det_vgl_beta = (double*) qmckl_malloc(context, mem_info);

      if (det_vgl_beta == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_vgl_beta",
                               NULL);
      }
      ctx->det.det_vgl_beta = det_vgl_beta;
    }

    qmckl_exit_code rc;
    if (ctx->det.type == 'G') {
      rc = qmckl_compute_det_vgl_beta(context,
                                 ctx->det.det_num_beta,
                                 ctx->det.walk_num,
                                 ctx->electron.up_num,
                                 ctx->electron.down_num,
                                 ctx->electron.num,
                                 ctx->det.mo_index_beta,
                                 ctx->mo_basis.mo_num,
                                 ctx->mo_basis.mo_vgl,
                                 ctx->det.det_vgl_beta);
    } else {
      return qmckl_failwith( context,
                             QMCKL_FAILURE,
                             "compute_det_vgl_beta",
                             "Not yet implemented");
    }
    if (rc != QMCKL_SUCCESS) {
      return rc;
    }

    ctx->det.det_vgl_beta_date = ctx->date;
  }

  return QMCKL_SUCCESS;
}
    #+end_src
*** Compute alpha
   :PROPERTIES:
   :Name:     qmckl_compute_det_vgl_alpha
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

    #+NAME: qmckl_compute_det_vgl_alpha_args
    | Variable         | Type                                                       | In/Out | Description                               |
    |------------------+------------------------------------------------------------+--------+-------------------------------------------|
    | ~context~        | ~qmckl_context~                                            | in     | Global state                              |
    | ~det_num_alpha~  | ~int64_t~                                                  | in     | Number of determinants                    |
    | ~walk_num~       | ~int64_t~                                                  | in     | Number of walkers                         |
    | ~alpha_num~      | ~int64_t~                                                  | in     | Number of electrons                       |
    | ~beta_num~       | ~int64_t~                                                  | in     | Number of electrons                       |
    | ~elec_num~       | ~int64_t~                                                  | in     | Number of electrons                       |
    | ~mo_index_alpha~ | ~int64_t[det_num_alpha][walk_num][alpha_num]~              | in     | MO indices for electrons                  |
    | ~mo_num~         | ~int64_t~                                                  | in     | Number of MOs                             |
    | ~mo_vgl~         | ~double[5][elec_num][mo_num]~                              | in     | Value, gradients and Laplacian of the MOs |
    | ~det_vgl_alpha~  | ~double[det_num_alpha][walk_num][5][alpha_num][alpha_num]~ | out    | Value, gradients and Laplacian of the Det |

    #+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_det_vgl_alpha_f(context, &
     det_num_alpha, walk_num, alpha_num, beta_num, elec_num, &
     mo_index_alpha, mo_num, mo_vgl, det_vgl_alpha) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  integer*8, intent(in)             :: det_num_alpha
  integer*8, intent(in)             :: walk_num
  integer*8, intent(in)             :: alpha_num
  integer*8, intent(in)             :: beta_num
  integer*8, intent(in)             :: elec_num
  integer*8, intent(in)             :: mo_num
  integer*8, intent(in)             :: mo_index_alpha(alpha_num, walk_num, det_num_alpha)
  double precision, intent(in)      :: mo_vgl(mo_num, elec_num, 5)
  double precision, intent(inout)   :: det_vgl_alpha(alpha_num, alpha_num, 5, walk_num, det_num_alpha)
  integer*8 :: idet, iwalk, ielec, mo_id, imo

  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 (alpha_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  do idet  = 1, det_num_alpha
  do iwalk = 1, walk_num
    do ielec = 1, alpha_num
      do imo = 1, alpha_num
        mo_id = mo_index_alpha(imo,iwalk,idet)
        ! Value
        det_vgl_alpha(imo, ielec, 1, iwalk, idet) = mo_vgl(mo_id, ielec, 1)

        ! Grad_x
        det_vgl_alpha(imo, ielec, 2, iwalk, idet) = mo_vgl(mo_id, ielec, 2)

        ! Grad_y
        det_vgl_alpha(imo, ielec, 3, iwalk, idet) = mo_vgl(mo_id, ielec, 3)

        ! Grad_z
        det_vgl_alpha(imo, ielec, 4, iwalk, idet) = mo_vgl(mo_id, ielec, 4)

        ! Lap
        det_vgl_alpha(imo, ielec, 5, iwalk, idet) = mo_vgl(mo_id, ielec, 5)
      end do
    end do
  end do
  end do

end function qmckl_compute_det_vgl_alpha_f
    #+end_src

    #+CALL: generate_c_header(table=qmckl_compute_det_vgl_alpha_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_vgl_alpha"))

   #+RESULTS:
   #+begin_src c :tangle (eval h_func) :comments org
   qmckl_exit_code qmckl_compute_det_vgl_alpha (
         const qmckl_context context,
         const int64_t det_num_alpha,
         const int64_t walk_num,
         const int64_t alpha_num,
         const int64_t beta_num,
         const int64_t elec_num,
         const int64_t* mo_index_alpha,
         const int64_t mo_num,
         const double* mo_vgl,
         double* const det_vgl_alpha );
   #+end_src

