class HepDataMCPlot: public TNamed

 Default constructor

 Normal constructor

 Default destructor

 Set DATA histogram

 Add MC histogram to stack

 Add grouped MC histogram to stack

 Grouped legend ?

 Draw this object
 - by default, two pads are drawn, one for the stack and one for
   the significance. Best results are obtained if drawn in a
   Canvas of specified height and width (with default config)

               width      height
   No ratio:    700         500
    1 ratio:    700         633
    2 ratio:    700         765


 Options available:
   "NOSTACK" - Overlay MC histograms rather than stack them
   "NOLEG"   - Do not draw a legend
   "NORM"    - Normalize the plots to Integral of 1 in case of "nostack" option. Use the option like hist->Draw("nostack,norm").
   !!!ATTENTION!!! The histograms are scaled after the option "norm". You have to close root and restart it to get again the unnormalized plots

 Strip filesystem path from the full path of the given directory

 Set title of x-axis

 Set title of y-axis

 Set range of x-axis

 Set range of x-axis

 Set range of y-axis

 Needs to be called before plot is drawn!

 Set range of y-axis of ratio plot

 Needs to be called before plot is drawn!

 Set no. of X axis divisions

 Set no. of Y axis divisions

 Browse plotter in TBrowser

 Draw legend

 In case of gswitched on grouping of histograms only the group
 entries but not the entries inside the groupe will be displayed

 Draw enlarged legend clone into the current pad.
 The pad is cleaned before

 Switch grouping of histograms on or off

 Compute distance from point px,py

 Draw all histograms of the MC stack

 Draw all histograms of the MC stack

 Draw DATA histogram

 Draw DATA MC ratio

 Draw Significance

 Draw Significance

 Draw MC error band

 Include normalisation uncertainties in error band

 Draw the Data error bars even for 0 data entry bins

 Draw the marker for bins with no data

 Draw MC error band

 Add overflow to last bin and underflow to first bin

 Internal helper function.

 Creates the graph for drawing (asymmetric) errors. For large
 entries numbers the errors are taken from the given histogram
 (as well as the xy-positions). For low numbers (<33) the errors
 are estimated by the FeldmanCousins method.

 Computes upper and lower errors for given number of events in
 bin of histogram h.
 For low numbers (<33) the errors
 are estimated by the FeldmanCousins method.

 Compute the normalization uncertainty per bin

 For each grouped template an uncertainty must be provided

 Prepares fit using TFractionFitter

 HepTemplate objects are created from the list of MC samples.
 Per default, sample groups are treated as one template.
 Set single_samples to TRUE, if you want to fit each single
 sample.
 If prepare_effs is set to TRUE, cut efficiencies are calculated
 and assigned to the template objects. For that, it is assumed
 that the number of entries in the fit histogram is equal to the
 number of events after all cuts applied. The denominator for the
 efficiencies is taken from the event info histogram. In case of
 folders a weighted sum is calculated. The efficiencies are probably
 needed to calculate cross sections from the fit results.

 Perform the fit

 Create TFractionFitter instance. Start values and constraints
 given to template objects are set and the fit is started.
 Returns the return value from TFractionFitter.

 Draw fitted MC histogram stack together with data

 Get template fraction for specific template

 Get template fraction error for specific template

 Get template cut efficiency for specific template

 Performs a rebinning of the stacked plot.
 Rebinning is applied to all histograms
 (data and MC).

 Scales the complete MC hist stack by the given scale

 Scales only a group of histograms by the given scale

 Draw ATLAS + label

 Functions taken from official ATLAS style

 Adjust position in case user adds more space to the right margin
 x += 0.05 - gStyle->GetPadRightMargin();

 Draw latex text on given position

 Functions taken from official ATLAS style

 set current style to ATLASstyle

 Print event yield table

 Options available:
   "SPLIT" - Print table for all samples. If this option is
             not given, only the grouped sample will be
             listed (default).

 Add overflow/underflow bin to first/last bin

 Draw MC histograms in overlay mode

 Setup color scheme for non-stacked mode

 Saves group-histograms and single sample histograms in a
 given file.

 The name of the histograms consists of the folder/sample name
 and a suffix, e.g. "ttbar_jesup"

 Saves group-histograms and single sample histograms and
 returns a list of histograms

 The name of the histograms consists of the folder/sample name
 and a suffix, e.g. "ttbar_jesup"

 Print S/B and S/sqrt(B) for all bins

 Draw MC histograms in stacked mode


 In case of stacked histogram mode draw the histograms in
 filled mode with their fill color. Use the histogram line
 colour of the current style for drawing the histogram
 outline

 Setup colour scheme for stacked mode

 In case of grouped drawing mode set the line and fill
 attributes of the grouped histograms first. The histograms
 within one group get all the same colour for filling and the
 histogram line so that they appear as a single histogram

 Setup Pads for drawing the stack and ratio-plots

 Draw Data/MC ratio

 The data/mc ratio is plotted with dotted markers and their
 uncertainty corresponds to the relative uncertainty from data.
 Furthermore the uncertainty on the prediction (i.e. MC/MC) is
 shown as shaded uncertainty band.

