added non_hermit_dav
This commit is contained in:
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parent
4b715bfcd9
commit
7f653b9eee
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utils
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Load Diff
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subroutine bi_ortho_gram_schmidt(wi,vi,n,ni,wk,wk_schmidt)
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implicit none
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BEGIN_DOC
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! you enter with a set of "ni" BI-ORTHONORMAL vectors of length "n"
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!
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! vi(j,i) = <j|vi>, wi(j,i) = <j|wi>, <vi|wj> = delta_{ij} S_ii, S_ii =<vi|wi>
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!
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! and a vector vk(j) = <j|vk>
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!
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! you go out with a vector vk_schmidt(j) = <j|vk_schmidt>
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!
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! which is Gram-Schmidt orthonormalized with respect to the "vi"
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!
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! <vi|wk_schmidt> = 0
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!
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! |wk_schmidt> = |wk> - \sum_{i=1}^ni (<vi|wk>/<vi|wi>) |wi>
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!
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! according to Eq. (5), (6) of Computers Structures, Vol 56, No. 4, pp 605-613, 1995
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!
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! https://doi.org/10.1016/0045-7949(94)00565-K
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END_DOC
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integer, intent(in) :: n,ni
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double precision, intent(in) :: wi(n,ni),vi(n,ni),wk(n)
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double precision, intent(out):: wk_schmidt(n)
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double precision :: vi_wk,u_dot_v,tmp,u_dot_u
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double precision, allocatable :: sii(:)
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integer :: i,j
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allocate( sii(ni) )
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wk_schmidt = wk
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do i = 1, ni
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sii(i) = u_dot_v(vi(1,i),wi(1,i),n)
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enddo
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! do i = 1, n
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! print*,i,'wk',wk(i)
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! enddo
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! print*,''
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! print*,''
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do i = 1, ni
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! print*,'i',i
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! Gram-Schmidt
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vi_wk = u_dot_v(vi(1,i),wk,n)
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vi_wk = vi_wk / sii(i)
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! print*,''
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do j = 1, n
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! print*,j,vi_wk,wi(j,i)
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wk_schmidt(j) -= vi_wk * wi(j,i)
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enddo
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enddo
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tmp = u_dot_u(wk_schmidt,n)
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tmp = 1.d0/dsqrt(tmp)
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wk_schmidt = tmp * wk_schmidt
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! do j = 1, n
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! print*,j,'wk_scc',wk_schmidt(j)
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! enddo
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! pause
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end
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BEGIN_PROVIDER [ integer, n_mat]
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implicit none
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n_mat = 2
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, h_non_hermit, (n_mat, n_mat)]
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&BEGIN_PROVIDER [ double precision, h_non_hermit_transp, (n_mat, n_mat)]
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&BEGIN_PROVIDER [ double precision, reigvec_ht, (n_mat, n_mat)]
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&BEGIN_PROVIDER [ double precision, leigvec_ht, (n_mat, n_mat)]
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&BEGIN_PROVIDER [ double precision, eigval_ht, (n_mat)]
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&BEGIN_PROVIDER [ integer, n_real_ht, (n_mat)]
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implicit none
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integer :: i,j
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do i = 1, n_mat
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read(33,*)h_non_hermit(i,1:n_mat)
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enddo
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print*,''
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print*,'H_mat '
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print*,''
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do i = 1, n_mat
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write(*,'(1000(F16.10,X))')h_non_hermit(i,:)
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enddo
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do i = 1, n_mat
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do j = 1, n_mat
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h_non_hermit_transp(j,i) = h_non_hermit(i,j)
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enddo
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enddo
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call non_hrmt_real_diag(n_mat,h_non_hermit,reigvec_ht,leigvec_ht,n_real_ht,eigval_ht)
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END_PROVIDER
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subroutine hcalc_r_tmp(v,u,N_st,sze) ! v = H u
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implicit none
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BEGIN_DOC
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! Template of routine for the application of H
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!
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! Here, it is done with the Hamiltonian matrix
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!
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! on the set of determinants of psi_det
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!
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! Computes $v = H | u \rangle$
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!
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END_DOC
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integer, intent(in) :: N_st,sze
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double precision, intent(in) :: u(sze,N_st)
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double precision, intent(inout) :: v(sze,N_st)
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integer :: i,j,istate
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v = 0.d0
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do istate = 1, N_st
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do j = 1, sze
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do i = 1, sze
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v(i,istate) += h_non_hermit(i,j) * u(j,istate)
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! print*,i,j,h_non_hermit(i,j),u(j,istate)
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enddo
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enddo
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enddo
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print*,'HU'
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do i = 1, sze
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print*,v(i,1)
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enddo
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end
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subroutine hcalc_l_tmp(v,u,N_st,sze) ! v = H^\dagger u
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implicit none
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BEGIN_DOC
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! Template of routine for the application of H
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!
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! Here, it is done with the Hamiltonian matrix
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!
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! on the set of determinants of psi_det
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!
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! Computes $v = H | u \rangle$
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!
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END_DOC
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integer, intent(in) :: N_st,sze
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double precision, intent(in) :: u(sze,N_st)
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double precision, intent(inout) :: v(sze,N_st)
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integer :: i,j,istate
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v = 0.d0
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do istate = 1, N_st
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do j = 1, sze
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do i = 1, sze
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v(i,istate) += h_non_hermit_transp(i,j) * u(j,istate)
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enddo
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enddo
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enddo
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print*,'HU'
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do i = 1, sze
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print*,v(i,1)
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enddo
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end
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File diff suppressed because it is too large
Load Diff
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@ -0,0 +1,669 @@
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subroutine non_hrmt_diag_split_degen_bi_orthog(n, A, leigvec, reigvec, n_real_eigv, eigval)
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BEGIN_DOC
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!
