## \file
## \ingroup tutorial_roostats
## \notebook
## Comparison of MCMC and PLC in a multi-variate gaussian problem
##
## This tutorial produces an N-dimensional multivariate Gaussian
## with a non-trivial covariance matrix.  By default N=4 (called "dim").
##
## A subset of these are considered parameters of interest.
## This problem is tractable analytically.
##
## We use this mainly as a test of Markov Chain Monte Carlo
## and we compare the result to the profile likelihood ratio.
##
## We use the proposal helper to create a customized
## proposal function for this problem.
##
## For N=4 and 2 parameters of interest it takes about 10-20 seconds
## and the acceptance rate is 37%
##
## \macro_image
## \macro_output
## \macro_code
##
## \date July 2022
## \authors Artem Busorgin, Kevin Belasco and Kyle Cranmer (C++ version)

import ROOT

dim = 4
nPOI = 2

# let's time this challenging example
t = ROOT.TStopwatch()
t.Start()

xVec = []
muVec = []
poi = set()

# make the observable and means
for i in range(dim):
    name = "x{}".format(i)
    x = ROOT.RooRealVar(name, name, 0, -3, 3)
    xVec.append(x)

    mu_name = "mu_x{}".format(i)
    mu_x = ROOT.RooRealVar(mu_name, mu_name, 0, -2, 2)
    muVec.append(mu_x)

# put them into the list of parameters of interest
for i in range(nPOI):
    poi.add(muVec[i])

# make a covariance matrix that is all 1's
cov = ROOT.TMatrixDSym(dim)
for i in range(dim):
    for j in range(dim):
        if i == j:
            cov[i, j] = 3.0
        else:
            cov[i, j] = 1.0

# now make the multivariate Gaussian
mvg = ROOT.RooMultiVarGaussian("mvg", "mvg", xVec, muVec, cov)

# --------------------
# make a toy dataset
data = mvg.generate(xVec, 100)

# now create the model config for this problem
w = ROOT.RooWorkspace("MVG")
modelConfig = ROOT.RooStats.ModelConfig(w)
modelConfig.SetPdf(mvg)
modelConfig.SetParametersOfInterest(poi)

# -------------------------------------------------------
# Setup calculators

# MCMC
# we want to setup an efficient proposal function
# using the covariance matrix from a fit to the data
fit = mvg.fitTo(data, Save=True)
ph = ROOT.RooStats.ProposalHelper()
ph.SetVariables(fit.floatParsFinal())
ph.SetCovMatrix(fit.covarianceMatrix())
ph.SetUpdateProposalParameters(True)
ph.SetCacheSize(100)
pdfProp = ph.GetProposalFunction()

# now create the calculator
mc = ROOT.RooStats.MCMCCalculator(data, modelConfig)
mc.SetConfidenceLevel(0.95)
mc.SetNumBurnInSteps(100)
mc.SetNumIters(10000)
mc.SetNumBins(50)
mc.SetProposalFunction(pdfProp)

mcInt = mc.GetInterval()
poiList = mcInt.GetAxes()

# now setup the profile likelihood calculator
plc = ROOT.RooStats.ProfileLikelihoodCalculator(data, modelConfig)
plc.SetConfidenceLevel(0.95)
plInt = plc.GetInterval()

# make some plots
mcPlot = ROOT.RooStats.MCMCIntervalPlot(mcInt)

c1 = ROOT.TCanvas()
mcPlot.SetLineColor(ROOT.kGreen)
mcPlot.SetLineWidth(2)
mcPlot.Draw()

plPlot = ROOT.RooStats.LikelihoodIntervalPlot(plInt)
plPlot.Draw("same")

if len(poiList) == 1:
    p = poiList.at(0)
    print("MCMC interval: [{}, {}]".format(mcInt.LowerLimit(p), mcInt.UpperLimit(p)))

if len(poiList) == 2:
    p0 = poiList.at(0)
    p1 = poiList.at(1)
    scatter = ROOT.TCanvas()
    print("MCMC interval on p0: [{}, {}]".format(mcInt.LowerLimit(p0), mcInt.UpperLimit(p0)))
    print("MCMC interval on p1: [{}, {}]".format(mcInt.LowerLimit(p1), mcInt.UpperLimit(p1)))

    # MCMC interval on p0: [-0.2, 0.6]
    # MCMC interval on p1: [-0.2, 0.6]

    mcPlot.DrawChainScatter(p0, p1)
    scatter.Update()
    scatter.SaveAs("MultivariateGaussianTest_scatter.png")

t.Stop()
t.Print()

c1.SaveAs("MultivariateGaussianTest_plot.png")

# TODO: The MCMCCalculator has to be destructed first. Otherwise, we can get
# segmentation faults depending on the destruction order, which is random in
# Python. Probably the issue is that some object has a non-owning pointer to
# another object, which it uses in its destructor. This should be fixed either
# in the design of RooStats in C++, or with phythonizations.
del mc