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https://gitlab.com/scemama/qp_plugins_scemama.git
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312 lines
8.3 KiB
FortranFixed
312 lines
8.3 KiB
FortranFixed
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program RSVD_ijHkl_det
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BEGIN_DOC
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!
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! decompose < di dj | H | dk dl > by a RSVD:
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!
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! H_{ik jl} = < di dj | H | dk dl >
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! = \sum_{s=1}^{n_svd} U_{ik s} V_{jl s}
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! = \sum_{s=1}^{n_svd} U_{ik s} U_{jl s}
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!
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! where n_svd << min( NaxNa , NbxNb )
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!
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END_DOC
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read_wf = .true.
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TOUCH read_wf
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call run()
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end
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subroutine run()
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implicit none
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integer(bit_kind) :: det1(N_int,2), det2(N_int,2)
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integer :: degree, i_state
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double precision :: h12
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integer*8 :: dim_Hdet
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integer*8, allocatable :: Hdet_ik(:), Hdet_jl(:)
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double precision, allocatable :: Hdet_v(:)
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integer :: dim_U , dim_V, dim_RSVD
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double precision :: t_beg, t_end
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call wall_time(t_beg)
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i_state = 1
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det1(:,1) = psi_det_alpha_unique(:,1)
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det2(:,1) = psi_det_alpha_unique(:,1)
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det1(:,2) = psi_det_beta_unique(:,1)
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det2(:,2) = psi_det_beta_unique(:,1)
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call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int)
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call get_excitation_degree(det1,det2,degree,N_int)
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call i_H_j(det1, det2, N_int, h12)
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! sparse representation of < di dj | H | dk dl >
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!dim_Hdet = 7486379362
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dim_Hdet = 1000000
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allocate( Hdet_ik(dim_Hdet), Hdet_jl(dim_Hdet), Hdet_v(dim_Hdet) )
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call const_ij_hdet_kl_sparse(dim_hdet, hdet_ik, hdet_jl, hdet_v)
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! decompose Hdet by a Randomized SVD
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dim_U = n_det_alpha_unique * n_det_alpha_unique
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dim_V = n_det_beta_unique * n_det_beta_unique
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dim_RSVD = min(dim_U, dim_V)
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dim_RSVD = min(5000, dim_RSVD)
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call perform_RSVD(dim_U, dim_V, dim_RSVD, dim_Hdet, Hdet_ik, Hdet_jl, Hdet_v)
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deallocate( Hdet_ik, Hdet_jl, Hdet_v )
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call wall_time(t_end)
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print *, ' end after (min)', (t_end-t_beg)/60.d0
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end
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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!
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subroutine const_ij_Hdet_kl_sparse(dim_Hdet, Hdet_ik, Hdet_jl, Hdet_v)
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implicit none
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integer*8, intent(in) :: dim_Hdet
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integer*8, intent(out) :: Hdet_ik(dim_Hdet), Hdet_jl(dim_Hdet)
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double precision, intent(out) :: Hdet_v(dim_Hdet)
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integer(bit_kind) :: det1(N_int,2), det2(N_int,2)
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integer :: degree
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integer :: na, nb, i, j, k, l, ii
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double precision :: h12
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double precision :: t1, t2
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print *, ""
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print *, " start const_ij_Hdet_kl_sparse"
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call wall_time(t1)
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na = n_det_alpha_unique
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nb = n_det_beta_unique
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ii = 0
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(i,j,k,l,ii,h12,det1,det2,degree) &
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!$OMP SHARED(na,nb,psi_det_alpha_unique,psi_det_beta_unique, &
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!$OMP N_int,Hdet_ik,Hdet_jl,Hdet_v)
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!$OMP DO
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do l = 1, nb
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det2(:,2) = psi_det_beta_unique(:,l)
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do j = 1, nb
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det1(:,2) = psi_det_beta_unique(:,j)
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call get_excitation_degree_spin(det1(1,2),det2(1,2),degree,N_int)
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if(degree .gt. 2) cycle
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do k = 1, na
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det2(:,1) = psi_det_alpha_unique(:,k)
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do i = 1, na
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det1(:,1) = psi_det_alpha_unique(:,i)
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call get_excitation_degree(det1,det2,degree,N_int)
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if(degree .gt. 2) cycle
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call i_H_j(det1, det2, N_int, h12)
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if(dabs(h12) .le. (1d-15)) cycle
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ii = ii + 1
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Hdet_ik(ii) = (i-1)*na + k
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Hdet_jl(ii) = (j-1)*na + l
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Hdet_v (ii) = h12
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enddo
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enddo
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call wall_time(t2)
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print *, " end const_ij_Hdet_kl_sparse after (min) ", (t2-t1)/60.
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print *, ""
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if( ii .ne. dim_Hdet) then
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print*, ' error in const_ij_Hdet_kl_sparse'
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print*, ' dim supposed = ', dim_Hdet
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print*, ' dim foundedi = ', ii
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stop
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end if
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return
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end subroutine const_ij_Hdet_kl_sparse
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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!
