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January 9, January 3, It defines:. The color numbers specified in this palette can be viewed by selecting the menu entry Colors in the View menu of the canvas menu bar. A TPaletteAxis object is used to display the color palette when drawing 2D histograms. It is added to the histogram list of functions. It can be retrieved and its attributes can be changed with:.

The palette can be interactively moved and resized. The context menu can be used to set the axis attributes. For example, to draw the 2-D histogram h2 using all default attributes except the viewing angles, one can do:. Operators can be put in any order in the option and must be separated by a space " ". No space characters should be put in an operator.

All the available operators are described below. The following tables summarize all the possible combinations of both groups:. Next example sets line color to 2, line type to 1 and line width to 2. Note that if pa is not specified, the histogram line attributes are used:. Sometimes the displayed region is rather large. When displaying all channels the pictures become very dense and complicated. It is very difficult to understand the overall shape of data. Only the channels coinciding with given nodes are displayed.

Allowed values are 0, 90, and degrees. Note that the X and Y axis are always linear. For sophisticated shading Light, Height and LightHeight Display Modes Groups the color palette starts from the basic pen color see pa function. There is a predefined number of color levels Color in every level is calculated by adding the increments of the r , g , b components to the previous level.

Using this function one can change the color increments between two neighboring color levels. The function does not apply on the Simple Display Modes Group. The default values are: 1,1,1. When the level of a component reaches the limit value one can choose either smooth transition by decreasing the limit value or a sharp modulo transition continuing with 0 value.

This allows various visual effects. One can choose from the following set of the algorithms:. This function does not apply on Simple display modes group. Default value is 0. In Light and LightHeight display modes groups the color palette is calculated according to the fictive light source position in 3-d space.

This function does not apply for Simple and Height display modes groups. Default is: lp ,, The surface picture is composed of triangles. The edges of the neighboring triangles can be smoothed shaded. The shadow can be painted as well. The function does not apply on Simple display modes group. The possible values for shading are:. The function does not apply on other display modes groups and display modes. Default value is: b 0. This function applies only on for the Contours display mode.

One can change the width between horizontal slices and thus their density. Default value: cw For LightHeight display modes group one can change the weight between both shading algorithms. The function does not apply on other display modes groups. Default value is lhw 0. In addition to the surface drawn using any above given algorithm one can display channel marks.

One can control the color as well as the width, height in pixels and the style of the marks. The possible styles are:. In addition to the surface drawn using any above given algorithm one can display grid using the color parameter. The parameter enable can be set to:. By default a 3D scatter plot is drawn.

Using a TCutG object, it is possible to draw a 2D histogram sub-range. Up to 16 cuts may be specified in the cut string delimited by "[.. Currently only the following drawing options are sensitive to the cuts option: col , box , scat , hist , lego , surf and cartesian coordinates only.

The following script creates two histograms; the second histogram is the bins integral of the first one. It shows a procedure to draw the two histograms in the same pad and it draws the scale of the second histogram using a new vertical axis on the right side.

By default, a histogram drawing includes the statistics box. The parameter option can contain:. With the option "same" , the statistic box is not redrawn. With the option "sames" , it is re-drawn. If it hides the previous statistics box, you can change its position with the next lines where h is the histogram pointer :.

See the description of these classes for the list of options. The TPad ::SetTicks method specifies the type of tick marks on the axis. Use TPad ::SetTicks tx,ty to set these options. See also the methods of TAxis that set specific axis attributes. If multiple color-filled histograms are drawn on the same pad, the fill area may hide the axis tick marks.

One can force the axis redrawing over all the histograms by calling:. Because the axis title is an attribute of the axis, you have to get the axis first and then call TAxis ::SetTitle. The histogram title and the axis titles can be any TLatex string. The titles are part of the persistent histogram.

For example if you wanted to write E with a subscript T you could use this:. It is also possible to specify the histogram title and the axis titles at creation time. This makes an identical copy of the original histogram including all associated errors and functions:.

The following statements create a ROOT file and store a histogram on the file. Because TH1 derives from TNamed , the key identifier on the file is the histogram name:. The parameter option is a character string that specifies:.