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! routine which returns the sorted REAL EIGENVALUES ONLY and corresponding LEFT/RIGHT eigenvetors
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!
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! of a non hermitian matrix A(n,n)
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!
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! n_real_eigv is the number of real eigenvalues, which might be smaller than the dimension "n"
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!
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END_DOC
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implicit none
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integer, intent(in) :: n
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double precision, intent(in) :: A(n,n)
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integer, intent(out) :: n_real_eigv
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double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
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double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
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integer :: i, j, n_degen,k , iteration
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double precision :: shift_current
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double precision :: r,thr,accu_d, accu_nd
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integer, allocatable :: iorder_origin(:),iorder(:)
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double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
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double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
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double precision, allocatable :: im_part(:),re_part(:)
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double precision :: accu,thr_cut, thr_norm=1d0
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thr_cut = 1.d-15
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print*,'Computing the left/right eigenvectors ...'
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print*,'Using the degeneracy splitting algorithm'
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! initialization
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shift_current = 1.d-15
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iteration = 0
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print*,'***** iteration = ',iteration
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! pre-processing the matrix :: sorting by diagonal elements
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allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
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allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
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! print*,'Aw'
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do i = 1, n
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iorder_origin(i) = i
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diag_elem(i) = A(i,i)
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! write(*,'(100(F16.10,X))')A(:,i)
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enddo
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call dsort(diag_elem, iorder_origin, n)
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do i = 1, n
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do j = 1, n
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A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
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enddo
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enddo
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allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
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allocate(im_part(n),iorder(n))
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allocate( S(n,n) )
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Aw = A_save
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call cancel_small_elmts(aw,n,thr_cut)
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call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
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do i = 1, n
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im_part(i) = -dabs(WI(i))
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iorder(i) = i
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enddo
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call dsort(im_part, iorder, n)
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n_real_eigv = 0
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do i = 1, n
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if(dabs(WI(i)).lt.1.d-20)then
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n_real_eigv += 1
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else
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! print*,'Found an imaginary component to eigenvalue'
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! print*,'Re(i) + Im(i)',WR(i),WI(i)
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endif
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enddo
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if(n_real_eigv.ne.n)then
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shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
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print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
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print*,'Splitting the degeneracies by ',shift_current
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else
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print*,'All eigenvalues are real !'
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endif
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do while(n_real_eigv.ne.n)
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iteration += 1
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print*,'***** iteration = ',iteration
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if(shift_current.gt.1.d-3)then
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print*,'shift_current > 1.d-3 !!'
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print*,'Your matrix intrinsically contains complex eigenvalues'
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stop
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endif
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Aw = A_save
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call cancel_small_elmts(Aw,n,thr_cut)
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call split_matrix_degen(Aw,n,shift_current)
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call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
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n_real_eigv = 0
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do i = 1, n
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if(dabs(WI(i)).lt.1.d-20)then
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n_real_eigv+= 1
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else
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! print*,'Found an imaginary component to eigenvalue'
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! print*,'Re(i) + Im(i)',WR(i),WI(i)
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endif
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enddo
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if(n_real_eigv.ne.n)then
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do i = 1, n
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im_part(i) = -dabs(WI(i))
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iorder(i) = i
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enddo
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call dsort(im_part, iorder, n)
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shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
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print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
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print*,'Splitting the degeneracies by ',shift_current
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else
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print*,'All eigenvalues are real !'
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endif
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enddo
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!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
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do i = 1, n
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eigval(i) = WR(i)
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iorder(i) = i
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enddo
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call dsort(eigval,iorder,n)
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do i = 1, n
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! print*,'eigval(i) = ',eigval(i)
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reigvec_tmp(:,i) = VR(:,iorder(i))
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leigvec_tmp(:,i) = Vl(:,iorder(i))
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enddo
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!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
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! check bi-orthogonality
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call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, .false.)
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print *, ' accu_nd bi-orthog = ', accu_nd
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if( accu_nd .lt. 1d-10 ) then
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print *, ' bi-orthogonality: ok'
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else
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print *, ' '
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print *, ' bi-orthogonality: not imposed yet'
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print *, ' '
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print *, ' '
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print *, ' orthog between degen eigenvect'
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print *, ' '
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double precision, allocatable :: S_nh_inv_half(:,:)
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allocate(S_nh_inv_half(n,n))
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logical :: complex_root
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deallocate(S_nh_inv_half)
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call impose_orthog_degen_eigvec(n, eigval, reigvec_tmp)
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call impose_orthog_degen_eigvec(n, eigval, leigvec_tmp)
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call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, .false.)
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if( accu_nd .lt. 1d-10 ) then
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print *, ' bi-orthogonality: ok'
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else
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print*,'New vectors not bi-orthonormals at ',accu_nd
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call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp, S)
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call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, .false.)
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if( accu_nd .lt. 1d-10 ) then
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print *, ' bi-orthogonality: ok'
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else
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print*,'New vectors not bi-orthonormals at ',accu_nd
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print*,'Must be a deep problem ...'
