2021-02-22 16:25:05 +01:00
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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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subroutine run
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implicit none
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include 'constants.include.F'
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double precision, allocatable :: A(:,:), U(:,:), V(:,:), D(:)
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integer :: r, i, j, k, l, m, n, iter, iter_max
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double precision, allocatable :: Z(:,:), P(:,:), Yt(:,:), UYt(:,:), r1(:,:)
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! !!!
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m = n_det_alpha_unique
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n = n_det_beta_unique
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r = n
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print *, 'matrix:', m,'x',n
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print *, 'N det:', N_det
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print *, 'rank = ', r
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iter_max = 20
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! !!!
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allocate( Z(m,r) , P(n,r) ) ! Z(m,r) = A(m,n) @ P(n,r)
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Z(:,:) = 0.d0
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! !!!
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! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
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! first we apply a RSVD for a pre-fixed rank (r)
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! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l,r1)
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allocate(r1(N_det,2))
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!$OMP DO
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do l=1,r
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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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2021-05-03 15:21:05 +02:00
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j = psi_bilinear_matrix_columns(k)
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2021-02-22 16:25:05 +01:00
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Z(i,l) = Z(i,l) + psi_bilinear_matrix_values(k,1) * 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 iterations
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! !!!
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do iter=1,iter_max
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! !!!
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print *, 'Power iteration ', iter, '/', 20
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! !!!
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! P(n,r) = At(n,m) @ Z(m,r)
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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
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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,1) * Z(i,l)
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enddo
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enddo
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!$OMP END DO
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! !!!
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! Z(m,r) = A(m,n) @ P(n,r)
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! !!!
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!$OMP BARRIER
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!$OMP DO
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do l=1,r
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Z(:,l) = 0.d0
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do k=1,N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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Z(i,l) = Z(i,l) + psi_bilinear_matrix_values(k,1) * P(j,l)
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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! !!!
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! Compute QR: at return: Q is Z(m,r)
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! !!!
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call ortho_qr(Z,size(Z,1),m,r)
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! !!!
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enddo
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! !!!
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! Y(r,n) = Zt(r,m) @ A(m,n) or Yt(n,r) = At(n,m) @ Z(m,r)
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! !!!
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allocate(Yt(n,r))
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!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
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!$OMP DO
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do l=1,r
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do k=1,n
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Yt(k,l) = 0.d0
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enddo
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do k=1,N_det
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i = psi_bilinear_matrix_rows(k)
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j = psi_bilinear_matrix_columns(k)
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Yt(j,l) = Yt(j,l) + Z(i,l) * psi_bilinear_matrix_values(k,1)
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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! !!!
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! Y = UY @ D @ Vt or Yt = V @ Dt @ UYt
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! !!!
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allocate(D(r),V(n,r), UYt(r,r))
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! !!!
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call svd(Yt,size(Yt,1),V,size(V,1),D,UYt,size(UYt,1),n,r)
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deallocate(Yt)
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! !!!
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! U(m,r) = Z(m,r) @ UY(r,r) or U = Z @ (UYt).T
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! !!!
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allocate(U(m,r))
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call dgemm('N','T',m,r,r,1.d0,Z,size(Z,1),UYt,size(UYt,1),0.d0,U,size(U,1))
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deallocate(UYt,Z)
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! !!!
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!do i=1,r
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! print *, i, real(D(i)), real(D(i)**2), real(sum(D(1:i)**2))
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! if (D(i) < 1.d-15) then
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! k = i
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! exit
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! endif
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!enddo
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!print *, 'threshold: ', 2.858 * D(k/2)
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! !!!
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! Build the new determinant: U @ D @ Vt
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! !!!
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!!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l)
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!!$OMP DO
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!!
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!print *, 'ok 1'
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!N_det = m * n
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!print *, 'ok 11'
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!TOUCH N_det
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!psi_bilinear_matrix_values(:,1) = 0.d0
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!TOUCH psi_bilinear_matrix_values
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! print *, size(psi_bilinear_matrix_values,1), size(D), size(U,1), size(U,2), size(V,1), size(V,2)
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print*, PSI_energy(1) + nuclear_repulsion
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psi_bilinear_matrix(:,:,:) = 0.d0
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do r = 1, n
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call generate_all_alpha_beta_det_products
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do i = 1, N_det_beta_unique
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do j = 1, N_det_alpha_unique
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psi_bilinear_matrix(j,i,1) = 0.d0
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do l = 1, r
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psi_bilinear_matrix(j,i,1) = psi_bilinear_matrix(j,i,1) + D(l) * U(j,l) * V(i,l)
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enddo
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enddo
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enddo
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TOUCH psi_bilinear_matrix
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call update_wf_of_psi_bilinear_matrix(.False.)
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2021-03-12 13:13:49 +01:00
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print*, r, PSI_energy(1) + nuclear_repulsion, s2_values(1) !CI_energy(1)
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call save_wavefunction()
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2021-02-22 16:25:05 +01:00
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enddo
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deallocate(U,D,V)
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! !!!
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end
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