TFractionFitter

 TFractionFitter default constructor.

 TFractionFitter constructor. Does a complete initialisation (including
 consistency checks, default fit range as the whole histogram but without
 under- and overflows, and declaration of the fit parameters). Note that
 the histograms are not copied, only references are used.
 Arguments:
     data: histogram to be fitted
     MCs:  array of TH1* corresponding template distributions

 TFractionFitter default destructor

 Change the histogram to be fitted to. Notes:
 - Parameter constraints and settings are retained from a possible previous fit.
 - Modifying the dimension or number of bins results in an error (in this case
   rather instantiate a new TFractionFitter object)

 Change the histogram for template number <parm>. Notes:
 - Parameter constraints and settings are retained from a possible previous fit.
 - Modifying the dimension or number of bins results in an error (in this case
   rather instantiate a new TFractionFitter object)

 Set bin by bin weights for template number <parm> (the parameter numbering
 follows that of the input template vector).
 Weights can be "unset" by passing a null pointer.
 Consistency of the weights histogram with the data histogram is checked at
 this point, and an error in case of problems.

 Give direct access to the underlying minimisation class. This can be
 used e.g. to modify parameter values or step sizes.

 Function for internal use, checking parameter validity
 An invalid parameter results in an error.

 Set the X range of the histogram to be used in the fit.
 Use ReleaseRangeX() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower X bin number
     high: upper X bin number

 Release restrictions on the X range of the histogram to be used in the fit.

 Set the Y range of the histogram to be used in the fit (2D or 3D histograms only).
 Use ReleaseRangeY() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower Y bin number
     high: upper Y bin number

 Release restrictions on the Y range of the histogram to be used in the fit.

 Set the Z range of the histogram to be used in the fit (3D histograms only).
 Use ReleaseRangeY() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower Y bin number
     high: upper Y bin number

 Release restrictions on the Z range of the histogram to be used in the fit.

 Constrain the values of parameter number <parm> (the parameter numbering
 follows that of the input template vector).
 Use UnConstrain() to remove this constraint.

 Remove the constraints on the possible values of parameter <parm>.

 Function used internally to check the consistency between the
 various histograms. Checks are performed on nonexistent or empty
 histograms, the precise histogram class, and the number of bins.
 In addition, integrals over the "allowed" bin ranges are computed.
 Any inconsistency results in a error.

 Perform the fit with the default UP value.
 The value returned is the minimisation status.

 Set UP to the given value (see class TMinuit), and perform a MINOS minimisation.

 Obtain the fit result for parameter <parm> (the parameter numbering
 follows that of the input template vector).

 Return the "template prediction" corresponding to the fit result (this is not
 the same as the weighted sum of template distributions, as template statistical
 uncertainties are taken into account).
 Note that the name of this histogram will simply be the same as that of the
 "data" histogram, prefixed with the string "Fraction fit to hist: ".

 Used internally to obtain the bin ranges according to the dimensionality of
 the histogram and the limits set by hand.

 Used internally to compute the likelihood value.

 Function used internally to obtain the template prediction in the individual bins

 Return the likelihood ratio Chi-squared (chi2) for the fit.
 The value is computed when the fit is executed successfully.
 Chi2 calculation is based on the "likelihood ratio" lambda,
 lambda = L(y;n) / L(m;n),
 where L(y;n) is the likelihood of the fit result <y> describing the data <n>
 and L(m;n) is the likelihood of an unknown "true" underlying distribution
 <m> describing the data <n>. Since <m> is unknown, the data distribution is
 used instead,
 lambda = L(y;n) / L(n;n).
 Note that this ratio is 1 if the fit is perfect. The chi2 value is then
 computed according to
 chi2 = -2*ln(lambda).
 This parameter can be shown to follow a Chi-square distribution. See for
 example S. Baker and R. Cousins, "Clarification of the use of chi-square
 and likelihood functions in fits to histograms", Nucl. Instr. Meth. A221, 
 pp. 437-442 (1984)

 return the number of degrees of freedom in the fit
 the fNDF parameter has been previously computed during a fit.
 The number of degrees of freedom corresponds to the number of points
 used in the fit minus the number of templates.

 return the fit probability

 Method used internally to compute the likelihood ratio chi2
 See the function GetChisquare() for details

 Return the adjusted MC template (Aji) for template (parm).
 Note that the (Aji) times fractions only sum to the total prediction
 of the fit if all weights are 1.