#+TITLE: Examples
#+STARTUP: latexpreview
#+SETUPFILE: docs/theme.setup

  
* Accessing sparse quantities
** Fortran
  :PROPERTIES:
  :header-args:    :tangle  print_energy.f90
  :END:
   
   #+begin_src f90
program print_energy
  use trexio
  implicit none

  character*(128)  :: filename   ! Name of the input file
  integer          :: rc         ! Return code for error checking
  integer(8)       :: f          ! TREXIO file handle
  character*(128)  :: err_msg    ! Error message
   #+end_src

   This program computes the energy as:

   \[
   E = E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\,
   +\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j
   \rangle\; \textrm{ with } \; 0 < i,j,k,l \le n
   \]
   One needs to read from the TREXIO file:

   - $n$ :: The number of molecular orbitals
   - $E_{\text{NN}}$ :: The nuclear repulsion energy 
   - $\gamma_{ij}$ :: The one-body reduced density matrix 
   - $\langle j |h| i \rangle$ :: The one-electron Hamiltonian integrals 
   - $\Gamma_{ijkl}$ :: The two-body reduced density matrix 
   - $\langle k l  | i j \rangle$ :: The electron repulsion integrals


   #+begin_src f90
  integer                       :: n
  double precision              :: E, E_nn
  double precision, allocatable :: D(:,:), h0(:,:)
  double precision, allocatable :: G(:,:,:,:), W(:,:,:,:)
   #+end_src

*** Declare Temporary variables

   #+begin_src f90
  integer                       :: i, j, k, l, m
  integer(8), parameter         :: BUFSIZE = 100000_8
  integer(8)                    :: offset, icount, size_max
  integer                       :: buffer_index(4,BUFSIZE)
  double precision              :: buffer_values(BUFSIZE)

  double precision, external    :: ddot   ! BLAS dot product
   #+end_src

*** Obtain the name of the TREXIO file from the command line, and open it for reading

   #+begin_src f90
  call getarg(1, filename)

  f = trexio_open (filename, 'r', TREXIO_HDF5, rc)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error opening TREXIO file: '//trim(err_msg)
     stop
  end if
   #+end_src

*** Read the nuclear repulsion energy

   #+begin_src f90
  rc = trexio_read_nucleus_repulsion(f, E_nn)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading nuclear repulsion: '//trim(err_msg)
     stop
  end if
   #+end_src

*** Read the number of molecular orbitals

    #+begin_src f90
  rc = trexio_read_mo_num(f, n)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading number of MOs: '//trim(err_msg)
     stop
  end if
    #+end_src

*** Allocate memory

    #+begin_src f90
  allocate( D(n,n), h0(n,n) )
  allocate( G(n,n,n,n), W(n,n,n,n) )
  G(:,:,:,:) = 0.d0
  W(:,:,:,:) = 0.d0
    #+end_src

*** Read one-electron quantities
    
    #+begin_src f90
  rc = trexio_has_mo_1e_int_core_hamiltonian(f)
  if (rc /= TREXIO_SUCCESS) then
     stop 'No core hamiltonian in file'
  end if
  
  rc = trexio_read_mo_1e_int_core_hamiltonian(f, h0)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading core Hamiltonian: '//trim(err_msg)
     stop
  end if
  
  
  rc = trexio_has_rdm_1e(f)
  if (rc /= TREXIO_SUCCESS) then
     stop 'No 1e RDM in file'
  end if
  
  rc = trexio_read_rdm_1e(f, D)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading one-body RDM: '//trim(err_msg)
     stop
  end if
    #+end_src
  
*** Read two-electron quantities
    
    Reading is done with OpenMP. Each thread reads its own buffer, and
    the buffers are then processed in parallel.

    Reading the file requires a lock, so it is done in a critical
    section. The ~offset~ variable is shared, and it is incremented in
    the critical section. For each read, the function returns in
    ~icount~ the number of read integrals, so this variable needs also
    to be protected in the critical section when modified.
    
