Re: [eigen] Clarification on the documentation for SparseSelfAdjointView::RankUpdate

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

answered there:
http://forum.kde.org/viewtopic.php?f=74&t=95552&sid=a52d201181d55e50c3105c1213caddaf

gael

On Thu, Jun 16, 2011 at 11:41 PM, Douglas Bates <bates@xxxxxxxxxxxxx> wrote:
> The documentation for this method states
>
>
>    /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
>      * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
>      *
>      * \returns a reference to \c *this
>      *
>      * Note that it is faster to set alpha=0 than initializing the
> matrix to zero
>      * and then keep the default value alpha=1.
>      *
>      * To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
>      * call this function with u.adjoint().
>      */
>
> The second-last paragraph is what has confused me.  I want to evaluate
> the Lower triangle of Z.adjoint() * ZLam so I am doing it as
>
>    SparseMatrix<double>  ZtZ;
>    ZtZ.selfadjointView<Lower>().rankUpdate(Z.adjoint(),
> 0.).rankUpdate(Z.adjoint());
>
> Is that what is meant - that I should do the
> .rankUpdate(Zlam.adjoint(), 0) then do the rankUpdate(Zlam.adjoint())?
>
> A second question, if I may: What would be an effective way of
> evaluating, as a sparse matrix, (I + Z'Z)?  I think I would want to
> initialize the result to the identity then apply the rankUpdate method
> but I want to be sure that I don't accidentally create a dense, square
> matrix along the way.
>
>
>