Re: [eigen] Fast method for computing Gramian Matrix

[Mark Borgerding <mark@xxxxxxxxxxxxxx>]

On 03/29/2012 01:18 AM, Douglas Bates wrote:
> On Thu, Mar 29, 2012 at 3:50 AM, Mark Borgerding<mark@xxxxxxxxxxxxxx>  wrote:
> > (sorry for hitting send too soon)
> >
> > http://en.wikipedia.org/wiki/Gramian_matrix
> >
> > What is the fastest way to compute MM' when M is wide?
> > The diagonal elements are the norm-squared of the rows of M. The result is
> > Hermitian.
> >
> > Is there an optimized method in Eigen or otherwise?
> I have used the rankUpdate method for a selfadjoint view to calculate
> this.  I assume that it is an efficient way to calculate the result
> but I haven't done any timings.
>
>
> MatrixXcd MMt(M.rows(), M.rows();
> MMt.setZero().selfadjointView<Eigen::Upper>().rankUpdate(M);
Thanks.  That cut the time to about 80% of the full matrix product.

Is there an elegant way to recover the full, square self-adjoint matrix 
from a SelfAdjointView ?
I've been adding the SA view to its own adjoint and then subtracting the 
original diagonal.