Add Lyapunov / Sylvester solver

[dlfivefifty]

There is no Lyapunov / Sylvester solver built-in to Julia, for solving

AXB + CXD = F

This could be fixed by wrapping the LAPack xTRSYL routine.

[lindahua]

+1

[stevengj]

Seems worthwhile and low-cost. What would the interface look like?

[jiahao]

I'm in favor of just putting in the LAPACK wrapper for now and deferring a higher-level interface to a symbolic rewrite rule in the same vein as #48. Or we could just do the simple thing and define a new solvesylvester function.

[dlfivefifty]

You could call the function lyap to match matlab

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On 15 Feb 2014, at 3:47 am, Jiahao Chen notifications@github.com wrote:

I'm in favor of just putting in the LAPACK wrapper for now and deferring a higher-level interface to a symbolic rewrite rule in the same vein as #48. Or we could just do the simple thing and define a new solvesylvester function.

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[lsorber]

@dlfivefifty lyap also solves Sylvester equations. Imho, maybe lyap tries to do too much and its functionality should be split into smaller pieces in Julia.

[atisharma]

Would a wrapper to SLICOT be a suitable response?

[mschauer]

As I understood, SLICOT is not really free, http://slicot.org/obtaining-slicot

[atisharma]

SLICOT 4.5 is GPL v3.0. SLICOT 5.0 does indeed look non-free from their website. But strangely it is available in the Debian main repo, and Debian are pretty strict about licencing.

Writing good Lyapunov / Riccati solvers is not that easy and if the SLICOT licence is acceptable it would be preferable to a reimplementation. Perhaps using SLICOT 4.5?

https://github.com/jcrist/Slicot.jl is attempting to create a Julia SLICOT wrapper.

[mschauer]

Ah, tricky. Could be that they had 5.0 for a limited time on the website under GPL and then removed the link, so that version 5.0 would be free as well, http://www.dynare.org/pipermail/dev/2011-July/001230.html .

[johnmyleswhite]

I think we'd generally try to avoid pulling something GPL3 into Base. Seems better suited for a package.

[dlfivefifty]

I've implemented my own lyap in Julia for the time being. If anyone is interested you can find it as part of ApproxFun:

https://github.com/dlfivefifty/ApproxFun/blob/master/src/PDE/lyap.jl

[mschauer]

@dlfivefifty Cool, thank you for implementing it. I would like to use your implementation for the time. Could you put your lyap.jl public domain or under a licence?

[dlfivefifty]

As far as I'm concerned it's public domain, but if you require an official license I'm happy to give it to you

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On Jun 26, 2014, at 10:54 PM, "M. Schauer" notifications@github.com wrote:

@dlfivefifty Cool, than you for implementing it. I would like to use your implementation for the time. Could you put your lyap.jl public domain or under a licence?

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[mschauer]

Ok, cool. I also have a look at the xTRSYL

[mschauer]

I gave it a try, if somebody familiar with Julia-LAPACK interaction could have a look, that would be nice, https://gist.github.com/mschauer/e967a2f1e7dc745c23e7 including naive implementation for comparison.
With some guidance I can make a pull request, or somebody else takes over.