ProcessMCMC.cpp

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//MaCh3 includes
#include "Fitters/OscProcessor.h"
#include "Manager/Manager.h"
 
 
inline void ProcessMCMC(const std::string& inputFile);
inline void MultipleProcessMCMC();
inline void CalcBayesFactor(MCMCProcessor* Processor);
inline void CalcSavageDickey(MCMCProcessor* Processor);
inline void CalcBipolarPlot(MCMCProcessor* Processor);
inline void CalcParameterEvolution(MCMCProcessor* Processor);
inline void GetTrianglePlot(MCMCProcessor* Processor);
inline void DiagnoseCovarianceMatrix(MCMCProcessor* Processor, const std::string& inputFile);
inline TH2D* TMatrixIntoTH2D(TMatrixDSym* Matrix, const std::string& title);
inline void KolmogorovSmirnovTest(const std::vector<std::unique_ptr<MCMCProcessor>>& Processor,
                                  const std::unique_ptr<TCanvas>& Posterior,
                                  const TString& canvasname);
int nFiles;
std::vector <std::string> FileNames;
std::vector <std::string> TitleNames;
std::string config;
 
int main(int argc, char *argv[]) 
{
  SetMaCh3LoggerFormat();
  nFiles = 0;
  if (argc != 3 && argc !=6 && argc != 8)
  {
    MACH3LOG_ERROR("How to use: ");
    MACH3LOG_ERROR("  single chain: {} <Config> <MCMM_ND_Output.root>", argv[0]);
    MACH3LOG_ERROR("  two chain:    {} <Config> <MCMM_ND_Output_1.root> <Title 1> <MCMC_ND_Output_2.root> <Title 2>", argv[0]);
    MACH3LOG_ERROR("  three chain:  {} <Config> <MCMM_ND_Output_1.root> <Title 1> <MCMC_ND_Output_2.root> <Title 2> <MCMC_ND_Output_3.root> <Title 3>", argv[0]);
    throw MaCh3Exception(__FILE__ , __LINE__ );
  }
 
  config = argv[1];
  YAML::Node card_yaml = M3OpenConfig(config);
  if (!CheckNodeExists(card_yaml, "ProcessMCMC")) {
    MACH3LOG_ERROR("The 'ProcessMCMC' node is not defined in the YAML configuration.");
    throw MaCh3Exception(__FILE__ , __LINE__ );
  }
 
  if (argc == 3)
  {
    MACH3LOG_INFO("Producing single fit output");
    std::string filename = argv[2];
    ProcessMCMC(filename);
  }
  // If we want to compare two or more fits (e.g. binning changes or introducing new params/priors)
  else if (argc == 6 || argc == 8)
  {
    MACH3LOG_INFO("Producing two fit comparison");
    FileNames.push_back(argv[2]);
    TitleNames.push_back(argv[3]);
 
    FileNames.push_back(argv[4]);
    TitleNames.push_back(argv[5]);
    //KS: If there is third file add it
    if(argc == 8)
    {
      FileNames.push_back(argv[6]);
      TitleNames.push_back(argv[7]);
    }
 
    MultipleProcessMCMC();
  }
  return 0;
}
 
std::map<std::string, std::pair<double, double>> GetCustomBinning(const YAML::Node& Settings)
{
  std::map<std::string, std::pair<double, double>> CustomBinning;
  if (Settings["CustomBinEdges"]) {
    const YAML::Node& edges = Settings["CustomBinEdges"];
 
    for (const auto& node : edges) {
      std::string key = node.first.as<std::string>();
      auto values = node.second.as<std::vector<double>>();
 
      if (values.size() == 2) {
        CustomBinning[key] = std::make_pair(values[0], values[1]);
        MACH3LOG_DEBUG("Adding custom binning {} with {:.4f}, {:.4f}", key, values[0], values[1]);
      } else {
        MACH3LOG_ERROR("Invalid number of values for key: {}", key);
        throw MaCh3Exception(__FILE__ , __LINE__ );
      }
    }
  }
  return CustomBinning;
}
 
void ProcessMCMC(const std::string& inputFile)
{
  MACH3LOG_INFO("File for study: {} with config  {}", inputFile, config);
  // Make the processor)
  auto Processor = std::make_unique<OscProcessor>(inputFile);
 
