added dav_dressed_ext_rout.irp.f

INSTALL.rst

@@ -209,7 +209,7 @@ ZeroMQ and its Fortran binding
 
 .. code:: bash
 
-   cp f77_zmq_free.h ${QP_ROOT}/src/ZMQ/f77_zmq.h
+   cp f77_zmq_free.h ${QP_ROOT}/src/zmq/f77_zmq.h
 
 
 Zlib

src/ao_basis/aos_in_r.irp.f

@@ -12,21 +12,21 @@ double precision function ao_value(i,r)
  integer :: power_ao(3)
  double precision :: accu,dx,dy,dz,r2
  num_ao = ao_nucl(i)
- power_ao(1:3)= ao_power(i,1:3)
+! power_ao(1:3)= ao_power(i,1:3)
- center_ao(1:3) = nucl_coord(num_ao,1:3)
+! center_ao(1:3) = nucl_coord(num_ao,1:3)
- dx = (r(1) - center_ao(1))
+! dx = (r(1) - center_ao(1))
- dy = (r(2) - center_ao(2))
+! dy = (r(2) - center_ao(2))
- dz = (r(3) - center_ao(3))
+! dz = (r(3) - center_ao(3))
- r2 = dx*dx + dy*dy + dz*dz
+! r2 = dx*dx + dy*dy + dz*dz
- dx = dx**power_ao(1)
+! dx = dx**power_ao(1)
- dy = dy**power_ao(2)
+! dy = dy**power_ao(2)
- dz = dz**power_ao(3)
+! dz = dz**power_ao(3)
 
  accu = 0.d0
- do m=1,ao_prim_num(i)
+! do m=1,ao_prim_num(i)
-   beta = ao_expo_ordered_transp(m,i)
+!   beta = ao_expo_ordered_transp(m,i)
-   accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2)
+!   accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2)
- enddo
+! enddo
  ao_value = accu * dx * dy * dz
 
