Re: finding approximate 'least common factor'

[Przemek Klosowski]

On 05/25/2011 12:46 PM, Thomas Shores wrote:
> On 05/24/2011 10:41 AM, Przemek Klosowski 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 ]
>
> It might help to have a little more information about the data, the
> nature of the error distribution, and what you intend to find.  For

The data is actually nominal capacity data of a series of batteries, and
I am trying to figure if they are built by paralleling several basic 
cells. Even if they were, the quoted number wouldn't have to be an even 
integer of the basic cell, because it's nominal and there are other 
physical effects of joining the cells. I don't know what's the error 
distribution, but it's gotta to be on the order of plus-minus a hundred 
or two.

> example, is the basic quantum an integer?  If so, this is a discrete
> problem which may not lend itself easily to continuous methods  or
> models (e.g., classical linear programming vs integer programming).

No, it doesn't have to be integer, although the numbers are such that 
anything +-50 is equivalent

> Also, if you believe ~650 to be an approximate quantum, this means that
> there is nearly 50% error in your last two data points, which is pretty
> extreme.  Could error in other points be comparable?  And finally, I
> think you may mean an approximate "greatest common divisor" since, after
> all, glancing at the data gives a perfectly accurate quantum of 50.

Right, this is all fuzzy, but take a look at the data, and it does make 
sense that they are made out of basic units that give 600 or so mAh 
capacity.