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
  
  const bool PlotCorr = GetFromManager<bool>(Settings["PlotCorr"], false);
 
  Processor->SetExcludedTypes(GetFromManager<std::vector<std::string>>(Settings["ExcludedTypes"], {}));
  Processor->SetExcludedNames(GetFromManager<std::vector<std::string>>(Settings["ExcludedNames"], {}));
  Processor->SetExcludedGroups(GetFromManager<std::vector<std::string>>(Settings["ExcludedGroups"], {}));
 
  //Apply additional cuts to 1D posterior
  Processor->SetPosterior1DCut(GetFromManager<std::string>(Settings["Posterior1DCut"], ""));
 
  if(PlotCorr) Processor->SetOutputSuffix("_drawCorr");
  //KS:Turn off plotting detector and some other setting, should be via some config
  Processor->SetPlotRelativeToPrior(GetFromManager<bool>(Settings["PlotRelativeToPrior"], false));
  Processor->SetPrintToPDF(GetFromManager<bool>(Settings["PrintToPDF"], true));
 
  //KS: Whether you want prior error bands for parameters with flat prior or not
  Processor->SetPlotErrorForFlatPrior(GetFromManager<bool>(Settings["PlotErrorForFlatPrior"], true));
  Processor->SetFancyNames(GetFromManager<bool>(Settings["FancyNames"], true));
  Processor->SetPlotBinValue(GetFromManager<bool>(Settings["PlotBinValue"], false));
  //KS: Plot only 2D posteriors with correlations greater than 0.2
  Processor->SetPost2DPlotThreshold(GetFromManager<double>(Settings["Post2DPlotThreshold"], 0.2));
 
  Processor->Initialise();
 
  if(Settings["BurnInSteps"]) {
    Processor->SetStepCut(Settings["BurnInSteps"].as<int>());
  } else {
    MACH3LOG_WARN("BurnInSteps not set, defaulting to 20%");
    Processor->SetStepCut(static_cast<int>(Processor->GetnSteps()/5));
  }
  if(Settings["MaxEntries"]) {
    Processor->SetEntries(Get<int>(Settings["MaxEntries"], __FILE__, __LINE__));
  }
  if(Settings["NBins"]) {
    Processor->SetNBins(Get<int>(Settings["NBins"], __FILE__, __LINE__));
  }
  if(Settings["Thinning"])
  {
    if(Settings["Thinning"][0].as<bool>()){
      Processor->ThinMCMC(Settings["Thinning"][1].as<int>());
    }
  }
  // Make the postfit
  Processor->MakePostfit(GetCustomBinning(Settings));
  Processor->DrawPostfit();
  //KS: Should set via config whether you want below or not
  if(GetFromManager<bool>(Settings["MakeCredibleIntervals"], true)) {
    Processor->MakeCredibleIntervals(GetFromManager<std::vector<double>>(Settings["CredibleIntervals"], {0.99, 0.90, 0.68}),
                                     GetFromManager<std::vector<short int>>(Settings["CredibleIntervalsColours"], {436, 430, 422}),
                                     GetFromManager<bool>(Settings["CredibleInSigmas"], false));
  }
  if(GetFromManager<bool>(Settings["CalcBayesFactor"], true))  CalcBayesFactor(Processor.get());
  if(GetFromManager<bool>(Settings["CalcSavageDickey"], true)) CalcSavageDickey(Processor.get());
  if(GetFromManager<bool>(Settings["CalcBipolarPlot"], false)) CalcBipolarPlot(Processor.get());
  if(GetFromManager<bool>(Settings["CalcParameterEvolution"], false)) CalcParameterEvolution(Processor.get());
 
  if(PlotCorr)
  {
    Processor->SetSmoothing(GetFromManager<bool>(Settings["Smoothing"], true));
    // Make the covariance matrix
    //We have different treatment for multithread
    Processor->CacheSteps();
    //KS: Since we cached let's make fancy violins :)
    if(GetFromManager<bool>(Settings["MakeViolin"], true)) Processor->MakeViolin();
    Processor->MakeCovariance_MP();
 
