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Posted to user@commons.apache.org by Yaqiang Wang <ya...@gmail.com> on 2022/09/20 07:44:05 UTC
Re: Use non-linear least squares to fit a function
Unfortunately, I can not figure out how to calculate partial gradients
using DerivativeStructure, so I used a simple way to calculate the
gradients of the parameters (
https://github.com/meteoinfo/MeteoInfo/blob/9586b1a850721e418370a8a3d90af1e8fea03674/meteoinfo-math/src/main/java/org/meteoinfo/math/optimize/MyParametricUnivariateFunction.java).
The result looks reasonable:
http://www.meteothink.org/downloads/temp/curve_fit.png.
Regards
Yaqiang
On Tue, Aug 2, 2022 at 7:34 PM Gilles Sadowski <gi...@gmail.com> wrote:
> Hello.
>
> Le mar. 2 août 2022 à 10:42, Yaqiang Wang <ya...@gmail.com> a
> écrit :
> >
> > Gilles,
> >
> > What I gather from the documentation is that the intended purpose is
> > > to track the values of some function and all its derivatives when the
> > > function is defined programmatically (using the usual arithmetical
> > > operators, and generalizations of the functions defined in the "Math"
> > > JDK class). IIUC, one gains automatic access to the derivatives
> > > without defining them analytically (only the function need be defined).
> > >
> >
> > Yes, the function is defined programmatically.
>
> Perhaps have a look at
>
> https://commons.apache.org/proper/commons-math/commons-math4-legacy/apidocs/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunction.html
> The associated unit test could also help figure out how to use
> "DerivativeStructure":
>
> https://commons.apache.org/proper/commons-math/commons-math4-legacy/xref-test/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunctionTest.html
>
> >
> > How is "function" defined here?
> > >
> >
> > "function" is a ParameUnivariateFunction instance which implements
> > UnivariateFunction interface with parameters (
> >
> https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-math/src/main/java/org/meteoinfo/math/optimize/ParamUnivariateFunction.java
> ).
> > Its is used to wrap the Jython function (
> >
> https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-lab/pylib/mipylib/numeric/optimize/minpack.py#L78-L135
> > ).
> >
> > The test Jython script and result figure from current curve_fit function
> > can be found here:
> http://www.meteothink.org/downloads/temp/curve_fit-1.png
> > , http://www.meteothink.org/downloads/temp/curve_fit-2.png,
> > http://www.meteothink.org/downloads/temp/curve_fit-3.png.
> >
> > Your code of gradient method (as below) was also tested with good result
> (
> > http://www.meteothink.org/downloads/temp/curve_fit-4.png). But of
> course it
> > can only work for that specific function.
>
> Sure, but I still can't figure out where the problem is: Do you want to
> implement the fitting using numerical derivatives because the gradient
> cannot be expressed simply, or just to save one input (the equivalent
> of the code below)?
> In the latter case, I believe that "DerivativeStructure" could do it. But
> so should it, with a package that performs symbolic differentiation (?).
>
> > public double[] gradient(double x, double ... parameters) {
> > > final double a = parameters[0];
> > > final double b = parameters[1];
> > > final double c = parameters[2];
> > > final double[] grad = new double[3];
> > > grad[0] = Math.exp(-b * x);
> > > grad[1] = -a * x * grad[0];
> > > grad[2] = 1;
> > > return grad;
> > > }
> > >
>
> Regards,
> Gilles
>
> P.S. If you succeed in framing the solution to your problem with
> "DrivativeStructure",
> we are interested in documenting it in "SimpleCurveFitter".
>
> >>> [...]
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
> For additional commands, e-mail: user-help@commons.apache.org
>
>
--
*************************************************
Dr. Yaqiang Wang
Chinese Academy of Meteorological Sciences (CAMS)
46, Zhong-Guan-Cun South Avenue
Beijing, 100081
China
yaqiang.wang@gmail.com
www.meteothink.org
**************************************************
Re: Use non-linear least squares to fit a function
Posted by Yaqiang Wang <ya...@gmail.com>.
I found the solution to calculate partial gradients of the parameters
unsing FiniteDifferencesDifferentiator and DerivativeStructure:
https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-math/src/main/java/org/meteoinfo/math/optimize/MyParametricUnivariateFunction.java.
A test case was also added:
https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-math/src/test/java/org/meteoinfo/math/optimize/FiniteDifferencesDifferentiatorTest.java
.
Hope this will be helpful on this issue.