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stop
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endif
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endif
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endif
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!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
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do i = 1, n
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do j = 1, n
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VR(iorder_origin(j),i) = reigvec_tmp(j,i)
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VL(iorder_origin(j),i) = leigvec_tmp(j,i)
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enddo
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enddo
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!! RECOMPUTING THE EIGENVALUES
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eigval = 0.d0
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do i = 1, n
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iorder(i) = i
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accu = 0.d0
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do j = 1, n
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accu += VL(j,i) * VR(j,i)
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do k = 1, n
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eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
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enddo
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enddo
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eigval(i) *= 1.d0/accu
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! print*,'eigval(i) = ',eigval(i)
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enddo
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!! RESORT JUST TO BE SURE
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call dsort(eigval, iorder, n)
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do i = 1, n
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do j = 1, n
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reigvec(j,i) = VR(j,iorder(i))
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leigvec(j,i) = VL(j,iorder(i))
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enddo
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enddo
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print*,'Checking for final reigvec/leigvec'
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shift_current = max(1.d-10,shift_current)
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print*,'Thr for eigenvectors = ',shift_current
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call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, shift_current, thr_norm, .false.)
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call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S, .false.)
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print *, ' accu_nd bi-orthog = ', accu_nd
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if( accu_nd .lt. 1d-10 ) then
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print *, ' bi-orthogonality: ok'
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else
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print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
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print*,'Eigenvectors are not bi orthonormal ..'
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print*,'accu_nd = ',accu_nd
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stop
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endif
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end
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subroutine non_hrmt_diag_split_degen_s_inv_half(n, A, leigvec, reigvec, n_real_eigv, eigval)
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BEGIN_DOC
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!
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! routine which returns the sorted REAL EIGENVALUES ONLY and corresponding LEFT/RIGHT eigenvetors
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!
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! of a non hermitian matrix A(n,n)
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!
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! n_real_eigv is the number of real eigenvalues, which might be smaller than the dimension "n"
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!
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END_DOC
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implicit none
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integer, intent(in) :: n
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double precision, intent(in) :: A(n,n)
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integer, intent(out) :: n_real_eigv
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double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
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double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
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integer :: i, j, n_degen,k , iteration
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double precision :: shift_current
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double precision :: r,thr,accu_d, accu_nd
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integer, allocatable :: iorder_origin(:),iorder(:)
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double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
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double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
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double precision, allocatable :: im_part(:),re_part(:)
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double precision :: accu,thr_cut, thr_norm=1.d0
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double precision, allocatable :: S_nh_inv_half(:,:)
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logical :: complex_root
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thr_cut = 1.d-15
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print*,'Computing the left/right eigenvectors ...'
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print*,'Using the degeneracy splitting algorithm'
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! initialization
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shift_current = 1.d-15
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iteration = 0
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print*,'***** iteration = ',iteration
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! pre-processing the matrix :: sorting by diagonal elements
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allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
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allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
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! print*,'Aw'
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do i = 1, n
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iorder_origin(i) = i
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diag_elem(i) = A(i,i)
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! write(*,'(100(F16.10,X))')A(:,i)
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enddo
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call dsort(diag_elem, iorder_origin, n)
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do i = 1, n
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do j = 1, n
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A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
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enddo
|
||||
enddo
|
||||
|
||||
allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
|
||||
allocate(im_part(n),iorder(n))
|
||||
allocate( S(n,n) )
|
||||
allocate(S_nh_inv_half(n,n))
|
||||
|
||||
|
||||
Aw = A_save
|
||||
call cancel_small_elmts(aw,n,thr_cut)
|
||||
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
||||
do i = 1, n
|
||||
im_part(i) = -dabs(WI(i))
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(im_part, iorder, n)
|
||||
n_real_eigv = 0
|
||||
do i = 1, n
|
||||
if(dabs(WI(i)).lt.1.d-20)then
|
||||
n_real_eigv += 1
|
||||
else
|
||||
! print*,'Found an imaginary component to eigenvalue'
|
||||
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
||||
endif
|
||||
enddo
|
||||
if(n_real_eigv.ne.n)then
|
||||
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
||||
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
||||
print*,'Splitting the degeneracies by ',shift_current
|
||||
else
|
||||
print*,'All eigenvalues are real !'
|
||||
endif
|
||||
|
||||
|
||||
do while(n_real_eigv.ne.n)
|
||||
iteration += 1
|
||||
print*,'***** iteration = ',iteration
|
||||
if(shift_current.gt.1.d-3)then
|
||||
print*,'shift_current > 1.d-3 !!'
|
||||
print*,'Your matrix intrinsically contains complex eigenvalues'
|
||||
stop
|
||||
endif
|
||||
Aw = A_save
|
||||
! thr_cut = shift_current
|
||||
call cancel_small_elmts(Aw,n,thr_cut)
|
||||
call split_matrix_degen(Aw,n,shift_current)
|
||||
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
||||
n_real_eigv = 0
|
||||
do i = 1, n
|
||||
if(dabs(WI(i)).lt.1.d-20)then
|
||||
n_real_eigv+= 1
|
||||
else
|
||||
! print*,'Found an imaginary component to eigenvalue'
|
||||
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
||||
endif
|
||||
enddo
|
||||
if(n_real_eigv.ne.n)then
|
||||
do i = 1, n
|
||||
im_part(i) = -dabs(WI(i))
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(im_part, iorder, n)
|
||||
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
||||
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
||||
print*,'Splitting the degeneracies by ',shift_current
|
||||
else
|
||||
print*,'All eigenvalues are real !'
|
||||
endif
|
||||
enddo
|
||||
!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
|
||||
do i = 1, n
|
||||
eigval(i) = WR(i)
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(eigval,iorder,n)
|
||||
do i = 1, n
|
||||
! print*,'eigval(i) = ',eigval(i)
|
||||
reigvec_tmp(:,i) = VR(:,iorder(i))
|
||||
leigvec_tmp(:,i) = Vl(:,iorder(i))
|
||||
enddo
|
||||
|
||||
!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
|
||||
! check bi-orthogonality
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, .false.)