 end

src/dav_general_mat/dav_dressed_ext_rout.irp.f

@@ -0,0 +1,485 @@
+subroutine davidson_general_ext_rout_dressed(u_in,H_jj,energies,sze,N_st,N_st_diag,dressing_state,dressing_vec,idress,converged,hcalc)
+  use mmap_module
+  implicit none
+  BEGIN_DOC
+  ! Davidson diagonalization.
+  !
+  ! u_in : guess coefficients on the various states. Overwritten
+  !   on exit
+  !
+  ! sze : leftmost dimension of u_in
+  !
+  ! sze : Number of determinants
+  !
+  ! N_st : Number of eigenstates
+  !
+  ! Initial guess vectors are not necessarily orthonormal
+  END_DOC
+  integer, intent(in)              :: sze, N_st, N_st_diag,idress
+  double precision, intent(inout)  :: u_in(sze,N_st_diag)
+  double precision,  intent(inout) :: H_jj(sze)
+  double precision, intent(out)    :: energies(N_st_diag)
+  double precision, intent(in)     :: dressing_vec(sze,N_st)
+  integer, intent(in)              :: dressing_state
+  logical, intent(out)             :: converged
+  external hcalc
+
+  double precision :: f
+
+  integer                        :: iter
+  integer                        :: i,j,k,l,m
+
+  double precision, external     :: u_dot_v, u_dot_u
+
+  integer                        :: k_pairs, kl
+
+  integer                        :: iter2, itertot
+  double precision, allocatable  :: y(:,:), h(:,:), lambda(:)
+  double precision, allocatable  :: s_tmp(:,:)
+  double precision               :: diag_h_mat_elem
+  double precision, allocatable  :: residual_norm(:)
+  character*(16384)              :: write_buffer
+  double precision               :: to_print(2,N_st)
+  double precision               :: cpu, wall
+  integer                        :: shift, shift2, itermax, istate
+  double precision               :: r1, r2, alpha
+  logical                        :: state_ok(N_st_diag*davidson_sze_max)
+  integer                        :: nproc_target
+  integer                        :: order(N_st_diag)
+  double precision               :: cmax
+  double precision, allocatable  :: U(:,:), overlap(:,:)
+  double precision, pointer      :: W(:,:)
+  logical                        :: disk_based
+  double precision               :: energy_shift(N_st_diag*davidson_sze_max)
+  !!!! TO CHANGE !!!!
+  integer :: idx_dress(1)
+  idx_dress = idress
+
+
+  if (dressing_state > 0) then
+    do k=1,N_st
+      do i=1,sze
+        H_jj(i)  += u_in(i,k) * dressing_vec(i,k)
+      enddo
+    enddo
+  endif
+
+  l = idx_dress(1)
+  f = 1.0d0/u_in(l,1)
+
+  include 'constants.include.F'
+
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, y, h, lambda
+  if (N_st_diag*3 > sze) then
+    print *,  'error in Davidson :'
+    print *,  'Increase n_det_max_full to ', N_st_diag*3
+    stop -1
+  endif
+
+  itermax = max(2,min(davidson_sze_max, sze/N_st_diag))+1
+  itertot = 0
+
+  if (state_following) then
+    allocate(overlap(N_st_diag*itermax, N_st_diag*itermax))
+  else
+    allocate(overlap(1,1))  ! avoid 'if' for deallocate
+  endif
+  overlap = 0.d0
+
+
+  provide threshold_davidson !nthreads_davidson
+  call write_time(6)
+  write(6,'(A)') ''
+  write(6,'(A)') 'Davidson Diagonalization'
+  write(6,'(A)') '------------------------'
+  write(6,'(A)') ''
+
+  ! Find max number of cores to fit in memory
+  ! -----------------------------------------
+
+  nproc_target = nproc
+  double precision :: rss
+  integer :: maxab
+!  maxab = max(N_det_alpha_unique, N_det_beta_unique)+1
+  maxab = sze
+
+  m=1
+  disk_based = .False.
+  call resident_memory(rss)
+  do
+    r1 = 8.d0 *                                   &! bytes
+         ( dble(sze)*(N_st_diag*itermax)          &! U
+         + 1.0d0*dble(sze*m)*(N_st_diag*itermax)  &! W
+         + 3.0d0*(N_st_diag*itermax)**2           &! h,y,s_tmp
+         + 1.d0*(N_st_diag*itermax)               &! lambda
+         + 1.d0*(N_st_diag)                       &! residual_norm
+                                                   ! In H_u_0_nstates_zmq
+         + 2.d0*(N_st_diag*N_det)                 &! u_t, v_t, on collector
+         + 2.d0*(N_st_diag*N_det)                 &! u_t, v_t, on slave
+         + 0.5d0*maxab                            &! idx0 in H_u_0_nstates_openmp_work_*
+         + nproc_target *                         &! In OMP section
+           ( 1.d0*(N_int*maxab)                   &! buffer
+           + 3.5d0*(maxab) )                      &! singles_a, singles_b, doubles, idx
+         ) / 1024.d0**3
+
+    if (nproc_target == 0) then
+      call check_mem(r1,irp_here)
+      nproc_target = 1
+      exit
+    endif
+
+    if (r1+rss < qp_max_mem) then
+      exit
+    endif
+
+    if (itermax > 4) then
+      itermax = itermax - 1
+    else if (m==1.and.disk_based_davidson) then
+      m=0
+      disk_based = .True.
+      itermax = 6
+    else
+      nproc_target = nproc_target - 1
+    endif
+
+  enddo
+  nthreads_davidson = nproc_target