Regards
Yaqiang
On Tue, Sep 20, 2022 at 3:44 PM Yaqiang Wang <ya...@gmail.com> wrote:
> Unfortunately, I can not figure out how to calculate partial gradients
> using DerivativeStructure, so I used a simple way to calculate the
> gradients of the parameters (
> https://github.com/meteoinfo/MeteoInfo/blob/9586b1a850721e418370a8a3d90af1e8fea03674/meteoinfo-math/src/main/java/org/meteoinfo/math/optimize/MyParametricUnivariateFunction.java).
> The result looks reasonable:
> http://www.meteothink.org/downloads/temp/curve_fit.png.
>
> Regards
> Yaqiang
>
> On Tue, Aug 2, 2022 at 7:34 PM Gilles Sadowski <gi...@gmail.com>
> wrote:
>
>> Hello.
>>
>> Le mar. 2 août 2022 à 10:42, Yaqiang Wang <ya...@gmail.com> a
>> écrit :
>> >
>> > Gilles,
>> >
>> > What I gather from the documentation is that the intended purpose is
>> > > to track the values of some function and all its derivatives when the
>> > > function is defined programmatically (using the usual arithmetical
>> > > operators, and generalizations of the functions defined in the "Math"
>> > > JDK class). IIUC, one gains automatic access to the derivatives
>> > > without defining them analytically (only the function need be
>> defined).
>> > >
>> >
>> > Yes, the function is defined programmatically.
>>
>> Perhaps have a look at
>>
>> https://commons.apache.org/proper/commons-math/commons-math4-legacy/apidocs/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunction.html
>> The associated unit test could also help figure out how to use
>> "DerivativeStructure":
>>
>> https://commons.apache.org/proper/commons-math/commons-math4-legacy/xref-test/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunctionTest.html
>>
>> >
>> > How is "function" defined here?
>> > >
>> >
>> > "function" is a ParameUnivariateFunction instance which implements
>> > UnivariateFunction interface with parameters (
>> >
>> https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-math/src/main/java/org/meteoinfo/math/optimize/ParamUnivariateFunction.java
>> ).
>> > Its is used to wrap the Jython function (
>> >
>> https://github.com/meteoinfo/MeteoInfo/blob/master/meteoinfo-lab/pylib/mipylib/numeric/optimize/minpack.py#L78-L135
>> > ).
>> >
>> > The test Jython script and result figure from current curve_fit function
>> > can be found here:
>> http://www.meteothink.org/downloads/temp/curve_fit-1.png
>> > , http://www.meteothink.org/downloads/temp/curve_fit-2.png,
>> > http://www.meteothink.org/downloads/temp/curve_fit-3.png.
>> >
>> > Your code of gradient method (as below) was also tested with good
>> result (
>> > http://www.meteothink.org/downloads/temp/curve_fit-4.png). But of
>> course it
>> > can only work for that specific function.
>>
>> Sure, but I still can't figure out where the problem is: Do you want to
>> implement the fitting using numerical derivatives because the gradient
>> cannot be expressed simply, or just to save one input (the equivalent
>> of the code below)?
>> In the latter case, I believe that "DerivativeStructure" could do it. But
>> so should it, with a package that performs symbolic differentiation (?).
>>
>> > public double[] gradient(double x, double ... parameters) {
>> > > final double a = parameters[0];
>> > > final double b = parameters[1];
>> > > final double c = parameters[2];
>> > > final double[] grad = new double[3];
>> > > grad[0] = Math.exp(-b * x);
>> > > grad[1] = -a * x * grad[0];
>> > > grad[2] = 1;
>> > > return grad;
>> > > }
>> > >
>>
>> Regards,
>> Gilles
>>
>> P.S. If you succeed in framing the solution to your problem with
>> "DrivativeStructure",
>> we are interested in documenting it in "SimpleCurveFitter".
>>
>> >>> [...]
>>
>> ---------------------------------------------------------------------
>> To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
>> For additional commands, e-mail: user-help@commons.apache.org
>>
>>
>
> --
> *************************************************
> Dr. Yaqiang Wang
> Chinese Academy of Meteorological Sciences (CAMS)
> 46, Zhong-Guan-Cun South Avenue
> Beijing, 100081
> China
>
> yaqiang.wang@gmail.com
>
> www.meteothink.org
> **************************************************
>
--
*************************************************
Dr. Yaqiang Wang
Chinese Academy of Meteorological Sciences (CAMS)
46, Zhong-Guan-Cun South Avenue
Beijing, 100081
China
yaqiang.wang@gmail.com
www.meteothink.org
**************************************************