What is the most efficient way of obtaining the orthogonal column space of a matrix?

[stevengj]

@stevengj

QR factors are stored in an implicit form that makes indexing slow, but they can be quickly multiplied by vectors. To get the first n columns, try multiplying Q by the first n columns of the identity matrix.

In particular, try qr(X).Q * Matrix(I, size(X)...), and you should find that it is much faster than an SVD.

@Oscar_Smith

I think I have a PR that fixes this, but it stalled out. I really should revive it though because it’s a dumb performance cliff.

Yes, it’s pretty common to want to slice a Q matrix and we really should provide a fast algorithm for it.