Bin the KS distances in a histogram, and then take the integral of all the KS values above the value obtained from the original data to Monte Carlo distribution. The function returns the integral. TH1 ::Smooth - smoothes the bin contents of a 1D histogram.

TH1 ::GetMean int axis - returns the mean value along axis. TH1 ::GetStdDev int axis - returns the sigma distribution along axis. Then h3 is created and filled with the asymmetry between h1 and h2 ; h1 and h2 are left intact. TH1 ::Reset - resets the bin contents and errors of a histogram. By default, histogram statistics are computed at fill time using the unbinned data used to update the bin content. See the documentation on THGetStats.

This is useful if you want to keep track of the mean and standard deviation of the dataset you are visualizing with the histogram, but it can lead to some unintuitive results. For example, suppose you have a histogram with one bin between 0 and , then you fill it with a Gaussian dataset with mean 20 and standard deviation Next, zoom in on the Gaussian:.

What happened? Well, GetMean and GetStdDev and many other TH1 functions return the statistics for bins in range ; this is because the histogram only stores the contents of its bins, not the coordinates of the values used to fill it.

This remains true even if you zoom out:. To mark the X axis as having no range, you can call. If you want ROOT to consistently return the statistics of the binned dataset stored in the histogram and not those of the dataset used to fill it, you can call THResetStats. This will delete the statistics originally calculated at fill time and replace them with those calculated from the bins; note that you cannot later retrieve the original statistics—they are lost.

Continuing the example above,. If you fill the histogram again, the statistics will be a mix of binned and unbinned:. By default, a histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead.

This can always be done before or after filling. Bin labels will be automatically drawn with the histogram. You change that and draw the value of char[0] as an integer by adding an arithmetic operation to the expression as shown below. When using the options 2 or 3 above, the labels are automatically added to the list THashList of labels for a given axis. By default, an axis is drawn with the order of bins corresponding to the filling sequence.

It is possible to reorder the axis alphabetically or by increasing or decreasing values. When using the option second above, new labels are added by doubling the current number of bins in case one label does not exist yet.

When the filling is terminated, it is possible to trim the number of bins to match the number of active labels by calling:. Here axis may be X, Y, or Z. This operation is automatic when using TTree ::Draw. The THStack does not own the objects in the list. By default, THStack ::Draw draws the histograms stacked as shown in the left pad in the picture above. If the option "nostack" is used, the histograms are superimposed as if they were drawn one at a time using the "same" draw option.

The right pad in this picture illustrates the THStack drawn with the "nostack" option. TH2Poly is a 2D Histogram class allowing to define polygonal bins of arbitrary shape. TH2PolyBin is a very simple class containing the vertices and contents of the polygonal bin as well as several related functions.

Bins are defined using one of the AddBin methods. The bin definition should be done before filling. Profile histograms are in many cases an elegant replacement of two-dimensional histograms. The relationship of two quantities X and Y can be visualized by a two-dimensional histogram or a scatter-plot; its representation is not particularly satisfactory, except for sparse data. If Y is an unknown [but single-valued] function of X, it can be displayed by a profile histogram with much better precision than by a scatter-plot.

The following shows the contents [capital letters] and the values shown in the graphics [small letters] of the elements for bin j. When you fill a profile histogram with TProfile. Fill x,y :. In the special case where s[j] is zero, when there is only one entry per bin, e[j] is computed from the average of the s[j] for all bins. This approximation is used to keep the bin during a fit operation. The TProfile constructor takes up to eight arguments. The first five parameters are similar to TH1D constructor.

All values of y are accepted at filling time. To fill a profile histogram, you must use TProfile ::Fill function. Note that when filling the profile histogram the method TProfile ::Fill checks if the variable y is between fYmin and fYmax. If a minimum or maximum value is set for the Y scale before filling, then all values below ylow or above yup will be discarded. Setting the minimum or maximum value for the Y scale before filling has the same effect as calling the special TProfile constructor above where ylow and yup are specified.

The last parameter is the build option. If a bin has N data points all with the same value Y, which is the case when dealing with integers, the spread in Y for that bin is zero, and the uncertainty assigned is also zero, and the bin is ignored in making subsequent fits. That it is only in the case where the Y variable is some sort of counting statistics, following a Poisson distribution.

