qr error for matrices with 0 columns

[StephenVavasis]

Function qr in 0.6 works fine for matrices with 0 columns, but not in 0.7.0-beta2:

julia> F = qr(zeros(4,0))
WARNING: Base.qr is deprecated: it has been moved to the standard library package `LinearAlgebra`.
Add `using LinearAlgebra` to your imports.
 in module Main
LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}
Q factor:
4×4 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
 1.0  0.0  0.0  0.0
 0.0  1.0  0.0  0.0
 0.0  0.0  1.0  0.0
 0.0  0.0  0.0  1.0
R factor:
Error showing value of type LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}:
ERROR: ArgumentError: the requested diagonal, 0, must be at least 1 and at most 1 in an 0-by-0 matrix

[KristofferC]

The computation seems to work, it's just the display that errors?

[StephenVavasis]

It's true that not displaying the answer prevents the problem from occurring immediately, but the it still occurs later:

julia> F = qr(zeros(4,0));

julia> R = Matrix(F.R)
ERROR: ArgumentError: the requested diagonal, 0, must be at least 1 and at most 1 in an 0-by-0 matrix
Stacktrace:
 [1] triu!(::Array{Float64,2}, ::Int64) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v0.7\LinearAlgebra\src\dense.jl:175
 [2] triu! at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v0.7\LinearAlgebra\src\generic.jl:237 [inlined]
 [3] getproperty(::LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}, ::Symbol) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v0.7\LinearAlgebra\src\qr.jl:419
 [4] top-level scope at none:0

[andreasnoack]

julia> triu!(randn(0,0));
ERROR: ArgumentError: the requested diagonal, 0, must be at least 1 and at most 1 in an 0-by-0 matrix
Stacktrace:
 [1] triu!(::Array{Float64,2}, ::Int64) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v0.7/LinearAlgebra/src/dense.jl:175
 [2] triu!(::Array{Float64,2}) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v0.7/LinearAlgebra/src/generic.jl:237
 [3] top-level scope at none:0

We added some checks to the triu/l functions to catch potential user errors but so far these checks have mainly been causing problems. I think we should seriously consider to revert the change that introduced the checks.

[StefanKarpinski]

100%. We need to either do the looser bounds or delete the checks altogether. Not super urgent since loosening the bounds can be done at any time, but these bounds checks seem mostly annoying.

[chenxlieee]

julia> a=[1 2 3; 4 5 6; 7 8 9]
3×3 Array{Int64,2}:
1 2 3
4 5 6
7 8 9

julia> using LinearAlgebra: qr

julia> q,r=qr(a)
LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}
Q factor:
3×3 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
-0.123091 0.904534 0.408248
-0.492366 0.301511 -0.816497
-0.86164 -0.301511 0.408248
R factor:
3×3 Array{Float64,2}:
-8.12404 -9.60114 -11.0782
0.0 0.904534 1.80907
0.0 0.0 -8.88178e-16

julia> q
3×3 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
-0.123091 0.904534 0.408248
-0.492366 0.301511 -0.816497
-0.86164 -0.301511 0.408248

julia> r
3×3 Array{Float64,2}:
-8.12404 -9.60114 -11.0782
0.0 0.904534 1.80907
0.0 0.0 -8.88178e-16

It seems the q and r matrices are not compact. Since the rank of "a" is 2, the size of the compact "q" and "r" should be 3 × 2 and 2 × 3, respectively.

[StephenVavasis]

With respect to the previous comment, I don't see anything wrong with the output from qr in your posting. Could you say more precisely what is the issue you are raising?

[andreasnoack]

Fixed by JuliaLang/julia#28480

[StephenVavasis]

With respect to the comment from @chenxlieee , plain QR is not suitable for use as a rank estimator. For rank estimation, use either pivoted QR or, for greatest robustness, SVD.