[scilab-Users] lsqrsolve

[ray joseph]

Gary,

Please let me know if this describes your experiment.

You have N sets of data.  You want to fit each one with its own Gaussian
curve.  You are not trying to determine the statistical distribution of the
magnitude of the numbers in each of the sets, but are addressing the
magnitudes of the sequence of numbers as if they were the range of (produced
from) a function on a sequentially ordered set of integers.  Such as:
yi = A*exp(-((xi-m)^2)/(2*s^2))

To do a least squared fit of (xi,yi) wrt (A,m,s):

Take the ln of both sides:
ln(yi) = ln(A) + -((xi-m)^2)/(2*s^2)

by letting -2*s^2 = 1/q, the above can be written:
ln(yi) = ln(A) + q*((xi-m)^2)
ln(yi) = ln(A) + q*(xi^2 - xi*m + m^2)
ln(yi) = ln(A) + q*xi^2 - q*xi*m + q*m^2)

If you do this for each of the j sets, each will have an independently fit
set (Aj,mj,sj).


Ray



----- Original Message ----- 
From: "Gary Nelson" <gnelson at quantasonics.com>
To: <users at lists.scilab.org>
Sent: Monday, May 17, 2010 5:57 PM
Subject: Re: [scilab-Users] lsqrsolve



Suppose I have a dataset that has N maxima and I want to fit a gaussian to
each one, and minimize the least square error between the sum of N gaussians
and the dataset.
I have tried this manually by tinkering the parameters and it clearly can be
done to good effect.
The datasets have 250 to 500 samples -- a smooth sequence of  positive
numbers with maxima that are plausibly gaussian shaped
Initial guess could be a set of amplitudes whose time locations are taken
from central difference positive to negative transits. I found that manual
tweaking by moving centers a fraction of a sample left or right would change
lsqerror, then tweaking amplitudes, then tweaking sigmas -- a couple
interations and the visible fit would be very good.

Now, how do I do this more rigorously?

Thanks

On May 4, 2010, at 7:57 PM, ray joseph wrote:

> Gary,
>
> I am sorry that I am bypassing your original request; but if you calculate
> the mean and standard deviation of your data set, you will get the two
> parameters.  Using the solver will be a fun exercise.
>
> Ray
>
> ----- Original Message ----- 
> From: "Gary Nelson" <gnelson at quantasonics.com>
> To: <users at lists.scilab.org>
> Sent: Tuesday, May 04, 2010 2:12 PM
> Subject: Re: [scilab-Users] lsqrsolve
>
>
> I would like to fit a gaussian to some data samples using least squares.
> The gaussian has two parameters -- amplitude and width (sigma).
>
> I would like to use 6 to 12 samples that span a maximum and provide a
first
> guess of the amplitude and width.
>
> After reading the manual on lsqsolve, it seems like it will do the job,
but
> I would appreciate some guidance to make it work.
>
> Thanks
>
> Gary Nelson
>
>
> On Apr 7, 2010, at 2:12 AM, Samuel Gougeon wrote:
>
>> ----- Message d'origine -----
>> De : Maso Ricci
>> Date : 31/03/2010 12:18:
>>> Hi,
>>>
>>> I am using the lsqrsolve function to fit some data.
>>> I wonder whether lsqrsolve accepts contrains in order to force the
> solution to be positive.
>>>
>>> thanks in advance for any comments and suggestions
>> Did you check the leastsq() function based on the optim() one ? Its 'b',
> binf, bsup
>> sequence of 3 input arguments allow to specify some boundaries.
>> So, for instance, if the solution you are searching for is a scalar that
> must be positive,
>> just set 'b',0,%inf. see help leastsq()
>>
>> HTH
>> Samuel
>>
>>
>
> Gary Nelson
> gnelson at quantasonics.com
>
>
>
>
>

Gary Nelson
gnelson at quantasonics.com