+  TOUCH nthreads_davidson
+  call write_int(6,N_st,'Number of states')
+  call write_int(6,N_st_diag,'Number of states in diagonalization')
+  call write_int(6,sze,'Number of determinants')
+  call write_int(6,nproc_target,'Number of threads for diagonalization')
+  call write_double(6, r1, 'Memory(Gb)')
+  if (disk_based) then
+    print *, 'Using swap space to reduce RAM'
+  endif
+
+  !---------------
+
+  write(6,'(A)') ''
+  write_buffer = '====='
+  do i=1,N_st
+    write_buffer = trim(write_buffer)//' ================ ==========='
+  enddo
+  write(6,'(A)') write_buffer(1:6+41*N_st)
+  write_buffer = 'Iter'
+  do i=1,N_st
+    write_buffer = trim(write_buffer)//'       Energy        Residual '
+  enddo
+  write(6,'(A)') write_buffer(1:6+41*N_st)
+  write_buffer = '====='
+  do i=1,N_st
+    write_buffer = trim(write_buffer)//' ================ ==========='
+  enddo
+  write(6,'(A)') write_buffer(1:6+41*N_st)
+
+
+  allocate(W(sze,N_st_diag*itermax))
+
+  allocate(                                                          &
+      ! Large
+      U(sze,N_st_diag*itermax),                                      &
+
+      ! Small
+      h(N_st_diag*itermax,N_st_diag*itermax),                        &
+      y(N_st_diag*itermax,N_st_diag*itermax),                        &
+      s_tmp(N_st_diag*itermax,N_st_diag*itermax),                    &
+      residual_norm(N_st_diag),                                      &
+      lambda(N_st_diag*itermax))
+
+  h = 0.d0
+  U = 0.d0
+  y = 0.d0
+  s_tmp = 0.d0
+
+
+  ASSERT (N_st > 0)
+  ASSERT (N_st_diag >= N_st)
+  ASSERT (sze > 0)
+
+  ! Davidson iterations
+  ! ===================
+
+  converged = .False.
+
+  do k=N_st+1,N_st_diag
+    do i=1,sze
+        call random_number(r1)
+        call random_number(r2)
+        r1 = dsqrt(-2.d0*dlog(r1))
+        r2 = dtwo_pi*r2
+        u_in(i,k) = r1*dcos(r2) * u_in(i,k-N_st)
+    enddo
+    u_in(k,k) = u_in(k,k) + 10.d0
+  enddo
+  ! Normalize all states 
+  do k=1,N_st_diag
+    call normalize(u_in(1,k),sze)
+  enddo
+  ! Copy from the guess input "u_in" to the working vectors "U"
+
+  do k=1,N_st_diag
+    do i=1,sze
+      U(i,k) = u_in(i,k)
+    enddo
+  enddo
+
+
+  do while (.not.converged)
+    itertot = itertot+1
+    if (itertot == 8) then
+      exit
+    endif
+
+    do iter=1,itermax-1
+
+      shift  = N_st_diag*(iter-1)
+      shift2 = N_st_diag*iter
+
+      if ((iter > 1).or.(itertot == 1)) then
+        ! Compute |W_k> = \sum_i |i><i|H|u_k>
+        ! -----------------------------------
+         ! Gram-Schmidt to orthogonalize all new guess with the previous vectors 
+          call ortho_qr(U,size(U,1),sze,shift2)
+          call ortho_qr(U,size(U,1),sze,shift2)
+          !    it does W = H U with W(sze,N_st_diag),U(sze,N_st_diag)
+          !    where sze is the size of the vector, N_st_diag is the number of states 
+          call hcalc(W(1,shift+1),U(1,shift+1),N_st_diag,sze)
+      else
+         ! Already computed in update below
+         continue
+      endif
+
+      if (dressing_state > 0) then
+
+        if (N_st == 1) then
+
+
+          do istate=1,N_st_diag
+            do i=1,sze
+              W(i,shift+istate) += dressing_vec(i,1) *f * U(l,shift+istate)
+              W(l,shift+istate) += dressing_vec(i,1) *f * U(i,shift+istate)
+            enddo
+
+          enddo
+
+        else
+          print*,'Not implemented yet for multi state ...'
+          stop
+!          call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, &
+!            psi_coef, size(psi_coef,1), &
+!            U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
+!
+!          call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, &
+!            dressing_vec, size(dressing_vec,1), s_tmp, size(s_tmp,1), &
+!            1.d0, W(1,shift+1), size(W,1))
+!
+!
+!          call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, &
+!            dressing_vec, size(dressing_vec,1), &
+!            U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1))
+!
+!          call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, &
+!            psi_coef, size(psi_coef,1), s_tmp, size(s_tmp,1), &
+!            1.d0, W(1,shift+1), size(W,1))
+
+        endif
+      endif
+
+      ! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
+      ! -------------------------------------------
+
+      call dgemm('T','N', shift2, shift2, sze,                       &
+          1.d0, U, size(U,1), W, size(W,1),                          &
+          0.d0, h, size(h,1))
+      call dgemm('T','N', shift2, shift2, sze,                       &
+          1.d0, U, size(U,1), U, size(U,1),                          &
+          0.d0, s_tmp, size(s_tmp,1))
+
+      ! Diagonalize h
+      ! ---------------
+
+       integer :: lwork, info
+       double precision, allocatable :: work(:)
+
+       y = h
