diff --git a/devel/svdwf/Evar_TruncSVD.irp.f b/devel/svdwf/Evar_TruncSVD.irp.f
new file mode 100644
index 0000000..ce88d64
--- /dev/null
+++ b/devel/svdwf/Evar_TruncSVD.irp.f
@@ -0,0 +1,451 @@
+program Evar_TruncSVD
+  implicit none
+  BEGIN_DOC
+! study energy variation with truncated SVD
+  END_DOC
+  read_wf = .True.
+  TOUCH read_wf
+  ! !!!
+  call run()
+  ! !!!
+end
+! !!!
+subroutine run
+  ! !!!
+  implicit none
+  include 'constants.include.F'
+  ! !!!
+  integer                       :: m, n, i_state
+  double precision              :: error_thr, error_RRRSVD, norm_psi, norm_SVD, err_verif, err_tmp
+  integer                       :: i, j, k, l, It, PowerIt
+  integer                       :: It_max, PowerIt_max, nb_oversamp
+  integer                       :: r_init, delta_r, low_rank
+  double precision, allocatable :: B_old(:,:), Q_old(:,:)
+  double precision, allocatable :: UB(:,:), D(:), Vt(:,:), U(:,:)
+  double precision, allocatable :: P(:,:), r1(:,:)
+  double precision, allocatable :: Q_new(:,:), Q_tmp(:,:), Q_mult(:,:)
+  double precision, allocatable :: B_new(:,:), B_tmp(:,:)
+  double precision, allocatable :: URSVD(:,:), DRSVD(:), VtRSVD(:,:)
+  double precision, allocatable :: Uverif(:,:), Dverif(:), Vtverif(:,:), Averif(:,:)
+  double precision, allocatable :: Uezfio(:,:,:), Dezfio(:,:), Vezfio(:,:,:)
+  double precision :: tmp
+  ! !!!
+  i_state = 1
+  m       = n_det_alpha_unique
+  n       = n_det_beta_unique
+  ! !!!
+  !open(111, file = 'data_to_python.txt', action = 'WRITE' )  
+  !  do k = 1, N_det
+  !    write(111, '(I8, 5X, I8, 5X, E15.7)' ) psi_bilinear_matrix_rows(k), psi_bilinear_matrix_columns(k), psi_bilinear_matrix_values(k,i_state)
+  !  end do  
+  !close(111)
+  ! !!!
+  ! !!!
+  print *, 'matrix:', m,'x',n
+  print *, 'N det:', N_det
+  ! !!!
+  r_init  = 78 !!!42
+  delta_r = 1
+  ! !!!
+  PowerIt_max = 10
+  nb_oversamp = 10
+  ! !!!
+  It_max    = 10
+  error_thr = 1.d-3 !not stable if less thant 0.001
+  ! !!!
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!! ~      Rank Revealing Randomized SVD      ~ !!! !
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!!
+  norm_psi = 0.d0
+  do k = 1, N_det
+    norm_psi = norm_psi + psi_bilinear_matrix_values(k,i_state) * psi_bilinear_matrix_values(k,i_state)
+  enddo
+  ! !!!
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!!  build initial QB decomposition !!! !
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!!
+  allocate( Q_old(m, r_init) )
+  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,k,l,r1)
+  allocate( r1(N_det,2) )
+  !$OMP DO
+  do l = 1, r_init
+    Q_old(:,l) = 0.d0
+    call random_number(r1)
+    r1(:,1) = dsqrt(-2.d0*dlog(r1(:,1)))
+    r1(:,1) = r1(:,1) * dcos(dtwo_pi*r1(:,2))
+    do k = 1, N_det
+      i          = psi_bilinear_matrix_rows(k)
+      Q_old(i,l) = Q_old(i,l) + psi_bilinear_matrix_values(k,i_state) * r1(k,1)
+    enddo
+  enddo
+  !$OMP END DO
+  deallocate(r1)
+  !$OMP END PARALLEL
+  ! !!!
+  ! power scheme
+  ! !!!
+  allocate( P(n, r_init) ) 
+  do PowerIt = 1, PowerIt_max
+    ! !!!
+    call my_ortho_qr(Q_old, size(Q_old,1), m, r_init)
+    ! !!!
