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random svd
This commit is contained in:
Abdallah AMMAR
parent
e3bc5b8c40
commit
4724e9f6f0
451
devel/svdwf/Evar_TruncSVD.irp.f
Normal file
451
devel/svdwf/Evar_TruncSVD.irp.f
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@ -0,0 +1,451 @@
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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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r_init = 78
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delta_r = 5
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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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error_thr = 1.d-3 !! don't touche it but rather increase r_init
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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 )
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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
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B_old(i,l) = B_tmp(i,l)
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enddo
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enddo
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deallocate( Q_tmp , B_tmp )
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! !!!
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print *, It, low_rank, error_RRRSVD
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! !!!
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enddo
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! !!!
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !
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! !!!
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allocate( UB(low_rank,low_rank), D(low_rank), Vt(low_rank,n) )
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call svd_s(B_old, size(B_old,1), UB, size(UB,1), D, Vt, size(Vt,1), low_rank, n)
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deallocate(B_old)
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print*, 'ok 1'
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! !!!
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allocate( U(m,low_rank) )
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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))
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deallocate( Q_old,UB )
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print*, 'ok 2'
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! !!!
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!!
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allocate( URSVD(m,low_rank), DRSVD(low_rank), VtRSVD(low_rank,n) )
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call RSVD( i_state, low_rank, PowerIt_max, nb_oversamp, URSVD, DRSVD, VtRSVD )
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print*, 'ok 3'
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! !!!
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!!
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allocate( Averif(m,n), Uverif(m,n), Dverif(n), Vtverif(n,n) )
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do i = 1, n
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Averif(:,i) = 1d-16
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enddo
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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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Averif(i,j) = psi_bilinear_matrix_values(k,i_state)
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enddo
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call svd_s( Averif, size(Averif,1), Uverif, size(Uverif,1), Dverif, Vtverif, size(Vtverif,1), m, n)
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print*, 'ok 4'
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! !!!
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err_verif = 0.d0
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do j = 1, n
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do i = 1, m
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err_tmp = 0.d0
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do l = 1, low_rank
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err_tmp = err_tmp + Dverif(l) * Uverif(i,l) * Vtverif(l,j)
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enddo
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err_verif = err_verif + ( Averif(i,j) - err_tmp )**2.d0
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enddo
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enddo
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print*, 'err verif (%) = ', 100.d0 * dsqrt(err_verif/norm_psi)
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! !!!
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! ~ !!! !
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! !!!
|
||||
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 = 10
|
||||
! !!!
|
||||
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
|
||||
@ -1 +1,2 @@
|
||||
determinants
|
||||
davidson_undressed
|
||||
|
||||
10
devel/svdwf/QR.py
Normal file
10
devel/svdwf/QR.py
Normal file
@ -0,0 +1,10 @@
|
||||
# !!!
|
||||
import numpy as np
|
||||
# !!!
|
||||
def QR_fact(X):
|
||||
Q, R = np.linalg.qr(X, mode="reduced")
|
||||
D = np.diag( np.sign( np.diag(R) ) )
|
||||
Qunique = np.dot(Q,D)
|
||||
#Runique = np.dot(D,R)
|
||||
return(Qunique)
|
||||
# !!!
|
||||
68
devel/svdwf/R3SVD_AMMAR.py
Normal file
68
devel/svdwf/R3SVD_AMMAR.py
Normal file
@ -0,0 +1,68 @@
|
||||
# !!!
|
||||
import numpy as np
|
||||
from QR import QR_fact
|
||||
from RSVD import powit_RSVD
|
||||
# !!!
|
||||
def R3SVD_AMMAR(A, t, delta_t, npow, nb_oversamp, err_thr, maxit, tol):
