Re: finding approximate 'least common factor'

[Przemek Klosowski]

On 05/26/2011 05:26 PM, Jordi Gutiérrez Hermoso wrote:
> On 24 May 2011 10:41, Przemek Klosowski<address@hidden>  wrote:
> > I have numbers which are approximately (but not exactly) an integer number
> > of some basic quantity. How would you estimate that basic quantum? For
> > instance, if the data is:
> >
> > a= [5500 3800 3300 3800 4000 5500 2600 3800 5500 2500 4000 6000 4000 450
> > 1550 1000 3800 5300 5300 1800 3800 1550 2500 3300 1300 2500 3300 2500 1550
> > 5500 2200 3500 3300 2200 1300 800 2200 1000 2500 5300 3000 2200 2200 2200
> > 4000 2400 2200 5500 4000 800 2200 2600 450 450 ]
> [snip]
> > Can anyone think of a more precise numerical algorithm?
>
> The subject of this thread should be about greatest, not least common
> factor, right?

Right, sorry.

> So it's a problem about finding the relative mininum of the following
> objective functions:
>
>       f = @(x) norm(fmod(bsxfun(@rdivide, a(:), x(:)'),1),"columns");
>
> i.e. looking at the x that minimises the norm of the fractional part
> of the vector a divided by a proposed quantum x.

Yes, but this looks separately at each multiple---i.e. dips at 600 give 
a tiny minimum, and dips at 1200 also give a tiny mininum, but together 
they signify a better agreement that each of them separately would 
indicate. My original method kind-of took that into account, actually.

>       gcd(num2cell(a){:})

let's not forget  0, and 1.  :)