|
||||
print *, ' accu_nd bi-orthog = ', accu_nd
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print *, ' '
|
||||
print *, ' bi-orthogonality: not imposed yet'
|
||||
if(complex_root)then
|
||||
print *, ' '
|
||||
print *, ' '
|
||||
print *, ' orthog between degen eigenvect'
|
||||
print *, ' '
|
||||
! bi-orthonormalization using orthogonalization of left, right and then QR between left and right
|
||||
call impose_orthog_degen_eigvec(n, eigval, reigvec_tmp) ! orthogonalization of reigvec
|
||||
call impose_orthog_degen_eigvec(n, eigval, leigvec_tmp) ! orthogonalization of leigvec
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S)
|
||||
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'New vectors not bi-orthonormals at ', accu_nd
|
||||
call get_inv_half_nonsymmat_diago(S, n, S_nh_inv_half, complex_root)
|
||||
if(complex_root)then
|
||||
call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp) ! bi-orthonormalization using QR
|
||||
else
|
||||
print*,'S^{-1/2} exists !!'
|
||||
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
||||
endif
|
||||
endif
|
||||
else ! the matrix S^{-1/2} exists
|
||||
print*,'S^{-1/2} exists !!'
|
||||
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
||||
endif
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, .false.)
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'New vectors not bi-orthonormals at ',accu_nd
|
||||
print*,'Must be a deep problem ...'
|
||||
stop
|
||||
endif
|
||||
endif
|
||||
|
||||
!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
VR(iorder_origin(j),i) = reigvec_tmp(j,i)
|
||||
VL(iorder_origin(j),i) = leigvec_tmp(j,i)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!! RECOMPUTING THE EIGENVALUES
|
||||
eigval = 0.d0
|
||||
do i = 1, n
|
||||
iorder(i) = i
|
||||
accu = 0.d0
|
||||
do j = 1, n
|
||||
accu += VL(j,i) * VR(j,i)
|
||||
do k = 1, n
|
||||
eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
|
||||
enddo
|
||||
enddo
|
||||
eigval(i) *= 1.d0/accu
|
||||
! print*,'eigval(i) = ',eigval(i)
|
||||
enddo
|
||||
!! RESORT JUST TO BE SURE
|
||||
call dsort(eigval, iorder, n)
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
reigvec(j,i) = VR(j,iorder(i))
|
||||
leigvec(j,i) = VL(j,iorder(i))
|
||||
enddo
|
||||
enddo
|
||||
print*,'Checking for final reigvec/leigvec'
|
||||
shift_current = max(1.d-10,shift_current)
|
||||
print*,'Thr for eigenvectors = ',shift_current
|
||||
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, shift_current, thr_norm, .false.)
|
||||
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S, .false.)
|
||||
print *, ' accu_nd bi-orthog = ', accu_nd
|
||||
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
|
||||
print*,'Eigenvectors are not bi orthonormal ..'
|
||||
print*,'accu_nd = ',accu_nd
|
||||
stop
|
||||
endif
|
||||
|
||||
end
|
||||
|
||||
|
||||
subroutine non_hrmt_fock_mat(n, A, leigvec, reigvec, n_real_eigv, eigval)
|
||||
|
||||
BEGIN_DOC
|
||||
!
|
||||
! routine returning the eigenvalues and left/right eigenvectors of the TC fock matrix
|
||||
!
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: A(n,n)
|
||||
integer, intent(out) :: n_real_eigv
|
||||
double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
|
||||
double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
|
||||
|
||||
integer :: i, j, n_degen,k , iteration
|
||||
double precision :: shift_current
|
||||
double precision :: r,thr,accu_d, accu_nd
|
||||
integer, allocatable :: iorder_origin(:),iorder(:)
|
||||
double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
|
||||
double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
|
||||
double precision, allocatable :: im_part(:),re_part(:)
|
||||
double precision :: accu,thr_cut
|
||||
double precision, allocatable :: S_nh_inv_half(:,:)
|
||||
logical :: complex_root
|
||||
|
||||
|
||||
thr_cut = 1.d-15
|
||||
print*,'Computing the left/right eigenvectors ...'
|
||||
print*,'Using the degeneracy splitting algorithm'
|
||||
! initialization
|
||||
shift_current = 1.d-15
|
||||
iteration = 0
|
||||
print*,'***** iteration = ',iteration
|
||||
|
||||
|
||||
! pre-processing the matrix :: sorting by diagonal elements
|
||||
allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
|
||||
allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
|
||||
! print*,'Aw'
|
||||
do i = 1, n
|
||||
iorder_origin(i) = i
|
||||
diag_elem(i) = A(i,i)
|
||||
! write(*,'(100(F16.10,X))')A(:,i)
|
||||
enddo
|
||||
call dsort(diag_elem, iorder_origin, n)
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
|
||||
enddo
|
||||
enddo
|
||||
|
||||
allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
|
||||
allocate(im_part(n),iorder(n))
|
||||
allocate( S(n,n) )
|
||||
allocate(S_nh_inv_half(n,n))
|
||||
|
||||
|
||||
Aw = A_save
|
||||
call cancel_small_elmts(aw,n,thr_cut)
|
||||
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
||||
do i = 1, n
|
||||
im_part(i) = -dabs(WI(i))
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(im_part, iorder, n)
|
||||
n_real_eigv = 0
|
||||
do i = 1, n
|
||||
if(dabs(WI(i)).lt.1.d-20)then
|
||||
n_real_eigv += 1
|
||||
else
|
||||
! print*,'Found an imaginary component to eigenvalue'
|
||||
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
||||
endif
|
||||
enddo
|
||||
if(n_real_eigv.ne.n)then
|
||||
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
||||
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
||||
print*,'Splitting the degeneracies by ',shift_current
|
||||
else
|
||||
print*,'All eigenvalues are real !'