+    !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+    !$OMP DO
+    do l = 1, r_init
+      P(:,l) = 0.d0
+      do k = 1, N_det
+        i      = psi_bilinear_matrix_rows(k)
+        j      = psi_bilinear_matrix_columns(k)
+        P(j,l) = P(j,l) + psi_bilinear_matrix_values(k,i_state) * Q_old(i,l)
+      enddo
+    enddo
+    !$OMP END DO
+    !$OMP END PARALLEL
+    ! !!!
+    call my_ortho_qr(P, size(P,1), n, r_init)
+    ! !!!
+    !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+    !$OMP DO
+    do l = 1, r_init
+      Q_old(:,l) = 0.d0
+      do k = 1 , N_det
+        i          = psi_bilinear_matrix_rows(k)
+        j          = psi_bilinear_matrix_columns(k)
+        Q_old(i,l) = Q_old(i,l) + psi_bilinear_matrix_values(k,i_state) * P(j,l)
+      enddo
+    enddo
+    !$OMP END DO
+    !$OMP END PARALLEL
+    ! !!!
+  enddo
+  deallocate( P )
+  ! !!!
+  call my_ortho_qr(Q_old, size(Q_old,1), m, r_init)
+  ! !!!
+  allocate( B_old(r_init,n) )
+  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+  !$OMP DO
+  do l = 1, r_init
+    B_old(l,:) = 0.d0
+    do k = 1, N_det
+      i          = psi_bilinear_matrix_rows(k)
+      j          = psi_bilinear_matrix_columns(k)
+      B_old(l,j) = B_old(l,j) + Q_old(i,l) * psi_bilinear_matrix_values(k,i_state)
+    enddo
+  enddo
+  !$OMP END DO
+  !$OMP END PARALLEL
+  norm_SVD = 0.d0
+  do j = 1, n
+    do l = 1, r_init
+      norm_SVD = norm_SVD + B_old(l,j) * B_old(l,j)
+    enddo
+  enddo
+  error_RRRSVD  = dabs( norm_psi - norm_SVD ) / norm_psi
+  It       = 1
+  low_rank = r_init
+  print *, It, low_rank, error_RRRSVD
+  ! !!!
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!! incrementally build up QB decomposition !!! !
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!!
+  do while( ( error_RRRSVD.gt.error_thr ).and.( It.lt.It_max ).and.( low_rank.lt.(min(m,n)-delta_r) ) )
+    ! !!!
+    allocate( Q_new(m,delta_r) ) 
+    allocate( r1(N_det, 2) )
+    do l = 1, delta_r
+      Q_new(:,l) = 0.d0
+      call random_number(r1)
+      r1(:,1) = dsqrt(-2.d0*dlog(r1(:,1)))
+      r1(:,1) = r1(:,1) * dcos(dtwo_pi*r1(:,2))
+      do k = 1, N_det
+        i          = psi_bilinear_matrix_rows(k)
+        Q_new(i,l) = Q_new(i,l) + psi_bilinear_matrix_values(k,i_state) * r1(k,1)
+      enddo
+    enddo
+    deallocate(r1)
+    ! !!!
+    ! orthogonalization with Q_old:  Q_new = Q_new - Q_old @ Q_old.T @ Q_new
+    ! !!!
+    !allocate( Q_mult(m,m) )
+    !call dgemm( 'N', 'T', m, m, low_rank, +1.d0, Q_old,  size(Q_old,1),  Q_old, size(Q_old,1), 0.d0, Q_mult, size(Q_mult,1) )
+    !!do i = 1, m
+    !!  do j = 1, m
+    !!    Q_mult(j,i) = 0.d0
+    !!    do l = 1, low_rank
+    !!      Q_mult(j,i) = Q_mult(j,i) +  Q_old(i,l) * Q_old(j,l)
+    !!    enddo
+    !!  enddo
+    !!enddo
+    !!call dgemm( 'N', 'N', m, delta_r, m,  -1.d0, Q_mult, size(Q_mult,1), Q_new, size(Q_new,1), 1.d0, Q_new,  size(Q_new,1)  )
+    !do l = 1, delta_r
+    !  do i = 1, m
+    !    tmp = 0.d0
+    !    do j = 1, m
+    !      tmp = tmp + Q_mult(i,j) * Q_new(j,l)
+    !    enddo
+    !    Q_new(i,l) = Q_new(i,l) - tmp
+    !  enddo
+    !enddo
+    !deallocate( Q_mult )
+    ! !!!
