Hello.
Le mar. 11 août 2020 à 12:08, Christoph Läubrich
<lae...@googlemail.com.invalid> a écrit :
>
> Thanks for your patience, maybe a better/simpler example would be [1], I
> want to find the best fit using LSB
"LSB" ?
> under the constraint that the height
> of the curve never is above 0.7 (even though without constrains the
> optimizer would find a better solution around 8.5).
It occurs to me that this would be more properly defined as a
least-square problem by assigning an error bar (weight) to each
data point.
> So my first idea way to copy/extend GausianCurveFitter to accept some
> kind of "maxHeight(...)", adjust the function to return INF for
> h>maxHeight, I was just unsure that return INF is allowed (per
> definition) as it is not mentioned anywhere in the userdocs. And if I
> want to limit others (like max position) it would work the same way.
Hopefully "infinity" will not cause an issue; you could try and check.
[Then if it does, just use any suitably large value.]
> In my final problem I need to limit the height, width and position of
> the bell-curve to fall into certain bounds, but there is no direct
> relation (e.g. width must be three times the height).
Then, width is totally correlated (to height) and there are only
2 parameters to fit (height and mean); hence it's probably better
(and more efficient) to use that fact instead of defining the
correlation as a constraint i.e. define (untested):
---CUT---
public class MyFunc implements ParametricUnivariateFunction {
public double value(double x, double ... param) {
final double diff = x - param[1]; // param[1] is the mean.
final double norm = param[0]; // param[0] is the height.
final double s = 3 * norm; // "constraint".
final double i2s2 = 1 / (2 * s * s);
return Gaussian.value(diff, norm, i2s2);
}
// And similarly for the "gradient":
//
https://gitbox.apache.org/repos/asf?p=commons-math.git;a=blob;f=src/main/java/org/apache/commons/math4/analysis/function/Gaussian.java;h=08dcac0d4d37179bc85a7071c84a6cb289c09f02;hb=HEAD#l143
}
---CUT---
to be passed to "SimpleCurveFitter".
Regards,
Gilles
>
>
>
> [1]
> https://crlbucophysics101.files.wordpress.com/2015/02/gaussian.png?w=538&h=294
>
>
>
>
> Am 11.08.20 um 11:18 schrieb Gilles Sadowski:
> > Hi.
> >
> > 2020-08-11 8:51 UTC+02:00, Christoph Läubrich
> > <lae...@googlemail.com.invalid>:
> >> Hi Gilles,
> >>
> >>
> >> Just to make clear I don't suspect any error with GausianCurveFitter, I
> >> just don't understand how the advice in the user-doc to restrict
> >> parameter (for general problems) could be applied to a concrete problem
> >> and thus chosen GausianCurvefitter as an example as it uses
> >> LeastSquaresBuilder.
> >>
> >> I also noticed that Gaussian Fitter has a restriction on parameters
> >> (norm can't be negative) that is handled in a third way (returning
> >> Double.POSITIVE_INFINITY instead of Parameter Validator) not mentioned
> >> in the userdoc at all, so I wonder if this is a general purpose solution
> >> for restricting parameters (seems the simplest approach).
> >
> > I'd indeed suggest to first try the same trick as in "GaussianCurveFitter"
> > (i.e. return a "high" value for arguments outside a known range).
> > That way, you only have to define a suitable "ParametricUnivariateFunction"
> > and pass it to "SimpleCurveFitter".
> >
> > One case for the "ParameterValidator" is when some of the model
> > parameters might be correlated to others.
> > But using it makes it necessary that you handle yourself all the
> > arguments to be passed to the "LeastSquaresProblem".
> >
> >> To take the gausian example for my use case, consider an observed signal
> >> similar to [1], given I know (from other source as the plain data) for
> >> example that the result must be found in the range of 2...3 and I wanted
> >> to restrict valid solutions to this area. The same might apply to the
> >> norm: I know it must be between a given range and I want to restrict the
> >> optimizer here even though there might be a solution outside of the
> >> range that (compared of the R^2) fits better, e.g. a gausian fit well
> >> inside the -1..1.
> >>
> >> I hope it is a little bit clearer.
> >
> > I'm not sure. The picture shows a function that is not a Gaussian.
> > Do you mean that you want to fit only *part* of the data with a
> > function that would not fit well *all* the data?
> >
> > Regards,
> > Gilles
> >
> >>
> >>
> >> [1]
> >> https://ascelibrary.org/cms/asset/6ca2b016-1a4f-4eed-80da-71219777cac1/1.jpg
> >>
> >> Am 11.08.20 um 00:42 schrieb Gilles Sadowski:
> >>> Hello.
> >>>
> >>> Le lun. 10 août 2020 à 17:09, Christoph Läubrich
> >>> <lae...@googlemail.com.invalid> a écrit :
> >>>>
> >>>> The userguide [1] mentions that it is currently not directly possible to
> >>>> contrain parameters directly but suggest one can use the
> >>>> ParameterValidator, is there any example code for both mentioned
> >>>> alternatives?
> >>>>
> >>>> For example GaussianCurveFitter uses LeastSquaresBuilder and I wan't to
> >>>> archive that the mean is within a closed bound e.g from 5 to 6 where my
> >>>> datapoints ranges from 0..90, how would this be archived?
> >>>
> >>> Could you set up a unit test as a practical example of what
> >>> you need to achieve?
> >>>
> >>>> I'm especially interested because the FUNCTION inside
> >>>> GaussianCurveFitter seems to reject invalid values (e.g. negative
> >>>> valuenorm) by simply return Double.POSITIVE_INFINITY instead of using
> >>>> either approach described in the user-docs.
> >>>
> >>> What I don't quite get is why you need to force the mean within a
> >>> certain range; if the data match a Gaussian with a mean within that
> >>> range, I would assume that the fitter will find the correct value...
> >>> Sorry if I missed something. Hopefully the example will clarify.
> >>>
> >>> Best,
> >>> Gilles
> >>>
> >>>>
> >>>>
> >>>> [1]
> >>>> https://commons.apache.org/proper/commons-math/userguide/leastsquares.html
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