This is the default case. An example is an ADC measurement. The next figure shows the graphic output of this simple example of a profile histogram. This will draw the outline of the TProfile. To create a regular histogram from a profile histogram, use the method TProfile ::ProjectionX. The 'prof' and 'profs' options in the TTree ::Draw method generate a profile histogram TProfile , given a two dimensional expression in the tree, or a TProfile2D given a three dimensional expression.

Note that you can specify 'prof' or 'profs' : 'prof' generates a TProfile with error on the mean, 'profs' generates a TProfile with error on the spread. It is in many cases an elegant replacement of a three-dimensional histogram. The relationship of three measured quantities X, Y and Z can be visualized by a three-dimensional histogram or scatter-plot; its representation is not particularly satisfactory, except for sparse data.

If Z is an unknown but single-valued function of X,Y , it can be displayed with a TProfile2D with better precision than by a scatter-plot. The following shows the cumulated contents capital letters and the values displayed small letters of the elements for cell i,j. When you fill a profile histogram with TProfile2D. Fill x,y,z :. In the special case where s[i,j] is zero, when there is only one entry per cell, e[i,j] is computed from the average of the s[i,j] for all cells.

This approximation is used to keep the cell during a fit operation. The TPie class allows to create a Pie Chart representation of a one dimensional data set. The possible options to draw a TPie are:. The method SetLabelFormat is used to customize the label format.

The format string must contain one of these modifiers:. In combination with some other draw options an outer line is drawn on top of the histogram. The binning tab has two different layouts. One is for a histogram, which is not drawn from an ntuple. The other one is available for a histogram, which is drawn from an ntuple. In this case, the rebin algorithm can create a rebinned histogram from the original data i.

Rebin with a slider and the number of bins shown in the field below the slider. The number of bins can be changed to any number, which divides the number of bins of the original histogram. A click on the Apply button will delete the origin histogram and will replace it by the rebinned one on the screen. A click on the Ignore button will restore the origin histogram. Using this slider the effect of binning the data into bins can be made visible statistical fluctuations.

It is also possible to set the upper and lower limit in fields below the slider. Then the changes on the histogram are only updated, when the Slider is released. This should be activated if the redrawing of the histogram is time consuming. The Rebinning tab has two different layouts. One is for a histogram that is not drawn from an ntuple; the other one is available for a histogram, which is drawn from an ntuple.

To see the differences do for example:. Rebin with sliders one for the x, one for the y-axis and the number of bins shown in the field below them can be changed to any number, which divides the number of bins of the original histogram. Selecting the Apply button will delete the origin histogram and will replace it by the rebinned one on the screen.

Selecting the Ignore the origin histogram will be restored. This should be activated if the redrawing of the histogram is too time consuming. A graph is a graphics object made of two arrays X and Y, holding the x,y coordinates of n points. The TGraph class supports the general case with non-equidistant points, and the special case with equidistant points.

Graphs are created with the TGraph constructor. First, we define the arrays of coordinates and then create the graph. The coordinates can be arrays of doubles or floats. An alternative constructor takes only the number of points n. It is expected that the coordinates will be set later.

The default constructor can also be used. Further calls to SetPoint will extend the internal vectors. The various drawing options for a graph are explained in TGraph::PaintGraph. They are:. This option only applies to the TGraphAsymmErrors. The options are not case sensitive and they can be concatenated in most cases. Let us look at some examples. This code will only work if n, x, and y is defined.

The previous example defines these. You need to set the fill color, because by default the fill color is white and will not be visible on a white canvas. You also need to give it an axis, or the bar chart will not be displayed properly. This code will only work if n , x , y are defined. The first example defines them. You also need to give it an axis, or the filled polygon will not be displayed properly. Next is an example:. To control the size of the lines at the end of the error bars when option 1 is chosen use SetEndErrorSize np.

It inherits the various draw format options from TGraph. You can set the following additional options for drawing:. The low value is the length of the error bar to the left and down, the high value is the length of the error bar to the right and up. The TGraphBentErrors is drawn by default with error bars and small horizontal and vertical lines at the end of the error bars.