|
||||
# !!!
|
||||
# build initial QB decomposition
|
||||
# !!!
|
||||
n = A.shape[1]
|
||||
G = np.random.randn(n, t)
|
||||
normA = np.linalg.norm(A, ord='fro')**2
|
||||
i_it = 0
|
||||
rank = 0
|
||||
Y = np.dot(A,G)
|
||||
# The power scheme
|
||||
for j in range(npow):
|
||||
Q = QR_fact(Y)
|
||||
Q = QR_fact( np.dot(A.T,Q) )
|
||||
Y = np.dot(A,Q)
|
||||
# orthogonalization process
|
||||
Q_old = QR_fact(Y)
|
||||
B = np.dot(Q_old.T,A)
|
||||
normB = np.linalg.norm(B, ord='fro')**2
|
||||
# error percentage
|
||||
errpr = abs( normA - normB ) / normA
|
||||
rank += t
|
||||
i_it += 1
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
# !!!
|
||||
# incrementally build up QB decomposition
|
||||
# !!!
|
||||
while ( (errpr>err_thr) and (i_it<maxit) and (rank<=min(A.shape)-delta_t) ): #
|
||||
G = np.random.randn(n, delta_t)
|
||||
Y = np.dot(A,G)
|
||||
#Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
|
||||
# power scheme
|
||||
for j in range(npow):
|
||||
Q = QR_fact(Y)
|
||||
Q = QR_fact( np.dot(A.T,Q) )
|
||||
Y = np.dot(A,Q)
|
||||
Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
|
||||
Q_new = QR_fact(Y)
|
||||
B_new = np.dot(Q_new.T,A)
|
||||
# build up approximate basis
|
||||
Q_old = np.append(Q_new, Q_old, axis=1)
|
||||
#B = np.append(B_new, B, axis=0)
|
||||
normB += np.linalg.norm(B_new, ord='fro')**2
|
||||
errpr = abs( normA - normB ) / normA
|
||||
rank += delta_t
|
||||
i_it += 1
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
# !!!
|
||||
#UL, SL, VLT = np.linalg.svd(B, full_matrices=0)
|
||||
#UL = np.dot(Q_old,UL)
|
||||
# !!!
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
UL, SL, VLT = powit_RSVD(A, rank, npow, nb_oversamp)
|
||||
#return UL, SL, VLT
|
||||
# !!!
|
||||
rank = SL.shape[0]
|
||||
new_r = rank
|
||||
for i in range(rank):
|
||||
if( SL[i] <= tol ):
|
||||
new_r = i
|
||||
break
|
||||
return UL[:,:(new_r)], SL[:(new_r)], VLT[:(new_r),:]
|
||||
# !!!
|
||||
58
devel/svdwf/R3SVD_LiYu.py
Normal file
58
devel/svdwf/R3SVD_LiYu.py
Normal file
@ -0,0 +1,58 @@
|
||||
# !!!
|
||||
import numpy as np
|
||||
from QR import QR_fact
|
||||
# !!!
|
||||
def R3SVD_LiYu(A, t, delta_t, npow, err_thr, maxit):
|
||||
# !!!
|
||||
# build initial QB decomposition
|
||||
# !!!
|
||||
n = A.shape[1]
|
||||
G = np.random.randn(n, t) # n x t Gaussian random matrix
|
||||
normA = np.linalg.norm(A, ord='fro')**2
|
||||
i_it = 0
|
||||
rank = 0
|
||||
Y = np.dot(A,G)
|
||||
# The power scheme
|
||||
for j in range(npow):
|
||||
Q = QR_fact(Y)
|
||||
Q = QR_fact( np.dot(A.T,Q) )
|
||||
Y = np.dot(A,Q)
|
||||
# orthogonalization process
|
||||
Q_old = QR_fact(Y)
|
||||
B = np.dot(Q_old.T,A)
