SUB2IND4UP Linear index from subscripts of upper triangular matrix (only elements above diagonal)

Single index for given subscripts of a 2D upper matrix, (no elements over the diagonal)

Description

IND = SUB2IND4UP(I, J) returns the linear index equivalent to the row and column subscripts I and J

Let ind be a vector of indexes for entries of some upper triangular matrix. The entries are selected vertically so that:

       ind = 1 is associated to entry (1, 2)
       ind = 2 is associated to entry (1, 3)
       ind = 3 is associated to entry (2, 3)
       ind = 4 is associated to entry (1, 4)
       ...
       ind = N * (N - 1) / 2 is associated to entry (N - 1, N)

***********************************************************************

EXAMPLE

If
             A = rand(10);
and
             b = A(find(triu(A, 1)));
then, given subscripts
             I = [1:9];
and
             J = [2:10];
for matrix A, these are equivalent to indices
             IND = sub2ind4up(I, J);
for vector b. In fact:
             all(A(sub2ind(size(A), I, J)) == b(IND)')

ans =
           1

This is obtained without even knowing about size(A)

***********************************************************************

See also SUB2IND, IND2SUB, FIND.

• MATLAB release: MATLAB 7 (R14)

[Bruno Luong]

Why restrict on one level upper diagonal? It is too restrictive. It should be able to handle lower and upper, with all the shift, positive or negative.

[Francesco Pozzi]

% Note that if
A = rand(10);
% and
b = A(find(triu(A, 1)));
% then, given subscripts
I = [1:9];
% and
J = [2:10];
% for matrix A, these are equivalent to
IND = sub2ind4up(I, J);
% for vector b. Infact:
all(A(sub2ind([10, 10], I, J)) == b(IND)')
%
% ans =
%
% 1
%
% This is obtained without even knowing about size(A).