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 <yaqiang.w...@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 <gillese...@gmail.com> > wrote: > >> Hello. >> >> Le mar. 2 août 2022 à 10:42, Yaqiang Wang <yaqiang.w...@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-unsubscr...@commons.apache.org >> For additional commands, e-mail: user-h...@commons.apache.org >> >> > > -- > ************************************************* > Dr. Yaqiang Wang > Chinese Academy of Meteorological Sciences (CAMS) > 46, Zhong-Guan-Cun South Avenue > Beijing, 100081 > China > > yaqiang.w...@gmail.com > > www.meteothink.org > ************************************************** > -- ************************************************* Dr. Yaqiang Wang Chinese Academy of Meteorological Sciences (CAMS) 46, Zhong-Guan-Cun South Avenue Beijing, 100081 China yaqiang.w...@gmail.com www.meteothink.org **************************************************