   #+CALL: generate_c_interface(table=qmckl_compute_det_vgl_alpha_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_vgl_alpha"))

    #+RESULTS:
    #+begin_src f90 :tangle (eval f) :comments org :exports none
    integer(c_int32_t) function qmckl_compute_det_vgl_alpha &
        (context, &
         det_num_alpha, &
         walk_num, &
         alpha_num, &
         beta_num, &
         elec_num, &
         mo_index_alpha, &
         mo_num, &
         mo_vgl, &
         det_vgl_alpha) &
        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 :: det_num_alpha
      integer (c_int64_t) , intent(in)  , value :: walk_num
      integer (c_int64_t) , intent(in)  , value :: alpha_num
      integer (c_int64_t) , intent(in)  , value :: beta_num
      integer (c_int64_t) , intent(in)  , value :: elec_num
      integer (c_int64_t) , intent(in)          :: mo_index_alpha(alpha_num,walk_num,det_num_alpha)
      integer (c_int64_t) , intent(in)  , value :: mo_num
      real    (c_double ) , intent(in)          :: mo_vgl(mo_num,elec_num,5)
      real    (c_double ) , intent(out)         :: det_vgl_alpha(alpha_num,alpha_num,5,walk_num,det_num_alpha)

      integer(c_int32_t), external :: qmckl_compute_det_vgl_alpha_f
      info = qmckl_compute_det_vgl_alpha_f &
             (context, &
         det_num_alpha, &
         walk_num, &
         alpha_num, &
         beta_num, &
         elec_num, &
         mo_index_alpha, &
         mo_num, &
         mo_vgl, &
         det_vgl_alpha)

    end function qmckl_compute_det_vgl_alpha
    #+end_src

*** Compute beta
   :PROPERTIES:
   :Name:     qmckl_compute_det_vgl_beta
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

    #+NAME: qmckl_compute_det_vgl_beta_args
    | Variable        | Type                                                    | In/Out | Description                               |
    |-----------------+---------------------------------------------------------+--------+-------------------------------------------|
    | ~context~       | ~qmckl_context~                                         | in     | Global state                              |
    | ~det_num_beta~  | ~int64_t~                                               | in     | Number of determinants                    |
    | ~walk_num~      | ~int64_t~                                               | in     | Number of walkers                         |
    | ~alpha_num~     | ~int64_t~                                               | in     | Number of electrons                       |
    | ~beta_num~      | ~int64_t~                                               | in     | Number of electrons                       |
    | ~elec_num~      | ~int64_t~                                               | in     | Number of electrons                       |
    | ~mo_index_beta~ | ~int64_t[det_num_beta][walk_num][beta_num]~             | in     | Number of electrons                       |
    | ~mo_num~        | ~int64_t~                                               | in     | Number of MOs                             |
    | ~mo_vgl~        | ~double[5][elec_num][mo_num]~                           | in     | Value, gradients and Laplacian of the MOs |
    | ~det_vgl_beta~  | ~double[det_num_beta][walk_num][5][beta_num][beta_num]~ | out    | Value, gradients and Laplacian of the Det |

    #+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_det_vgl_beta_f(context, &
     det_num_beta, walk_num, alpha_num, beta_num, elec_num, &
     mo_index_beta, mo_num, mo_vgl, det_vgl_beta) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  integer*8, intent(in)             :: det_num_beta
  integer*8, intent(in)             :: walk_num
  integer*8, intent(in)             :: alpha_num
  integer*8, intent(in)             :: beta_num
  integer*8, intent(in)             :: elec_num
  integer*8, intent(in)             :: mo_num
  integer*8, intent(in)             :: mo_index_beta(beta_num,walk_num,det_num_beta)
  double precision, intent(in)      :: mo_vgl(mo_num, elec_num, 5)
  double precision, intent(inout)   :: det_vgl_beta(beta_num, beta_num, 5, walk_num, det_num_beta)
  integer*8 :: idet, iwalk, ielec, mo_id, imo

  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 (beta_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  do idet = 1, det_num_beta
  do iwalk = 1, walk_num
    do ielec = 1, beta_num
      do imo = 1, beta_num
        mo_id = mo_index_beta(imo, iwalk, idet)
        ! Value
        det_vgl_beta(imo, ielec, 1, iwalk, idet) = mo_vgl(mo_id, alpha_num + ielec, 1)

        ! Grad_x
        det_vgl_beta(imo, ielec, 2, iwalk, idet) = mo_vgl(mo_id, alpha_num + ielec, 2)

        ! Grad_y
        det_vgl_beta(imo, ielec, 3, iwalk, idet) = mo_vgl(mo_id, alpha_num + ielec, 3)

