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From jeesh <michaelwong8...@gmail.com>
Subject Re: [Math] Jacobian Matrix of f(x,y)
Date Sun, 03 Jul 2011 20:24:51 GMT
Thanks for the quick replies.  I'll see if I can get that to work and let
you know.

On Sun, Jul 3, 2011 at 10:54 AM, Luc Maisonobe [via Apache Commons] <
ml-node+3642029-1270943118-249529@n4.nabble.com> wrote:

> 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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--
Michael Wong

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