Re: [eigen] Blocking triangular Sylvester solver

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

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