Example
> a = rand(5,5)
a =
0.81 0.621 0.328 0.0767 0.818
0.909 0.845 0.799 0.647 0.367
0.293 0.132 0.0398 0.0221 0.191
0.743 0.0376 0.398 0.227 0.845
0.705 0.811 0.263 0.431 0.401
> res = qr(a)
res =
q r
> a - res.q*res.r
-1.11e-16 -3.33e-16 -3.89e-16 -1.11e-16 -2.22e-16
0 0 1.11e-16 1.11e-16 -1.67e-16
0 -5.55e-17 -9.71e-17 -1.42e-16 -2.78e-17
0 -6.94e-17 -2.22e-16 -5.55e-17 0
0 0 -5.55e-17 -5.55e-17 -5.55e-17
> res2 = qr(a,"p")
res2 =
p q r
> a*res2.p - res2.q*res.r
-1.11e-16 -3.33e-16 -3.89e-16 -1.11e-16 -2.22e-16
0 0 1.11e-16 1.11e-16 -1.67e-16
0 -5.55e-17 -9.71e-17 -1.42e-16 -2.78e-17
0 -6.94e-17 -2.22e-16 -5.55e-17 0
0 0 -5.55e-17 -5.55e-17 -5.55e-17