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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject Re: [Math] Jacobian Matrix of f(x,y)
Date Mon, 04 Jul 2011 18:44:18 GMT
```Hi Jeesh,

Le 04/07/2011 19:47, jeesh a écrit :
> Thanks!  I've got it to work!  One more quick question - how would I take the
> function&  parameters that the algorithm just spat out and then find the
> global max z value (and associated x,y coordinate) of the function?

from the former one. In the former problem, you had some sampling points
and wanted to have the parameters of your Gaussian.

Now you have a perfectly defined Gaussian function, using the parameters
you have estimated from the first problem, and you want to find the
maximum of this function. Is this right ?

If this is right, then you can simply compute analytically the maximum
since Gaussian function is really simple. Lets say you defined your
Gaussian function from parameters p0, p1, p2, p3, p4 as follows:

g(x, y) = p0 * exp(-(x-p1)^2/p2 - (y-p3)^2/p4)

Then the maximum is at (xmax, ymax) = (p1, p3) and the corresponding
zmax value is p0.

If you had a much more difficult function for which solving analytically
the extremum is not feasible, then you should use another optimization
algorithm (like PowellOptimizer or CMAESOptimizer) that deal with
multivariate real-valued functions.

Luc

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