+    ! power scheme
+    ! !!!
+    allocate( P(n, delta_r) )
+    do PowerIt = 1, PowerIt_max
+      ! !!!
+      call my_ortho_qr(Q_new, size(Q_new,1), m, delta_r)
+      ! !!!
+      do l = 1, delta_r
+        P(:,l) = 0.d0
+        do k = 1, N_det
+          i      = psi_bilinear_matrix_rows(k)
+          j      = psi_bilinear_matrix_columns(k)
+          P(j,l) = P(j,l) + psi_bilinear_matrix_values(k,i_state) * Q_new(i,l)
+        enddo
+      enddo
+      ! !!!
+      call my_ortho_qr(P, size(P,1), n, delta_r)
+      ! !!!
+      do l = 1, delta_r
+        Q_new(:,l) = 0.d0
+        do k = 1, N_det
+          i          = psi_bilinear_matrix_rows(k)
+          j          = psi_bilinear_matrix_columns(k)
+          Q_new(i,l) = Q_new(i,l) + psi_bilinear_matrix_values(k,i_state) * P(j,l)
+        enddo
+      enddo
+      ! !!!
+    enddo
+    deallocate( P )
+    ! !!!
+    ! orthogonalization with Q_old:  Q_new = Q_new - Q_old @ Q_old.T @ Q_new
+    ! !!!
+    allocate( Q_mult(m,m) )
+    call dgemm( 'N', 'T', m, m, low_rank, +1.d0, Q_old,  size(Q_old,1),  Q_old, size(Q_old,1), 0.d0, Q_mult, size(Q_mult,1) )
+    !do i = 1, m
+    !  do j = 1, m
+    !    Q_mult(j,i) = 0.d0
+    !    do l = 1, low_rank
+    !      Q_mult(j,i) = Q_mult(j,i) +  Q_old(i,l) * Q_old(j,l)
+    !    enddo
+    !  enddo
+    !enddo
+    !call dgemm( 'N', 'N', m, delta_r, m,  -1.d0, Q_mult, size(Q_mult,1), Q_new, size(Q_new,1), 1.d0, Q_new,  size(Q_new,1)  )
+    do l = 1, delta_r
+      do i = 1, m
+        tmp = 0.d0
+        do j = 1, m
+          tmp = tmp + Q_mult(i,j) * Q_new(j,l)
+        enddo
+        Q_new(i,l) = Q_new(i,l) - tmp
+      enddo
+    enddo
+    deallocate( Q_mult )
+    ! !!!
+    call my_ortho_qr(Q_new, size(Q_new,1), m, delta_r)
+    ! !!!
+    allocate( B_new(delta_r,n) )
+    do l = 1 , delta_r
+      B_new(l,:) = 0.d0
+      do k = 1 , N_det
+        i          = psi_bilinear_matrix_rows(k)
+        j          = psi_bilinear_matrix_columns(k)
+        B_new(l,j) = B_new(l,j) + Q_new(i,l) * psi_bilinear_matrix_values(k,i_state)
+      enddo
+    enddo
+    ! !!!
+    do j = 1, n
+      do l = 1, delta_r
+        norm_SVD = norm_SVD + B_new(l,j) * B_new(l,j)
+      enddo
+    enddo
+    ! !!!
+    error_RRRSVD = dabs( norm_psi - norm_SVD ) / norm_psi
+    It           = It + 1
+    low_rank     = low_rank + delta_r
+    ! !!!
+    ! build up approximate basis:
+    !         Q_old  = np.append(Q_new, Q_old, axis=1)
+    !         B      = np.append(B_new, B, axis=0)
+    ! !!!
+    allocate( Q_tmp(m,low_rank) , B_tmp(low_rank,n) )
+    ! !!!
+    !do l = 1, delta_r
+    !  do i = 1, m
+    !    Q_tmp(i,l) = Q_new(i,l)
+    !  enddo
+    !enddo
+    !do l = 1 , low_rank-delta_r
+    !  do i = 1, m
+    !    Q_tmp(i,l+delta_r) = Q_old(i,l)
+    !  enddo
+    !enddo
+    !do i = 1, n
+    !  do l = 1 , delta_r
+    !    B_tmp(l,i) = B_new(l,i)
+    !  enddo
+    !enddo
+    !do i = 1, n
+    !  do l = 1 , low_rank-delta_r
+    !    B_tmp(l+delta_r,i) = B_old(l,i)
+    !  enddo
+    !enddo
+    ! !!!