        ! Grad_z
        det_vgl_beta(imo, ielec, 4, iwalk, idet) = mo_vgl(mo_id, alpha_num + ielec, 4)

        ! Lap
        det_vgl_beta(imo, ielec, 5, iwalk, idet) = mo_vgl(mo_id, alpha_num + ielec, 5)
      end do
    end do
  end do
  end do

end function qmckl_compute_det_vgl_beta_f
    #+end_src

    #+CALL: generate_c_header(table=qmckl_compute_det_vgl_beta_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_vgl_beta"))

   #+RESULTS:
   #+begin_src c :tangle (eval h_func) :comments org
   qmckl_exit_code qmckl_compute_det_vgl_beta (
         const qmckl_context context,
         const int64_t det_num_beta,
         const int64_t walk_num,
         const int64_t alpha_num,
         const int64_t beta_num,
         const int64_t elec_num,
         const int64_t* mo_index_beta,
         const int64_t mo_num,
         const double* mo_vgl,
         double* const det_vgl_beta );
   #+end_src

   #+CALL: generate_c_interface(table=qmckl_compute_det_vgl_beta_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_vgl_beta"))

    #+RESULTS:
    #+begin_src f90 :tangle (eval f) :comments org :exports none
    integer(c_int32_t) function qmckl_compute_det_vgl_beta &
        (context, &
         det_num_beta, &
         walk_num, &
         alpha_num, &
         beta_num, &
         elec_num, &
         mo_index_beta, &
         mo_num, &
         mo_vgl, &
         det_vgl_beta) &
        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 :: det_num_beta
      integer (c_int64_t) , intent(in)  , value :: walk_num
      integer (c_int64_t) , intent(in)  , value :: alpha_num
      integer (c_int64_t) , intent(in)  , value :: beta_num
      integer (c_int64_t) , intent(in)  , value :: elec_num
      integer (c_int64_t) , intent(in)          :: mo_index_beta(beta_num,walk_num,det_num_beta)
      integer (c_int64_t) , intent(in)  , value :: mo_num
      real    (c_double ) , intent(in)          :: mo_vgl(mo_num,elec_num,5)
      real    (c_double ) , intent(out)         :: det_vgl_beta(beta_num,beta_num,5,walk_num,det_num_beta)

      integer(c_int32_t), external :: qmckl_compute_det_vgl_beta_f
      info = qmckl_compute_det_vgl_beta_f &
             (context, &
         det_num_beta, &
         walk_num, &
         alpha_num, &
         beta_num, &
         elec_num, &
         mo_index_beta, &
         mo_num, &
         mo_vgl, &
         det_vgl_beta)

    end function qmckl_compute_det_vgl_beta
    #+end_src

*** Test

     #+begin_src c :tangle (eval c_test) :exports none

#define walk_num chbrclf_walk_num
#define elec_num chbrclf_elec_num
#define shell_num chbrclf_shell_num
#define ao_num chbrclf_ao_num

int64_t elec_up_num   = chbrclf_elec_up_num;
int64_t elec_dn_num   = chbrclf_elec_dn_num;
double* elec_coord    = &(chbrclf_elec_coord[0][0][0]);
const int64_t   nucl_num      = chbrclf_nucl_num;
const double*   nucl_charge   = chbrclf_charge;
const double*   nucl_coord    = &(chbrclf_nucl_coord[0][0]);

rc = qmckl_set_electron_num (context, elec_up_num, elec_dn_num);
assert (rc == QMCKL_SUCCESS);

rc = qmckl_set_electron_walk_num (context, walk_num);
assert (rc == QMCKL_SUCCESS);

assert(qmckl_electron_provided(context));

rc = qmckl_set_electron_coord (context, 'N', elec_coord, walk_num*elec_num*3);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_nucleus_num (context, nucl_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_nucleus_coord (context, 'T', &(nucl_coord[0]), nucl_num*3);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_nucleus_charge(context, nucl_charge, nucl_num);
assert(rc == QMCKL_SUCCESS);

assert(qmckl_nucleus_provided(context));

const int64_t *  nucleus_index     =  &(chbrclf_basis_nucleus_index[0]);
const int64_t *  nucleus_shell_num =  &(chbrclf_basis_nucleus_shell_num[0]);
const int32_t *  shell_ang_mom     =  &(chbrclf_basis_shell_ang_mom[0]);
const int64_t *  shell_prim_num    =  &(chbrclf_basis_shell_prim_num[0]);
const int64_t *  shell_prim_index  =  &(chbrclf_basis_shell_prim_index[0]);
const double  *  shell_factor      =  &(chbrclf_basis_shell_factor[0]);
const double  *  exponent          =  &(chbrclf_basis_exponent[0]);
const double  *  coefficient       =  &(chbrclf_basis_coefficient[0]);
const double  *  prim_factor       =  &(chbrclf_basis_prim_factor[0]);
const double  *  ao_factor         =  &(chbrclf_basis_ao_factor[0]);

