Re: rank(gf) doesn't really work?

[David Bateman]

Lapo Luchini wrote:

> Maybe I'm missing some important point (e.g. "gfrank" is not defined) and this
> is really not supported, but it gives different result on gf() than on a normal
> array so just maybe it shuold work..?
>
> $ B=gf([0,1,0,0,1,1;
> 0,0,1,1,1,0;
> 0,1,1,1,0,0;
> 1,0,1,1,0,0;
> 1,1,0,1,0,0;
> 1,1,1,0,0,0]);
> $ D=gf([0,1,0,0,1,1;
> 0,0,1,1,1,0;
> 0,1,1,1,0,0;
> 1,0,1,1,0,0;
> 1,1,0,1,0,0;
> 0,1,1,0,0,0]);
> $ B+D
> ans =
> GF(2) array.
>
> Array elements =
>
>  0  0  0  0  0  0
>  0  0  0  0  0  0
>  0  0  0  0  0  0
>  0  0  0  0  0  0
>  0  0  0  0  0  0
>  1  0  0  0  0  0
> $ rank(B)
> ans = 6
> $ rank(D)
> ans = 4
>
> Then, if B is full-rank (6 out of 6) how can possibly D be rank 4 if the first 5
> lines are the very same 5 lines that in B were linearly independent?
>
> It just seems that it works, but only on square matrices, and it just ignores
> any other column:
> $ rank(B(1:5,1:5))
> ans = 4
> $ rank(B(1:5,2:6))
> ans = 5
> $ rank(B(1:5,:))
> ans = 4
>
> I would expect last line to be 5 as well. Maybe rank(B(1:5,:)) just uses the
> first 5 columns in the 5x6 matrix?
>
> Mhh...?
>
>    Lapo
>
>  
Yes this is a bug.. The rank function does an LU factorization of the 
galois array which pivots where it can and then attempts to count the 
rank deficiencies where it can't. Unfortunately, I messed this up. The 
relevant function is galois.cc (LU::factor) and the "info" variable. 
I'll look at it and try and fix it...

D.

--
David Bateman                                address@hidden
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 1 69 35 77 01 (Fax) 
91193 Gif-Sur-Yvette FRANCE

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