function [fcr,E]=verfullcolrank(A) % VERFULLCOLRANK Verified full column rank of a rectangular real matrix. % % This is an INTLAB file. It requires to have INTLAB installed under % MATLAB to function properly. % % For a rectangular real matrix A, % fcr=verfullcolrank(A) % either verifies full column rank of A, or verifies column rank % deficiency of A, or fails (yields no verified result): % % fcr= 1 A is verified to have full column rank (i.e., columns of A are linearly independent), % fcr= 0 A is verified not to have full column rank (i.e., columns of A are linearly dependent), % fcr=-1 no verified result. % % For full row rank, apply VERFULLCOLRANK to A'. % % Built-in function. % Copyright 2008 Jiri Rohn. % % WARRANTY % % Because the program is licensed free of charge, there is % no warranty for the program, to the extent permitted by applicable % law. Except when otherwise stated in writing the copyright holder % and/or other parties provide the program "as is" without warranty % of any kind, either expressed or implied, including, but not % limited to, the implied warranties of merchantability and fitness % for a particular purpose. The entire risk as to the quality and % performance of the program is with you. Should the program prove % defective, you assume the cost of all necessary servicing, repair % or correction. % % History % % 2007-11-02 first version % 2008-03-12 version for posting % 2008-04-05 column rank deficiency part added; E added % 2008-05-30 ZD, p-coded, called by VERFULLCOLRANK % [fcr,E]=zd(A); % computation done by ZD