    Processor->DrawCovariance();
    if(GetFromManager<bool>(Settings["MakeCovarianceYAML"], true)) Processor->MakeCovarianceYAML(GetFromManager<std::string>(Settings["CovarianceYAMLOutName"], "UpdatedCorrelationMatrix.yaml"), GetFromManager<std::string>(Settings["CovarianceYAMLMeansMethod"], "HPD"));
 
    auto const &MakeSubOptimality = Settings["MakeSubOptimality"];
    if(MakeSubOptimality[0].as<bool>()) Processor->MakeSubOptimality(MakeSubOptimality[1].as<int>());
 
    if(GetFromManager<bool>(Settings["MakeCredibleRegions"], false)) {
      Processor->MakeCredibleRegions(GetFromManager<std::vector<double>>(Settings["CredibleRegions"], {0.99, 0.90, 0.68}),
                                     GetFromManager<std::vector<short int>>(Settings["CredibleRegionStyle"], {2, 1, 3}),
                                     GetFromManager<std::vector<short int>>(Settings["CredibleRegionColor"], {413, 406, 416}),
                                     GetFromManager<bool>(Settings["CredibleInSigmas"], false), 
                                     GetFromManager<bool>(Settings["Draw2DPosterior"], true),
                                     GetFromManager<bool>(Settings["DrawBestFit"], true));
    }
    if(GetFromManager<bool>(Settings["GetTrianglePlot"], true)) GetTrianglePlot(Processor.get());
 
    //KS: When creating covariance matrix longest time is spend on caching every step, since we already cached we can run some fancy covariance stability diagnostic
    if(GetFromManager<bool>(Settings["DiagnoseCovarianceMatrix"], false)) DiagnoseCovarianceMatrix(Processor.get(), inputFile);
  }
  Processor->ProduceChi2(GetFromManager<std::string>(Settings["Chi2Group"], "Osc"));
  if(GetFromManager<bool>(Settings["JarlskogAnalysis"], true))          Processor->PerformJarlskogAnalysis();
  if(GetFromManager<bool>(Settings["ProducePMNSElements"], true))       Processor->ProducePMNSElements();
  if(GetFromManager<bool>(Settings["ProduceUnitarityTriangles"], true)) Processor->ProduceUnitarityTriangles();
  if(GetFromManager<bool>(Settings["MakePiePlot"], true))               Processor->MakePiePlot();
}
 
void MultipleProcessMCMC()
{
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  constexpr Color_t PosteriorColor[] = {kBlue-1, kRed, kGreen+2};
  //constexpr Style_t PosteriorStyle[] = {kSolid, kDashed, kDotted};
  nFiles = int(FileNames.size());
  std::vector<std::unique_ptr<MCMCProcessor>> Processor(nFiles);
 
  if(!Settings["BurnInSteps"]) {
    MACH3LOG_WARN("BurnInSteps not set, defaulting to 20%");
  }
 
  for (int ik = 0; ik < nFiles; ik++)
  {
    MACH3LOG_INFO("File for study: {}", FileNames[ik]);
    // Make the processor
    Processor[ik] = std::make_unique<MCMCProcessor>(FileNames[ik]);
    Processor[ik]->SetOutputSuffix(("_" + std::to_string(ik)).c_str());
 
