## \file
## \ingroup tutorial_roofit_main
## \notebook
## Multidimensional models: working with parameterized ranges to define non-rectangular
## regions for fitting and integration
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT


# Create 3D pdf
# -------------------------

# Define observable (x,y,z)
x = ROOT.RooRealVar("x", "x", 0, 10)
y = ROOT.RooRealVar("y", "y", 0, 10)
z = ROOT.RooRealVar("z", "z", 0, 10)

# Define 3 dimensional pdf
z0 = ROOT.RooRealVar("z0", "z0", -0.1, 1)
px = ROOT.RooPolynomial("px", "px", x, [0.0])
py = ROOT.RooPolynomial("py", "py", y, [0.0])
pz = ROOT.RooPolynomial("pz", "pz", z, [z0])
pxyz = ROOT.RooProdPdf("pxyz", "pxyz", [px, py, pz])

# Defined non-rectangular region R in (x, y, z)
# -------------------------------------------------------------------------------------

#
# R = Z[0 - 0.1*Y^2] * Y[0.1*X - 0.9*X] * X[0 - 10]
#

# Construct range parameterized in "R" in y [ 0.1*x, 0.9*x ]
ylo = ROOT.RooFormulaVar("ylo", "0.1*x", [x])
yhi = ROOT.RooFormulaVar("yhi", "0.9*x", [x])
y.setRange("R", ylo, yhi)

# Construct parameterized ranged "R" in z [ 0, 0.1*y^2 ]
zlo = ROOT.RooFormulaVar("zlo", "0.0*y", [y])
zhi = ROOT.RooFormulaVar("zhi", "0.1*y*y", [y])
z.setRange("R", zlo, zhi)

# Calculate integral of normalized pdf in R
# ----------------------------------------------------------------------------------

# Create integral over normalized pdf model over x,y, in "R" region
intPdf = pxyz.createIntegral({x, y, z}, {x, y, z}, "R")

# Plot value of integral as function of pdf parameter z0
frame = z0.frame(Title="Integral of pxyz over x,y, in region R")
intPdf.plotOn(frame)

c = ROOT.TCanvas("rf313_paramranges", "rf313_paramranges", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.6)
frame.Draw()

c.SaveAs("rf313_paramranges.png")