|
||||
endif
|
||||
|
||||
|
||||
do while(n_real_eigv.ne.n)
|
||||
iteration += 1
|
||||
print*,'***** iteration = ',iteration
|
||||
if(shift_current.gt.1.d-3)then
|
||||
print*,'shift_current > 1.d-3 !!'
|
||||
print*,'Your matrix intrinsically contains complex eigenvalues'
|
||||
stop
|
||||
endif
|
||||
Aw = A_save
|
||||
! thr_cut = shift_current
|
||||
call cancel_small_elmts(Aw,n,thr_cut)
|
||||
call split_matrix_degen(Aw,n,shift_current)
|
||||
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
||||
n_real_eigv = 0
|
||||
do i = 1, n
|
||||
if(dabs(WI(i)).lt.1.d-20)then
|
||||
n_real_eigv+= 1
|
||||
else
|
||||
! print*,'Found an imaginary component to eigenvalue'
|
||||
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
||||
endif
|
||||
enddo
|
||||
if(n_real_eigv.ne.n)then
|
||||
do i = 1, n
|
||||
im_part(i) = -dabs(WI(i))
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(im_part, iorder, n)
|
||||
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
||||
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
||||
print*,'Splitting the degeneracies by ',shift_current
|
||||
else
|
||||
print*,'All eigenvalues are real !'
|
||||
endif
|
||||
enddo
|
||||
!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
|
||||
do i = 1, n
|
||||
eigval(i) = WR(i)
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(eigval,iorder,n)
|
||||
do i = 1, n
|
||||
! print*,'eigval(i) = ',eigval(i)
|
||||
reigvec_tmp(:,i) = VR(:,iorder(i))
|
||||
leigvec_tmp(:,i) = Vl(:,iorder(i))
|
||||
enddo
|
||||
|
||||
!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
|
||||
! check bi-orthogonality
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S)
|
||||
print *, ' accu_nd bi-orthog = ', accu_nd
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print *, ' '
|
||||
print *, ' bi-orthogonality: not imposed yet'
|
||||
print *, ' '
|
||||
print *, ' '
|
||||
print *, ' Using impose_unique_biorthog_degen_eigvec'
|
||||
print *, ' '
|
||||
! bi-orthonormalization using orthogonalization of left, right and then QR between left and right
|
||||
call impose_unique_biorthog_degen_eigvec(n, eigval, mo_coef, leigvec_tmp, reigvec_tmp)
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S)
|
||||
print*,'accu_nd = ',accu_nd
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'New vectors not bi-orthonormals at ',accu_nd
|
||||
call get_inv_half_nonsymmat_diago(S, n, S_nh_inv_half,complex_root)
|
||||
if(complex_root)then
|
||||
print*,'S^{-1/2} does not exits, using QR bi-orthogonalization'
|
||||
call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp, S) ! bi-orthonormalization using QR
|
||||
else
|
||||
print*,'S^{-1/2} exists !!'
|
||||
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
||||
endif
|
||||
endif
|
||||
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S)
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'New vectors not bi-orthonormals at ',accu_nd
|
||||
print*,'Must be a deep problem ...'
|
||||
stop
|
||||
endif
|
||||
endif
|
||||
|
||||
!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
VR(iorder_origin(j),i) = reigvec_tmp(j,i)
|
||||
VL(iorder_origin(j),i) = leigvec_tmp(j,i)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!! RECOMPUTING THE EIGENVALUES
|
||||
eigval = 0.d0
|
||||
do i = 1, n
|
||||
iorder(i) = i
|
||||
accu = 0.d0
|
||||
do j = 1, n
|
||||
accu += VL(j,i) * VR(j,i)
|
||||
do k = 1, n
|
||||
eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
|
||||
enddo
|
||||
enddo
|
||||
eigval(i) *= 1.d0/accu
|
||||
! print*,'eigval(i) = ',eigval(i)
|
||||
enddo
|
||||
!! RESORT JUST TO BE SURE
|
||||
call dsort(eigval, iorder, n)
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
reigvec(j,i) = VR(j,iorder(i))
|
||||
leigvec(j,i) = VL(j,iorder(i))
|
||||
enddo
|
||||
enddo
|
||||
print*,'Checking for final reigvec/leigvec'
|
||||
shift_current = max(1.d-10,shift_current)
|
||||
print*,'Thr for eigenvectors = ',shift_current
|
||||
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec,shift_current)
|
||||
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S)
|
||||
print *, ' accu_nd bi-orthog = ', accu_nd
|
||||
|
||||
if( accu_nd .lt. 1d-10 ) then
|
||||
print *, ' bi-orthogonality: ok'
|
||||
else
|
||||
print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
|
||||
print*,'Eigenvectors are not bi orthonormal ..'
|
||||
print*,'accu_nd = ',accu_nd
|
||||
stop
|
||||
endif
|
||||
|
||||
end
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,53 @@
|
|||
subroutine h_non_hermite(v,u,Hmat,a,N_st,sze)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Template of routine for the application of H
|
||||
!
|
||||
! Here, it is done with the Hamiltonian matrix
|
||||
!
|
||||
! on the set of determinants of psi_det
|
||||
!
|
||||
! Computes $v = a * H | u \rangle$
|
||||
!