|
||||
normB = np.linalg.norm(B, ord='fro')**2
|
||||
# error percentage
|
||||
errpr = abs( normA - normB ) / normA
|
||||
rank += t
|
||||
i_it += 1
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
# !!!
|
||||
# incrementally build up QB decomposition
|
||||
# !!!
|
||||
while ( (errpr>err_thr) and (i_it<maxit) and (rank<=min(A.shape)-delta_t) ): #
|
||||
G = np.random.randn(n, delta_t) # n x delta_t Gaussian random matrix
|
||||
Y = np.dot(A,G)
|
||||
Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
|
||||
# power scheme
|
||||
for j in range(npow):
|
||||
Q = QR_fact(Y)
|
||||
Q = QR_fact( np.dot(A.T,Q) )
|
||||
Y = np.dot(A,Q)
|
||||
Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
|
||||
Q_new = QR_fact(Y)
|
||||
B_new = np.dot(Q_new.T,A)
|
||||
# build up approximate basis
|
||||
Q_old = np.append(Q_new, Q_old, axis=1)
|
||||
B = np.append(B_new, B, axis=0)
|
||||
rank += delta_t
|
||||
i_it += 1
|
||||
normB += np.linalg.norm(B_new, ord='fro')**2
|
||||
errpr = abs( normA - normB ) / normA
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
# !!!
|
||||
print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
|
||||
UL, SL, VLT = np.linalg.svd(B, full_matrices=0)
|
||||
UL = np.dot(Q_old,UL)
|
||||
# !!!
|
||||
return UL, SL, VLT
|
||||
# !!!
|
||||
114
devel/svdwf/RSVD.irp.f
Normal file
114
devel/svdwf/RSVD.irp.f
Normal file
@ -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
|
||||
20
devel/svdwf/RSVD.py
Normal file
20
devel/svdwf/RSVD.py
Normal file
@ -0,0 +1,20 @@
|
||||
# !!!
|
||||
import numpy as np
|
||||
from QR import QR_fact
|
||||
# !!!
|
||||
def powit_RSVD(X, new_r, nb_powit, nb_oversamp):
|
||||
# !!!
|
||||
G = np.random.randn(X.shape[1], new_r+nb_oversamp)
|
||||
Q = QR_fact( np.dot(X,G) )
|
||||
# !!!
|
||||
for _ in range(nb_powit):
|
||||
Q = QR_fact( np.dot(X.T,Q) )
|
||||
Q = QR_fact( np.dot(X,Q) )
|
||||
# !!!
|
||||
Y = np.dot(Q.T,X)
|
||||
# !!!
|
||||
U, S, VT = np.linalg.svd(Y, full_matrices=0)
|
||||
U = np.dot(Q,U)
|
||||
return U[:,:(new_r)], S[:(new_r)], VT[:(new_r),:]
|
||||
# !!!
|
||||
# !!!
|
||||
127
devel/svdwf/linear_algebra.irp.f
Normal file
127
devel/svdwf/linear_algebra.irp.f
Normal file
@ -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
|
||||
123
devel/svdwf/pyth_RSVD.py
Normal file
123
devel/svdwf/pyth_RSVD.py
Normal file
@ -0,0 +1,123 @@
|
||||
#!/usr/bin/env python3
|
||||
# !!!
|
||||
import os, sys
|
||||
# !!!
|
||||
#QP_PATH=os.environ["QMCCHEM_PATH"]
|
||||
#sys.path.insert(0,QMCCHEM_PATH+"/EZFIO/Python/")
|
||||
# !!!
|
||||
from ezfio import ezfio
|
||||
from datetime import datetime
|
||||
import numpy as np
|
||||
from scipy.sparse.linalg import svds
|
||||
from R3SVD_LiYu import R3SVD_LiYu
|
||||
from RSVD import powit_RSVD
|
||||
from R3SVD_AMMAR import R3SVD_AMMAR
|
||||
import time
|
||||
# !!!
|
||||
fmt = '%5d' + 2 * ' %e'
|
||||
# !!!
|
||||
if __name__ == "__main__":
|
||||
# !!!
|
||||
if len(sys.argv) != 2:
|
||||
print("Usage: %s <EZFIO_DIRECTORY>"%sys.argv[0])
|
||||
sys.exit(1)
|
||||
filename = sys.argv[1]
|
||||
ezfio.set_file(filename)
