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qp2/src/utils_trust_region/vec_to_mat_index.irp.f

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2023-04-18 13:01:25 +02:00
! Vector to matrix indexes
! *Compute the indexes p,q of a matrix element with the vector index i*
! Vector (i) -> lower diagonal matrix (p,q), p > q
! If a matrix is antisymmetric it can be reshaped as a vector. And the
! vector can be reshaped as an antisymmetric matrix
! \begin{align*}
! \begin{pmatrix}
! 0 & -1 & -2 & -4 \\
! 1 & 0 & -3 & -5 \\
! 2 & 3 & 0 & -6 \\
! 4 & 5 & 6 & 0
! \end{pmatrix}
! \Leftrightarrow
! \begin{pmatrix}
! 1 & 2 & 3 & 4 & 5 & 6
! \end{pmatrix}
! \end{align*}
! !!! Here the algorithm only work for the lower diagonal !!!
! Input:
! | i | integer | index in the vector |
! Ouput:
! | p,q | integer | corresponding indexes in the lower diagonal of a matrix |
! | | | p > q, |
! | | | p -> row, |
! | | | q -> column |
subroutine vec_to_mat_index(i,p,q)
include 'pi.h'
!BEGIN_DOC
! Compute the indexes (p,q) of the element in the lower diagonal matrix knowing
! its index i a vector
!END_DOC
implicit none
! Variables
! in
integer,intent(in) :: i
! out
integer, intent(out) :: p,q
! internal
integer :: a,b
double precision :: da
da = 0.5d0*(1+ sqrt(1d0+8d0*DBLE(i)))
a = INT(da)
if ((a*(a-1))/2==i) then
p = a-1
else
p = a
endif
b = p*(p-1)/2
! Matrix element indexes
p = p + 1
q = i - b
end subroutine