const char typ = 'G';

assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_type (context, typ);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_shell_num (context, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_prim_num (context, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_nucleus_index (context, nucleus_index, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_nucleus_shell_num (context, nucleus_shell_num, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_shell_ang_mom (context, shell_ang_mom, shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_shell_factor  (context, shell_factor, shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_shell_prim_num (context, shell_prim_num, shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_shell_prim_index (context, shell_prim_index, shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_exponent (context, exponent, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_coefficient (context, coefficient, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));

rc = qmckl_set_ao_basis_prim_factor (context, prim_factor, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_ao_basis_ao_num(context, chbrclf_ao_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_ao_basis_ao_factor (context, ao_factor, chbrclf_ao_num);
assert(rc == QMCKL_SUCCESS);

assert(qmckl_ao_basis_provided(context));


double ao_vgl[5][walk_num][elec_num][chbrclf_ao_num];

rc = qmckl_get_ao_basis_ao_vgl(context, &(ao_vgl[0][0][0][0]), (int64_t) 5*walk_num*elec_num*chbrclf_ao_num);
assert (rc == QMCKL_SUCCESS);

/* Set up MO data */
const int64_t mo_num = chbrclf_mo_num;
rc = qmckl_set_mo_basis_mo_num(context, mo_num);
assert (rc == QMCKL_SUCCESS);

const double  * mo_coefficient          =  &(chbrclf_mo_coef[0]);

rc = qmckl_set_mo_basis_coefficient(context, mo_coefficient);
assert (rc == QMCKL_SUCCESS);

assert(qmckl_mo_basis_provided(context));

double mo_vgl[5][elec_num][chbrclf_mo_num];
rc = qmckl_get_mo_basis_vgl(context, &(mo_vgl[0][0][0]));
assert (rc == QMCKL_SUCCESS);

/* Set up determinant data */

const int64_t det_num_alpha = 1;
const int64_t det_num_beta  = 1;
int64_t mo_index_alpha[det_num_alpha][walk_num][elec_up_num];
int64_t mo_index_beta[det_num_alpha][walk_num][elec_dn_num];

int i, j, k;
for(k = 0; k < det_num_alpha; ++k)
  for(i = 0; i < walk_num; ++i)
    for(j = 0; j < elec_up_num; ++j)
      mo_index_alpha[k][i][j] = j + 1;
for(k = 0; k < det_num_beta; ++k)
  for(i = 0; i < walk_num; ++i)
    for(j = 0; j < elec_up_num; ++j)
      mo_index_beta[k][i][j] = j + 1;

rc = qmckl_set_determinant_type (context, typ);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_determinant_walk_num (context, walk_num);
assert (rc == QMCKL_SUCCESS);

rc = qmckl_set_determinant_det_num_alpha (context, det_num_alpha);
assert (rc == QMCKL_SUCCESS);

rc = qmckl_set_determinant_det_num_beta (context, det_num_beta);
assert (rc == QMCKL_SUCCESS);

rc = qmckl_set_determinant_mo_index_alpha (context, &(mo_index_alpha[0][0][0]));
assert (rc == QMCKL_SUCCESS);

rc = qmckl_set_determinant_mo_index_beta (context, &(mo_index_beta[0][0][0]));
assert (rc == QMCKL_SUCCESS);

// Get slater-determinant

double det_vgl_alpha[det_num_alpha][walk_num][5][elec_up_num][elec_up_num];
double det_vgl_beta[det_num_beta][walk_num][5][elec_dn_num][elec_dn_num];

rc = qmckl_get_det_vgl_alpha(context, &(det_vgl_alpha[0][0][0][0][0]));
assert (rc == QMCKL_SUCCESS);

rc = qmckl_get_det_vgl_beta(context, &(det_vgl_beta[0][0][0][0][0]));
assert (rc == QMCKL_SUCCESS);

     #+end_src

** Inverse of Determinant matrix
   :PROPERTIES:
   :Name:     qmckl_compute_det_inv_matrix
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

*** Get

    #+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code qmckl_get_det_inv_matrix_alpha(qmckl_context context, double* const det_inv_matrix_alpha);
qmckl_exit_code qmckl_get_det_inv_matrix_beta(qmckl_context context, double* const det_inv_matrix_beta);
qmckl_exit_code qmckl_get_det_adj_matrix_alpha(qmckl_context context, double* const det_adj_matrix_alpha);
qmckl_exit_code qmckl_get_det_adj_matrix_beta(qmckl_context context, double* const det_adj_matrix_beta);
qmckl_exit_code qmckl_get_det_alpha(qmckl_context context, double* const det_adj_matrix_alpha);
qmckl_exit_code qmckl_get_det_beta(qmckl_context context, double* const det_adj_matrix_beta);
    #+end_src