+       lwork = -1
+       allocate(work(1))
+       call dsygv(1,'V','U',shift2,y,size(y,1), &
+          s_tmp,size(s_tmp,1), lambda, work,lwork,info)
+       lwork = int(work(1))
+       deallocate(work)
+       allocate(work(lwork))
+       call dsygv(1,'V','U',shift2,y,size(y,1), &
+          s_tmp,size(s_tmp,1), lambda, work,lwork,info)
+       deallocate(work)
+       if (info /= 0) then
+         stop 'DSYGV Diagonalization failed'
+       endif
+
+      ! Compute Energy for each eigenvector
+      ! -----------------------------------
+
+      call dgemm('N','N',shift2,shift2,shift2,                       &
+          1.d0, h, size(h,1), y, size(y,1),                          &
+          0.d0, s_tmp, size(s_tmp,1))
+
+      call dgemm('T','N',shift2,shift2,shift2,                       &
+          1.d0, y, size(y,1), s_tmp, size(s_tmp,1),                  &
+          0.d0, h, size(h,1))
+
+      do k=1,shift2
+        lambda(k) = h(k,k)
+      enddo
+
+      if (state_following) then
+
+        overlap = -1.d0
+        do k=1,shift2
+          do i=1,shift2
+            overlap(k,i) = dabs(y(k,i))
+          enddo
+        enddo
+        do k=1,N_st
+          cmax = -1.d0
+          do i=1,N_st
+            if (overlap(i,k) > cmax) then
+              cmax = overlap(i,k)
+              order(k) = i
+            endif
+          enddo
+          do i=1,N_st_diag
+            overlap(order(k),i) = -1.d0
+          enddo
+        enddo
+        overlap = y
+        do k=1,N_st
+          l = order(k)
+          if (k /= l) then
+            y(1:shift2,k) = overlap(1:shift2,l)
+          endif
+        enddo
+        do k=1,N_st
+          overlap(k,1) = lambda(k)
+        enddo
+
+      endif
+
+
+      ! Express eigenvectors of h in the determinant basis
+      ! --------------------------------------------------
+
+      call dgemm('N','N', sze, N_st_diag, shift2,                    &
+          1.d0, U, size(U,1), y, size(y,1), 0.d0, U(1,shift2+1), size(U,1))
+      call dgemm('N','N', sze, N_st_diag, shift2,                    &
+          1.d0, W, size(W,1), y, size(y,1), 0.d0, W(1,shift2+1), size(W,1))
+
+      ! Compute residual vector and davidson step
+      ! -----------------------------------------
+
+      !$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,k)
+      do k=1,N_st_diag
+        do i=1,sze
+          U(i,shift2+k) =  &
+            (lambda(k) * U(i,shift2+k) - W(i,shift2+k) )      &
+              /max(H_jj(i) - lambda (k),1.d-2)
+        enddo
+
+        if (k <= N_st) then
+          residual_norm(k) = u_dot_u(U(1,shift2+k),sze)
+          to_print(1,k) = lambda(k) + nuclear_repulsion
+          to_print(2,k) = residual_norm(k)
+        endif
+      enddo
+      !$OMP END PARALLEL DO
+
+
+      if ((itertot>1).and.(iter == 1)) then
+        !don't print
+        continue
+      else
+        write(*,'(1X,I3,1X,100(1X,F16.10,1X,E11.3))') iter-1, to_print(1:2,1:N_st)
+      endif
+
+      ! Check convergence
+      if (iter > 1) then
+          converged = dabs(maxval(residual_norm(1:N_st))) < threshold_davidson
+      endif
+
+      do k=1,N_st
+        if (residual_norm(k) > 1.d8) then
+          print *, 'Davidson failed'
+          stop -1
+        endif
+      enddo
+      if (converged) then
+        exit
+      endif
+
+      logical, external :: qp_stop
+      if (qp_stop()) then
+        converged = .True.
+        exit
+      endif
+
+
+    enddo
+
+    ! Re-contract U and update W
+    ! --------------------------------
+
+    call dgemm('N','N', sze, N_st_diag, shift2, 1.d0,      &
+        W, size(W,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
+    do k=1,N_st_diag
+      do i=1,sze
+        W(i,k) = u_in(i,k)
+      enddo
+    enddo
+
+    call dgemm('N','N', sze, N_st_diag, shift2, 1.d0,      &
+        U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
+
+    do k=1,N_st_diag
+      do i=1,sze
+        U(i,k) = u_in(i,k)
+      enddo
+    enddo
+
+  enddo
+
+
+  call nullify_small_elements(sze,N_st_diag,U,size(U,1),threshold_davidson_pt2)
+  do k=1,N_st_diag
+    do i=1,sze
+      u_in(i,k) = U(i,k)
+    enddo
+  enddo
+
+  do k=1,N_st_diag
+    energies(k) = lambda(k)
+  enddo
+  write_buffer = '======'
+  do i=1,N_st
+    write_buffer = trim(write_buffer)//' ================ ==========='
+  enddo
+  write(6,'(A)') trim(write_buffer)
+  write(6,'(A)') ''
+  call write_time(6)
+
+  deallocate(W)
+
+  deallocate (                                                       &
+      residual_norm,                                                 &
+      U, overlap,                                                    &
+      h, y, s_tmp,                                                   &
+      lambda                                                         &
+      )
+  FREE nthreads_davidson
+end
+
+
+
+
+
+
+

