2021-04-08 16:42:42 +02:00
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program Evar_TruncSVD
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implicit none
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BEGIN_DOC
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! study energy variation with truncated SVD
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END_DOC
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read_wf = .True.
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TOUCH read_wf
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! !!!
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call run()
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! !!!
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end
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! !!!
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subroutine run
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! !!!
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implicit none
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include 'constants.include.F'
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! !!!
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integer :: m, n, i_state
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double precision :: error_thr, error_RRRSVD, norm_psi, norm_SVD, err_verif, err_tmp
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integer :: i, j, k, l, It, PowerIt
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integer :: It_max, PowerIt_max, nb_oversamp
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integer :: r_init, delta_r, low_rank
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double precision, allocatable :: B_old(:,:), Q_old(:,:)
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double precision, allocatable :: UB(:,:), D(:), Vt(:,:), U(:,:)
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double precision, allocatable :: P(:,:), r1(:,:)
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double precision, allocatable :: Q_new(:,:), Q_tmp(:,:), Q_mult(:,:)
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double precision, allocatable :: B_new(:,:), B_tmp(:,:)
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double precision, allocatable :: URSVD(:,:), DRSVD(:), VtRSVD(:,:)
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double precision, allocatable :: Uverif(:,:), Dverif(:), Vtverif(:,:), Averif(:,:)
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double precision, allocatable :: Uezfio(:,:,:), Dezfio(:,:), Vezfio(:,:,:)
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double precision :: tmp
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! !!!
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i_state = 1
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m = n_det_alpha_unique
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n = n_det_beta_unique
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! !!!
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!open(111, file = 'data_to_python.txt', action = 'WRITE' )
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! do k = 1, N_det
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! 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)
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! end do
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!close(111)
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! !!!
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! !!!
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print *, 'matrix:', m,'x',n
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print *, 'N det:', N_det
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! !!!
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2021-04-08 17:16:12 +02:00
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r_init = 78
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delta_r = 5
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2021-04-08 16:42:42 +02:00
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! !!!
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PowerIt_max = 10
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nb_oversamp = 10
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! !!!
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It_max = 10
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2021-04-08 17:16:12 +02:00
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error_thr = 1.d-3 !! don't touche it but rather increase r_init
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2021-04-08 16:42:42 +02:00
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! !!!
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!! ~ Rank Revealing Randomized SVD ~ !!! !
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!!
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norm_psi = 0.d0
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do k = 1, N_det
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norm_psi = norm_psi + psi_bilinear_matrix_values(k,i_state) * psi_bilinear_matrix_values(k,i_state)
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enddo
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! !!!
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!! build initial QB decomposition !!! !
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!!
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allocate( Q_old(m, r_init) )
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,k,l,r1)
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allocate( r1(N_det,2) )
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!$OMP DO
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do l = 1, r_init
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Q_old(:,l) = 0.d0
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call random_number(r1)
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r1(:,1) = dsqrt(-2.d0*dlog(r1(:,1)))
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r1(:,1) = r1(:,1) * dcos(dtwo_pi*r1(:,2))
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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Q_old(i,l) = Q_old(i,l) + psi_bilinear_matrix_values(k,i_state) * r1(k,1)
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enddo
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enddo
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!$OMP END DO
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deallocate(r1)
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!$OMP END PARALLEL
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! !!!
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! power scheme
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! !!!
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allocate( P(n, r_init) )
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do PowerIt = 1, PowerIt_max
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! !!!
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call my_ortho_qr(Q_old, size(Q_old,1), m, r_init)
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! !!!
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
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!$OMP DO
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do l = 1, r_init
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P(:,l) = 0.d0
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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P(j,l) = P(j,l) + psi_bilinear_matrix_values(k,i_state) * Q_old(i,l)
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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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! !!!
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call my_ortho_qr(P, size(P,1), n, r_init)
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! !!!
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
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!$OMP DO
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do l = 1, r_init
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Q_old(:,l) = 0.d0
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do k = 1 , N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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Q_old(i,l) = Q_old(i,l) + psi_bilinear_matrix_values(k,i_state) * P(j,l)
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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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! !!!
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enddo
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deallocate( P )
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! !!!
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call my_ortho_qr(Q_old, size(Q_old,1), m, r_init)
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! !!!
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allocate( B_old(r_init,n) )
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
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!$OMP DO
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do l = 1, r_init
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B_old(l,:) = 0.d0
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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B_old(l,j) = B_old(l,j) + Q_old(i,l) * psi_bilinear_matrix_values(k,i_state)
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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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norm_SVD = 0.d0
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do j = 1, n
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do l = 1, r_init
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norm_SVD = norm_SVD + B_old(l,j) * B_old(l,j)
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enddo
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enddo
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error_RRRSVD = dabs( norm_psi - norm_SVD ) / norm_psi
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It = 1
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low_rank = r_init
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print *, It, low_rank, error_RRRSVD
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! !!!
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!! incrementally build up QB decomposition !!! !
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!!
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do while( ( error_RRRSVD.gt.error_thr ).and.( It.lt.It_max ).and.( low_rank.lt.(min(m,n)-delta_r) ) )
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! !!!
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allocate( Q_new(m,delta_r) )
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allocate( r1(N_det, 2) )
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do l = 1, delta_r
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Q_new(:,l) = 0.d0
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call random_number(r1)
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r1(:,1) = dsqrt(-2.d0*dlog(r1(:,1)))
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r1(:,1) = r1(:,1) * dcos(dtwo_pi*r1(:,2))
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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Q_new(i,l) = Q_new(i,l) + psi_bilinear_matrix_values(k,i_state) * r1(k,1)
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enddo
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enddo
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deallocate(r1)
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! !!!
