Re: [eigen] Blocking triangular Sylvester solver

[Chen-Pang He <jdh8@xxxxxxxxxxxxxx>]

Thanks for your advice.  Now I am trying

- Recursive blocked algorithm
- Vectorization only

which are much easier for even quasitriangular matrices.

I wrote my own kernels to eliminate temporaries, but they are
really redundant with triangular solvers. :-(

Sincerely,
Chen-Pang

在 2014 七月 8 週二 18:34:12，Gael Guennebaud 寫道:
> Hi,
> 
> trying to directly write a cache-friendly implementation is probably a bit
> too difficult. I'd recommend to first have a working implementation based
> on vector-vector operations and then see how to leverage more efficient
> matrix-vector or even matrix-matrix operations.
> 
> Moreover, it would be better to write a high-level blocking strategy as in
> the PartialPivLU and LLT solvers and let the existing triangular solver and
> matrix products deal with the nasty details. Such an approach should lead
> to a much simpler code, with less redundancy, and the result will be more
> future proof as the internal matrix product kernels are subject to change
> from one version to the other.
> 
> cheers,
> gael
> 
> 
> On Fri, Jul 4, 2014 at 7:34 PM, Chen-Pang He <jdh8@xxxxxxxxxxxxxx> wrote:
> 
> > I am writing Sylvester-like solvers.  I began with triangular Sylvester
> > equation.  Now I have done with vectors, i.e. when the solution is a
> > column-vector or a row-vector.
> >
> > However, when I look at Eigen/src/Core/products/TriangularSolverMatrix.h,
> > I see
> > different blocking methods for on-the-left and on-the-right.  What is the
> > best
> > blocking when the solution is a general matrix?
> >
> > The attachment is my current work.  The TODO comment marks where I got
> > stuck.
> >
> > Regards,
> > Chen-Pang