|
||||
END_DOC
|
||||
integer, intent(in) :: N_st,sze
|
||||
double precision, intent(in) :: u(sze,N_st), Hmat(sze,sze), a
|
||||
double precision, intent(inout) :: v(sze,N_st)
|
||||
integer :: i,j,k
|
||||
do k = 1, N_st
|
||||
do j = 1, sze
|
||||
do i = 1, sze
|
||||
v(i,k) += a * u(j,k) * Hmat(i,j)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
end
|
||||
|
||||
|
||||
subroutine exp_tau_H(u,v,hmat,tau,et,N_st,sze)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! realises v = (1 - tau (H - et)) u
|
||||
END_DOC
|
||||
integer, intent(in) :: N_st,sze
|
||||
double precision, intent(in) :: hmat(sze,sze), u(sze,N_st), tau, et
|
||||
double precision, intent(out):: v(sze,N_st)
|
||||
double precision :: a
|
||||
integer :: i,j
|
||||
v = (1.d0 + tau * et) * u
|
||||
a = -1.d0 * tau
|
||||
call h_non_hermite(v,u,Hmat,a,N_st,sze)
|
||||
end
|
||||
|
||||
double precision function project_phi0(u,Hmat0,N_st,sze)
|
||||
implicit none
|
||||
integer, intent(in) :: N_st,sze
|
||||
double precision, intent(in) :: u(sze,N_st), Hmat0(sze)
|
||||
integer :: j
|
||||
project_phi0 = 0.d0
|
||||
do j = 1, sze
|
||||
project_phi0 += u(j,1) * Hmat0(j)
|
||||
enddo
|
||||
project_phi0 *= 1.d0 / u(1,1)
|
||||
end
|
||||
|
||||
|
|
@ -0,0 +1,325 @@
|
|||
|
||||
subroutine get_inv_half_svd(matrix, n, matrix_inv_half)
|
||||
|
||||
BEGIN_DOC
|
||||
! :math:`X = S^{-1/2}` obtained by SVD
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: matrix(n,n)
|
||||
double precision, intent(out) :: matrix_inv_half(n,n)
|
||||
|
||||
integer :: num_linear_dependencies
|
||||
integer :: LDA, LDC
|
||||
integer :: info, i, j, k
|
||||
double precision, parameter :: threshold = 1.d-6
|
||||
double precision, allocatable :: U(:,:),Vt(:,:), D(:),matrix_half(:,:),D_half(:)
|
||||
|
||||
double precision :: accu_d,accu_nd
|
||||
|
||||
LDA = size(matrix, 1)
|
||||
LDC = size(matrix_inv_half, 1)
|
||||
if(LDA .ne. LDC) then
|
||||
print*, ' LDA != LDC'
|
||||
stop
|
||||
endif
|
||||
|
||||
print*, ' n = ', n
|
||||
print*, ' LDA = ', LDA
|
||||
print*, ' LDC = ', LDC
|
||||
|
||||
double precision,allocatable :: WR(:),WI(:),VL(:,:),VR(:,:)
|
||||
allocate(WR(n),WI(n),VL(n,n),VR(n,n))
|
||||
call lapack_diag_non_sym(n,matrix,WR,WI,VL,VR)
|
||||
do i = 1, n
|
||||
print*,'WR,WI',WR(i),WI(i)
|
||||
enddo
|
||||
|
||||
|
||||
allocate(U(LDC,n), Vt(LDA,n), D(n))
|
||||
|
||||
call svd(matrix, LDA, U, LDC, D, Vt, LDA, n, n)
|
||||
double precision, allocatable :: tmp1(:,:),tmp2(:,:),D_mat(:,:)
|
||||
allocate(tmp1(n,n),tmp2(n,n),D_mat(n,n),matrix_half(n,n),D_half(n))
|
||||
D_mat = 0.d0
|
||||
do i = 1,n
|
||||
D_mat(i,i) = D(i)
|
||||
enddo
|
||||
! matrix = U D Vt
|
||||
! tmp1 = U D
|
||||
tmp1 = 0.d0
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
, U, size(U, 1), D_mat, size(D_mat, 1) &
|
||||
, 0.d0, tmp1, size(tmp1, 1) )
|
||||
! tmp2 = tmp1 X Vt = matrix
|
||||
tmp2 = 0.d0
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
, tmp1, size(tmp1, 1), Vt, size(Vt, 1) &
|
||||
, 0.d0, tmp2, size(tmp2, 1) )
|
||||
print*,'Checking the recomposition of the matrix'
|
||||
accu_nd = 0.d0
|
||||
accu_d = 0.d0
|
||||
do i = 1, n
|
||||
accu_d += dabs(tmp2(i,i) - matrix(i,i))
|
||||
do j = 1, n
|
||||
if(i==j)cycle
|
||||
accu_nd += dabs(tmp2(j,i) - matrix(j,i))
|
||||
enddo
|
||||
enddo
|
||||
print*,'accu_d =',accu_d
|
||||
print*,'accu_nd =',accu_nd
|
||||
print*,'passed the recomposition'
|
||||
|
||||
num_linear_dependencies = 0
|
||||
do i = 1, n
|
||||
if(abs(D(i)) <= threshold) then
|
||||
D(i) = 0.d0
|
||||
num_linear_dependencies += 1
|
||||
else
|
||||
ASSERT (D(i) > 0.d0)
|
||||
D_half(i) = dsqrt(D(i))
|
||||
D(i) = 1.d0 / dsqrt(D(i))
|
||||
endif
|
||||
enddo
|
||||
write(*,*) ' linear dependencies', num_linear_dependencies
|
||||
