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57 lines
1.4 KiB
Fortran
57 lines
1.4 KiB
Fortran
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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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