    Processor[ik]->SetExcludedTypes(GetFromManager<std::vector<std::string>>(Settings["ExcludedTypes"], {}));
    Processor[ik]->SetExcludedNames(GetFromManager<std::vector<std::string>>(Settings["ExcludedNames"], {}));
    Processor[ik]->SetExcludedGroups(GetFromManager<std::vector<std::string>>(Settings["ExcludedGroups"], {}));
 
    //Apply additional cuts to 1D posterior
    Processor[ik]->SetPosterior1DCut(GetFromManager<std::string>(Settings["Posterior1DCut"], ""));
 
    Processor[ik]->SetPlotRelativeToPrior(GetFromManager<bool>(Settings["PlotRelativeToPrior"], false));
    Processor[ik]->SetFancyNames(GetFromManager<bool>(Settings["FancyNames"], true));
    Processor[ik]->Initialise();
 
    if(Settings["BurnInSteps"]) {
      Processor[ik]->SetStepCut(Settings["BurnInSteps"].as<int>());
    }else {
      Processor[ik]->SetStepCut(static_cast<int>(Processor[ik]->GetnSteps()/5));
    }
 
    if(Settings["MaxEntries"]) {
      Processor[ik]->SetEntries(Get<int>(Settings["MaxEntries"], __FILE__, __LINE__));
    }
    if(Settings["NBins"]) {
      Processor[ik]->SetNBins(Get<int>(Settings["NBins"], __FILE__, __LINE__));
    }
  }
 
  Processor[0]->MakePostfit(GetCustomBinning(Settings));
  Processor[0]->DrawPostfit();
  // Get edges from first histogram to ensure all params use same binning
  std::map<std::string, std::pair<double, double>> ParamEdges;
  for(int i = 0; i < Processor[0]->GetNParams(); ++i) {
    // Get the histogram for the i-th parameter
    TH1D* hist = Processor[0]->GetHpost(i);
    if (!hist) {
      MACH3LOG_DEBUG("Histogram for parameter {} is null.", i);
      continue;
    }
 
    // Get the parameter name (title of the histogram)
    std::string paramName = hist->GetTitle();
 
    // Get the axis limits (edges)
    TAxis* axis = hist->GetXaxis();
    double xmin = axis->GetXmin();
    double xmax = axis->GetXmax();
 
    MACH3LOG_DEBUG("Adding bin edges for {} equal to {:.4f}, {:.4f}",paramName, xmin, xmax);
    // Insert into the map
    ParamEdges[paramName] = std::make_pair(xmin, xmax);
  }
 
  //KS: Multithreading here is very tempting but there are some issues with root that need to be resovled :(
  for (int ik = 1; ik < nFiles; ik++)
  {
    // Make the postfit
    Processor[ik]->MakePostfit(ParamEdges);
    Processor[ik]->DrawPostfit();
  }
 
  // Open a TCanvas to write the posterior onto
  auto Posterior = std::make_unique<TCanvas>("PosteriorMulti", "PosteriorMulti", 0, 0, 1024, 1024);
  gStyle->SetOptStat(0);
  gStyle->SetOptTitle(0);
  Posterior->SetGrid();
  Posterior->SetBottomMargin(0.1f);
  Posterior->SetTopMargin(0.05f);
  Posterior->SetRightMargin(0.03f);
  Posterior->SetLeftMargin(0.15f);
  
  // First filename: keep path, just remove ".root"
  // Would be nice to specify outpath in a later update
  size_t pos = FileNames[0].rfind(".root");
  std::string base = (pos == std::string::npos) ? FileNames[0] : FileNames[0].substr(0, pos);
  TString canvasname = base;
 
  // Remaining filenames: strip path and ".root"
  // So if you have /path/to/file1.root and /path/to/file2.root or /another/path/to/file2.root, canvasname = /path/to/file1_file2.root
  for (int ik = 1; ik < nFiles; ik++) {
    pos = FileNames[ik].find_last_of('/');
    base = (pos == std::string::npos) ? FileNames[ik] : FileNames[ik].substr(pos + 1);
    pos = base.rfind(".root");
    if (pos != std::string::npos) base = base.substr(0, pos);
    canvasname += "_" + TString(base);
  }
  
  canvasname = canvasname +".pdf[";
 
