From 9cdb127e33acf006bd1719f4a43063d72b294782 Mon Sep 17 00:00:00 2001
From: Emmanuel Giner <giner.emmanuel@gmail.com>
Date: Fri, 2 Jul 2021 16:18:13 +0200
Subject: [PATCH] added dav_general_mat to src

---
 src/dav_general_mat/NEED               |   1 +
 src/dav_general_mat/README.rst         |   4 +
 src/dav_general_mat/dav_ext_rout.irp.f | 444 +++++++++++++++++++++++++
 src/dav_general_mat/dav_general.irp.f  | 435 ++++++++++++++++++++++++
 src/dav_general_mat/test_dav.irp.f     |  42 +++
 5 files changed, 926 insertions(+)
 create mode 100644 src/dav_general_mat/NEED
 create mode 100644 src/dav_general_mat/README.rst
 create mode 100644 src/dav_general_mat/dav_ext_rout.irp.f
 create mode 100644 src/dav_general_mat/dav_general.irp.f
 create mode 100644 src/dav_general_mat/test_dav.irp.f

diff --git a/src/dav_general_mat/NEED b/src/dav_general_mat/NEED
new file mode 100644
index 00000000..711fbf96
--- /dev/null
+++ b/src/dav_general_mat/NEED
@@ -0,0 +1 @@
+davidson_undressed
diff --git a/src/dav_general_mat/README.rst b/src/dav_general_mat/README.rst
new file mode 100644
index 00000000..5407a206
--- /dev/null
+++ b/src/dav_general_mat/README.rst
@@ -0,0 +1,4 @@
+========
+test_dav
+========
+
diff --git a/src/dav_general_mat/dav_ext_rout.irp.f b/src/dav_general_mat/dav_ext_rout.irp.f
new file mode 100644
index 00000000..79c39b1f
--- /dev/null
+++ b/src/dav_general_mat/dav_ext_rout.irp.f
@@ -0,0 +1,444 @@
+
+subroutine davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,hcalc)
+  use mmap_module
+  implicit none
+  BEGIN_DOC
+  ! Davidson diagonalization with specific diagonal elements of the H matrix
+  !
+  ! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
+  !
+  ! u_in : guess coefficients on the various states. Overwritten on exit
+  !
+  ! dim_in : leftmost dimension of u_in
+  !
+  ! sze : Number of determinants
+  !
+  ! N_st : Number of eigenstates
+  !
+  ! N_st_diag_in : Number of states in which H is diagonalized. Assumed > sze
+  !
+  ! Initial guess vectors are not necessarily orthonormal
+  !
+  ! 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
+  double precision,  intent(in)   :: H_jj(sze)
+  double precision, intent(inout) :: u_in(dim_in,N_st_diag_in)
+  double precision, intent(out)   :: energies(N_st)
+  external hcalc
+
+  integer                        :: iter, N_st_diag
+  integer                        :: i,j,k,l,m
+  logical, intent(inout)         :: converged
+
+  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  :: 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
+  integer                        :: nproc_target
+  integer                        :: order(N_st_diag_in)
+  double precision               :: cmax
+  double precision, allocatable  :: U(:,:), overlap(:,:)!, S_d(:,:)
+  double precision, pointer      :: W(:,:)
+  logical                        :: disk_based
+  double precision               :: energy_shift(N_st_diag_in*davidson_sze_max)
+
+  include 'constants.include.F'
+
+  N_st_diag = N_st_diag_in
+  !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 = sze 
+
+  m=1
+  disk_based = .False.
+  call resident_memory(rss)
+  do
+    r1 = 8.d0 *                                   &! bytes
+         ( dble(sze)*(N_st_diag*itermax)          &! U
+         + 1.d0*dble(sze*m)*(N_st_diag*itermax)  &! W
+         + 2.0d0*(N_st_diag*itermax)**2           &! h,y
+         + 2.d0*(N_st_diag*itermax)               &! s2,lambda
+         + 1.d0*(N_st_diag)                       &! residual_norm
+                                                   ! In H_S2_u_0_nstates_zmq
+         + 3.d0*(N_st_diag*N_det)                 &! u_t, v_t, s_t on collector
+         + 3.d0*(N_st_diag*N_det)                 &! u_t, v_t, s_t on slave
+         + 0.5d0*maxab                            &! idx0 in H_S2_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 basis functions')
+  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)
+
+
+!  if (disk_based) then
+!    ! 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
+      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),                        &
+      residual_norm(N_st_diag),                                      &
+      lambda(N_st_diag*itermax))
+
+  h = 0.d0
+  U = 0.d0
+  y = 0.d0
+
+
+  ASSERT (N_st > 0)
+  ASSERT (N_st_diag >= N_st)
+  ASSERT (sze > 0)
+
+  ! Davidson iterations
+  ! ===================
+
+  converged = .False.