 Setup axis labels and axis range

 Title size needs to be rescaled when using ratio plots. Size
 depends whether axis is redrawn in the ratio pad or main pad.

 Draw Significance

 Given two ROOT histograms (with the same binning!) containing the
 observed and expected counts, create and return a histogram showing
 the significance of their bin-to-bin discrepancies.

 If the histogram representing the expectation (second input
 parameter) has non-zero bin "errors", these are considered the
 standard deviations representing the full uncertainty and the
 significance is computed accordingly, unless this is disabled (third
 parameter).

 The last input pointer is the pull histogram, which is filled with
 all z-values, without discarding the bins for which the p-value is
 larger than 0.5: in case of ideal match, the pulls follow a standard
 normal distribution.  A typical binnin for the pulls is from -5 to
 +5 with 20 bins.



 Code from
 "Plotting the Differences Between Data and Expectation"
 by Georgios Choudalakis and Diego Casadei
 Eur. Phys. J. Plus 127 (2012) 25
 http://dx.doi.org/10.1140/epjp/i2012-12025-y
 (http://arxiv.org/abs/1111.2062)


 This code is covered by the GNU General Public License:
 http://www.gnu.org/licenses/gpl.html

 Diego Casadei <casadei@cern.ch> 7 Dec 2011

 Normal quantile computed following Peter John Acklam's
 pseudo-code algorithm for rational approximation
 (pjacklam@online.no)
 http://home.online.no/~pjacklam/notes/invnorm

 The algorithm below assumes p is the input and x is the output.

  Coefficients in rational approximations.
  a(1) <- -3.969683028665376e+01
  a(2) <-  2.209460984245205e+02
  a(3) <- -2.759285104469687e+02
  a(4) <-  1.383577518672690e+02
  a(5) <- -3.066479806614716e+01
  a(6) <-  2.506628277459239e+00

  b(1) <- -5.447609879822406e+01
  b(2) <-  1.615858368580409e+02
  b(3) <- -1.556989798598866e+02
  b(4) <-  6.680131188771972e+01
  b(5) <- -1.328068155288572e+01

  c(1) <- -7.784894002430293e-03
  c(2) <- -3.223964580411365e-01
  c(3) <- -2.400758277161838e+00
  c(4) <- -2.549732539343734e+00
  c(5) <-  4.374664141464968e+00
  c(6) <-  2.938163982698783e+00

  d(1) <-  7.784695709041462e-03
  d(2) <-  3.224671290700398e-01
  d(3) <-  2.445134137142996e+00
  d(4) <-  3.754408661907416e+00

  Define break-points.

  p_low  <- 0.02425
  p_high <- 1 - p_low

  Rational approximation for lower region.

  if 0 < p < p_low
     q <- sqrt(-2*log(p))
x <- (((((c(1)*q+c(2))*q+c(3))*q+c(4))*q+c(5))*q+c(6))
           ((((d(1)*q+d(2))*q+d(3))*q+d(4))*q+1)
  endif

  Rational approximation for central region.

  if p_low <= p <= p_high
     q <- p - 0.5
     r <- q*q
x <- (((((a(1)*r+a(2))*r+a(3))*r+a(4))*r+a(5))*r+a(6))*q
          (((((b(1)*r+b(2))*r+b(3))*r+b(4))*r+b(5))*r+1)
  endif

  Rational approximation for upper region.

  if p_high < p < 1
     q <- sqrt(-2*log(1-p))
x <- -(((((c(1)*q+c(2))*q+c(3))*q+c(4))*q+c(5))*q+c(6))
            ((((d(1)*q+d(2))*q+d(3))*q+d(4))*q+1)
  endif

 The absolute value of the relative error (x_approx - x)/x is
 <= 1.15e-9 for all input values p which can be represented in
 IEEE double precision arithmetic.




 Code from
 "Plotting the Differences Between Data and Expectation"
 by Georgios Choudalakis and Diego Casadei
 Eur. Phys. J. Plus 127 (2012) 25
 http://dx.doi.org/10.1140/epjp/i2012-12025-y
 (http://arxiv.org/abs/1111.2062)


 This code is covered by the GNU General Public License:
 http://www.gnu.org/licenses/gpl.html

 p-value for Poisson distribution, no uncertainty on the parameter


 Diego Casadei <casadei@cern.ch>   Oct 2011
 Last update: 4 Nov 2011 (using incomplete Gamma from ROOT)


 Consider Poi(k|nExp) and compute the p-value which corresponds to
 the observation of nObs counts.