+    do i = 1, m
+      do l = 1, low_rank-delta_r
+        Q_tmp(i,l) = Q_old(i,l)
+      enddo
+      do l = 1, delta_r
+        Q_tmp(i,l+low_rank-delta_r) = Q_new(i,l)
+      enddo
+    enddo
+    do i = 1, n
+      do l = 1 , low_rank-delta_r
+        B_tmp(l,i) = B_old(l,i)
+      enddo
+      do l = 1 , delta_r
+        B_tmp(l+low_rank-delta_r,i) = B_new(l,i)
+      enddo
+    enddo
+    ! !!!
+    deallocate( Q_old, B_old, Q_new, B_new )
+    allocate( Q_old(m,low_rank) , B_old(low_rank,n) )
+    ! !!!
+    do l = 1, low_rank
+      do i = 1, m
+        Q_old(i,l) = Q_tmp(i,l)
+      enddo
+    enddo
+    do l = 1, n
+      do i = 1, low_rank
+        B_old(i,l) = B_tmp(i,l)
+      enddo
+    enddo
+    deallocate( Q_tmp , B_tmp )
+    ! !!!
+  print *, It, low_rank, error_RRRSVD
+  ! !!!
+  enddo
+  ! !!!
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!!
+  allocate( UB(low_rank,low_rank), D(low_rank), Vt(low_rank,n) )
+  call svd_s(B_old, size(B_old,1), UB, size(UB,1), D, Vt, size(Vt,1), low_rank, n)
+  deallocate(B_old)
+  print*, 'ok 1'
+  ! !!!
+  allocate( U(m,low_rank) )
+  call dgemm('N', 'N', m, low_rank, low_rank, 1.d0, Q_old, size(Q_old,1), UB, size(UB,1), 0.d0, U, size(U,1))
+  deallocate( Q_old,UB )
+  print*, 'ok 2'
+  ! !!!
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!!
+  allocate( URSVD(m,low_rank), DRSVD(low_rank), VtRSVD(low_rank,n) )
+  call RSVD( i_state, low_rank, PowerIt_max, nb_oversamp, URSVD, DRSVD, VtRSVD )
+  print*, 'ok 3'
+  ! !!!
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!!
+  allocate( Averif(m,n), Uverif(m,n), Dverif(n), Vtverif(n,n) )
+  do i = 1, n
+    Averif(:,i) = 1d-16
+  enddo
+  do k = 1, N_det
+    i           = psi_bilinear_matrix_rows(k)
+    j           = psi_bilinear_matrix_columns(k)
+    Averif(i,j) = psi_bilinear_matrix_values(k,i_state)
+  enddo
+  call svd_s( Averif, size(Averif,1), Uverif, size(Uverif,1), Dverif, Vtverif, size(Vtverif,1), m, n)
+  print*, 'ok 4'
+  ! !!!
+  err_verif = 0.d0
+  do j = 1, n
+    do i = 1, m
+    err_tmp = 0.d0
+    do l = 1, low_rank
+      err_tmp = err_tmp + Dverif(l) * Uverif(i,l) * Vtverif(l,j)
+    enddo
+    err_verif = err_verif + ( Averif(i,j) - err_tmp )**2.d0
+    enddo
+  enddo
+  print*, 'err verif (%) = ', 100.d0 * dsqrt(err_verif/norm_psi)
+  ! !!!
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
+  ! !!!
+  open(111, file = 'singular_values.txt', action = 'WRITE' )  
+    do i = 1, low_rank  
+      write(111, '(I8, 5X, E15.7, 2(5X, E15.7, E15.7) )' ) i, Dverif(i), D(i), 100.d0*dabs(D(i)-Dverif(i))/Dverif(i), DRSVD(i), 100.d0*dabs(DRSVD(i)-Dverif(i))/Dverif(i)
+    end do  
+  close(111)
+  ! !!!
+  !deallocate( Averif, Uverif, Dverif, Vtverif )
+  ! !!!
+  low_rank = 12
+  ! !!!
