Re: [eigen] Blocking triangular Sylvester solver |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] Blocking triangular Sylvester solver*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Tue, 8 Jul 2014 18:34:12 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; bh=Rfgtrim+KNPzjMb679wan9VQXYSvVRLqroifdqgGXr4=; b=VTGsiblLwaQ+OeCgmnVfxz8eUbNZZT+EpfVPYT329e+oEyGKrTgZ/mJAD+TvhulMEk rEY6EDovXtaN3ZVMXY/b2GsAU/7lpaD17Jw16iY+fehhWVmNkPJROB1/4q9k8Nl3qXX1 FL7iMbVm0wY6k2Rg5rVO4hNJKiRlyBh23GT7YvrEMt1yVCVYwE5/KEaepll/qysSPRFW SntUatIpfQEHSuJxC7s4fCDeAqoBX3nrVjumSNFhv0SbR+7LIHguG9FC0Gd61szFy/RA xB7GGfWfGt5jrE1wN2GlUCfJwEyGfhyFVRqccQic76MZG5qUS7humT5O1TdtH2xSPDmq TgQw==

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

**Follow-Ups**:**Re: [eigen] Blocking triangular Sylvester solver***From:*Chen-Pang He

**References**:**[eigen] Blocking triangular Sylvester solver***From:*Chen-Pang He

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