    #+begin_src c :comments org :tangle (eval c) :noweb yes  :exports none
qmckl_exit_code qmckl_get_det_inv_matrix_alpha(qmckl_context context, double * const det_inv_matrix_alpha) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num * ctx->electron.up_num * ctx->electron.up_num;
  memcpy(det_inv_matrix_alpha, ctx->det.det_inv_matrix_alpha, sze * sizeof(double));

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_inv_matrix_beta(qmckl_context context, double * const det_inv_matrix_beta) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num * ctx->electron.down_num * ctx->electron.down_num;
  memcpy(det_inv_matrix_beta, ctx->det.det_inv_matrix_beta, sze * sizeof(double));

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_adj_matrix_alpha(qmckl_context context, double * const det_adj_matrix_alpha) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num * ctx->electron.up_num * ctx->electron.up_num;
  memcpy(det_adj_matrix_alpha, ctx->det.det_adj_matrix_alpha, sze * sizeof(double));

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_adj_matrix_beta(qmckl_context context, double * const det_adj_matrix_beta) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num * ctx->electron.down_num * ctx->electron.down_num;
  memcpy(det_adj_matrix_beta, ctx->det.det_adj_matrix_beta, sze * sizeof(double));

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_alpha(qmckl_context context, double * const det_value_alpha) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_alpha(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num;
  memcpy(det_value_alpha, ctx->det.det_value_alpha, sze * sizeof(double));

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_get_det_beta(qmckl_context context, double * const det_value_beta) {

  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;

  rc = qmckl_provide_mo_vgl(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_vgl_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

  rc = qmckl_provide_det_inv_matrix_beta(context);
  if (rc != QMCKL_SUCCESS) return rc;

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

  size_t sze = ctx->det.det_num_alpha * ctx->det.walk_num;
  memcpy(det_value_beta, ctx->det.det_value_beta, sze * sizeof(double));

  return QMCKL_SUCCESS;
}
    #+end_src


*** Provide

    #+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_det_inv_matrix_alpha(qmckl_context context);
qmckl_exit_code qmckl_provide_det_inv_matrix_beta(qmckl_context context);
    #+end_src

    #+begin_src c :comments org :tangle (eval c) :noweb yes  :exports none
qmckl_exit_code qmckl_provide_det_inv_matrix_alpha(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->nucleus.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if(!(ctx->electron.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if (!ctx->ao_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_ao_basis",
                           NULL);
  }

  if (!ctx->mo_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

  if (!ctx->det.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

 /* Compute if necessary */
  if (ctx->electron.coord_new_date > ctx->det.det_inv_matrix_alpha_date) {

 /* Allocate array */
    if (ctx->det.det_inv_matrix_alpha == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_alpha *
                      ctx->electron.up_num * ctx->electron.up_num * sizeof(double);
      double* det_inv_matrix_alpha = (double*) qmckl_malloc(context, mem_info);

      if (det_inv_matrix_alpha == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_inv_matrix_alpha",
                               NULL);
      }
      ctx->det.det_inv_matrix_alpha = det_inv_matrix_alpha;
    }

    if (ctx->det.det_adj_matrix_alpha == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_alpha *
                      ctx->electron.up_num * ctx->electron.up_num * sizeof(double);
      double* det_adj_matrix_alpha = (double*) qmckl_malloc(context, mem_info);

      if (det_adj_matrix_alpha == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_adj_matrix_alpha",
                               NULL);
      }
      ctx->det.det_adj_matrix_alpha = det_adj_matrix_alpha;
    }

    if (ctx->det.det_value_alpha == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_alpha * sizeof(double);
      double* det_value_alpha = (double*) qmckl_malloc(context, mem_info);

      if (det_value_alpha == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_value_alpha",
                               NULL);
      }
      ctx->det.det_value_alpha = det_value_alpha;
    }

    qmckl_exit_code rc;
    if (ctx->det.type == 'G') {
      rc = qmckl_compute_det_inv_matrix_alpha(context,
                                        ctx->det.det_num_alpha,
                                        ctx->det.walk_num,
                                        ctx->electron.up_num,
                                        ctx->det.det_vgl_alpha,
                                        ctx->det.det_value_alpha,
                                        ctx->det.det_adj_matrix_alpha,
                                        ctx->det.det_inv_matrix_alpha);
    } else {
      return qmckl_failwith( context,
                             QMCKL_FAILURE,
                             "compute_det_inv_matrix_alpha",
                             "Not yet implemented");
    }
    if (rc != QMCKL_SUCCESS) {
      return rc;
    }

    ctx->det.det_value_alpha_date = ctx->date;
    ctx->det.det_adj_matrix_alpha_date = ctx->date;
    ctx->det.det_inv_matrix_alpha_date = ctx->date;
  }

  return QMCKL_SUCCESS;
}

qmckl_exit_code qmckl_provide_det_inv_matrix_beta(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->nucleus.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if(!(ctx->electron.provided)) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_electron",
                           NULL);
  }

  if (!ctx->ao_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_ao_basis",
                           NULL);
  }

  if (!ctx->mo_basis.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

  if (!ctx->det.provided) {
    return qmckl_failwith( context,
                           QMCKL_NOT_PROVIDED,
                           "qmckl_mo_basis",
                           NULL);
  }

