QR factorization does not show Q factor

[cafaxo]

On current master, I get

julia> qr(randn(2,2))
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor:
2×2 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}
R factor:
2×2 Matrix{Float64}:
 -2.3358  -0.951623
  0.0     -0.608775

The actual matrix should be printed after Q factor:.

[dkarrasch]

This was also changed in #46196 on purpose. Qs are not readily accessible in memory, their components need to be computed one by one, so printing them like a matrix is costly. If you're interested in seeing the matrix representation of something that is not in matrix format, you should call Matrix(qr(...).Q).

[dkarrasch]

Can this be closed?

[cafaxo]

I think we shouldn't care too much about cost when printing / showing a struct.

[dkarrasch]

I've looked into it. It's a pretty big deal, after all. We have some matrix printing code that does all computations regarding alignment of elements, fill-up with ellipses etc. That's specialized to AbstractVecOrMat, which AbstractQ isn't. Removing the type constraints in Julia Base doesn't seem like an option, the other options are (i) first compute the entire matrix and display it as usual (that is certainly expensive and may make the repl look like it stalled, I think we were discussing this over at SparseArrays.jl with @jishnub IIRC), or (ii) duplicate the printing code, which is also bad. All the effort for printing something like a matrix that isn't a matrix. 🤔

[jishnub]

Is there a different way to show it, perhaps by summarising the struct fields? The current display might confuse users who might expect some value to be printed after the type

[cafaxo]

Why not just print Matrix(Q)? Was the matrix previously allocated when printing Q?

[jishnub]

Given that AbstractQ used to be an AbstractMatrix, it could avail the show methods for AbstractArrays that only needed to compute a handful of elements. Now that it's not an AbstractMatrix anymore, it lacks an efficient show method. Computing the entire matrix representation will be expensive and may allocate considerably, which is unnecessary for an object that isn't really a Matrix.

[dkarrasch]

Is that more expensive than before?

Of course. You'd allocate an entirely new matrix in memory.

Was the matrix previously allocated when printing Q?

No, for big Q's, you'd only want to print the "corners" of the "matrix". In that case, you better compute only those that are required for printing, instead of first computing everything and then use only the corners. That's what used to be done. Printing works via getindex, and for Q's that means computing columns or elements etc.

[dkarrasch]

What if we change the output to

julia> qr(randn(2,2))
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor: 2×2 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}
R factor:
2×2 Matrix{Float64}:
 -2.3358  -0.951623
  0.0     -0.608775

? Like remove the line break between "Q factor" and the summary of Q. If one really wants to inspect Q, one will be always better off computing the entire matrix, or columns of interest. Anything is better than elementwise.