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Fitting in AIDA

Fitting in AIDA. General Concepts Requirements JAIDA Examples Interfaces Overview Conclusions. General Concepts. The main players: Data Set the actual data, i.e. an Histogram Model or Function a set of parametric shapes to describe the data Fitter

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Fitting in AIDA

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  1. Fitting in AIDA • General Concepts • Requirements • JAIDA • Examples • Interfaces Overview • Conclusions

  2. General Concepts • The main players: • Data Set • the actual data, i.e. an Histogram • Model or Function • a set of parametric shapes to describe the data • Fitter • the engine that finds the best fit between the data and the model by changing a set of paramters • Fit Method • the method used by the fitter to evaluate the “best fit”, i.e. Chi2, Least Squares etc. • Fit Result • the actual result of a fit • new set of parameters • covariance matrix • contours • scans • Optimizer • the engine that calculates the minimum (or maximum) of the problem

  3. User General Concepts Optimizing Optimizer Model/Function Result

  4. Fit Method Data Set Model/Function User General Concepts Fitting Optimizer Fitter Fit Result

  5. Requirements • Easy to use and configure • change fit method • change data set • change model • Easy access to pool of optimizers • Minuit is a must, but not the only product. Many optimizers are available. • Accept user-provided custom functions • Straightforward way to build complicated models • Add, multiply and convolute (analytically when possible)

  6. Requirements • Same interface for binned and unbinned fits • binned fit to histogram • unbinned fit to a tuple • Similar interfaces for fitting and optimization • Multiple fit methods supported • least squares • chi2 • …user defined (advanced) • Support for simultaneous fits • fits over different data sets

  7. JAIDA • JAIDA is our Java implementation of AIDA • http://java.freehep.org/jaida/index.html • Fitting implementation: • fit methods • least squares • “leastsquares”, “ls” • chi2 • “chi2”, “chisquared” • clever chi2 • “cleverchi2”, cleverchisquared” • binned maximum likelihood • “bml”, “binnedmaxlikelihood”, binnedmaximumlikelihood” • unbinned maximum likelihood • “uml”, “unbinnedmaxlikelihood”, “unbinnedmaximumlikelihood” • engines • Minuit • Uncmin (pure java code)

  8. JAIDA • built-in functions • gaussian “g” • “amplitude”, “mean”, “sigma” • exponential “e” • “amplitude”, “exponent” • polynomials “p0”,”p1”,… • “p1”,”p2”… • Clear distinction between optimization and error analysis • easy to adopt new optimizers • The examples below are based on JAIDA • other implementations might have different fit methods or optimizers.

  9. Examples Binned fit to an IHistogram //Create the factories … IFitter fitter = af.createFitFactory().createFitter(); //Perform the fit IFitResult result = fitter.fit(hist,”g”); //Plot the result IPlotter p = af.createPlotterFactory().create(); p.region(0).plot(hist); p.region(0).plot(result.fittedFunction()); p.show()

  10. Examples Binned fit to a 2D Histogram //Create the factories … IFunctionfactory funcFactory = af.createFunctionFactory( tree ); IFitter fitter = af.createFitFactory().createFitter("chi2","minuit"); //Create a scripted function, a sum of two gaussians IFunction func = funcFactory.createFunctionFromScript("twoDdistr",2,"N*(a*exp( -(x[0]-mu0)*(x[0]-mu0)/(2*s0*s0) )+(1-a)*exp( -(x[0]-mu1)*(x[0]-mu1)/(2*s1*s1) ))*exp( -(x[1]-mu2)*(x[1]-mu2)/(2*s2*s2) )","N,a,mu0,s0,mu1,s1,mu2,s2","",null); //Set the initial parameters double[] initialPars = { 1, 0.8, 5, 1, 5, 2, 0, 1}; func.setParameters( initialPars ); //Control the parameters and set constraints fitter.fitParameterSettings("mu2").setFixed(true); fitter.fitParameterSettings("a").setBounds(0.5,0.9); fitter.fitParameterSettings("a").setStepSize(0.001); fitter.fitParameterSettings("s1").setBounds(2,4); fitter.fitParameterSettings("s1").setStepSize(0.1); fitter.setConstraint("s0 = s2"); fitter.setConstraint("mu0 = mu1"); //Perform the fit IFitResult fitResult = fitter.fit(hist2d,func);

