On Wed, 9 Sep 2015 18:45:51 +0200, Thom Brown wrote:
Hi!
I think I'm beginning to understand now (thanks to your awesome
explanations). Yes, wow, calculating the derivatives of F(t) wrt to
the
parameters isn't that hard. I thought way too complicated, I'm
afraid.
Now I'm just unsure about one thing:
[Since the model "F(t)" refers to earlier times, I guess that you'll
have
to create a specific class in order to look up the correct "S", "b"
and
"I".]
After thinking about it, do you mean I should solve my problem like
that:
MultivariateJacobianFunction distanceToCurrentF = new
MultivariateJacobianFunction() {
public Pair<RealVector, RealMatrix> value(final RealVector
params) {
Vector3D approx = new Vector3D(params.getEntry(0),
params.getEntry(1), params.getEntry(2)); //get current estimations of
alpha, beta and gamma
RealVector value = new
ArrayRealVector(observedValues.length);
RealMatrix jacobian = new
Array2DRowRealMatrix(observedValues.length, 3); // can I even use
Array2DRowRealMatrix if I have 3 columns?
for (int i = 0; i < observedValues.length; ++i) {
Vector o = observedValues[i];
// calculate current values using
helper.calculate...();
double modelF = (helper.getCurrentS() +
helper.getCurrentB()) * helper.getCurrentI(i);
value.setEntry(i, modelF);
jacobian.setEntry(i, 0, derivative of dF/dalpha);
jacobian.setEntry(i, 1, derivative of dF/dbeta);
jacobian.setEntry(i, 2, derivative of dF/dgamma);
}
return new Pair<RealVector, RealMatrix>(value, jacobian);
}
};
Is that somehow correct?
I'd think so; that should be the idea. [But no warranty...]
I'm unsure because in the example were vectors
used for geometrical points and thus, I'm wondering if I can use an
Array2DRowRealMatrix
Sure.
or if I need something else?
And as for the optimization step:
double[] prescribedValues = new double[observedValues.length];
Arrays.fill(prescribedValues, alpha, beta, gamma); // this will not
work, because I cannot use Arrays.fill() with two additional
parameters, what else should I use here? As in: what else can I use
to
process my target?
Remember that "target" must contain the measurements (i.e. the
observed values of the model function "F"), not the parameters of
the model.
However, I'm not sure how everything plays out.
If I had to do the work, I'd take the case described there:
http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc436.htm
as a unit test.
// least squares problem to solve : modeled radius should be close
to target radius
LeastSquaresProblem problem = new LeastSquaresBuilder().
start(new double[] { 0.0, 1.0 } /* I
suppose I cannot add two further double arrays representing beta and
gamma in that way? Do I need a RealVector instead? Like a RealVector
that contains three Real Vector with the boundaries for alpha, beta
and gamma?*/).
Yes, you have to have an "initial guess" for each of the parameters
of the model.
model(distancesToCurrentF).
target(prescribedValues).
lazyEvaluation(false).
maxEvaluations(1000).
maxIterations(1000).
build();
LeastSquaresOptimizer.Optimum optimum = new
LevenbergMarquardtOptimizer().optimize(problem);
I hope this gets formatted in a readable way as my posts are somewhat
strangely formatted after submitting them. :P
[I guess that it's because everything is aligned in a variable-width
font, while the ML use a fixed-width font.]
Best regards,
Gilles
Thanks again for answering my questions and giving me all that input!
It's
highly appreciated.
Best regards
Thom
PS: sorry for my rough English, I'm obviously struggling along with
finding
the best/right terms describing mathematical issues. :P
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