+  err_verif = 0.d0
+  do j = 1, n
+    do i = 1, m
+    err_tmp = 0.d0
+    do l = 1, low_rank
+      err_tmp = err_tmp + Dverif(l) * Uverif(i,l) * Vtverif(l,j)
+    enddo
+    err_verif = err_verif + ( Averif(i,j) - err_tmp )**2.d0
+    enddo
+  enddo
+  print*, 'err verif (%) = ', 100.d0 * dsqrt(err_verif/norm_psi)
+  ! !!!
+  print*, 'low_rank =', low_rank
+  allocate(Uezfio(m,low_rank,1), Dezfio(low_rank,1), Vezfio(n,low_rank,1))
+  do l = 1, low_rank
+    Dezfio(l,1) = Dverif(l)
+    do j = 1, m
+      Uezfio(j,l,1) = Uverif(j,l)
+    enddo
+    do j = 1, n
+      Vezfio(j,l,1) = Vtverif(l,j)
+    enddo
+  enddo
+  deallocate( U, D, Vt )
+  ! !!!
+  call ezfio_set_spindeterminants_n_det(N_det)
+  call ezfio_set_spindeterminants_n_states(N_states)
+  call ezfio_set_spindeterminants_n_det_alpha(n_det_alpha_unique)
+  call ezfio_set_spindeterminants_n_det_beta(n_det_beta_unique)
+  call ezfio_set_spindeterminants_psi_coef_matrix_rows(psi_bilinear_matrix_rows)
+  call ezfio_set_spindeterminants_psi_coef_matrix_columns(psi_bilinear_matrix_columns)
+  call ezfio_set_spindeterminants_psi_coef_matrix_values(psi_bilinear_matrix_values)
+  ! !!!
+  call ezfio_set_spindeterminants_n_svd_coefs(low_rank)
+  call ezfio_set_spindeterminants_psi_svd_alpha(Uezfio)
+  call ezfio_set_spindeterminants_psi_svd_beta(Vezfio )
+  call ezfio_set_spindeterminants_psi_svd_coefs(Dezfio)
+  deallocate(Uezfio, Dezfio, Vezfio)
+  ! !!!
+  !print*, PSI_energy(1) + nuclear_repulsion
+  !psi_bilinear_matrix(:,:,:) = 0.d0
+  !do low_rank = n, n
+  !  call generate_all_alpha_beta_det_products
+  !  do i = 1, N_det_beta_unique
+  !    do j = 1, N_det_alpha_unique
+  !      psi_bilinear_matrix(j,i,1) = 0.d0
+  !      do l = 1, r
+  !        psi_bilinear_matrix(j,i,1) = psi_bilinear_matrix(j,i,1) + D(l) * U(j,l) * V(i,l)
+  !      enddo
+  !    enddo
+  !  enddo
+  !  TOUCH psi_bilinear_matrix
+  !  call update_wf_of_psi_bilinear_matrix(.False.)
+  !  print*, low_rank, PSI_energy(1) + nuclear_repulsion !CI_energy(1)
+  !enddo
+  !deallocate(U,D,V)
+  ! !!!
+end
diff --git a/devel/svdwf/RSVD.irp.f b/devel/svdwf/RSVD.irp.f
new file mode 100644
index 0000000..f25ad1f
--- /dev/null
+++ b/devel/svdwf/RSVD.irp.f
@@ -0,0 +1,114 @@
+! !!!
+subroutine RSVD( i_state, low_rank, PowerIt_max, nb_oversamp, URSVD, DRSVD, VtRSVD )
+  ! !!!
+  BEGIN_DOC
+  ! standard RSVD for a prefixed rank
+  END_DOC
+  ! !!!
+  implicit none
+  include 'constants.include.F'
+  ! !!!
+  integer, intent(in)           :: i_state, low_rank, PowerIt_max, nb_oversamp
+  double precision, intent(out) :: URSVD(n_det_alpha_unique,low_rank), DRSVD(low_rank), VtRSVD(low_rank,n_det_beta_unique)
+  ! !!!
+  integer                       :: i, j, k, l, PowerIt, m, n 
+  double precision, allocatable :: r1(:,:), Q(:,:), P(:,:), B(:,:)
+  double precision, allocatable :: UB(:,:), D(:), Vt(:,:), U(:,:)
+  ! !!!
+  m = n_det_alpha_unique
+  n = n_det_beta_unique
+  ! !!!
+  ! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
+  ! !!!
