[GAP Forum] GAP to MATLAB?

[dmitrii.pasechnik at cs.ox.ac.uk]

Dear Joey,
On Wed, Oct 16, 2019 at 12:06:16PM +0000, Iverson, Joseph W [MATH] wrote:
> 
> Does anybody know of a way to efficiently get matrices (say with cyclotomic entries) from GAP to MATLAB? For instance, is there a package to export matrices as .mat files? 
> 
> I have been getting by with a jerry-rigged solution where I make GAP print a matrix like
> A:=[[1,0],[0,1]];;
> to a file "A.m" containing a single string like
> "A=[1,0;0,1];".
> Then I have MATLAB read the file as a script. That works fine for small matrices, but for large ones (or for 3-tensors consisting of lots of matrices) it is prohibitively slow, both for GAP to print to the file and for MATLAB to interpret the result. 
> 
> For a sense of scale, at the moment I would like to export 95040 matrices each of size 540x540 to MATLAB, preferably as a 3-tensor so that I can easily iterate through the list. (The matrices are the image of a representation of M12 having degree 540.)

What kind of task are do going to do on these matrices?
I believe you can do a lot in SageMath, which has a fast (lib)GAP
interface, and many more numerical
and matrix tools than GAP. E.g. we recently have been working on solving
semidefinite optimisation problems using GAP output (needed to
block-diagonalise certain combinatorial data).

We (mostly, my former student) also have a GAP package that would block-diagonalise for you your
representation (into block-diagonal matrix with irredicible blocks).
https://gitlab.com/kaashif/decomp
which might help a lot with whatever linear algebra tasks you might want
to do with your representation of degree 540.

HTH
Dima


> 
> Best regards,
> Joey Iverson
> 
> Assistant Professor
> Department of Mathematics
> Iowa State University
> 
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum