QR that returns permutation matrix?

[j.e....@gmail.com]

Hey all,

Is there QR decomposition in gonum that returns the Permutation matrix/vector too?

This is useful for variable selection/responding to multicollinearity.

I'm referring to P in this matlab documentation:

https://www.mathworks.com/help/matlab/ref/qr.html

[Q,R,P] = qr(A) additionally returns a permutation matrix P such that A*P = Q*R. If A is full, the permutation matrix is chosen so that abs(diag(R)) is decreasing.

example

example

[Q,R,P] = qr(A,outputForm) specifies whether to return the permutation information P as a matrix or a vector. For example, if outputForm is "vector", then A(:,P) = Q*R. The default value of outputForm is "matrix" such that A*P = Q*R.

So that one can do things like

https://math.stackexchange.com/questions/759208/multicollinearity-and-svd

I didn't see one, searching gonum in github.... or maybe gonum has a different factorization already, to do the same thing?  Or it could be easily added.  GSL 

seems to have it; i.e.  

http://gnu.ist.utl.pt/software/gsl/manual/html_node/QR-Decomposition-with-Column-Pivoting.html

Thanks.

[Vladimír Chalupecký]

Hi,

We do have QR factorization with column pivoting in Gonum as long as you don't mind accessing it through a Lapack-like interface for now, see lapack/gonum/dgeqp3.go (the implementation is in pure Go).

I'd be happy to add a wrapping type like PivotedQR to the mat package for convenient usage. The need for a permutation matrix type is a hurdle but maybe it's just that I haven't thought deep enough about it (which I haven't). There's already another factorization that needs it (PivotedCholesky, https://github.com/gonum/gonum/pull/1780), so that's two reasons to try to make progress. I'll see what I can do.

Vladimir