 /* Compute if necessary */
  if (ctx->electron.coord_new_date > ctx->det.det_inv_matrix_beta_date) {

 /* Allocate array */
    if (ctx->det.det_inv_matrix_beta == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_beta *
                      ctx->electron.down_num * ctx->electron.down_num * sizeof(double);
      double* det_inv_matrix_beta = (double*) qmckl_malloc(context, mem_info);

      if (det_inv_matrix_beta == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_inv_matrix_beta",
                               NULL);
      }
      ctx->det.det_inv_matrix_beta = det_inv_matrix_beta;
    }

    if (ctx->det.det_adj_matrix_beta == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_beta *
                      ctx->electron.down_num * ctx->electron.down_num * sizeof(double);
      double* det_adj_matrix_beta = (double*) qmckl_malloc(context, mem_info);

      if (det_adj_matrix_beta == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_adj_matrix_beta",
                               NULL);
      }
      ctx->det.det_adj_matrix_beta = det_adj_matrix_beta;
    }

    if (ctx->det.det_value_beta == NULL) {

      qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
      mem_info.size = ctx->det.walk_num * ctx->det.det_num_beta * sizeof(double);
      double* det_value_beta = (double*) qmckl_malloc(context, mem_info);

      if (det_value_beta == NULL) {
        return qmckl_failwith( context,
                               QMCKL_ALLOCATION_FAILED,
                               "qmckl_det_value_beta",
                               NULL);
      }
      ctx->det.det_value_beta = det_value_beta;
    }

    qmckl_exit_code rc;
    if (ctx->det.type == 'G') {
      rc = qmckl_compute_det_inv_matrix_beta(context,
                                        ctx->det.det_num_beta,
                                        ctx->det.walk_num,
                                        ctx->electron.down_num,
                                        ctx->det.det_vgl_beta,
                                        ctx->det.det_value_beta,
                                        ctx->det.det_adj_matrix_beta,
                                        ctx->det.det_inv_matrix_beta);
    } else {
      return qmckl_failwith( context,
                             QMCKL_FAILURE,
                             "compute_det_inv_matrix_beta",
                             "Not yet implemented");
    }
    if (rc != QMCKL_SUCCESS) {
      return rc;
    }

    ctx->det.det_value_beta_date = ctx->date;
    ctx->det.det_adj_matrix_beta_date = ctx->date;
    ctx->det.det_inv_matrix_beta_date = ctx->date;
  }

  return QMCKL_SUCCESS;
}
    #+end_src

*** Compute alpha
   :PROPERTIES:
   :Name:     qmckl_compute_det_inv_matrix_alpha
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

   #+NAME: qmckl_det_inv_matrix_alpha_args
    | Variable               | Type                                                       | In/Out | Description                                                  |
    |------------------------+------------------------------------------------------------+--------+--------------------------------------------------------------|
    | ~context~              | ~qmckl_context~                                            | in     | Global state                                                 |
    | ~det_num_alpha~        | ~int64_t~                                                  | in     | Number of determinants                                       |
    | ~walk_num~             | ~int64_t~                                                  | in     | Number of walkers                                            |
    | ~alpha_num~            | ~int64_t~                                                  | in     | Number of electrons                                          |
    | ~det_vgl_alpha~        | ~double[det_num_alpha][walk_num][5][alpha_num][alpha_num]~ | in     | determinant matrix Value, gradients and Laplacian of the MOs |
    | ~det_value_alpha~      | ~double[det_num_alpha][walk_num]~                          | out    | value of determinant matrix                                  |
    | ~det_adj_matrix_alpha~ | ~double[det_num_alpha][walk_num][alpha_num][alpha_num]~    | out    | adjoint of determinant matrix                                |
    | ~det_inv_matrix_alpha~ | ~double[det_num_alpha][walk_num][alpha_num][alpha_num]~    | out    | inverse of determinant matrix                                |

    #+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_det_inv_matrix_alpha_f(context, &
     det_num_alpha, walk_num, alpha_num, det_vgl_alpha, det_value_alpha, det_adj_matrix_alpha, det_inv_matrix_alpha) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  integer*8, intent(in)             :: det_num_alpha
  integer*8, intent(in)             :: walk_num
  integer*8, intent(in)             :: alpha_num
  double precision, intent(in)      :: det_vgl_alpha(alpha_num, alpha_num, 5, walk_num, det_num_alpha)
  double precision, intent(inout)   :: det_value_alpha(walk_num, det_num_alpha)
  double precision, intent(inout)   :: det_adj_matrix_alpha(alpha_num, alpha_num, walk_num, det_num_alpha)
  double precision, intent(inout)   :: det_inv_matrix_alpha(alpha_num, alpha_num, walk_num, det_num_alpha)
  double precision,dimension(:,:),allocatable  :: matA
  double precision                  :: det_l
  integer*8 :: idet, iwalk, ielec, mo_id, imo, LDA, res, i, j

  allocate(matA(alpha_num, alpha_num))

