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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject Re: [Math] Jacobian Matrix of f(x,y)
Date Sun, 03 Jul 2011 14:53:12 GMT
Le 03/07/2011 14:47, jeesh a écrit :
> Hi everyone,

Hi Jeesh,

> I'm somewhat new to java, but I'm looking to build a least squares
> optimization routine for a 2D Gaussian Fit based on this link (about half
> way down) http://commons.apache.org/math/userguide/optimization.html.
>
> Just a general question - how would I go about structuring the Jacobian
> matrix for a two component function?

You can organize the rows as you want. In the quadratic example of the 
user guide page you cite, the rows correspond to simply to different 
measurement points. For simplicity, they have been put in x increasing 
order, but they could have been put in any order. So in your case, you 
could choose something like:

   index 0  : (x0, y0)
   index 1  : (x0, y1)
   index 2  : (x0, y2)
   ...
   index n-1: (x0, yn-1)
   index n  : (x1, y0)
   index n+1: (x1, y1)
   ...

or the other way round:

   index 0  : (x0, y0)
   index 1  : (x1, y0)
   index 2  : (x2, y0)
   ...
   index m-1: (xm-1, y0)
   index m  : (x0, y1)
   index m+1: (x1, y1)
   ...

or even a random order, and your (xi,yj) samples may even not be 
regularly spaced but could be random points.

Once you have chose some ordering, you should use the same order for the 
rows of the jacobian matrix and the values of the function as returned 
by the respectively the jacobian method and the value method of your 
DifferentiableMultivariateVectorialFunction implementation. The same 
order should also be used for the target array you pass to the optimize 
method of the optimizer.

best regards,
Luc

>
> Any help would be appreciated.
>
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