|
||||
matrix_inv_half = 0.d0
|
||||
matrix_half = 0.d0
|
||||
do k = 1, n
|
||||
if(D(k) /= 0.d0) then
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
! matrix_inv_half(i,j) = matrix_inv_half(i,j) + U(i,k) * D(k) * Vt(k,j)
|
||||
matrix_inv_half(i,j) = matrix_inv_half(i,j) + U(i,k) * D(k) * Vt(j,k)
|
||||
matrix_half(i,j) = matrix_half(i,j) + U(i,k) * D_half(k) * Vt(j,k)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
enddo
|
||||
print*,'testing S^1/2 * S^1/2= S'
|
||||
! tmp1 = S^1/2 X S^1/2
|
||||
tmp1 = 0.d0
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
, matrix_half, size(matrix_half, 1), matrix_half, size(matrix_half, 1) &
|
||||
, 0.d0, tmp1, size(tmp1, 1) )
|
||||
accu_nd = 0.d0
|
||||
accu_d = 0.d0
|
||||
do i = 1, n
|
||||
accu_d += dabs(tmp1(i,i) - matrix(i,i))
|
||||
do j = 1, n
|
||||
if(i==j)cycle
|
||||
accu_nd += dabs(tmp1(j,i) - matrix(j,i))
|
||||
enddo
|
||||
enddo
|
||||
print*,'accu_d =',accu_d
|
||||
print*,'accu_nd =',accu_nd
|
||||
|
||||
! print*,'S inv half'
|
||||
! do i = 1, n
|
||||
! write(*, '(1000(F16.10,X))') matrix_inv_half(i,:)
|
||||
! enddo
|
||||
|
||||
double precision, allocatable :: pseudo_inverse(:,:),identity(:,:)
|
||||
allocate( pseudo_inverse(n,n),identity(n,n))
|
||||
call get_pseudo_inverse(matrix,n,n,n,pseudo_inverse,n,threshold)
|
||||
|
||||
! S^-1 X S = 1
|
||||
! identity = 0.d0
|
||||
! call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
! , matrix, size(matrix, 1), pseudo_inverse, size(pseudo_inverse, 1) &
|
||||
! , 0.d0, identity, size(identity, 1) )
|
||||
print*,'Checking S^-1/2 X S^-1/2 = S^-1 ?'
|
||||
! S^-1/2 X S^-1/2 = S^-1 ?
|
||||
tmp1 = 0.d0
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
,matrix_inv_half, size(matrix_inv_half, 1), matrix_inv_half, size(matrix_inv_half, 1) &
|
||||
, 0.d0, tmp1, size(tmp1, 1) )
|
||||
accu_nd = 0.d0
|
||||
accu_d = 0.d0
|
||||
do i = 1, n
|
||||
accu_d += dabs(1.d0 - pseudo_inverse(i,i))
|
||||
do j = 1, n
|
||||
if(i==j)cycle
|
||||
accu_nd += dabs(tmp1(j,i) - pseudo_inverse(j,i))
|
||||
enddo
|
||||
enddo
|
||||
print*,'accu_d =',accu_d
|
||||
print*,'accu_nd =',accu_nd
|
||||
|
||||
stop
|
||||
!
|
||||
! ! ( S^-1/2 x S ) x S^-1/2
|
||||
! Stmp2 = 0.d0
|
||||
! call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
! , Stmp, size(Stmp, 1), matrix_inv_half, size(matrix_inv_half, 1) &
|
||||
! , 0.d0, Stmp2, size(Stmp2, 1) )
|
||||
|
||||
! S^-1/2 x ( S^-1/2 x S )
|
||||
! Stmp2 = 0.d0
|
||||
! call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
! , matrix_inv_half, size(matrix_inv_half, 1), Stmp, size(Stmp, 1) &
|
||||
! , 0.d0, Stmp2, size(Stmp2, 1) )
|
||||
|
||||
! do i = 1, n
|
||||
! do j = 1, n
|
||||
! if(i==j) then
|
||||
! accu_d += Stmp2(j,i)
|
||||
! else
|
||||
! accu_nd = accu_nd + Stmp2(j,i) * Stmp2(j,i)
|
||||
! endif
|
||||
! enddo
|
||||
! enddo
|
||||
! accu_nd = dsqrt(accu_nd)
|
||||
! print*, ' after S^-1/2: sum of off-diag S elements = ', accu_nd
|
||||
! print*, ' after S^-1/2: sum of diag S elements = ', accu_d
|
||||
! do i = 1, n
|
||||
! write(*,'(1000(F16.10,X))') Stmp2(i,:)
|
||||
! enddo
|
||||
|
||||
!double precision :: thresh
|
||||
!thresh = 1.d-10
|
||||
!if( accu_nd.gt.thresh .or. dabs(accu_d-dble(n)).gt.thresh) then
|
||||
! stop
|
||||
!endif
|
||||
|
||||
end subroutine get_inv_half_svd
|
||||
|
||||
! ---
|
||||
|
||||
subroutine get_inv_half_nonsymmat_diago(matrix, n, matrix_inv_half, complex_root)
|
||||
|
||||
BEGIN_DOC
|
||||
! input: S = matrix
|
||||
! output: S^{-1/2} = matrix_inv_half obtained by diagonalization
|
||||
!
|
||||
! S = VR D VL^T
|
||||
! = VR D^{1/2} D^{1/2} VL^T
|
||||
! = VR D^{1/2} VL^T VR D^{1/2} VL^T
|
||||
! = S^{1/2} S^{1/2} with S = VR D^{1/2} VL^T
|
||||
!
|
||||
! == > S^{-1/2} = VR D^{-1/2} VL^T
|
||||
!
