Data and categories: tools for manipulation of (un)binned datasets
Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, April 17, 2024 at 11:18 AM.
from __future__ import print_function
import ROOT
import math
WVE Add reduction by range
Binned (RooDataHist) and unbinned datasets (RooDataSet) share many properties and inherit from a common abstract base class (RooAbsData), provides an interface for all operations that can be performed regardless of the data format
x = ROOT.RooRealVar("x", "x", -10, 10)
y = ROOT.RooRealVar("y", "y", 0, 40)
c = ROOT.RooCategory("c", "c")
c.defineType("Plus", +1)
c.defineType("Minus", -1)
False
ROOT.RooDataSet is an unbinned dataset (a collection of points in N-dimensional space)
d = ROOT.RooDataSet("d", "d", {x, y, c})
Unlike ROOT.RooAbsArgs (ROOT.RooAbsPdf, ROOT.RooFormulaVar,....) datasets are not attached to the variables they are constructed from. Instead they are attached to an internal clone of the supplied set of arguments
Fill d with dummy values
for i in range(1000):
x.setVal(i / 50 - 10)
y.setVal(math.sqrt(1.0 * i))
if i % 2:
c.setLabel("Plus")
else:
c.setLabel("Minus")
# We must explicitly refer to x,y, here to pass the values because
# d is not linked to them (as explained above)
if i < 3:
print(x, y, c)
print(type(x))
d.add({x, y, c})
d.Print("v")
print("")
RooRealVar::x = -10 L(-10 - 10) RooRealVar::y = 0 L(0 - 40) { {"Minus" , -1}, {"Plus" , 1} } <class cppyy.gbl.RooRealVar at 0x93b4110> RooRealVar::x = -9.98 L(-10 - 10) RooRealVar::y = 1 L(0 - 40) { {"Minus" , -1}, {"Plus" , 1} } <class cppyy.gbl.RooRealVar at 0x93b4110> RooRealVar::x = -9.96 L(-10 - 10) RooRealVar::y = 1.41421 L(0 - 40) { {"Minus" , -1}, {"Plus" , 1} } <class cppyy.gbl.RooRealVar at 0x93b4110> DataStore d (d) Contains 1000 entries Observables: 1) y = 31.607 L(0 - 40) "y" 2) x = 9.98 L(-10 - 10) "x" 3) c = Plus(idx = 1) "c"
The get() function returns a pointer to the internal copy of the RooArgSet(x,y,c) supplied in the constructor
row = d.get()
row.Print("v")
print("")
1) 0x971bda0 RooRealVar:: y = 31.607 L(0 - 40) "y" 2) 0x971ad40 RooRealVar:: x = 9.98 L(-10 - 10) "x" 3) 0x95f6460 RooCategory:: c = Plus(idx = 1) "c"
Get with an argument loads a specific data point in row and returns a pointer to row argset. get() always returns the same pointer, unless an invalid row number is specified. In that case a null ptr is returned
d.get(900).Print("v")
print("")
1) 0x971bda0 RooRealVar:: y = 30 L(0 - 40) "y" 2) 0x971ad40 RooRealVar:: x = 8 L(-10 - 10) "x" 3) 0x95f6460 RooCategory:: c = Minus(idx = -1) "c"
The reduce() function returns a dataset which is a subset of the original
print("\n >> d1 has only columns x,c")
d1 = d.reduce({x, c})
d1.Print("v")
print("\n >> d2 has only column y")
d2 = d.reduce({y})
d2.Print("v")
print("\n >> d3 has only the points with y>5.17")
d3 = d.reduce("y>5.17")
d3.Print("v")
print("\n >> d4 has only columns x, for data points with y>5.17")
d4 = d.reduce({x, c}, "y>5.17")
d4.Print("v")
>> d1 has only columns x,c >> d2 has only column y >> d3 has only the points with y>5.17 >> d4 has only columns x, for data points with y>5.17 DataStore d (d) Contains 1000 entries Observables: 1) c = Plus(idx = 1) "c" 2) x = 9.98 L(-10 - 10) "x" DataStore d (d) Contains 1000 entries Observables: 1) y = 31.607 L(0 - 40) "y" [#1] INFO:InputArguments -- The formula y>5.17 claims to use the variables (y,x,c) but only (y) seem to be in use. inputs: y>5.17 DataStore d (d) Contains 973 entries Observables: 1) y = 31.607 L(0 - 40) "y" 2) x = 9.98 L(-10 - 10) "x" 3) c = Plus(idx = 1) "c" DataStore d (d) Contains 973 entries Observables: 1) c = Plus(idx = 1) "c" 2) x = 9.98 L(-10 - 10) "x"
The merge() function adds two data set column-wise
print("\n >> merge d2(y) with d1(x,c) to form d1(x,c,y)")
d1.merge(d2)
d1.Print("v")
>> merge d2(y) with d1(x,c) to form d1(x,c,y) DataStore d (d) Contains 1000 entries Observables: 1) c = Plus(idx = 1) "c" 2) x = 9.98 L(-10 - 10) "x" 3) y = 31.607 L(0 - 40) "y"
The append() function adds two datasets row-wise
