iscoplanar

 ISCOPLANAR - Test for coplanar controls.

  [c,cols] = iscoplanar(B)
 
 Given a control effectiveness matrix B (k x m), the function returns
 c = 1 if there are k columns in B that are linearly dependent.
 The columns indexes of all such combinations are gathered in cols.
 
 Example:

   B = [1 1 0;0 0 1]
   [c,cols] = iscoplanar(B)

0001 function [c,cols] = iscoplanar(B)
0002   
0003 % ISCOPLANAR - Test for coplanar controls.
0004 %
0005 %  [c,cols] = iscoplanar(B)
0006 %
0007 % Given a control effectiveness matrix B (k x m), the function returns
0008 % c = 1 if there are k columns in B that are linearly dependent.
0009 % The columns indexes of all such combinations are gathered in cols.
0010 %
0011 % Example:
0012 %
0013 %   B = [1 1 0;0 0 1]
0014 %   [c,cols] = iscoplanar(B)
0015   
0016 % Dimensions
0017   [k,m] = size(B);
0018   
0019   % Construct all n combinations of k columns.
0020   C = nchoosek(1:m,k);
0021   n = nchoosek(m,k);
0022   
0023   c = 0;
0024   cols = [];
0025   % Check all k x k submatrices of B.
0026   for i = 1:n
0027     Bsub = B(:,C(i,:));
0028     if qrank(Bsub) < k
0029       % Coplanar controls detected
0030       c = 1;
0031       cols = [cols ; C(i,:)];
0032     end
0033   end