This option is interesting to superimpose systematic errors on top of a graph with statistical errors. The TGraphPolar class creates a polar graph including error bars. It uses the class TGraphPolargram to draw the polar axis. This is useful to show exclusion zones. This drawing mode is activated when the absolute value of the graph line width set thanks to SetLineWidth is greater than The current fill area attributes are used to draw the hatched zone.

A TGraphQQ allows drawing quantile-quantile plots. Such plots can be drawn for two datasets, or for one dataset and a theoretical distribution function. Quantile-quantile plots are used to determine whether two samples come from the same distribution. A qq-plot draws the quantiles of one dataset against the quantile of the other. The quantiles of the dataset with fewer entries are on Y-axis, with more entries - on X-axis.

A straight line, going through 0. It represents a robust linear fit, not sensitive to the extremes of the datasets. If the datasets come from the same distribution, points of the plot should fall approximately on the 45 degrees line. If they have the same distribution function, but different parameters of location or scale, they should still fall on the straight line, but not the 45 degrees one.

The greater their departure from the straight line, the more evidence there is that the datasets come from different distributions. Quantile-quantile plots are used to determine if the dataset comes from the specified theoretical distribution, such as normal. A qq-plot draws quantiles of the dataset against quantiles of the specified theoretical distribution. Note, that density, not CDF should be specified a straight line, going through 0.

It represents a robust linear fit, not sensitive to the extremes of the dataset. As in the two datasets case, departures from straight line indicate departures from the specified distribution. Next picture shows an example of a qq-plot of a dataset from N 3, 2 distribution and TMath::Gaus 0, 1 theoretical function. Fitting parameters are estimates of the distribution mean and sigma. Use TMultiGraph::Add to add a new graph to the list. The TMultiGraph owns the objects in the list.

The drawing and fitting options are the same as for TGraph. This class is a set of N points x[i] , y[i] , z[i] in a non-uniform grid. Several visualization techniques are implemented, including Delaunay triangulation. Note that in any of last three cases, the SetPoint method can be used to change a data point or to add a new one.

If the data point index i is greater than the size of the internal arrays, they are automatically extended. A hidden surface drawing technique is used. The surface is painted with the current fill area color. The edges of the triangles are painted with the current line color;. In this case, an intermediate 2D histogram is filled using the Delaunay triangles technique to interpolate the data set. The existing X,Y,Z points can be randomly scattered. The algorithm works by joining the existing points to make Delaunay triangles in X,Y.

These are then used to define flat planes in X,Y,Z over which to interpolate. The interpolated surface thus takes the form of tessellating triangles at various angles. Output can take the form of a 2D histogram or a vector. The triangles found can be drawn in 3D. This software cannot be guaranteed to work under all circumstances. It was originally written to work with a few hundred points in an XY space with similar X and Y ranges.

C that produces the next figure. It is useful to perform fits with errors on a 2D graph. The graph Fit method in general works the same way as the THFit. To give the axis of a graph a title you need to draw the graph first, only then does it actually have an axis object. Once drawn, you set the title by getting the axis and calling the TAxis::SetTitle method, and if you want to center it, you can call the TAxis::CenterTitle method.

Assuming that n, x, and y are defined. Next code sets the titles of the x and y axes. C , gerrors. C , zdemo. C , and gerrors2. To zoom a graph you can create a histogram with the desired axis range first. Draw the empty histogram and then draw the graph using the existing axis from the histogram. The class TGraphEditor provides the user interface for setting the following graph attributes interactively:. To fit a histogram you can use the Fit Panel on a visible histogram via the context menu, or you can use the THFit method.

The Fit Panel, which is limited, is best for prototyping. The histogram needs to be drawn in a pad before the Fit Panel is invoked. The method THFit is more powerful and is used in scripts and programs. To fit a histogram programmatically, you can use the THFit method. Here is the signatures of THFit and an explanation of the parameters:. One can also use the function name. This name may be one of ROOT pre-defined function names or a user-defined function. See the next paragraph for the list of pre-defined functions.

