Code covered by the BSD License

# Don't let that INV go past your eyes; to solve that system, FACTORIZE!

### Tim Davis (view profile)

14 May 2009 (Updated )

A simple-to-use object-oriented method for solving linear systems and least-squares problems.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

factorization_qrt_dense
```classdef factorization_qrt_dense < factorization
%FACTORIZATION_QRT_DENSE A' = Q*R where A is full.

% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com

methods

function F = factorization_qrt_dense (A, fail_if_singular)
%FACTORIZATION_QRT_DENSE : A' = Q*R
[m, n] = size (A) ;
if (m > n)
error ('FACTORIZE:wrongdim', 'QR(A'') method requires m<=n.') ;
end
[f.Q, f.R] = qr (A',0) ;
F.A_condest = cheap_condest (get_diag (f.R), fail_if_singular) ;
F.A = A ;
F.Factors = f ;
F.A_rank = rank_est (f.R, m, n) ;
F.kind = 'dense economy QR factorization: A'' = Q*R' ;
end

function e = error_check (F)
%ERROR_CHECK : return relative 1-norm of error in factorization
% meant for testing only
f = F.Factors ;
e = norm (F.A' - f.Q*f.R, 1) / norm (F.A, 1) ;
end

function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBCLASS x = A\b using a dense QR factorization of A'
% minimum 2-norm solution of an underdetermined system
% x = Q * (R' \ b)
f = F.Factors ;
opUT.UT = true ;
opUT.TRANSA = true ;
y = b ;
if (issparse (y))
y = full (y) ;
end
x = f.Q * linsolve (f.R, y, opUT) ;
end

function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using dense QR of A'
% least-squares solution of a overdetermined problem
% x = (R \ (Q' * b'))'
f = F.Factors ;
opU.UT = true ;
y = f.Q' * b' ;
if (issparse (y))
y = full (y) ;
end
x = linsolve (f.R, y, opU)' ;
end
end
end
```