TransformToOnes.m

% B = TransformToOnes (clovec)
%
% Returns the similarity transformation matrix that 
% converts the given column vector to a vector of ones.
% It works even if clovec has zero entries.
% 
% Parameters
% ----------
% clovec : matrix, shape(M,1)
%     The original closing vector
% 
% Returns
% -------
% B : matrix, shape(M,M)
%     The matrix by which B*clovec = ones holds  
 
function B = TransformToOnes (clovec)
 
    % construct permutation matrix to move at least one non-zero element to the first position
    % to acchieve it, the code below sorts it in a reverse order
    m = length(clovec);
    
    [~,ix] = sort(-clovec);
    P = zeros(m);
    for i=1:m
        P(i,ix(i)) = 1.0;
    end
    cp = P*clovec;
 
    % construct transformation matrix B for which B*rp=1 holds
    B = zeros(m);
    for i=1:m
        B(i,1:i) = 1.0 / sum(cp(1:i,1));
    end
    % construct matrix B for which B*r=1 holds
    B = B*P;
end