Here is the list of fitting options:. To be used when the histogram represents counts. To be used when the histogram has been filled with weights different than 1. The expected error is instead estimated from the the square-root of the bin function value. Note that in case of pre-defined functions some default initial values and limits are set.

By default, polN functions are fitted by the linear fitter. By default, the fitted function object is added to the histogram and is drawn in the current pad. The signature for fitting a TGraph is exactly the same as for the TH1. Here we will show how to create the TF1 class that is used for fitting histograms and graphs.

To fit a histogram with a predefined function, simply pass the name of the function in the first parameter of THFit. For example, this line fits histogram object hist with a Gaussian. The initial parameter values and eventual limits for pre-defined functions are set automatically. For overriding the default limits values use the fit option B. The list of pre-defined functions that can be used with the Fit method is the following:. There are three ways to create a TF1.

Using a function that you have defined. This can be a free function or a functor object or a particular member function of a class. You can also use a TF1 object in the constructor of another TF1. The second way to construct a TF1 is to add parameters to the expression. Here we use two parameters:. The parameter index is enclosed in square brackets. To set the initial parameters explicitly you can use:. This sets parameter 0 to You can also use SetParameters to set multiple parameters at once.

This sets parameter 0 to 10 and parameter 1 to 5. We can now draw the TF1 :. The third way to build a TF1 is to define a function yourself and then pass the function pointer to the constructor. A function for a TF1 constructor needs to have this exact signature:. Each element contains a dimension. For a 1D histogram only x[0] is used, for a 2D histogram x[0] and x[1] is used, and for a 3D histogram x[0] , x[1] , and x[2] are used.

For histograms, only 3 dimensions apply, but this method is also used to fit other objects, for example an ntuple could have 10 dimensions. This array contains the current values of parameters when it is called by the fitting function. C illustrates how to fit a 1D histogram with a user-defined function.

First we declare the function. The advantage of the function object is that it can have a state and reference therefore what-ever other object the user needs, without using globals. This is an example to define first the function object. We will show here some configuration actions that can or must be done when fitting histogram or graph using the Fit method.

Parameters must be initialized before invoking the Fit method. The setting of the parameter initial values is automatic for the predefined functions: poln , exp , gaus , and landau. When a function is not predefined, the fit parameters must be initialized to some value as close as possible to the expected values before calling the fit function. When the lower and upper limits are equal, the parameter is fixed. Next two statements fix parameter 4 at Note that you are not forced to set the limits for all parameters.

For example, if you fit a function with 6 parameters, you can:. By default, THFit will fit the function on the defined histogram range. In this example, the fit will be limited to -3 to 3, the range specified in the TF1 constructor. C and multifit. C as more completed examples. It shows how to use several Gaussian functions with different parameters on separate sub ranges of the same histogram. When fitting simple functions, such as a Gaussian, the initial values of the parameters are automatically computed by ROOT.

In the more complicated case of the sum of 3 Gaussian functions, the initial values of parameters must be set. In this particular case, the initial values are taken from the result of the individual fits. C also illustrates how to fit several functions on the same histogram. By default a Fit command deletes the previously fitted function in the histogram object. You can combine functions to fit a histogram with their sum as it is illustrated in the macro FitDemo. We have a function that is the combination of a background and Lorentzian peak.

Each function contributes 3 parameters:. This script creates a histogram and fits it with the combination of two functions. First we define the two functions and the combination function:. Here we will show how to obtain the result of the fit fitted function, parameter values, errors and eventually the covariance and correlation matrix.

A call to THFit adds the fitted function to this list. Given a histogram h , one can retrieve the associated function with:. If the histogram or graph is made persistent, the list of associated functions is also persistent. Retrieve a pointer to the function with the THGetFunction method. Then you can retrieve the fit parameters from the function TF1 with calls such as:.

Using the fit option S one can access the full result of the fit including the covariance and correlation matrix. See later the paragraph TFitResult. By default, for each bin, the sum of weights is computed at fill time. One can also call THSumw2 to force the storage and computation of the sum of the square of weights per bin.

If Sumw2 has been called, the error per bin is computed as the sqrt sum of squares of weights ; otherwise, the error is set equal to the sqrt bin content. To return the error for a given bin number, do:. Empty bins are excluded in the fit when using the Chi-square fit method.