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (det_num_alpha <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  if (alpha_num <= 0) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  LDA = alpha_num
  do idet = 1, det_num_alpha
     do iwalk = 1, walk_num
        ! Value
        matA(1:alpha_num,1:alpha_num) = &
             det_vgl_alpha(1:alpha_num, 1:alpha_num, 1, iwalk, idet)

        res = qmckl_adjugate(context,                 &
             alpha_num, matA, LDA,                    &
             det_adj_matrix_alpha(1:alpha_num, 1:alpha_num, iwalk, idet), &
             int(size(det_adj_matrix_alpha,1),8),     &
             det_l)

        det_inv_matrix_alpha(1:alpha_num, 1:alpha_num, iwalk, idet) = &
             (1.d0/det_l) * &
             det_adj_matrix_alpha(1:alpha_num, 1:alpha_num, iwalk, idet)

        det_value_alpha(iwalk, idet) = det_l
     end do
  end do

  deallocate(matA)
end function qmckl_compute_det_inv_matrix_alpha_f
    #+end_src

   #+CALL: generate_c_header(table=qmckl_det_inv_matrix_alpha_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_inv_matrix_alpha"))

   #+RESULTS:
   #+begin_src c :tangle (eval h_func) :comments org
   qmckl_exit_code qmckl_compute_det_inv_matrix_alpha (
         const qmckl_context context,
         const int64_t det_num_alpha,
         const int64_t walk_num,
         const int64_t alpha_num,
         const double* det_vgl_alpha,
         double* const det_value_alpha,
         double* const det_adj_matrix_alpha,
         double* const det_inv_matrix_alpha );
   #+end_src

    #+CALL: generate_c_interface(table=qmckl_det_inv_matrix_alpha_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_inv_matrix_alpha"))

    #+RESULTS:
    #+begin_src f90 :tangle (eval f) :comments org :exports none
    integer(c_int32_t) function qmckl_compute_det_inv_matrix_alpha &
        (context, &
         det_num_alpha, &
         walk_num, &
         alpha_num, &
         det_vgl_alpha, &
         det_value_alpha, &
         det_adj_matrix_alpha, &
         det_inv_matrix_alpha) &
        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 :: det_num_alpha
      integer (c_int64_t) , intent(in)  , value :: walk_num
      integer (c_int64_t) , intent(in)  , value :: alpha_num
      real    (c_double ) , intent(in)          :: det_vgl_alpha(alpha_num,alpha_num,5,walk_num,det_num_alpha)
      real    (c_double ) , intent(out)         :: det_value_alpha(walk_num,det_num_alpha)
      real    (c_double ) , intent(out)         :: det_adj_matrix_alpha(alpha_num,alpha_num,walk_num,det_num_alpha)
      real    (c_double ) , intent(out)         :: det_inv_matrix_alpha(alpha_num,alpha_num,walk_num,det_num_alpha)

      integer(c_int32_t), external :: qmckl_compute_det_inv_matrix_alpha_f
      info = qmckl_compute_det_inv_matrix_alpha_f &
             (context, &
         det_num_alpha, &
         walk_num, &
         alpha_num, &
         det_vgl_alpha, &
         det_value_alpha, &
         det_adj_matrix_alpha, &
         det_inv_matrix_alpha)

    end function qmckl_compute_det_inv_matrix_alpha
    #+end_src

*** Compute beta
   :PROPERTIES:
   :Name:     qmckl_compute_det_inv_matrix_beta
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

    #+NAME: qmckl_det_inv_matrix_beta_args
    | Variable              | Type                                                    | In/Out | Description                                                  |
    |-----------------------+---------------------------------------------------------+--------+--------------------------------------------------------------|
    | ~context~             | ~qmckl_context~                                         | in     | Global state                                                 |
    | ~det_num_beta~        | ~int64_t~                                               | in     | Number of determinants                                       |
    | ~walk_num~            | ~int64_t~                                               | in     | Number of walkers                                            |
    | ~beta_num~            | ~int64_t~                                               | in     | Number of electrons                                          |
    | ~det_vgl_beta~        | ~double[det_num_beta][walk_num][5][beta_num][beta_num]~ | in     | determinant matrix Value, gradients and Laplacian of the MOs |
    | ~det_value_beta~      | ~double[det_num_beta][walk_num]~                        | out    | value of determinant matrix                                  |
    | ~det_adj_matrix_beta~ | ~double[det_num_beta][walk_num][beta_num][beta_num]~    | out    | adjoint of determinant matrix                                |
    | ~det_inv_matrix_beta~ | ~double[det_num_beta][walk_num][beta_num][beta_num]~    | out    | inverse of determinant matrix                                |