  11. Examples Unbinned Fit //Create the factories … IFunctionfactory funcFactory = af.createFunctionFactory( tree ); IFitFactory fitf = af.createFitFactory(); IFitter fitter = fitf.createFitter(“uml",“uncmin"); IFitData data = fitf.createFitData(); ITupleFactory tupf = af.createTupleFactory(tree); //Create a function, control the parameters, set bounds and constraints… //… //Get and ITuple and create an IEvaluator for its columns ITuple tuple = (ITuple) tree.find(“myTuple”); IEvaluator eval = tupf.createEvaluator(“sqrt(px*px + py*py)”); //Connect the data set to the ITuple through the IEvaluator data.createConnection(tuple, eval); //Perform the fit IFitResult fitResult = fitter.fit(data,func);

  12. Interfaces Overview The factories • From IAnalysisFactory • IFitFactory createFitFactory() • IFunctionFactory createFunctionFactory(ITree) • IFitFactory creates • fitters • data sets (for advanced data handling) • e.g. select columns from tuple • IFunctionFactory creates • functions

  13. Interfaces Overview IFitFactory • Methods • IFitData createFitData() • IFitter createFitter(fitMethod,engine) • Through IFitData connections to all the AIDA data objects are established • IFitter is the main fitting engine

  14. Interfaces Overview IFunctionFactory • IFunction creatFunctionByName(name,model) • IFunction createFunctionFromScript(……) • IFunction cloneFunction(name, function) • IFunctionCatalog catalog() • “byName” are built-in functions • “fromScript” are scripted functions • user-defined functions • e.g. define “Gauss+Gauss+Pol1+…” to be “myFavoriteFunc” • …that can be added to a function catalog for future use

  15. Interfaces Overview IFitter • Do the fit • IFitResult fit(“data”,”model”,”pars”) • IDataPointSet createContour(IFitData, IFitResult…..) • IDataPointSet createScan1D(IFitData, IFunction…) • Configure the fitter • void setFitMethod(String) • String fitMethodName() • void setEngine(String) • String engineName() • void setUseFunctionGradient(boolean) • boolean userFunctionGradient() • Control the parameters in the fit • IFitParameterSetting fitParameterSettings(String) • String[] listParameterSettings() • void resetParameterSettings()

  16. Interfaces Overview IFitter • Constraints • void setConstraint(String) • String[] constraints() • void resetConstraints() • The fitter does not change the function; the fitted parameters are in the IFitResult

  17. Interfaces Overview IFitResult • Fit outcome • int fitStatus() • int ndf() • double quality() • Fit info • String fitMethodName() • String engineName() • String dataDescription() • String[] constraints() • Fitted function • IFunction fittedFunction() • String[] fittedParameterNames() • double fittedParameter(String) • double fittedParameters() • IFitParameterSettings fitParameterSettings(String) • Errors • double covMatrixElement(int,int) • double[] errors() • double[] errorsMinus() • double[] errorsPlus()

  18. Interfaces Overview IFitData • Connect the data • create1DConnection(…) • create2DConnection(…) • create3DConnection(…) • createConnection(…) • Ranges • IRangeSet range(int) • Utils • String dataDescription() • int dimension() • reset()

  19. Interfaces Overview IFunction • General • double value(double[]) • double[] gradient(double[] x) • int dimension() • int numberOfParameters() • boolean providesGradient() • Variables • String variableName(int) • String[] variableNames() • Parameters • String[] parameterNames() • double[] parameters() • double parameter(String) • int indexOfParameter(String) • void setParameter(String,double) • void setParameters(double[])

  20. Interfaces Overview IFitParameterSettings • Control a parameter • Bounds • double lowerBound() • void setLowerBound(double) • double upperBound() • void setUpperBound() • boolean isBound() • void setBounds(double, double) • void removeBounds() • Step • void setStepSize(double) • double stepSize() • Fix • boolean isFixed() • void setFixed(boolean) • Other • void reset() • String name()

  21. Conclusions • AIDA has a complete set of interfaces for fitting • flexible interfaces • room for improvements • JAIDA future: • Extend the pool of optimizers • Implement more built-in functions • Allow model-building

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