+
+  ! Initialize from N_st to N_st_diat with gaussian random numbers
+  ! to be sure to have overlap with any eigenvectors
+  do k=N_st+1,N_st_diag
+    u_in(k,k) = 10.d0
+    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)
+    enddo
+  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
+
+      ! 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))
+
+      ! Diagonalize h y = lambda y
+      ! ---------------
+
+      call lapack_diag(lambda,y,h,size(h,1),shift2)
+
+      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
+        do k=1,N_st
+          l = order(k)
+          if (k /= l) then
+            lambda(k) = overlap(l,1)
+          endif
+        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) 
+          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,F11.6,1X,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.e8) 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
+
+    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
+      call ortho_qr(U,size(U,1),sze,N_st_diag)
+      call ortho_qr(U,size(U,1),sze,N_st_diag)
+    do j=1,N_st_diag
+      k=1
+      do while ((k<sze).and.(U(k,j) == 0.d0))
+        k = k+1
+      enddo
+      if (U(k,j) * u_in(k,j) < 0.d0) then
+        do i=1,sze
+          W(i,j) = -W(i,j)
+        enddo
+      endif
+    enddo
+  enddo
+
+  do k=1,N_st
+    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, h,                                                 &
+      y,                                                             &
+      lambda                                                         &
+      )
+  deallocate(overlap)
+  FREE nthreads_davidson
+end
+
+subroutine hcalc_template(v,u,N_st,sze)
+  use bitmasks
+  implicit none
+  BEGIN_DOC
+  ! Template of routine for the application of H
+  !
+  ! Here, it is done with the Hamiltonian matrix 
+  !
+  ! on the set of determinants of psi_det 
+  !
+  ! Computes $v = H | u \rangle$ 
+  !
+  END_DOC
+  integer, intent(in)              :: N_st,sze
+  double precision, intent(in)     :: u(sze,N_st)
+  double precision, intent(inout)  :: v(sze,N_st)
+  integer :: i,j,istate
+  v = 0.d0
+  do istate = 1, N_st
+   do i = 1, sze
+    do j = 1, sze
+      v(i,istate) += H_matrix_all_dets(j,i) * u(j,istate)
+    enddo
+   enddo
+  enddo
+end
+
+
+
+
+
+
diff --git a/src/dav_general_mat/dav_general.irp.f b/src/dav_general_mat/dav_general.irp.f
new file mode 100644
index 00000000..5ddc7fc0
--- /dev/null
+++ b/src/dav_general_mat/dav_general.irp.f
@@ -0,0 +1,435 @@
+
+subroutine davidson_general(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,h_mat)
+  use mmap_module
+  implicit none
+  BEGIN_DOC
+  ! Davidson diagonalization with specific diagonal elements of the H matrix
+  !
+  ! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
+  !
+  ! u_in : guess coefficients on the various states. Overwritten on exit
+  !
+  ! dim_in : leftmost dimension of u_in
+  !
+  ! sze : Number of determinants
+  !
+  ! N_st : Number of eigenstates
+  !
+  ! N_st_diag_in : Number of states in which H is diagonalized. Assumed > sze
+  !
+  ! Initial guess vectors are not necessarily orthonormal
+  END_DOC
+  integer, intent(in)             :: dim_in, sze, N_st, N_st_diag_in
+  double precision,  intent(in)   :: H_jj(sze),h_mat(sze,sze)
+  double precision, intent(inout) :: u_in(dim_in,N_st_diag_in)
+  double precision, intent(out)   :: energies(N_st)
+
+  integer                        :: iter, N_st_diag
+  integer                        :: i,j,k,l,m
+  logical, intent(inout)         :: converged
+
+  double precision, external     :: u_dot_v, u_dot_u
+
+  integer                        :: k_pairs, kl
+
+  integer                        :: iter2, itertot
+  double precision, allocatable  :: y(:,:), h(:,:), lambda(:)
+  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
+  integer                        :: nproc_target
+  integer                        :: order(N_st_diag_in)
+  double precision               :: cmax
+  double precision, allocatable  :: U(:,:), overlap(:,:)!, S_d(:,:)
+  double precision, pointer      :: W(:,:)
+  logical                        :: disk_based
+  double precision               :: energy_shift(N_st_diag_in*davidson_sze_max)
+
+  include 'constants.include.F'
+
+  N_st_diag = N_st_diag_in
+  !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 = sze 
+
+  m=1
+  disk_based = .False.