When fitting an histogram representing counts i. When the histogram has been filled with weights different than one, a weighted likelihood method can be used and the errors retrieved from the fit are corrected following a procedure described in paragraph 8. You can change the statistics box to display the fit parameters with the TStyle::SetOptFit mode method. To display the Fit Panel right click on a histogram to pop up the context menu, and then select the menu entry Fit Panel.

Its goal is to replace the old Fit Panel and to provide more user friendly way for performing, exploring and comparing fits. The new fit panel is a modeless dialog, i. Its first prototype is a singleton application. When the Fit Panel is activated, users can select an object for fitting in the usual way, i.

If the selected object is suitable for fitting, the fit panel is connected with this object and users can perform fits by setting different parameters and options. You have a choice of several polynomials, a Gaussian, a Landau, and an Exponential function. The default one is Gaussian. The entered string is checked after the Enter key was pressed and an error message shows up, if the function string is not accepted.

The default one is Chi-square. The Binned Likelihood is recommended for bins with low statistics. Otherwise the minimization is done by Minuit, i. The Linear fitter can be selected only for functions linear in parameters for example - polN. Sliders settings are used if this option is set to On. It is possible to change both values simultaneously by pressing the left mouse button near to the slider center and moving it to a new position.

By default, the previously fitted function is deleted and replaced with the most recent one, so the list only contains one function. Setting this option to On will add the newly fitted function to the existing list of functions for the histogram. Note that the fitted functions are saved with the histogram when it is written to a ROOT file. By default, the function is drawn on the pad displaying the histogram.

When a fit is executed, the image of the function is drawn on the current pad. The advance option button is enabled only after having performed the fit and provides additional drawing options that can be used after having done the fit. Contour : to plot the confidence contour of two chosen parameters.

One can select the number of points to draw the contour more points might require more time to compute it , the parameters and the desired confidence level. Scan : to plot a scan of the minimization function likelihood or chi-squared around the minimum as function of the chosen parameter. Conf Interval : to plot the confidence interval of the fitted function as a filled coloured band around its central value.

One can select the desired confidence level for the band to be plotted. This set of options specifies the amount of feedback printed on the root command line after performed fits. Fit button - performs a fit taking different option settings via the Fit Panel interface. These classes can be classified in the following groups:. More information about the function interface and the multi-dimensional minimization in ROOT is given in the Mathematical Library chapter.

Using these classes instead of the interface provided directly in the ROOT data objects, like THFit allow are more fine control to configure and customise the fits. For example, using these classes a combined fit of several histograms can be performed. These steps are: 1. Create the input fit data object. Create the input model function. Configure the fit.

Perform the data fitting. Examine the result. The function DataRange::AddRange icoord,xmin,xmax adds a range in the coordinate icoord with lower value xmin and upper value xmax :. One can create an empty UnBinData object, iterate on the data and add the data point one by one, or directly create the UnBinData object from a data iterator. In this case the UnBinData object is created from an iterator or pointers to the data and the data are not copied inside.

In this case the data cannot be selected according to a specified range. All the data points will be included in the fit. In addition to the data points coordinates , which can be of arbitrary k dimensions, the class can be constructed from a vector of weights. This is an example of taking data from an histogram buffer of a TH1 object:.

In order to fit a data sets we need a model to describe our data, e. We can have an arbitrary number k of independent variables. For example, when fitting a k -dimensional histogram, the independent variables X are the bin center coordinates and Y is the bin weight.

The model function needs to be expressed as function of some unknown parameters. The fitting will find the best parameter value to describe the observed data. The user has also the possibility to provide a function object, which implements the derivatives of the function with respect to the parameters. This information might be useful for some types of fits.

The parameter derivatives of the model function can be useful to some minimization algorithms, such as Fumili. However, in general is better to leave the minimization algorithm e. Minuit to compute the needed derivatives using its own customised numerical differentiation algorithm. In order to not provide to the fitter the parameter derivatives, we explicitly passed in Fitter::SetFunction a false value. These are the possible allowed fit configurations:.

