Re: [eigen] GivensQR

[Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>]

On Wed, 19 Aug 2009, Benoit Jacob wrote:

> I was intrigued by the option of computing/storing only the sequence
> of Givens rotations, which doesn't seem like common practice at all; i
> was expecting a GivensQR class to compute/store Q and/or R according
> to what the user asked for.

The HouseholderQR class does something similar. It doesn't store Q but 
only the sequence of Householder reflections. The matrix Q is only 
computed when the user asks for it.

> So I wondered what was the use case for the approach of storing the
> sequence of Givens rotations, and it seems to me that the best use
> case for it should be when doing only 1 vector solve. Indeed, in that
> case, avoiding the overhead of computing Q or R should be the most
> beneficial.

Another use case is solving an overdetermined system in the least-square 
sense. You don't need to compute Q; you only need to be able to multiply Q 
with a vector.


Jitse