  Posterior->Print(canvasname);
  // Once the pdf file is open no longer need to bracket
  canvasname.ReplaceAll("[","");
 
  for(int i = 0; i < Processor[0]->GetNParams(); ++i) 
  {
    // This holds the posterior density
    std::vector<std::unique_ptr<TH1D>> hpost(nFiles);
    std::vector<std::unique_ptr<TLine>> hpd(nFiles);
    hpost[0] = M3::Clone(Processor[0]->GetHpost(i));
    hpost[0]->GetYaxis()->SetTitle("Posterior Density");
    bool Skip = false;
    for (int ik = 1 ; ik < nFiles;  ik++)
    {
      // KS: If somehow this chain doesn't given params we skip it
      const int Index = Processor[ik]->GetParamIndexFromName(hpost[0]->GetTitle());
      if(Index == M3::_BAD_INT_)
      {
        Skip = true;
        break;
      }
      hpost[ik] = M3::Clone(Processor[ik]->GetHpost(Index));
    }
 
    // Don't plot if this is a fixed histogram (i.e. the peak is the whole integral)
    if(hpost[0]->GetMaximum() == hpost[0]->Integral()*1.5 || Skip) {
      continue;
    }
    for (int ik = 0; ik < nFiles;  ik++)
    {
      RemoveFitter(hpost[ik].get(), "Gauss");
 
      // Set some nice colours
      hpost[ik]->SetLineColor(PosteriorColor[ik]);
      //hpost[ik]->SetLineStyle(PosteriorStyle[ik]);
      hpost[ik]->SetLineWidth(2);
 
      // Area normalise the distributions
      hpost[ik]->Scale(1./hpost[ik]->Integral());
    }
    TString Title;
    double Prior = 1.0;
    double PriorError = 1.0;
 
    Processor[0]->GetNthParameter(i, Prior, PriorError, Title);
 
    // Now make the TLine for the Asimov
    auto Asimov = std::make_unique<TLine>(Prior, hpost[0]->GetMinimum(), Prior, hpost[0]->GetMaximum());
    Asimov->SetLineColor(kRed-3);
    Asimov->SetLineWidth(2);
    Asimov->SetLineStyle(kDashed);
 
    // Make a nice little TLegend
    auto leg = std::make_unique<TLegend>(0.20, 0.7, 0.6, 0.97);
    leg->SetTextSize(0.03f);
    leg->SetFillColor(0);
    leg->SetFillStyle(0);
    leg->SetLineColor(0);
    leg->SetLineStyle(0);
    TString asimovLeg = Form("#splitline{Prior}{x = %.2f , #sigma = %.2f}", Prior, PriorError);
    leg->AddEntry(Asimov.get(), asimovLeg, "l");
 
    for (int ik = 0; ik < nFiles; ik++)
    {
      TString rebinLeg = Form("#splitline{%s}{#mu = %.2f, #sigma = %.2f}", TitleNames[ik].c_str(), hpost[ik]->GetMean(), hpost[ik]->GetRMS());
      leg->AddEntry(hpost[ik].get(),  rebinLeg, "l");
 
      hpd[ik] = std::make_unique<TLine>(hpost[ik]->GetBinCenter(hpost[ik]->GetMaximumBin()), hpost[ik]->GetMinimum(),
                                        hpost[ik]->GetBinCenter(hpost[ik]->GetMaximumBin()), hpost[ik]->GetMaximum());
      hpd[ik]->SetLineColor(hpost[ik]->GetLineColor());
      hpd[ik]->SetLineWidth(2);
      hpd[ik]->SetLineStyle(kSolid);
    }
 
