[GAP Forum] GAP to MATLAB?

Wed Oct 16 21:59:17 BST 2019

Dear Joey,
On Wed, Oct 16, 2019 at 06:31:46PM +0000, Iverson, Joseph W [MATH] wrote:
> 
> >> What kind of task are do going to do on these matrices?
> 
> Usually when I need to export to MATLAB it's because I need to do stuff with eigenvalues or with non-cyclotomic numbers. For instance, right now I need to convert this non-unitary representation to a unitary one (using the square root of a positive matrix) and then find a matrix for orthogonal projection onto an invariant subspace (with the aid of a spectral decomposition).

SageMath can do linear algebra on matrices of general algebraic numbers.

By the way, our GAP package should be able to do unitarization. We
figured out a procedure for this, described in the MSc thesis (which I
supervised) of the main author of the package, see Sect. A.1 of
http://users.ox.ac.uk/~coml0531/kaashif-thesis.pdf
but implementation isn't quite done yet (not tests ready, for sure).

The procedure involves taking square roots of a positive diagonal
matrix of cyclotomics (unsuprisingly) - probably this means that it might get slow. 
I guess one can do an "incomplete
unitarisation" - the invariant sesquilinear form will be diagonal, but 
not scalar, this would avoid taking roots.
> 
> >>     I believe you can do a lot in SageMath
> 
> Yes, I always have that in the back of my mind as a last resort, but I would like to avoid learning a whole new system if I can. In addition, many of my collaborators use MATLAB and I would like to stay on the same page as them.
<rant>
I honestly wish my university did not have a campus Matlab license - it has a side
effect that any non-Matlab software effort gets zero university funding :-(
Matlab for software is akin to Elsevier for maths journals - a huge
access-restricting costpost for little gain.
</rant>
>  
> Still, I wonder if a person could use Sage as a bridge to MATLAB. Does anybody know if it has a method to export .mat files, and if so, whether that method is compatible with the interface to GAP?

*.mat files are snapshots of Matlab memory, I don't see how one can
produce them outside of Matlab. (They are akin to Python's or GAP's IO
package serialisation).

What one can do is to create a MEX-file extension for Matlab, which
would embed libGAP and allow for efficient copying of data in memory:
https://en.wikipedia.org/wiki/MEX_file
(this is a kind of interface to (lib)GAP done in SageMath, and, IIRC, in a new
Julia-language based system Oscar https://oscar.computeralgebra.de/)

HTH
Dima

> 
> Dima, thanks also for pointing me to your package about block diagonalization. That is closely related to what I am doing, yes.
> 
> All the best,
> Joey Iverson
> 
> Assistant Professor
> Department of Mathematics
> Iowa State University
> 
> 
> 
> 
> On 10/16/19, 9:11 AM, "dmitrii.pasechnik at cs.ox.ac.uk" <dmitrii.pasechnik at cs.ox.ac.uk> wrote:
> 
>     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
>     > 
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