|
||||
# !!!
|
||||
N_det = ezfio.get_spindeterminants_n_det()
|
||||
A_rows = np.array(ezfio.get_spindeterminants_psi_coef_matrix_rows())
|
||||
A_cols = np.array(ezfio.get_spindeterminants_psi_coef_matrix_columns())
|
||||
A_vals = np.array(ezfio.get_spindeterminants_psi_coef_matrix_values())
|
||||
nrows, ncols = ezfio.get_spindeterminants_n_det_alpha(), ezfio.get_spindeterminants_n_det_beta()
|
||||
Y = np.zeros( (nrows, ncols) )
|
||||
for k in range(N_det):
|
||||
i = A_rows[k] - 1
|
||||
j = A_cols[k] - 1
|
||||
Y[i,j] = A_vals[0][k]
|
||||
print("# # # # # # # # # # # # # # # # # # # # # #")
|
||||
print('matrix dimensions = {} x {}'.format(nrows, ncols))
|
||||
print("# # # # # # # # # # # # # # # # # # # # # # \n")
|
||||
normY = np.linalg.norm(Y, ord='fro')
|
||||
print( normY )
|
||||
# !!!
|
||||
print('Full SVD:')
|
||||
t_beg = time.time()
|
||||
U, S_FSVD, VT = np.linalg.svd(Y, full_matrices=0)
|
||||
t_end = time.time()
|
||||
rank = S_FSVD.shape[0]
|
||||
energy = np.sum(np.square(S_FSVD)) / normY**2
|
||||
err_SVD = 100. * np.linalg.norm(Y - np.dot(U,np.dot(np.diag(S_FSVD),VT)), ord='fro') / normY
|
||||
print('rank = {}, energy = {}, error = {}%, CPU time = {} \n'.format(rank, energy, err_SVD, t_end-t_beg))
|
||||
# !!!
|
||||
np.savetxt('results_python/h2o_pseudo/SingValues_FullSVD.txt', np.transpose([ np.array(range(rank))+1, S_FSVD ]), fmt='%5d' + ' %e', delimiter=' ')
|
||||
# !!!
|
||||
t = 50
|
||||
delta_t = 10
|
||||
npow = 15
|
||||
err_thr = 1e-3
|
||||
maxit = 10
|
||||
# !!!
|
||||
print('RRR SVD Li & Yu:')
|
||||
t_beg = time.time()
|
||||
U, S_R3SVD, VT = R3SVD_LiYu(Y, t, delta_t, npow, err_thr, maxit)
|
||||
t_end = time.time()
|
||||
rank = S_R3SVD.shape[0]
|
||||
energy = np.sum( np.square(S_R3SVD) ) / normY**2
|
||||
err_SVD = 100. * np.linalg.norm(Y - np.dot(U,np.dot(np.diag(S_R3SVD),VT)), ord='fro') / normY
|
||||
print('nb Pow It = {}, rank = {}, energy = {}, error = {} %, CPU time = {}\n'.format(npow, rank, energy, err_SVD, t_end-t_beg))
|
||||
# !!!
|
||||
err_R3SVD = np.zeros( (rank) )
|
||||
for i in range(rank):
|
||||
err_R3SVD[i] = 100.0 * abs( S_FSVD[i] - S_R3SVD[i] ) / S_FSVD[i]
|
||||
np.savetxt('results_python/h2o_pseudo/SingValues_R3SVD.txt', np.transpose([ np.array(range(rank))+1, S_R3SVD, err_R3SVD ]), fmt=fmt, delimiter=' ')
