Hi.
On Mon, 7 Sep 2015 12:07:36 +0200, Thom Brown wrote:
I've read both guides (
http://commons.apache.org/proper/commons-math/userguide/optimization.html
and
http://commons.apache.org/proper/commons-math/userguide/leastsquares.html)
regarding optimization yet I'm still unsure about how to apply those
examples to my case.
What I want to do is to optimize the parameters alpha, beta and gamma
in
these three equations:
http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc435.htm
The code in the "o.a.c.m.fitting.leastsquares" package (second
reference
to the user guide, above) should be fine.
I'm afraid I lack the mathematical understanding to come up with an
appropriate function. I well understand the Quadratic Problem
example,
however, I'm kind of overwhelmed when trying to do this for my
problem (as
my equation has three parts).
So, if you have N observations (indexed by the time variable), you'll
have
3 * N measurements. And the "target" will be for example:
[S(t0), b(t0), I(t0), S(t1), b(t1), I(t1), ..., S(tN), b(tN), I(tN)]
Then you have to define the "model" function which has to match the
contents of the "target" array.
Do I need to derive the different parameters
as it was done in the example?
You must provide the Jacobian (in the "model" function), i.e. a matrix
where
each line corresponds to a measurement, and the columns must be the
partial
derivatives wrt the parameters (i.e. "alpha", "beta" and "gamma").
Is there a way to do that without
calculating derivatives?
Why would you, since the derivatives are relatively easy to provide?
I'd appreciate some help towards this task as I'm not making any
process at
the moment. I hope this is the right place to put the question.
It's the right place, I hope. ;-)
HTH,
Gilles
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