The initial parameter values can be set directly in the input model function object. However, for setting parameter bounds and step sizes to values different than the automatically computed ones, one needs to use the ROOT::Fit::ParameterSetting class. Only when the function is set, the number of parameter is known and automatically the FitConfig creates the corresponding ParameterSetting objects. When fitting, different minimizer can be used.

The can be implemented in different libraries and loaded ar run time by the plug-in manager system of ROOT. Each different minimizer e. Minuit, Minuit2, Fumili, etc. Within the same minimizer, thus within the same class implementing the Minimizer interface, different algorithms can exist. For example in the case of Minuit, we have Migrad, Simplex or Minimize. If the requested minimizer is not available in ROOT, the default one is used.

The list of available minimizer libraries currently available in ROOT, with their corresponding available algorithms is the following one. Some minimizers e. Minuit contain several algorithms that the user can choose. Others are based on a single algorithm e. Implement a dedicated minimization algorithm for least-square and likelihood fits. It has requirements on the type of method function to be used.

No specific algorithm exists. This minimizer can be used only for least-square fits. Minimizer based on simulated annealing. Genetic library libGenetic. Genetic minimizer based on an algorithm implemented in the TMVA package. The list of possible option that can be set are:. Note that not all the options are implemented by all the minimizers.

For example in Minuit is possible to set the maximum number of function calls, but not the maximum number of iterations. The Strategy and the Precision options apply instead only for Minuit and Minuit2. The class supports also setting global default values for the options, by using the static functions MinimizerOptions::SetDefault The list of the current option values can be inspected by using MinimizerOptions::Print. See the documentation of the particular minimizer to use for the list of possible additional options available.

Here we have now all the required input ingredients for the fit, the data and the function to fit. Depending on these we have now several different way to perform the fit, using the corresponding methods of the ROOT::Fit::Fitter class and depending on the type of input data. Above we described the pre-defined methods used for fitting. A user can also implement its own fitting methods, thus its version of the chi-square or likelihood function he wants to minimize.

In this case, the user does not really need to build as input a ROOT::Fit data set and model function as we described before. He can implements its own version of the method function using on its own data set objects and functions. A reference to the result object is obtained with the function Fitter::Result. The class has a self-explanatory API so, see its reference documentation for the possible information available after the fit.

One extra functionality offered by ROOT::Fit::FitResult is the possibility to compute the confidence intervals of the function after the fit. This is an example:. As explained before various minimization packages can be used when fitting in ROOT. We have seen before how to configure the Fitter class to use different minimization packages and different minimization options.

For example to select Minuit2 instead of Minuit for fitting an histogram do:. In the following we will give some brief description of the minimization packages. The packages all implement the ROOT::Math::Minimizer interface which can be use for finding the minimum of a multi-dimensional function.

The interface is documented in the Mathematical Library Chapter. The main changes are:. The variables in the various Minuit labeled common blocks have been changed to the TMinuit class data members. The include file Minuit. Instead of passing the FCN function in the argument list, the addresses of this function is stored as pointer in the data members of the class. This is by far more elegant and flexible in an interactive environment.

The member function SetFCN can be used to define this pointer. The ROOT static function Printf is provided to replace all format statements and to print on currently defined output file. By default fGraphicsMode is true. When calling the Minuit functions such as mncont , mnscan , or any Minuit command invoking mnplot , TMinuit::mnplot produces a TGraph object pointed by fPlot. One can retrieve this object with TMinuit ::GetPlot.

The value of FCN will in general depend on one or more variable parameters. Since the transformation is necessarily non-linear, it would transform a nice linear problem into a nasty non-linear one, which is the reason why limits should be avoided if not necessary.

In addition, the transformation does require some computer time, so it slows down the computation a little bit, and more importantly, it introduces additional numerical inaccuracy into the problem in addition to what is introduced in the numerical calculation of the FCN value. The effects of non-linearity and numerical round off both become more important as the external value gets closer to one of the limits expressed as the distance to nearest limit divided by distance between limits.

The user must therefore be aware of the fact that, for example, if they put limits of 0, on a parameter, then the values 0. Therefore, it is recommended that:. Limits on variable parameters should be used only when needed in order to prevent the parameter from taking on unphysical values. When a satisfactory minimum has been found using limits, the limits should then be removed if possible, in order to perform or re-perform the error analysis without limits.