|
||||
# !!!
|
||||
nb_oversamp = 10
|
||||
tol_SVD = 1e-10
|
||||
print('RRR SVD my version:')
|
||||
t_beg = time.time()
|
||||
U, S_MRSVD, VT = R3SVD_AMMAR(Y, t, delta_t, npow, nb_oversamp, err_thr, maxit, tol_SVD)
|
||||
t_end = time.time()
|
||||
rank = S_MRSVD.shape[0]
|
||||
energy = np.sum( np.square(S_MRSVD) ) / normY**2
|
||||
err_SVD = 100. * np.linalg.norm(Y - np.dot(U,np.dot(np.diag(S_MRSVD),VT)), ord='fro') / normY
|
||||
print('nb Pow It = {}, rank = {}, energy = {}, error = {} %, CPU time = {}\n'.format(npow, rank, energy, err_SVD, t_end-t_beg))
|
||||
# !!!
|
||||
err_MRSVD = np.zeros( (rank) )
|
||||
for i in range(rank):
|
||||
err_MRSVD[i] = 100.0 * abs( S_FSVD[i] - S_MRSVD[i] ) / S_FSVD[i]
|
||||
np.savetxt('results_python/h2o_pseudo/SingValues_MRSVD.txt', np.transpose([ np.array(range(rank))+1, S_MRSVD, err_MRSVD ]), fmt=fmt, delimiter=' ')
|
||||
# !!!
|
||||
trank = rank
|
||||
print("Truncated RSVD (pre-fixed rank = {} & oversampling parameter = {}):".format(trank,nb_oversamp))
|
||||
t_beg = time.time()
|
||||
U, S_RSVD, VT = powit_RSVD(Y, trank, npow, nb_oversamp)
|
||||
t_end = time.time()
|
||||
rank = S_RSVD.shape[0]
|
||||
energy = np.sum( np.square(S_RSVD) ) / normY**2
|
||||
err_SVD = 100. * np.linalg.norm( Y - np.dot(U,np.dot(np.diag(S_RSVD),VT)), ord="fro") / normY
|
||||
print('nb Pow It = {}, rank = {}, energy = {}, error = {} %, CPU time = {}\n'.format(npow, rank, energy, err_SVD, t_end-t_beg))
|
||||
# !!!
|
||||
err_RSVD = np.zeros( (rank) )
|
||||
for i in range(rank):
|
||||
err_RSVD[i] = 100.0 * abs( S_FSVD[i] - S_RSVD[i] ) / S_FSVD[i]
|
||||
np.savetxt('results_python/h2o_pseudo/SingValues_RSVD.txt', np.transpose([ np.array(range(rank))+1, S_RSVD, err_RSVD ]), fmt=fmt, delimiter=' ')
|
||||
# !!!
|
||||
print("Truncated SVD (scipy):")
|
||||
t_beg = time.time()
|
||||
U, S_TSVD, VT = svds(Y, min(trank, min(Y.shape[0],Y.shape[1])-1 ), which='LM')
|
||||
t_end = time.time()
|
||||
rank = S_TSVD.shape[0]
|
||||
energy = np.sum( np.square(S_TSVD) ) / normY**2
|
||||
err_SVD = 100. * np.linalg.norm( Y - np.dot(U, np.dot(np.diag(S_TSVD),VT) ), ord="fro") / normY
|
||||
print('rank = {}, energy = {}, error = {} %, CPU time = {}\n'.format(rank, energy, err_SVD, t_end-t_beg))
|
||||
# !!!
|
||||
err_TSVD = np.zeros( (rank) )
|
||||
for i in range(rank-1):
|
||||
for j in range(i+1,rank):
|
||||
if( S_TSVD[j] > S_TSVD[i]):
|
||||
S_TSVD[i], S_TSVD[j] = S_TSVD[j], S_TSVD[i]
|
||||
for i in range(rank):
|
||||
err_TSVD[i] = 100.0 * abs( S_FSVD[i] - S_TSVD[i] ) / S_FSVD[i]
|
||||
np.savetxt('results_python/h2o_pseudo/SingValues_TSVD.txt', np.transpose([ np.array(range(rank))+1, S_TSVD, err_TSVD ]), fmt=fmt, delimiter=' ')
|
||||
# !!!
|
||||
# !!!
|
||||
Loading…
x
Reference in New Issue
Block a user