print("\n >> append data points of d3 to d1")
d1.append(d3)
d1.Print("v")
>> append data points of d3 to d1 DataStore d (d) Contains 1973 entries Observables: 1) c = Plus(idx = 1) "c" 2) x = 9.98 L(-10 - 10) "x" 3) y = 31.607 L(0 - 40) "y"
A binned dataset can be constructed empty, an unbinned dataset, or from a ROOT native histogram (TH1,2,3)
print(">> construct dh (binned) from d(unbinned) but only take the x and y dimensions, ")
print(">> the category 'c' will be projected in the filling process")
>> construct dh (binned) from d(unbinned) but only take the x and y dimensions, >> the category 'c' will be projected in the filling process
The binning of real variables (like x,y) is done using their fit range 'get/setRange()' and number of specified fit bins 'get/setBins()'. Category dimensions of binned datasets get one bin per defined category state
x.setBins(10)
y.setBins(10)
dh = ROOT.RooDataHist("dh", "binned version of d", {x, y}, d)
dh.Print("v")
yframe = y.frame(Bins=10, Title="Operations on binned datasets")
dh.plotOn(yframe) # plot projection of 2D binned data on y
<cppyy.gbl.RooPlot object at 0xa124160>
DataStore dh (binned version of d) Contains 100 entries Observables: 1) y = 38 L(0 - 40) B(10) "y" 2) x = 9 L(-10 - 10) B(10) "x" Binned Dataset dh (binned version of d) Contains 100 bins with a total weight of 1000 Observables: 1) y = 38 L(0 - 40) B(10) "y" 2) x = 9 L(-10 - 10) B(10) "x"
Examine the statistics of a binned dataset
print(">> number of bins in dh : ", dh.numEntries())
print(">> sum of weights in dh : ", dh.sum(False))
>> number of bins in dh : 100 >> sum of weights in dh : 1000.0
accounts for bin volume
print(">> integral over histogram: ", dh.sum(True))
>> integral over histogram: 8000.0
Locate a bin from a set of coordinates and retrieve its properties
x.setVal(0.3)
y.setVal(20.5)
print(">> retrieving the properties of the bin enclosing coordinate (x,y) = (0.3,20.5) bin center:")
>> retrieving the properties of the bin enclosing coordinate (x,y) = (0.3,20.5) bin center:
load bin center coordinates in internal buffer
dh.get({x, y}).Print("v")
print(" weight = ", dh.weight()) # return weight of last loaded coordinates
weight = 76.0 1) 0x9da6000 RooRealVar:: y = 22 L(0 - 40) B(10) "y" 2) 0x9f09ec0 RooRealVar:: x = 1 L(-10 - 10) B(10) "x"
Reduce the 2-dimensional binned dataset to a 1-dimensional binned dataset
All reduce() methods are interfaced in RooAbsData. All reduction techniques demonstrated on unbinned datasets can be applied to binned datasets as well.
print(">> Creating 1-dimensional projection on y of dh for bins with x>0")
dh2 = dh.reduce({y}, "x>0")
dh2.Print("v")
>> Creating 1-dimensional projection on y of dh for bins with x>0 DataStore dh (binned version of d) Contains 10 entries Observables: 1) y = 38 L(0 - 40) B(10) "y" Binned Dataset dh (binned version of d) Contains 10 bins with a total weight of 500 Observables: 1) y = 38 L(0 - 40) B(10) "y"
Add dh2 to yframe and redraw
dh2.plotOn(yframe, LineColor="r", MarkerColor="r")
<cppyy.gbl.RooPlot object at 0xa124160>
[#1] INFO:Plotting -- RooPlot::updateFitRangeNorm: New event count of 500 will supersede previous event count of 1000 for normalization of PDF projections
Datasets can be persisted with ROOT I/O
print("\n >> Persisting d via ROOT I/O")
f = ROOT.TFile("rf402_datahandling.root", "RECREATE")
d.Write()
f.ls()
>> Persisting d via ROOT I/O TFile** rf402_datahandling.root TFile* rf402_datahandling.root KEY: RooDataSet d;1 d KEY: TProcessID ProcessID0;1 3fc07c80-fcac-11ee-ac50-942c8a89beef
To read back in future session:
ROOT.TFile f("rf402_datahandling.root") d = (ROOT.RooDataSet*) f.FindObject("d")
c = ROOT.TCanvas("rf402_datahandling", "rf402_datahandling", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
yframe.GetYaxis().SetTitleOffset(1.4)
yframe.Draw()
c.SaveAs("rf402_datahandling.png")
Info in <TCanvas::Print>: png file rf402_datahandling.png has been created
Draw all canvases
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()