Re: [eigen] on fuzzy comparisons

[Benoît Jacob <jacob@xxxxxxxxxxxxxxx>]

> *****************************************************************
> m1 << m2 if and only if we have m1*v << m2*v for all vectors v
> *****************************************************************
>
> Sounds reasonable doesn't it? I am very attached to the fact that this
> relation has such a simple geometrical meaning. The implemented algorithm
> amounts to check that for v running over the canonical basis, and this is
> equivalent to checking it for all vectors v.

sorry, i must correct that. The current solution checks that

m1 << m2 if and only if we have m1*v << m2*v for all vectors v

for v = e_1, ...., e_n, the n vectors of the canonical basis. This is in fact 
not equivalent to checking that for all vectors v, although one direction 
obvously is true -- if it's true for all vectors v, then in particular it's 
true for v = e_1, ... , e_n.

Now that we have matrixNorm() I am quite open to the idea of implementing 
matrix comparisons on top of it. At least that's mathematically satisfying. 
What's your opinion?

Cheers,
Benoit

Attachment: signature.asc
Description: This is a digitally signed message part.