New recursive constructions of Orthogonal Arrays

[ncohen]

Here they are ! They have been sitting on my HD for a long time :-P

Nathann

[git]

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

​004833a	trac #16347: Wilson's construction with two truncated groups
​f5069f0	trac #16347: Merged with 6.3.beta4
​f182d36	trac #16499: Cheap speedup in the OA recursive constructions
​70f7046	trac #16500: New recursive constructions of Orthogonal Arrays

[vdelecroix]

EDIT: deleted comment as I messed up ticket numbers...

[vdelecroix]

(Replying to comment:4) sorry, this comment was for #16430. Not this one!!

[ncohen]

Rebased on top of #16499. But....

sage -t --long latin_squares.py
    [40 tests, 35.08 s]

T_T

Nathann

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​0fa89d5	trac #16347: Wilson's construction with two truncated groups
​828ff22	trac #16437: cut the branches in W. dec. with two trunc. blocks
​8ebd21b	trac #16347: use is_sum_of_squares_pyx instead of two_squares
​0175134	trac #16347: doc + simplifications
​9ff5062	trac #16423: Table of MOLS from the handbook and comparison with Sage
​e64be98	trac #16423: tiny code improvement and alignment
​e948cf6	trac #16423: Aligning the alignment
​0a7d853	trac #16423: Broken doctests
​b329351	trac #16499: Cheap speedup in the OA recursive constructions
​770a28d	trac #16500: New recursive constructions of Orthogonal Arrays

[vdelecroix]

Hi Nathann,

Stupid questions to start:

• It would be nice to have references! You provide [AC07]_ for construction_3_4 but that's all.
• Why you did not move product, one_truncated_group and two_trucated_group in the recursive construction?
• Why not put the cache only for find_recursive_construction? (less cached function and less function calls)

Vicent

[ncohen]

Yo !

I updated the "find" functions a bit. Nothing smart, just common sense, and the MOLS_table function is fast again. Yeepeeeeeeeeee !!! :-P

• It would be nice to have references! You provide [AC07]_ for construction_3_4 but that's all.

Ahahahah. I had nothing else :-P

I tried to reverse-engineer the construction from the theorem's claim, and when I was not able too I asked Julian R. Abel for a hint. This being said, the explanations I give in the docstring are more or less like a proof.

• Why you did not move product, one_truncated_group and two_trucated_group in the recursive construction?

Because I thought that it would be abusing your kindness. I waste my health implementing those things, but I still try to makes patches somehow readable so that reviewing them will not be hell for you. I can add a commit for that if you don't mind. As I told you by email, "this is in the plan" :-P

• Why not put the cache only for find_recursive_construction? (less cached function and less function calls)

Because this function returns both OA and True/False answers. The find_* functions I cached only return immutable stuff.

Nathann

[git]

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

​a67c04f

trac #16500: New recursive constructions of Orthogonal Arrays

[vdelecroix]

Replying to ncohen:

• Why you did not move product, one_truncated_group and two_trucated_group in the recursive construction?

Because I thought that it would be abusing your kindness. I waste my health implementing those things, but I still try to makes patches somehow readable so that reviewing them will not be hell for you. I can add a commit for that if you don't mind. As I told you by email, "this is in the plan" :-P

Ok. Will see that later. I postponed to #16535 if you agree.

• Why not put the cache only for find_recursive_construction? (less cached function and less function calls)

Because this function returns both OA and True/False answers. The find_* functions I cached only return immutable stuff.

But why not having orthogonal_array implements the three lines that are right now in find_recursive_construction? My main concern is about readability. I would prefer

@cached_method
def find_recursive_construction(k,n):
    for find_c in [find_construction_3_3,
                   find_construction_3_4,
                   find_construction_3_5,
                   find_construction_3_6]:
        res = find_c(k,n)
        if res: return res

That way:

• you still have the freedom to update find_recursive_construction without touching orthogonal_array
• you keep an eye on who did what with the cache
• you perform the work of adapting your answer only in orthogonal_array
• if you changed your mind about the syntax existence=True and such you will not have to touch to find_recursive_construction
• the file orthogonal_array_recursive.py will look like a "dynamical" database in the very same way that database.py is a static one

Vincent

[ncohen]

Yo !