 When nObs > nExp there is an excess of observed events and

   p-value = P(n>=nObs|nExp) = \sum_{n=nObs}^{\infty} Poi(n|nExp)
           = 1 - \sum_{n=0}^{nObs-1} Poi(n|nExp)
           = 1 - e^{-nExp} \sum_{n=0}^{nObs-1} nExp^n / n!

 Otherwise (nObs <= nExp) there is a deficit and

   p-value = P(n<=nObs|nExp) = \sum_{n=0}^{nObs} Poi(n|nExp)
           = e^{-nExp} \sum_{n=0}^{nObs} nExp^n / n!



 Code from
 "Plotting the Differences Between Data and Expectation"
 by Georgios Choudalakis and Diego Casadei
 Eur. Phys. J. Plus 127 (2012) 25
 http://dx.doi.org/10.1140/epjp/i2012-12025-y
 (http://arxiv.org/abs/1111.2062)


 This code is covered by the GNU General Public License:
 http://www.gnu.org/licenses/gpl.html

  p-value for Poisson distribution when there is uncertainty on the
 parameter



 Diego Casadei <casadei@cern.ch>  6 Nov 2011
 Last update: 3 Mar 2012 (logarithms used only for big numbers)



 Consider Poi(k|nExp) and compute the p-value which corresponds to
 the observation of nObs counts, in the case of uncertain nExp whose
 variance is provided.

 The prior for nExp is a Gamma density which matches the expectation
 and variance provided as input.  The marginal model is provided by
 the Poisson-Gamma mixture, which is used to compute the p-value.

 Gamma density: the parameters are
  * a = shape param  [dimensionless]
  * b = rate param   [dimension: inverse of x]

   nExp ~ Ga(x|a,b) = [b^a/Gamma(a)] x^{a-1} exp(-bx)

 One has E[x] = a/b and V[x] = a/b^2 hence
  * b = E/V
  * a = E*b

 The integral of Poi(n|x) Ga(x|a,b) over x gives the (marginal)
 probability of observing n counts as

               b^a [Gamma(n+a) / Gamma(a)]
   P(n|a,b) = -----------------------------
                      n! (1+b)^{n+a}

 When nObs > nExp there is an excess of observed events and

   p-value = P(n>=nObs) = \sum_{n=nObs}^{\infty} P(n)
           = 1 - \sum_{n=0}^{nObs-1} P(n)

 Otherwise (nObs <= nExp) there is a deficit and

   p-value = P(n<=nObs) = \sum_{n=0}^{nObs} P(n)

 To compute the sum, we use the following recurrent relation:

   P(n=0) = [b/(1+b)]^a
   P(n=1) = [b/(1+b)]^a a/(1+b) = P(n=0) a/(1+b)
   P(n=2) = [b/(1+b)]^a a/(1+b) (a+1)/[2(1+b)] = P(n=1) (a+1)/[2(1+b)]
   ...        ...
   P(n=k) = P(n=k-1) (a+k-1) / [k(1+b)]

 and to avoid rounding errors, we work with logarithms.


 Code from
 "Plotting the Differences Between Data and Expectation"
 by Georgios Choudalakis and Diego Casadei
 Eur. Phys. J. Plus 127 (2012) 25
 http://dx.doi.org/10.1140/epjp/i2012-12025-y
 (http://arxiv.org/abs/1111.2062)


 This code is covered by the GNU General Public License:
 http://www.gnu.org/licenses/gpl.html

 Convert a p-value into a right-tail normal significance, i.e. into
 the number of Gaussian standard deviations which correspond to it.

 Code from
 "Plotting the Differences Between Data and Expectation"
 by Georgios Choudalakis and Diego Casadei
 Eur. Phys. J. Plus 127 (2012) 25
 http://dx.doi.org/10.1140/epjp/i2012-12025-y
 (http://arxiv.org/abs/1111.2062)


 This code is covered by the GNU General Public License:
 http://www.gnu.org/licenses/gpl.html

 Optimize binning for given HepDataMCPlot
 (this plot should have many bin (~100 - ~1000)

 To optimize the binning, the quantity Z_ij




 with




 is computed.  and  are parameters for adjusting the number of bins.

 The binning is determined in a iterative procedure. Starting with
  , then
  1) Compute 
  2) Check if 
  2.a) Condition is true  -> Merge all bins from i to j
                             Set j = i-1 and go back to 1)
  2.b) Condition is false -> Reduce i by one and go back to 1).

  Repeat this until i == 1.

 Scale factor of the overlay histogram (see
 SetDrawSignalOverlay())

 Flag for drawing the signal MC (assumed to be the least entry
 in the MC histogram stack) as overlay instead as part of the
 stack

 Add MC folder for grouping histograms

 Add MC single sample

function to design plot in ATLAS style

 Flag for drawing the signal MC (assumed to be the least
 entry in the MC histogram stack) as overlay instead as part of the
 stack