src/dav_general_mat/dav_ext_rout.irp.f

@@ -1,5 +1,5 @@
 
-subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,hcalc)
+subroutine davidson_general_ext_rout(u_in,H_jj,energies,sze,N_st,N_st_diag_in,converged,hcalc)
   use mmap_module
   implicit none
   BEGIN_DOC
@@ -9,7 +9,7 @@ subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_dia
   !
   ! u_in : guess coefficients on the various states. Overwritten on exit
   !
-  ! dim_in : leftmost dimension of u_in
+  ! sze : leftmost dimension of u_in
   !
   ! sze : Number of determinants
   !
@@ -21,9 +21,9 @@ subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_dia
   !
   ! hcalc subroutine to compute W = H U (see routine hcalc_template for template of input/output)
   END_DOC
-  integer, intent(in)             :: dim_in, sze, N_st, N_st_diag_in
+  integer, intent(in)             :: sze, N_st, N_st_diag_in
   double precision,  intent(in)   :: H_jj(sze)
-  double precision, intent(inout) :: u_in(dim_in,N_st_diag_in)
+  double precision, intent(inout) :: u_in(sze,N_st_diag_in)
   double precision, intent(out)   :: energies(N_st)
   external hcalc
 
@@ -157,19 +157,7 @@ subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_dia
   write(6,'(A)') write_buffer(1:6+41*N_st)
 
 
-!  if (disk_based) then
+  allocate(W(sze,N_st_diag*itermax))
-!    ! Create memory-mapped files for W and S
-!    type(c_ptr) :: ptr_w, ptr_s
-!    integer :: fd_s, fd_w
-!    call mmap(trim(ezfio_work_dir)//'davidson_w', (/int(sze,8),int(N_st_diag*itermax,8)/),&
-!        8, fd_w, .False., ptr_w)
-!    call mmap(trim(ezfio_work_dir)//'davidson_s', (/int(sze,8),int(N_st_diag*itermax,8)/),&
-!        4, fd_s, .False., ptr_s)
-!    call c_f_pointer(ptr_w, w, (/sze,N_st_diag*itermax/))
-!    call c_f_pointer(ptr_s, s, (/sze,N_st_diag*itermax/))
-!  else
-    allocate(W(sze,N_st_diag*itermax))
-!  endif
 
   allocate(                                                          &
       ! Large
@@ -398,7 +386,7 @@ subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_dia
   write(6,'(A)') ''
   call write_time(6)
 
