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From jeesh <michaelwong8...@gmail.com>
Subject Re: [Math] Jacobian Matrix of f(x,y)
Date Mon, 04 Jul 2011 19:14:25 GMT
Thanks a lot Luc!  I'm an undergrad with some limited math background but no
programming experience (before this project) so your help has really been
invaluable.

Keep up the good work,
Michael



On Mon, Jul 4, 2011 at 2:45 PM, Luc Maisonobe [via Apache Commons] <
ml-node+3644310-2041674435-249529@n4.nabble.com> wrote:

> 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?
>
> If I understand your needs, this is an additional, independent problem
> 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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-- 
Michael Wong


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