a difference_matrices module

[ncohen]

This commit creates a difference_matrices module which does not do much at the moment: it can creates DM for prime powers, and return DM from the database.

In the database, however, a lot changes as many OA were actually difference matrices. The constructors are turned into difference matrices constructors, and orthogonal_array now calls difference_matrix to get them.

All in all what this patch does is mostly code administration, but well, that's the way to go ...

Quasi-difference matrices will be handled later as there are some problems with them, in particular in the way orthogonal_array will query the future quasi_difference_matrix constructor.

Nathann

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8f10d94	trac #16797: is_difference_matrix
​aa097f6	trac #16797: Fit with the current definition until we can change everything at once
​5d21b8c	trac #16797: int * and ** instead of Python list
​8f29bd1	trac #16797: change int to int * in a malloc
​811e3e9	trac #16797: better malloc + better error msg
​1b8c2e3	trac #16797: More compact mallocs
​b78c347	trac #16797: Reorder the arguments to copy is_orthogonal_array
​dee4275	trac #16797: Merged with 6.4.beta0
​896f0e1	trac #16797: correct a row/column inversion
​2649805	trac #16846: a difference_matrices module

[ncohen]

Sorry for the diff in the database file, it's a bit hard to review with everything being mixed up by the diff algorithm... :-/

What happens there is simple: some DM_* functions are removed and replaced by their DM_* counterpart. No new constructor is added, it's only a rephrase of that code.

Nathann

[vdelecroix]

Hi Nathann,

Very nice that you did that!

I guess that difference matrices are interesting only over Abelian groups. Is that true? It would be nice to coordinate with difference families for input/output. For example, in #16802, in the database, you can ask a difference family with a given group and not only a fixed cardinality. It is not perfect, but I tried to start involving the group...

Vincent

[ncohen]

Yo !

I guess that difference matrices are interesting only over Abelian groups. Is that true?

I have no idea about that, but all examples I saw were on abelian groups indeed.

It would be nice to coordinate with difference families for input/output. For example, in #16802, in the database, you can ask a difference family with a given group and not only a fixed cardinality. It is not perfect, but I tried to start involving the group...

Hmmmmm... So a structure like that ?

DM_constructions = {
   order_of_the_group : {
     signature_of_the_abelian_group: [
         (k1,matrix_constructor1),
         (k2,matrix_constructor2)
         ]
     }
}

Having several difference families/matrices or OA and stuff is a hobby of yours, you know ? To me it's just not the interesting direction :-P

It can be done anyway but we have to do that later, this heap of patches is really getting dangerous. Plus Travis wrote a patch that is totally incompatible with this one, and there are like 10 tickets in linear order an needs_review at the moment :-P

Nathann

[vdelecroix]

Replying to ncohen:

Yo !

I guess that difference matrices are interesting only over Abelian groups. Is that true?

I have no idea about that, but all examples I saw were on abelian groups indeed.

Because you can not develop a difference matrix to get an OA if the group is non Abelian. But perhaps, difference matrices can be used for other purposes.

It would be nice to coordinate with difference families for input/output. For example, in #16802, in the database, you can ask a difference family with a given group and not only a fixed cardinality. It is not perfect, but I tried to start involving the group...

Hmmmmm... So a structure like that ?

DM_constructions = {
   order_of_the_group : {
     signature_of_the_abelian_group: [
         (k1,matrix_constructor1),
         (k2,matrix_constructor2)
         ]
     }
}

Might be better than what I did... I used {signature: DF}

Having several difference families/matrices or OA and stuff is a hobby of yours, you know ? To me it's just not the interesting direction :-P

Sometimes it is very important that your group is cyclic (for difference families or difference matrix)... so you want to be able to ask a given difference X over a cyclic group only.

It can be done anyway but we have to do that later, this heap of patches is really getting dangerous. Plus Travis wrote a patch that is totally incompatible with this one, and there are like 10 tickets in linear order an needs_review at the moment :-P

+1

Vincent

[ncohen]

Might be better than what I did... I used {signature: DF}

If you just want a difference family to exist in order to build a BIBD but don't know the exact decomposition you need to list everything :-/

Nathann

[ncohen]

Last 10 new commits:

​e6deb83	trac #16859: doc
​db53470	trac #16780: Merged with #16859 (need the resolvable incomplete OA)
​52c4fa0	trac #16780: resolvable incomplete OA are built with 2 lines
​7fe173a	trac #16780: review 2
​931a33f	trac #16780: repeat "parallel classes"
​5b8500b	trac #16864: designs/database.py: auto-generated doc index
​bfbad46	trac #16864: use Python string .format() + doc
​3ca48dc	trac #16817: OA for n=205,254,469,520,522,524,1262
​43034f4	trac #16846: a difference_matrices module
​3e0a79b	trac #16846: Remove obsolete functions

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​c92e9bf	trac #16846: a difference_matrices module
​fdab06e	trac #16846: Remove obsolete functions
​f7afe6f	trac #16846: Broken doctests

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f9e6569	trac #16817: docfix
​fd1bbc6	trac #16846: Merge with updated #16817

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​c66c19b

trac #16846: review

[vdelecroix]

I did

• removed TD_6_12
• OA_7_39 -> DM_39_6_1

As a consequence, doc builds... and test still pass.

If you like it, set to positive review.

Vincent

[ncohen]

The doc builds, and doctests pass. Thank you very much for this last review ! :-D

Nathann