+  allocate( Q(m, low_rank+nb_oversamp) )
+  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,k,l,r1)
+  allocate( r1(N_det,2) )
+  !$OMP DO
+  do l = 1, low_rank+nb_oversamp
+    Q(:,l) = 0.d0
+    call random_number(r1)
+    r1(:,1) = dsqrt(-2.d0*dlog(r1(:,1)))
+    r1(:,1) = r1(:,1) * dcos(dtwo_pi*r1(:,2))
+    do k = 1, N_det
+      i      = psi_bilinear_matrix_rows(k)
+      Q(i,l) = Q(i,l) + psi_bilinear_matrix_values(k,i_state) * r1(k,1)
+    enddo
+  enddo
+  !$OMP END DO
+  deallocate(r1)
+  !$OMP END PARALLEL
+  ! !!!
+  call ortho_qr(Q, size(Q,1), m, low_rank+nb_oversamp)
+  ! !!!
+  ! power scheme
+  ! !!!
+  allocate( P(n, low_rank+nb_oversamp) ) 
+  do PowerIt = 1, PowerIt_max
+    ! !!!
+    !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+    !$OMP DO
+    do l = 1, low_rank+nb_oversamp
+      P(:,l) = 0.d0
+      do k = 1, N_det
+        i      = psi_bilinear_matrix_rows(k)
+        j      = psi_bilinear_matrix_columns(k)
+        P(j,l) = P(j,l) + psi_bilinear_matrix_values(k,i_state) * Q(i,l)
+      enddo
+    enddo
+    !$OMP END DO
+    !$OMP END PARALLEL
+    ! !!!
+    call ortho_qr(P, size(P,1), n, low_rank+nb_oversamp)
+    ! !!!
+    !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+    !$OMP DO
+    do l = 1, low_rank+nb_oversamp
+      Q(:,l) = 0.d0
+      do k = 1 , N_det
+        i      = psi_bilinear_matrix_rows(k)
+        j      = psi_bilinear_matrix_columns(k)
+        Q(i,l) = Q(i,l) + psi_bilinear_matrix_values(k,i_state) * P(j,l)
+      enddo
+    enddo
+    !$OMP END DO
+    !$OMP END PARALLEL
+    ! !!!
+    call ortho_qr(Q, size(Q,1), m, low_rank+nb_oversamp)
+    ! !!!
+  enddo
+  deallocate(P)
+  ! !!!
+  allocate( B(low_rank+nb_oversamp,n) )
+  !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
+  !$OMP DO
+  do l = 1, low_rank+nb_oversamp
+    B(l,:) = 0.d0
+    do k = 1, N_det
+      i      = psi_bilinear_matrix_rows(k)
+      j      = psi_bilinear_matrix_columns(k)
+      B(l,j) = B(l,j) + psi_bilinear_matrix_values(k,i_state) * Q(i,l)
+    enddo
+  enddo
+  !$OMP END DO
+  !$OMP END PARALLEL
+  ! !!!
+  allocate( UB(low_rank+nb_oversamp,low_rank+nb_oversamp), D(low_rank+nb_oversamp), Vt(low_rank+nb_oversamp,n) )
+  call svd_s( B, size(B,1), UB, size(UB,1), D, Vt, size(Vt,1), low_rank+nb_oversamp, n)
+  deallocate(B)
+  allocate( U(m,low_rank+nb_oversamp) )
+  call dgemm('N', 'N', m, low_rank+nb_oversamp, low_rank+nb_oversamp, 1.d0, Q, size(Q,1), UB, size(UB,1), 0.d0, U, size(U,1))
+  deallocate( Q,UB )
+  ! !!!
+  do l = 1, low_rank
+    DRSVD(l) = D(l)
+    do i = 1, m
+      URSVD(i,l) = U(i,l)
+    enddo
+    do i = 1, n
+      VtRSVD(l,i) = Vt(l,i)
+    enddo
+  enddo
+  ! !!!
+  return
+  ! !!!
+end
diff --git a/devel/svdwf/linear_algebra.irp.f b/devel/svdwf/linear_algebra.irp.f
new file mode 100644
index 0000000..ed675f9
--- /dev/null
+++ b/devel/svdwf/linear_algebra.irp.f
@@ -0,0 +1,127 @@
+subroutine svd_s(A, LDA, U, LDU, D, Vt, LDVt, m, n)
+  implicit none
+  BEGIN_DOC
+  ! !!!
