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1.2 KiB
1.2 KiB
Matrix to vector index
Compute the index i of a vector element from the indexes p,q of a matrix element
Lower diagonal matrix (p,q), p > q -> vector (i)
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:
p,q | integer | indexes of a matrix element in the lower diagonal |
p > q, q -> column | ||
p -> row, | ||
q -> column |
Input:
i | integer | corresponding index in the vector |
subroutine mat_to_vec_index(p,q,i)
include 'pi.h'
implicit none
! Variables
! in
integer, intent(in) :: p,q
! out
integer, intent(out) :: i
! internal
integer :: a,b
double precision :: da
! Calculation
a = p-1
b = a*(a-1)/2
i = q+b
end subroutine