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! orthogonalization with Q_old: Q_new = Q_new - Q_old @ Q_old.T @ Q_new
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! !!!
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!allocate( Q_mult(m,m) )
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!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) )
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!!do i = 1, m
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!! do j = 1, m
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!! Q_mult(j,i) = 0.d0
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!! do l = 1, low_rank
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!! Q_mult(j,i) = Q_mult(j,i) + Q_old(i,l) * Q_old(j,l)
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!! enddo
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!! enddo
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!!enddo
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!!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) )
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!do l = 1, delta_r
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! do i = 1, m
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! tmp = 0.d0
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! do j = 1, m
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! tmp = tmp + Q_mult(i,j) * Q_new(j,l)
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! enddo
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! Q_new(i,l) = Q_new(i,l) - tmp
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! enddo
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!enddo
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!deallocate( Q_mult )
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! !!!
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! power scheme
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! !!!
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allocate( P(n, delta_r) )
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do PowerIt = 1, PowerIt_max
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! !!!
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call my_ortho_qr(Q_new, size(Q_new,1), m, delta_r)
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! !!!
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do l = 1, delta_r
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P(:,l) = 0.d0
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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P(j,l) = P(j,l) + psi_bilinear_matrix_values(k,i_state) * Q_new(i,l)
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enddo
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enddo
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! !!!
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call my_ortho_qr(P, size(P,1), n, delta_r)
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! !!!
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do l = 1, delta_r
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Q_new(:,l) = 0.d0
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do k = 1, N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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Q_new(i,l) = Q_new(i,l) + psi_bilinear_matrix_values(k,i_state) * P(j,l)
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enddo
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enddo
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! !!!
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enddo
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deallocate( P )
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! !!!
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! orthogonalization with Q_old: Q_new = Q_new - Q_old @ Q_old.T @ Q_new
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! !!!
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allocate( Q_mult(m,m) )
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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) )
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!do i = 1, m
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! do j = 1, m
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! Q_mult(j,i) = 0.d0
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! do l = 1, low_rank
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! Q_mult(j,i) = Q_mult(j,i) + Q_old(i,l) * Q_old(j,l)
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! enddo
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! enddo
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!enddo
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!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) )
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do l = 1, delta_r
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do i = 1, m
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tmp = 0.d0
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do j = 1, m
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tmp = tmp + Q_mult(i,j) * Q_new(j,l)
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enddo
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Q_new(i,l) = Q_new(i,l) - tmp
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enddo
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enddo
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deallocate( Q_mult )
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! !!!
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call my_ortho_qr(Q_new, size(Q_new,1), m, delta_r)
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! !!!
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allocate( B_new(delta_r,n) )
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do l = 1 , delta_r
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B_new(l,:) = 0.d0
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do k = 1 , N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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B_new(l,j) = B_new(l,j) + Q_new(i,l) * psi_bilinear_matrix_values(k,i_state)
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enddo
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enddo
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! !!!
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do j = 1, n
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do l = 1, delta_r
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norm_SVD = norm_SVD + B_new(l,j) * B_new(l,j)
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enddo
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enddo
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! !!!
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error_RRRSVD = dabs( norm_psi - norm_SVD ) / norm_psi
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It = It + 1
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low_rank = low_rank + delta_r
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! !!!
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! build up approximate basis:
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! Q_old = np.append(Q_new, Q_old, axis=1)
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! B = np.append(B_new, B, axis=0)
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! !!!
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allocate( Q_tmp(m,low_rank) , B_tmp(low_rank,n) )
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! !!!
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!do l = 1, delta_r
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! do i = 1, m
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! Q_tmp(i,l) = Q_new(i,l)
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! enddo
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!enddo
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!do l = 1 , low_rank-delta_r
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! do i = 1, m
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! Q_tmp(i,l+delta_r) = Q_old(i,l)
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! enddo
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!enddo
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!do i = 1, n
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! do l = 1 , delta_r
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! B_tmp(l,i) = B_new(l,i)
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! enddo
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!enddo
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!do i = 1, n
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! do l = 1 , low_rank-delta_r
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! B_tmp(l+delta_r,i) = B_old(l,i)
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! enddo
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!enddo
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! !!!
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do i = 1, m
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do l = 1, low_rank-delta_r
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Q_tmp(i,l) = Q_old(i,l)
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enddo
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do l = 1, delta_r
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Q_tmp(i,l+low_rank-delta_r) = Q_new(i,l)
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enddo
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enddo
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do i = 1, n
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do l = 1 , low_rank-delta_r
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B_tmp(l,i) = B_old(l,i)
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enddo
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do l = 1 , delta_r
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B_tmp(l+low_rank-delta_r,i) = B_new(l,i)
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|
|
enddo
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enddo
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! !!!
|
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|
|
|
deallocate( Q_old, B_old, Q_new, B_new )
|
|
|
|
|
allocate( Q_old(m,low_rank) , B_old(low_rank,n) )
|
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|
! !!!
|
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|
do l = 1, low_rank
|
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|
do i = 1, m
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|
Q_old(i,l) = Q_tmp(i,l)
|
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|
enddo
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|
enddo
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|
|
do l = 1, n
|
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|
|
|
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'
|
|
|
|
|
! !!!
|
|
|
|
|
! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
|
|
|
|
|
! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
|
|
|
|
|
! !!!
|
2021-07-28 17:19:18 +02:00
|
|
|
allocate( Averif(m,n), Uverif(m,m), Dverif(min(m,n)), Vtverif(n,n) )
|
2021-04-08 16:42:42 +02:00
|
|
|
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 )
|
|
|
|
|
! !!!
|
2021-04-08 16:31:31 +02:00
|
|
|
low_rank = 10
|
2021-04-08 16:42:42 +02:00
|
|
|
! !!!
|
|
|
|
|
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
|