Ok. Will see that later. I postponed to #16535 if you agree.

I will have to rebase what is currently above this patch, then.

Well.... does not matter...

But why not having orthogonal_array implements the three lines that are right now in find_recursive_construction?

Oh, you mean only the part that actually creates the design ? Yeah, why not !...

I will add a commit for that in a second.

Nathann

[git]

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

​41c50d5

trac #16500: Simplified find_recursive_construction

[vdelecroix]

Hi,

small commit at u/vdelecroix/16500

Be careful that a truncated OA is not an incomplete OA. In truncated OA you removed points in columns whereas in incomplete OA you have less blocks than an OA (but columns are not changed)... it is very confusing to read your doc. And moreover you use block or column indifferently but it would be better to have a unique name for that.

In the doc of the construction 3.4 there is

- If there exists an `OA(k,m+r+1)` the column of size `s` is truncated in
  order to intersect `B_0`.

- If there exists an `OA(k,m+r+1)`, the last column must not intersect `B_0`

which is contradictory!

The rest is fine except that there is no need to use linear programming to build an oval, see #16552.

Vincent

[ncohen]

Yo !

small commit at u/vdelecroix/16500

Looks good !

Be careful that a truncated OA is not an incomplete OA.

Arg yes yes, I always mix the two words ^^;

And moreover you use block or column indifferently but it would be better to have a unique name for that.

Do you mean "column or group" ? There are n^2 blocks in an OA(k,n) but k columns.

In the doc of the construction 3.4 there is

- If there exists an `OA(k,m+r+1)` the column of size `s` is truncated in
  order to intersect `B_0`.

- If there exists an `OA(k,m+r+1)`, the last column must not intersect `B_0`

which is contradictory!

I don't se how O_o

The rest is fine except that there is no need to use linear programming to build an oval, see #16552.

Oh ? Cool. Free ovals ! :-D

Nathann

[git]

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

​e1992ce

trac #16500: doc + speedup

[ncohen]

What exactly needs work ?

Nathann

[vdelecroix]

Replying to ncohen:

What exactly needs work ?

the doc of construction 3.4

[ncohen]

Then please answer my question above : what is wrong in those sentences ?

Nathann

[ncohen]

Oh. Right.

[git]

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

​697dd0c

trac #16500: Typoes in the doc

[vdelecroix]

This one was much easier once the Wilson construction is understood!

Do you already did the even more general construction from Brouwer-Rees 1982 (they consider generalization of truncated OA where the extra columns are partitioned in possibly more than two parts)?

Vincent

[ncohen]

Yo !

This one was much easier once the Wilson construction is understood!

Yep yep. That's what I will remember of design theory. Deadly scary stuff that becomes totally straightforward once you pay attention to it.

Still, a lot of stuff remains deadly scary in the field :-P

Do you already did the even more general construction from Brouwer-Rees 1982 (they consider generalization of truncated OA where the extra columns are partitioned in possibly more than two parts)?

Now yet, but I will have to. What scares me is not the implementation of the construction, but how to properly write the input part of the function T_T

Nathann

[ncohen]

This one was much easier once the Wilson construction is understood!

Some smarter comment: I believe that it is thanks to work like the one we do that we can get to understand such things. That's how it happened to me with LP : I had to implement very basic things 1000 times for Sage, and in the end I find myself understanding the basics properly, which would have NEVER happened if I had just had a book in front of me. Or even if it was in Sage's code.

When you implement Sage stuff you are forced to spend time on things you would quickly look at otherwise.

Nathann