    #+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_det_inv_matrix_beta_f(context, &
     det_num_beta, walk_num, beta_num, det_vgl_beta, det_value_beta, det_adj_matrix_beta, det_inv_matrix_beta) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  integer*8, intent(in)             :: det_num_beta
  integer*8, intent(in)             :: walk_num
  integer*8, intent(in)             :: beta_num
  double precision, intent(in)      :: det_vgl_beta(beta_num, beta_num, 5, walk_num, det_num_beta)
  double precision, intent(inout)   :: det_value_beta(walk_num, det_num_beta)
  double precision, intent(inout)   :: det_adj_matrix_beta(beta_num, beta_num, walk_num, det_num_beta)
  double precision, intent(inout)   :: det_inv_matrix_beta(beta_num, beta_num, walk_num, det_num_beta)
  double precision,dimension(:,:),allocatable  :: matA
  double precision                  :: det_l
  integer*8 :: idet, iwalk, ielec, mo_id, imo, LDA, res

  allocate(matA(beta_num, beta_num))

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (det_num_beta <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  if (beta_num <= 0) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  LDA = beta_num
  do idet = 1, det_num_beta
     do iwalk = 1, walk_num
        ! Value
        matA(1:beta_num,1:beta_num) = &
             det_vgl_beta(1:beta_num, 1:beta_num, 1, iwalk, idet)

        res = qmckl_adjugate(context,                 &
             beta_num, matA, LDA,                    &
             det_adj_matrix_beta(1, 1, iwalk, idet), &
             int(size(det_adj_matrix_beta,1),8),     &
             det_l)

        det_inv_matrix_beta(1:beta_num, 1:beta_num, iwalk, idet) = &
             (1.d0/det_l) * &
             det_adj_matrix_beta(1:beta_num, 1:beta_num, iwalk, idet)

        det_value_beta(iwalk, idet) = det_l
     end do
  end do


  deallocate(matA)
end function qmckl_compute_det_inv_matrix_beta_f
    #+end_src

    #+CALL: generate_c_header(table=qmckl_det_inv_matrix_beta_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_inv_matrix_beta"))

   #+RESULTS:
   #+begin_src c :tangle (eval h_func) :comments org
   qmckl_exit_code qmckl_compute_det_inv_matrix_beta (
         const qmckl_context context,
         const int64_t det_num_beta,
         const int64_t walk_num,
         const int64_t beta_num,
         const double* det_vgl_beta,
         double* const det_value_beta,
         double* const det_adj_matrix_beta,
         double* const det_inv_matrix_beta );
   #+end_src

    #+CALL: generate_c_interface(table=qmckl_det_inv_matrix_beta_args,rettyp=get_value("CRetType"),fname="qmckl_compute_det_inv_matrix_beta"))

    #+RESULTS:
    #+begin_src f90 :tangle (eval f) :comments org :exports none
    integer(c_int32_t) function qmckl_compute_det_inv_matrix_beta &
        (context, &
         det_num_beta, &
         walk_num, &
         beta_num, &
         det_vgl_beta, &
         det_value_beta, &
         det_adj_matrix_beta, &
         det_inv_matrix_beta) &
        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 :: det_num_beta
      integer (c_int64_t) , intent(in)  , value :: walk_num
      integer (c_int64_t) , intent(in)  , value :: beta_num
      real    (c_double ) , intent(in)          :: det_vgl_beta(beta_num,beta_num,5,walk_num,det_num_beta)
      real    (c_double ) , intent(out)         :: det_value_beta(walk_num,det_num_beta)
      real    (c_double ) , intent(out)         :: det_adj_matrix_beta(beta_num,beta_num,walk_num,det_num_beta)
      real    (c_double ) , intent(out)         :: det_inv_matrix_beta(beta_num,beta_num,walk_num,det_num_beta)

      integer(c_int32_t), external :: qmckl_compute_det_inv_matrix_beta_f
      info = qmckl_compute_det_inv_matrix_beta_f &
             (context, &
         det_num_beta, &
         walk_num, &
         beta_num, &
         det_vgl_beta, &
         det_value_beta, &
         det_adj_matrix_beta, &
         det_inv_matrix_beta)

    end function qmckl_compute_det_inv_matrix_beta
    #+end_src

*** Test                                                           :noexport:
     #+begin_src c :tangle (eval c_test) :exports none
// Get adjoint of the slater-determinant

double det_inv_matrix_alpha[det_num_alpha][walk_num][elec_up_num][elec_up_num];
double det_inv_matrix_beta[det_num_beta][walk_num][elec_dn_num][elec_dn_num];

rc = qmckl_get_det_inv_matrix_alpha(context, &(det_inv_matrix_alpha[0][0][0][0]));
assert (rc == QMCKL_SUCCESS);

rc = qmckl_get_det_inv_matrix_beta(context, &(det_inv_matrix_beta[0][0][0][0]));
assert (rc == QMCKL_SUCCESS);

     #+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