+  call resident_memory(rss)
+  do
+    r1 = 8.d0 *                                   &! bytes
+         ( dble(sze)*(N_st_diag*itermax)          &! U
+         + 1.d0*dble(sze*m)*(N_st_diag*itermax)  &! W
+         + 2.0d0*(N_st_diag*itermax)**2           &! h,y
+         + 2.d0*(N_st_diag*itermax)               &! s2,lambda
+         + 1.d0*(N_st_diag)                       &! residual_norm
+                                                   ! In H_S2_u_0_nstates_zmq
+         + 3.d0*(N_st_diag*N_det)                 &! u_t, v_t, s_t on collector
+         + 3.d0*(N_st_diag*N_det)                 &! u_t, v_t, s_t on slave
+         + 0.5d0*maxab                            &! idx0 in H_S2_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 basis functions')
+  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)
+
+
+!  if (disk_based) then
+!    ! 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
+      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),                        &
+      residual_norm(N_st_diag),                                      &
+      lambda(N_st_diag*itermax))
+
+  h = 0.d0
+  U = 0.d0
+  y = 0.d0
+
+
+  ASSERT (N_st > 0)
+  ASSERT (N_st_diag >= N_st)
+  ASSERT (sze > 0)
+
+  ! Davidson iterations
+  ! ===================
+
+  converged = .False.
+
+  ! Initialize from N_st to N_st_diat with gaussian random numbers
+  ! to be sure to have overlap with any eigenvectors
+  do k=N_st+1,N_st_diag
+    u_in(k,k) = 10.d0
+    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)
+    enddo
+  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-Smitt 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)
+
+!            call H_S2_u_0_nstates_openmp(W(1,shift+1),U(1,shift+1),N_st_diag,sze)
+            call hpsi                   (W(1,shift+1),U(1,shift+1),N_st_diag,sze,h_mat)
+      else
+         ! Already computed in update below
+         continue
+      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))
+
+      ! Diagonalize h y = lambda y
+      ! ---------------
+
+      call lapack_diag(lambda,y,h,size(h,1),shift2)
+
+      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
+        do k=1,N_st
+          l = order(k)
+          if (k /= l) then
+            lambda(k) = overlap(l,1)
+          endif
+        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) 
+          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,F11.6,1X,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.e8) 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
+
+    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
+      call ortho_qr(U,size(U,1),sze,N_st_diag)
+      call ortho_qr(U,size(U,1),sze,N_st_diag)
+    do j=1,N_st_diag
+      k=1
+      do while ((k<sze).and.(U(k,j) == 0.d0))
+        k = k+1
+      enddo
+      if (U(k,j) * u_in(k,j) < 0.d0) then
+        do i=1,sze
+          W(i,j) = -W(i,j)
+        enddo
+      endif
+    enddo
+  enddo
+
+  do k=1,N_st
+    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, h,                                                 &
+      y,                                                             &
+      lambda                                                         &
+      )
+  deallocate(overlap)
+  FREE nthreads_davidson
+end
+
+subroutine hpsi(v,u,N_st,sze,h_mat)
+  use bitmasks
+  implicit none
+  BEGIN_DOC
+  ! Computes $v = H | u \rangle$ and 
+  END_DOC
+  integer, intent(in)              :: N_st,sze
+  double precision, intent(in)     :: u(sze,N_st),h_mat(sze,sze)
+  double precision, intent(inout)  :: v(sze,N_st)
+  integer :: i,j,istate
+  v = 0.d0
+  do istate = 1, N_st
+   do i = 1, sze
+    do j = 1, sze
+      v(i,istate) += h_mat(j,i) * u(j,istate)
+    enddo
+   enddo
+  enddo
+end
+
+
+
+
+
+
diff --git a/src/dav_general_mat/test_dav.irp.f b/src/dav_general_mat/test_dav.irp.f
new file mode 100644
index 00000000..825cdde2
--- /dev/null
+++ b/src/dav_general_mat/test_dav.irp.f
@@ -0,0 +1,42 @@
+program test_dav
+  implicit none
+  BEGIN_DOC
+! TODO : Put the documentation of the program here
+  END_DOC
+  print *, 'Hello world'
+  read_wf = .True.
+  touch read_wf
+  PROVIDE threshold_davidson nthreads_davidson
+  call routine
+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
+ logical :: converged 
+ integer :: i,j
+ external hcalc_template
+ N_st = N_states
+ N_st_diag_in = N_states_diag
+ sze = N_det
+ dim_in = sze
+ dressing_state = 0
+ allocate(u_in(dim_in,N_st_diag_in),H_jj(sze),h_mat(sze,sze),energies(N_st))
+ u_in = 0.d0
+ do i = 1, N_st
+  u_in(1,i) = 1.d0
+ enddo
+ do i = 1, sze
+  do j = 1, sze
+   h_mat(j,i) = H_matrix_all_dets(j,i)
+  enddo
+  H_jj(i) = H_mat(i,i)
+ enddo
+ provide nthreads_davidson
+ call davidson_general(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,h_mat)
+ print*,'energies = ',energies + nuclear_repulsion
+ call davidson_general_ext_rout(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,hcalc_template)
+ print*,'energies = ',energies + nuclear_repulsion
+end
+