Minuit offers the user a choice of several minimization algorithms. It is a variable-metric method with inexact line search, a stable metric updating scheme, and checks for positive-definiteness. Its main weakness is that it depends heavily on knowledge of the first derivatives, and fails miserably if they are very inaccurate. If parameter limits are needed, in spite of the side effects, then the user should be aware of the following techniques to alleviate problems caused by limits:.

If MIGRAD converges normally to a point where no parameter is near one of its limits, then the existence of limits has probably not prevented Minuit from finding the right minimum. In the best case, where the minimum is far from any limits, Minuit will correctly transform the error matrix, and the parameter errors it reports should be accurate and very close to those you would have got without limits.

In other cases which should be more common, since otherwise you would not need limits , the very meaning of parameter errors becomes problematic. Mathematically, since the limit is an absolute constraint on the parameter, a parameter at its limit has no error, at least in one direction. The error matrix, which can assign only symmetric errors, then becomes essentially meaningless. For discussion of basic concepts, such as the meaning of the elements of the error matrix, or setting of exact confidence levels see the articles:.

Determining the statistical Significance of experimental Results. Eadie, D. Drijard, F. James, M. Roos, and B. Statistical Methods in Experimental Physics. North-Holland, Minuit always carries around its own current estimates of the parameter errors, which it will print out on request, no matter how accurate they are at any given point in the execution.

For example, at initialization, these estimates are just the starting step sizes as specified by the user. Minuit , when it prints out error values, also gives some indication of how reliable it thinks they are. If no mitigating adjective is given, then at least Minuit believes the errors are accurate, although there is always a small chance that Minuit has been fooled.

Some visible signs that Minuit may have been fooled:. Correlation coefficients exactly equal to zero, unless some parameters are known to be uncorrelated with the others. Correlation coefficients very close to one greater than 0. This indicates both an exceptionally difficult problem, and one which has been badly parameterized so that individual errors are not very meaningful because they are so highly correlated.

Parameter at limit. This condition, signaled by a Minuit warning message, may make both the function minimum and parameter errors unreliable. Therefore, if MIGRAD reports that it has found a non-positive-definite covariance matrix, this may be a sign of one or more of the following:.

On its way to the minimum, MIGRAD may have traversed a region that has unphysical behavior, which is of course not a serious problem as long as it recovers and leaves such a region. If the matrix is not positive-definite even at the minimum, this may mean that the solution is not well defined, for example that there are more unknowns than there are data points, or that the parameterization of the fit contains a linear dependence. If this is the case, then Minuit or any other program cannot solve your problem uniquely.

The error matrix will necessarily be largely meaningless, so the user must remove the under determinedness by reformulating the parameterization. Minuit cannot do this itself. It is possible that the apparent lack of positive-definiteness is due to excessive round off errors in numerical calculations in the user function , or not enough precision.

This is unlikely in general, but becomes more likely if the number of free parameters is very large, or if the parameters are badly scaled not all of the same order of magnitude , and correlations are large. In any case, whether the non-positive-definiteness is real or only numerical is largely irrelevant, since in both cases the error matrix will be unreliable and the minimum suspicious.

For questions of parameter dependence, see the discussion above on positive-definiteness. Possible other mathematical problems are the following:. Excessive numerical round off - be especially careful of exponential and factorial functions which get big very quickly and lose accuracy.

Starting too far from the solution - the function may have unphysical local minima, especially at infinity in some variables.

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The reason: "the -rand" option tells by default to use random file. Since user issues to use. I myself will bump into this error again. And ofcourse I will check StackOverflow R ha ha first!!! Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Collectives on Stack Overflow.

Learn more. Asked 1 year, 7 months ago. Modified 3 months ago. Viewed 27k times. When I run this command line, it appear this error. What should I do? Command : openssl req -new -x -days -key ca. Asma Asma 1 1 gold badge 3 3 silver badges 6 6 bronze badges. Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Help us improve our answers. Are the answers below sorted in a way that puts the best answer at or near the top?

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