**** Electron repulsion integrals

     #+begin_src f90
  rc = trexio_has_mo_2e_int_eri(f)
  if (rc /= TREXIO_SUCCESS) then
     stop 'No electron repulsion integrals in file'
  end if

  rc = trexio_read_mo_2e_int_eri_size (f, size_max)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading number of ERIs: '//trim(err_msg)
     stop
  end if

  offset = 0_8
  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &
  !$OMP   buffer_index, buffer_values, m)
  icount = BUFSIZE
  do while (icount == BUFSIZE)
    !$OMP CRITICAL
    if (offset < size_max) then
      rc = trexio_read_mo_2e_int_eri(f, offset, icount, buffer_index, buffer_values)
      offset = offset + icount
    else
      icount = 0
    end if
    !$OMP END CRITICAL
    do m=1,icount
      i = buffer_index(1,m)
      j = buffer_index(2,m)
      k = buffer_index(3,m)
      l = buffer_index(4,m)
      W(i,j,k,l) = buffer_values(m)
      W(k,j,i,l) = buffer_values(m)
      W(i,l,k,j) = buffer_values(m)
      W(k,l,i,j) = buffer_values(m)
      W(j,i,l,k) = buffer_values(m)
      W(j,k,l,i) = buffer_values(m)
      W(l,i,j,k) = buffer_values(m)
      W(l,k,j,i) = buffer_values(m)
    end do
  end do
  !$OMP END PARALLEL
     #+end_src

**** Reduced density matrix
     
     #+begin_src f90
  rc = trexio_has_rdm_2e(f)
  if (rc /= TREXIO_SUCCESS) then
     stop 'No two-body density matrix in file'
  end if

  rc = trexio_read_rdm_2e_size (f, size_max)
  if (rc /= TREXIO_SUCCESS) then
     call trexio_string_of_error(rc, err_msg)
     print *, 'Error reading number of 2-RDM elements: '//trim(err_msg)
     stop
  end if

  offset = 0_8
  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &
  !$OMP   buffer_index, buffer_values, m)
  icount = bufsize
  do while (offset < size_max)
    !$OMP CRITICAL
    if (offset < size_max) then
      rc = trexio_read_rdm_2e(f, offset, icount, buffer_index, buffer_values)
      offset = offset + icount
    else
      icount = 0
    end if
    !$OMP END CRITICAL
    do m=1,icount
      i = buffer_index(1,m)
      j = buffer_index(2,m)
      k = buffer_index(3,m)
      l = buffer_index(4,m)
      G(i,j,k,l) = buffer_values(m)
    end do
  end do
  !$OMP END PARALLEL

     #+end_src
    
*** Compute the energy
    
    When the orbitals are real, we can use
   \begin{eqnarray*}
   E &=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\,
   +\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j
   \rangle \\
     &=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle i | h | j \rangle\,
   +\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle i j | k l
   \rangle \\
   \end{eqnarray*}

    As $(n,m)$ 2D arrays are stored in memory as $(n \times m)$ 1D
    arrays, we could pass the matrices to the ~ddot~ BLAS function to
    perform the summations in a single call for the 1-electron quantities.
    Instead, we prefer to interleave the 1-electron (negative) and
    2-electron (positive) summations to have a better cancellation of
    numerical errors.
    
    Here $n^4$ can be larger than the largest possible 32-bit integer,
    so it is not safe to pass $n^4$ to the ~ddot~ BLAS
    function. Hence, we perform $n^2$ loops, using vectors of size $n^2$.
    
    #+begin_src f90

  E = 0.d0
  do l=1,n
    E = E + ddot( n, D(1,l), 1, h0(1,l), 1 ) 
    do k=1,n
       E = E + 0.5d0 * ddot( n*n, G(1,1,k,l), 1, W(1,1,k,l),  1 )
    end do
  end do
  E = E + E_nn

  print *, 'Energy: ', E
    #+end_src

*** Terminate
    
    #+begin_src f90
  deallocate( D, h0, G, W )

end program
    #+end_src