qp2/src/utils_trust_region/org/mat_to_vec_index.org

• Matrix to vector index

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