sub2ind4up(I, J)

function IND = sub2ind4up(I, J)
%SUB2IND4UP Linear index from subscripts of upper triangular matrix (only
%elements above diagonal)
%   SUB2IND4UP determines the equivalent single index corresponding to a
%   given set of subscript values for a 2D upper triangular matrix,
%   excluded all elements over the diagonal.
%
%   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
%
%       % 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 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.
%
% % ======================================================================
%
%   Author: Francesco Pozzi
%   E-mail: [e-mail]
%   Date: 1 May 2010
%
% % ======================================================================
%

% Check input
ctrl1 = isnumeric(I) & isreal(I) & isnumeric(J) & isreal(J);
if ctrl1
  I = I(:);
  J = J(:);
  ctrl2 = ~any(isnan(I)) & ~any(isinf(I)) & all(I > 0) & ~any(isnan(J)) & ~any(isinf(J)) & all(J > 0);
  if ~ctrl2
    error('Check indexes: they need to be positive integers!')
  else
    ctrl3 = all(I < J);
    if ~ctrl3
      error('Check indexes: in an upper triangular matrix row indexes need to be less than column indexes!')
    end
  end
else
  error('Check indexes: they need to be positive integers!')
end

IND = round(J .* (J - 3) / 2 + I + 1);