R'xQ' of mxn matrix with m<n not allowed

[evelyne-ringoot]

Hi all,

I would like to use the Q and R factors of matrices and their transposes and I'm running into some issues for an mxn matrix m<n.

julia> using LinearAlgebra

julia> m, n = 2, 3;

julia> a=randn(m,n)
2×3 Matrix{Float64}:

julia> b=randn(n,m)
3×2 Matrix{Float64}:

julia> qa,ra=qr(a)
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor:
2×2 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}:
R factor:
2×3 Matrix{Float64}:
julia> qb,rb=qr(b)
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor:
3×3 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}:
R factor:
2×2 Matrix{Float64}:

julia> qa*ra
2×3 Matrix{Float64}: # works fine
julia> qb*rb
3×2 Matrix{Float64}:  # works fine

julia> ra'*qa'  # works fine
3×2 Matrix{Float64}:
julia> rb'*qb'  # does not work
ERROR: DimensionMismatch: second dimension of C, 2, and first dimension of V, 3 must match
Stacktrace:
 [1] gemqrt!(side::Char, trans::Char, V::Matrix{Float64}, T::Matrix{Float64}, C::Matrix{Float64})
   @ LinearAlgebra.LAPACK Local\Programs\Julia-1.8.0\share\julia\stdlib\v1.8\LinearAlgebra\src\lapack.jl:2925
 [2] rmul!
   @ Local\Programs\Julia-1.8.0\share\julia\stdlib\v1.8\LinearAlgebra\src\qr.jl:789 [inlined]
 [3] *(adjA::Adjoint{Float64, Matrix{Float64}}, adjQ::Adjoint{Float64, LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}})
   @ LinearAlgebra Local\Programs\Julia-1.8.0\share\julia\stdlib\v1.8\LinearAlgebra\src\qr.jl:850
 [4] top-level scope
   @ REPL[41]:1

While there is definetly a work-around (manually padding with zeros), I wonder whether it might be worth allowing rb'*qb' in LinearAlgebra Base in the same way as qb*rb?

[dkarrasch]

This is resolved on current nightly, perhaps since JuliaLang/julia#46196.