mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-15 18:43:51 +01:00
57 lines
1.4 KiB
Fortran
57 lines
1.4 KiB
Fortran
|
subroutine bi_ortho_gram_schmidt(wi,vi,n,ni,wk,wk_schmidt)
|
||
|
|
implicit none
|
||
|
|
BEGIN_DOC
|
||
|
|
! you enter with a set of "ni" BI-ORTHONORMAL vectors of length "n"
|
||
|
|
!
|
||
|
|
! vi(j,i) = <j|vi>, wi(j,i) = <j|wi>, <vi|wj> = delta_{ij} S_ii, S_ii =<vi|wi>
|
||
|
|
!
|
||
|
|
! and a vector vk(j) = <j|vk>
|
||
|
|
!
|
||
|
|
! you go out with a vector vk_schmidt(j) = <j|vk_schmidt>
|
||
|
|
!
|
||
|
|
! which is Gram-Schmidt orthonormalized with respect to the "vi"
|
||
|
|
!
|
||
|
|
! <vi|wk_schmidt> = 0
|
||
|
|
!
|
||
|
|
! |wk_schmidt> = |wk> - \sum_{i=1}^ni (<vi|wk>/<vi|wi>) |wi>
|
||
|
|
!
|
||
|
|
! according to Eq. (5), (6) of Computers Structures, Vol 56, No. 4, pp 605-613, 1995
|
||
|
|
!
|
||
|
|
! https://doi.org/10.1016/0045-7949(94)00565-K
|
||
|
|
END_DOC
|
||
|
|
integer, intent(in) :: n,ni
|
||
|
|
double precision, intent(in) :: wi(n,ni),vi(n,ni),wk(n)
|
||
|
|
double precision, intent(out):: wk_schmidt(n)
|
||
|
|
double precision :: vi_wk,u_dot_v,tmp,u_dot_u
|
||
|
|
double precision, allocatable :: sii(:)
|
||
|
|
integer :: i,j
|
||
|
|
allocate( sii(ni) )
|
||
|
|
wk_schmidt = wk
|
||
|
|
do i = 1, ni
|
||
|
|
sii(i) = u_dot_v(vi(1,i),wi(1,i),n)
|
||
|
|
enddo
|
||
|
|
! do i = 1, n
|
||
|
|
! print*,i,'wk',wk(i)
|
||
|
|
! enddo
|
||
|
|
! print*,''
|
||
|
|
! print*,''
|
||
|
|
do i = 1, ni
|
||
|
|
! print*,'i',i
|
||
|
|
! Gram-Schmidt
|
||
|
|
vi_wk = u_dot_v(vi(1,i),wk,n)
|
||
|
|
vi_wk = vi_wk / sii(i)
|
||
|
|
! print*,''
|
||
|
|
do j = 1, n
|
||
|
|
! print*,j,vi_wk,wi(j,i)
|
||
|
|
wk_schmidt(j) -= vi_wk * wi(j,i)
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
tmp = u_dot_u(wk_schmidt,n)
|
||
|
|
tmp = 1.d0/dsqrt(tmp)
|
||
|
|
wk_schmidt = tmp * wk_schmidt
|
||
|
|
! do j = 1, n
|
||
|
|
! print*,j,'wk_scc',wk_schmidt(j)
|
||
|
|
! enddo
|
||
|
|
! pause
|
||
|
|
end
|