+  ! DGESVD computes the singular value decomposition (SVD) of a real
+  ! M-by-N matrix A, optionally computing the left and/or right singular
+  ! vectors. The SVD is written:
+  !      A = U * SIGMA * transpose(V)
+  ! where SIGMA is an M-by-N matrix which is zero except for its
+  ! min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
+  ! V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
+  ! are the singular values of A; they are real and non-negative, and
+  ! are returned in descending order.  The first min(m,n) columns of
+  ! U and V are the left and right singular vectors of A.
+  !
+  ! Note that the routine returns V**T, not V.
+  ! !!!
+  END_DOC
+
+  integer, intent(in)             :: LDA, LDU, LDVt, m, n
+  double precision, intent(in)    :: A(LDA,n)
+  double precision, intent(out)   :: U(LDU,min(m,n)), Vt(LDVt,n), D(min(m,n))
+  double precision,allocatable    :: work(:), A_tmp(:,:)
+  integer                         :: info, lwork, i, j, k
+
+
+   allocate (A_tmp(LDA,n))
+   do k=1,n
+     do i=1,m
+       A_tmp(i,k) = A(i,k) + 1d-16
+     enddo
+   enddo
+ 
+   ! Find optimal size for temp arrays
+   allocate(work(1))
+   lwork = -1
+   call dgesvd('A', 'S', m, n, A_tmp, LDA,                             &
+       D, U, LDU, Vt, LDVt, work, lwork, info)
+   ! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
+   lwork = max(int(work(1)), 5*MIN(M,N))
+   deallocate(work)
+
+   allocate(work(lwork))
+   call dgesvd('A','S', m, n, A_tmp, LDA,                             &
+       D, U, LDU, Vt, LDVt, work, lwork, info)
+   deallocate(A_tmp,work)
+
+   if (info /= 0) then
+     print *,  info, ': SVD in svds failed'
+     stop
+   endif
+ 
+   do j=1,min(m,n)
+     do i=1,m
+       if (dabs(U(i,j)) < 1.d-14)  U(i,j) = 0.d0
+     enddo
+   enddo
+ 
+   do j = 1, n
+     do i = 1, LDVt
+       if (dabs(Vt(i,j)) < 1.d-14) Vt(i,j) = 0.d0
+     enddo
+   enddo
+ 
+end
+
+
+
+
+
+
+subroutine my_ortho_qr(A,LDA,m,n)
+  implicit none
+  BEGIN_DOC
+  ! Orthogonalization using Q.R factorization
+  !
+  ! A : matrix to orthogonalize
+  !
+  ! LDA : leftmost dimension of A
+  !
+  ! m : Number of rows of A
+  !
+  ! n : Number of columns of A
+  !
+  END_DOC
+  integer, intent(in)             :: m, n, LDA
+  double precision, intent(inout) :: A(LDA,n)
+  integer                         :: LWORK, INFO, nTAU, ii, jj
+  double precision, allocatable   :: TAU(:), WORK(:)
+  double precision                :: Adorgqr(LDA,n)
+
+  allocate (TAU(min(m,n)), WORK(1))
+
+  LWORK=-1
+  call dgeqrf( m, n, A, LDA, TAU, WORK, LWORK, INFO )
+  ! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
+  LWORK=max(n,int(WORK(1)))
+
+  deallocate(WORK)
+  allocate(WORK(LWORK))
+  call dgeqrf(m, n, A, LDA, TAU, WORK, LWORK, INFO )
+  if(INFO.ne.0 ) then
+   print*, 'problem in DGEQRF'
+  endif
+
+  nTAU = size(TAU)
+  do jj = 1, n
+    do ii = 1, LDA
+      Adorgqr(ii,jj) = A(ii,jj)
+    enddo
+  enddo
+
+  LWORK=-1
+  call dorgqr(m, n, nTAU, Adorgqr, LDA, TAU, WORK, LWORK, INFO)
+  ! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
+  LWORK=max(n,int(WORK(1)))
+
+  deallocate(WORK)
+  allocate(WORK(LWORK))
+  call dorgqr(m, n, nTAU, A, LDA, TAU, WORK, LWORK, INFO)
+  if(INFO.ne.0 ) then
+   print*, 'problem in DORGQR'
+  endif
+
+
+  deallocate(WORK,TAU)
+end