three-arg mul! with Q factor of type LinearAlgebra.QRCompactWYQ is wrong

[Jutho]

Test:

using LinearAlgebra
A = randn(11,10);
Q, R = qr(A);
X = randn(11,10);
mul!(X, Q, R);
norm(X-A)

the problem is with this implementation:
https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/qr.jl#L752

mul!(C::StridedVecOrMat{T}, Q::AbstractQ{T}, B::StridedVecOrMat{T}) where {T} = lmul!(Q, copyto!(C, B))

This is only correct if C and B are of the same size, which here they are not.
The same holds for the other combinations (i.e. the methods on the lines below).

[r0cketr1kky]

I guess this test should work now @Jutho ! Kudos to this issue JuliaLang/julia#26007 and this PR JuliaLang/julia#34049

[Jutho]

I will have to test, I am not sure that it does. I have not fully studied what was changed by PR JuliaLang/julia#34049, but in this case what you want is

mul!(C::StridedVecOrMat{T}, Q::AbstractQ{T}, B::StridedVecOrMat{T}) where {T} = lmul!(Q, copyto!(fill!(C, 0), B))

i.e. if Q originates from the QR of an n x k matrix (n>k) , and B is k x k, and C is n x k, then in order compute C = Q*B using in place lmul!(Q, C), you want the matrix C to be such that it contains B in its first rows and zeros in its final rows. If C contains garbage in its final rows, this will still be the case after copyto!(C,B) if I understand correctly.

[r0cketr1kky]

Ahh yes, you're right! My bad!
Are you working on this issue @Jutho ?

[Jutho]

Currently not; I hope to have more time when the semester ends, if no-one has fixed it by then.