-    deallocate(W)
+  deallocate(W)
 
   deallocate (                                                       &
       residual_norm,                                                 &

src/dav_general_mat/test_dav.irp.f

@@ -8,12 +8,13 @@ program test_dav
   touch read_wf
   PROVIDE threshold_davidson nthreads_davidson
   call routine
+  call test_dav_dress
 end
 
 subroutine routine
  implicit none
  double precision, allocatable :: u_in(:,:), H_jj(:), energies(:),h_mat(:,:)
- integer :: dim_in,sze,N_st,N_st_diag_in,dressing_state
+ integer :: dim_in,sze,N_st,N_st_diag_in
  logical :: converged 
  integer :: i,j
  external hcalc_template
@@ -21,9 +22,8 @@ subroutine routine
  N_st_diag_in = N_states_diag
  sze = N_det
  dim_in = sze
- dressing_state = 0
  !!!! MARK THAT u_in mut dimensioned with "N_st_diag_in" as a second dimension 
- allocate(u_in(dim_in,N_st_diag_in),H_jj(sze),h_mat(sze,sze),energies(N_st))
+ allocate(u_in(dim_in,N_st_diag_in),H_jj(sze),h_mat(sze,sze),energies(N_st_diag_in))
  u_in = 0.d0
  do i = 1, N_st
   u_in(1,i) = 1.d0
@@ -42,7 +42,38 @@ subroutine routine
  print*,'energies = ',energies 
  !!! hcalc_template is the routine that computes v = H u 
  !!! and you can use the routine "davidson_general_ext_rout" 
- call davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,hcalc_template)
+ call davidson_general_ext_rout(u_in,H_jj,energies,sze,N_st,N_st_diag_in,converged,hcalc_template)
  print*,'energies = ',energies 
 end
 
+
+subroutine test_dav_dress
+ implicit none
+ double precision, allocatable :: u_in(:,:), H_jj(:), energies(:)
+ integer :: sze,N_st,N_st_diag_in,dressing_state
+ logical :: converged 
+ integer :: i,j
+ external hcalc_template
+ double precision, allocatable :: dressing_vec(:)
+ integer :: idress
+ N_st = N_states
+ N_st_diag_in = N_states_diag
+ sze = N_det
+ dressing_state = 0
+ idress = 1
+ !!!! MARK THAT u_in mut dimensioned with "N_st_diag_in" as a second dimension 
+ allocate(u_in(sze,N_st_diag_in),H_jj(sze),energies(N_st_diag_in))
+ allocate(dressing_vec(sze))
+ dressing_vec = 0.d0
+ u_in = 0.d0
+ do i = 1, N_st
+  u_in(1,i) = 1.d0
+ enddo
+ do i = 1, sze
+  H_jj(i) = H_matrix_all_dets(i,i) + nuclear_repulsion
+ enddo
+ print*,'dressing davidson '
+ call davidson_general_ext_rout_dressed(u_in,H_jj,energies,sze,N_st,N_st_diag_in,dressing_state,dressing_vec,idress,converged,hcalc_template)
+ print*,'energies(1) = ',energies(1)
+
+end

src/mo_basis/mos_in_r.irp.f

@@ -1,6 +1,9 @@
 
 subroutine give_all_mos_at_r(r,mos_array)
  implicit none
+ BEGIN_DOC
+! mos_array(i) = ith MO function evaluated at "r"
+ END_DOC
  double precision, intent(in) :: r(3)
  double precision, intent(out) :: mos_array(mo_num)
  double precision :: aos_array(ao_num)