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: matrix(n,n)
|
||||
logical, intent(out) :: complex_root
|
||||
double precision, intent(out) :: matrix_inv_half(n,n)
|
||||
|
||||
integer :: i, j
|
||||
double precision :: accu_d, accu_nd
|
||||
double precision, allocatable :: WR(:), WI(:), VL(:,:), VR(:,:), S(:,:), S_diag(:)
|
||||
double precision, allocatable :: tmp1(:,:), D_mat(:,:)
|
||||
|
||||
complex_root = .False.
|
||||
|
||||
matrix_inv_half = 0.D0
|
||||
print*,'Computing S^{-1/2}'
|
||||
|
||||
allocate(WR(n), WI(n), VL(n,n), VR(n,n))
|
||||
call lapack_diag_non_sym(n, matrix, WR, WI, VL, VR)
|
||||
|
||||
allocate(S(n,n))
|
||||
call check_biorthog(n, n, VL, VR, accu_d, accu_nd, S)
|
||||
print*,'accu_nd S^{-1/2}',accu_nd
|
||||
if(accu_nd.gt.1.d-10) then
|
||||
complex_root = .True. ! if vectors are not bi-orthogonal return
|
||||
print*,'Eigenvectors of S are not bi-orthonormal, skipping S^{-1/2}'
|
||||
return
|
||||
endif
|
||||
|
||||
allocate(S_diag(n))
|
||||
do i = 1, n
|
||||
S_diag(i) = 1.d0/dsqrt(S(i,i))
|
||||
if(dabs(WI(i)).gt.1.d-20.or.WR(i).lt.0.d0)then ! check that eigenvalues are real and positive
|
||||
complex_root = .True.
|
||||
print*,'Eigenvalues of S have imaginary part '
|
||||
print*,'WR(i),WI(i)',WR(i), WR(i)
|
||||
print*,'Skipping S^{-1/2}'
|
||||
return
|
||||
endif
|
||||
enddo
|
||||
deallocate(S)
|
||||
|
||||
if(complex_root) return
|
||||
|
||||
! normalization of vectors
|
||||
do i = 1, n
|
||||
if(S_diag(i).eq.1.d0) cycle
|
||||
do j = 1,n
|
||||
VL(j,i) *= S_diag(i)
|
||||
VR(j,i) *= S_diag(i)
|
||||
enddo
|
||||
enddo
|
||||
deallocate(S_diag)
|
||||
|
||||
allocate(tmp1(n,n), D_mat(n,n))
|
||||
|
||||
D_mat = 0.d0
|
||||
do i = 1, n
|
||||
D_mat(i,i) = 1.d0/dsqrt(WR(i))
|
||||
enddo
|
||||
deallocate(WR, WI)
|
||||
|
||||
! tmp1 = VR D^{-1/2}
|
||||
tmp1 = 0.d0
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
, VR, size(VR, 1), D_mat, size(D_mat, 1) &
|
||||
, 0.d0, tmp1, size(tmp1, 1) )
|
||||
deallocate(VR, D_mat)
|
||||
|
||||
! S^{-1/2} = tmp1 X VL^T
|
||||
matrix_inv_half = 0.d0
|
||||
call dgemm( 'N', 'T', n, n, n, 1.d0 &
|
||||
, tmp1, size(tmp1, 1), VL, size(VL, 1) &
|
||||
, 0.d0, matrix_inv_half, size(matrix_inv_half, 1) )
|
||||
deallocate(tmp1, VL)
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine bi_ortho_s_inv_half(n,leigvec,reigvec,S_nh_inv_half)
|
||||
implicit none
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: S_nh_inv_half(n,n)
|
||||
double precision, intent(inout) :: leigvec(n,n),reigvec(n,n)
|
||||
BEGIN_DOC
|
||||
! bi-orthonormalization of left and right vectors
|
||||
!
|
||||
! S = VL^T VR
|
||||
!
|
||||
! S^{-1/2} S S^{-1/2} = 1 = S^{-1/2} VL^T VR S^{-1/2} = VL_new^T VR_new
|
||||
!
|
||||
! VL_new = VL (S^{-1/2})^T
|
||||
!
|
||||
! VR_new = VR S^{^{-1/2}}
|
||||
END_DOC
|
||||
double precision,allocatable :: vl_tmp(:,:),vr_tmp(:,:)
|
||||
print*,'Bi-orthonormalization using S^{-1/2}'
|
||||
allocate(vl_tmp(n,n),vr_tmp(n,n))
|
||||
vl_tmp = leigvec
|
||||
vr_tmp = reigvec
|
||||
! VL_new = VL (S^{-1/2})^T
|
||||
call dgemm( 'N', 'T', n, n, n, 1.d0 &
|
||||
, vl_tmp, size(vl_tmp, 1), S_nh_inv_half, size(S_nh_inv_half, 1) &
|
||||
, 0.d0, leigvec, size(leigvec, 1) )
|
||||
! VR_new = VR S^{^{-1/2}}
|
||||
call dgemm( 'N', 'N', n, n, n, 1.d0 &
|
||||
, vr_tmp, size(vr_tmp, 1), S_nh_inv_half, size(S_nh_inv_half, 1) &
|
||||
, 0.d0, reigvec, size(reigvec, 1) )
|
||||
double precision :: accu_d, accu_nd
|
||||
double precision,allocatable :: S(:,:)
|
||||
allocate(S(n,n))
|
||||
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S)
|
||||
if(dabs(accu_d - n).gt.1.d-10 .or. accu_nd .gt.1.d-8 )then
|
||||
print*,'Pb in bi_ortho_s_inv_half !!'
|
||||
print*,'accu_d =',accu_d
|
||||
print*,'accu_nd =',accu_nd
|
||||
stop
|
||||
endif
|
||||
end
|
||||
Loading…
Reference in New Issue