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subroutine perform_RSVD(dim_U, dim_V, dim_RSVD, dim_Hdet, Hdet_ik, Hdet_jl, Hdet_v)
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include 'constants.include.F'
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implicit none
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integer, intent(in) :: dim_U, dim_V, dim_RSVD
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integer*8, intent(in) :: dim_Hdet
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integer*8, intent(in) :: Hdet_ik(dim_Hdet), Hdet_jl(dim_Hdet)
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double precision, intent(in) :: Hdet_v(dim_Hdet)
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integer :: na, nb
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integer :: iter, iter_max
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integer :: ii, rr, ik, jl
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double precision, allocatable :: GR(:,:)
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double precision, allocatable :: Z(:,:), P(:,:), Yt(:,:), UYt(:,:)
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double precision, allocatable :: U(:,:), V(:,:), D(:)
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na = n_det_alpha_unique
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nb = n_det_beta_unique
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! Z = Hdet x G
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! G: random gauss dist
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allocate( Z(dim_U,dim_RSVD) )
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Z(:,:) = 0
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!$OMP PARALLEL DEFAULT(NONE) PRIVATE(ii, rr, ik, GR) &
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!$OMP SHARED(dim_Hdet, dim_RSVD, Z, Hdet_ik, Hdet_v)
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allocate( GR(dim_Hdet,2) )
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!$OMP DO
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do rr = 1, dim_RSVD
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call random_number(GR)
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GR(:,1) = dsqrt(-2.d0*dlog(GR(:,1)))
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GR(:,1) = GR(:,1) * dcos(dtwo_pi*GR(:,2))
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do ii = 1, dim_Hdet
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ik = Hdet_ik(ii)
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!jl = Hdet_jl(ii)
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Z(ik,rr) = Z(ik,rr) + Hdet_v(ii) * GR(ii,1)
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enddo
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enddo
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!$OMP END DO
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deallocate(GR)
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!$OMP END PARALLEL
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! parameter
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iter_max = 10
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allocate( P(dim_V,dim_RSVD) )
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! ------------------------------------------------------------------------------------------
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! Power iterations
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!
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do iter = 1, iter_max
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print *, ' power iteration ', iter, '/', iter_max
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!$OMP PARALLEL DEFAULT(NONE) PRIVATE(ii, rr, ik, jl) &
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!$OMP SHARED(dim_Hdet, dim_RSVD, Z, P, Hdet_ik, Hdet_jl, Hdet_v)
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!$OMP DO
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! P = Hdet.T x Z
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do rr = 1, dim_RSVD
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P(:,rr) = 0.d0
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do ii = 1, dim_Hdet
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ik = Hdet_ik(ii)
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jl = Hdet_jl(ii)
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P(jl,rr) = P(jl,rr) + Hdet_v(ii) * Z(ik,rr)
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enddo
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enddo
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!$OMP END DO
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!$OMP BARRIER
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!$OMP DO
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do rr = 1, dim_RSVD
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Z(:,rr) = 0.d0
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do ii = 1, dim_Hdet
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ik = Hdet_ik(ii)
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jl = Hdet_jl(ii)
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Z(ik,rr) = Z(ik,rr) + Hdet_v(ii) * P(jl,rr)
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call ortho_qr(Z, size(Z,1), dim_U, dim_RSVD)
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enddo
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!
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! ------------------------------------------------------------------------------------------
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! Y = Z.T x Hdet
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! Yt = Hdet.T x Z
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allocate( Yt(dim_V,dim_RSVD) )
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!$OMP PARALLEL DEFAULT(NONE) PRIVATE(ii, rr, ik, jl) &
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!$OMP SHARED(dim_Hdet, dim_RSVD, Z, Yt, Hdet_ik, Hdet_jl, Hdet_v)
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!$OMP DO
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do rr = 1, dim_RSVD
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Yt(:,rr) = 0.d0
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do ii = 1, dim_Hdet
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ik = Hdet_ik(ii)
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jl = Hdet_jl(ii)
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Yt(jl,rr) = Yt(jl,rr) + Z(ik,rr) * Hdet_v(ii)
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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! Y = U x D x Vt
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! Yt = V x D x Ut
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allocate( D(dim_RSVD), V(dim_V,dim_RSVD), UYt(dim_RSVD,dim_RSVD) )
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call svd(Yt, size(Yt,1), V, size(V,1), D, UYt, size(UYt,1), dim_V, dim_RSVD)
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deallocate( Yt )
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! U = Z x UY
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allocate( U(dim_U,dim_RSVD) )
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call dgemm('N', 'T', dim_U, dim_RSVD, dim_RSVD, 1.d0, Z, size(Z,1), UYt, size(UYt,1), 0.d0, U, size(U,1))
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deallocate( UYt, Z )
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open(unit=41, file='u_det.txt', action='write')
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do rr = 1, dim_RSVD
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do ii = 1, dim_U
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write(41,*) U(ii,rr)
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enddo
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enddo
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close(41)
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! v = u because H is symmetric
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!open(unit=41, file='v_det.txt', action='write')
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! do rr = 1, dim_RSVD
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! do ii = 1, dim_V
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! write(41,*) V(ii,rr)
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! enddo
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! enddo
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!close(41)
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open(unit=41, file='d_det.txt', action='write')
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do rr = 1, dim_RSVD
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write(41,*) D(rr), sum( D(1:rr)**2 )
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enddo
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close(41)
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deallocate( U, D, V )
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end subroutine perform_RSVD
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! _________________________________________________________________________________________________
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! _________________________________________________________________________________________________
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