    // Find the maximum value to nicely resize hist
    double maximum = 0;
    for (int ik = 0; ik < nFiles; ik++) maximum = std::max(maximum, hpost[ik]->GetMaximum());
    for (int ik = 0; ik < nFiles; ik++) hpost[ik]->SetMaximum(1.3*maximum);
 
    hpost[0]->Draw("hist");
    for (int ik = 1; ik < nFiles; ik++) hpost[ik]->Draw("hist same");
    Asimov->Draw("same");
    for (int ik = 0; ik < nFiles; ik++) hpd[ik]->Draw("same");
    leg->Draw("same");
    Posterior->cd();
    Posterior->Print(canvasname);
  }//End loop over parameters
    
  // Finally draw the parameter plot onto the PDF
  // Close the .pdf file with all the posteriors
  Posterior->cd();
  Posterior->Clear();
 
  if(GetFromManager<bool>(Settings["PerformKStest"], true)) KolmogorovSmirnovTest(Processor, Posterior, canvasname);
  
  // Close the pdf file
  MACH3LOG_INFO("Closing pdf {}", canvasname);
  canvasname+="]";
  Posterior->Print(canvasname);
}
 
void CalcBayesFactor(MCMCProcessor* Processor)
{
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  std::vector<std::string> ParNames;
  std::vector<std::vector<double>> Model1Bounds;
  std::vector<std::vector<double>> Model2Bounds;
  std::vector<std::vector<std::string>> ModelNames;
  for (const auto& dg : Settings["BayesFactor"])
  {
    ParNames.push_back(dg[0].as<std::string>());
    ModelNames.push_back(dg[1].as<std::vector<std::string>>());
    Model1Bounds.push_back(dg[2].as<std::vector<double>>());
    Model2Bounds.push_back(dg[3].as<std::vector<double>>());
  }
 
  Processor->GetBayesFactor(ParNames, Model1Bounds, Model2Bounds, ModelNames);
}
 
void CalcSavageDickey(MCMCProcessor* Processor)
{
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  std::vector<std::string> ParNames;
  std::vector<double> EvaluationPoint;
  std::vector<std::vector<double>> Bounds;
  
  for (const auto& d : Settings["SavageDickey"])
  {
    ParNames.push_back(d[0].as<std::string>());
    EvaluationPoint.push_back(d[1].as<double>());
    Bounds.push_back(d[2].as<std::vector<double>>());
  }
  Processor->GetSavageDickey(ParNames, EvaluationPoint, Bounds);
}
 
void CalcParameterEvolution(MCMCProcessor* Processor)
{
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  std::vector<std::string> ParNames;
  std::vector<int> Intervals;
  for (const auto& d : Settings["ParameterEvolution"])
  {
    ParNames.push_back(d[0].as<std::string>());
    Intervals.push_back(d[1].as<int>());
  }
  Processor->ParameterEvolution(ParNames, Intervals);
}
 
void CalcBipolarPlot(MCMCProcessor* Processor)
{
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  std::vector<std::string> ParNames;
  for (const auto& d : Settings["BipolarPlot"])
  {
    ParNames.push_back(d[0].as<std::string>());
  }
  Processor->GetPolarPlot(ParNames);
}
 
void GetTrianglePlot(MCMCProcessor* Processor) {
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  for (const auto& dg : Settings["TrianglePlot"])
  {
    std::string ParName = dg[0].as<std::string>();
 
    std::vector<std::string> NameVec = dg[1].as<std::vector<std::string>>();
    Processor->MakeTrianglePlot(NameVec,
                                GetFromManager<std::vector<double>>(Settings["CredibleIntervals"], {0.99, 0.90, 0.68}),
                                GetFromManager<std::vector<short int>>(Settings["CredibleIntervalsColours"], {436, 430, 422}),
                                GetFromManager<std::vector<double>>(Settings["CredibleRegions"], {0.99, 0.90, 0.68}),
                                GetFromManager<std::vector<short int>>(Settings["CredibleRegionStyle"], {2, 1, 3}),
                                GetFromManager<std::vector<short int>>(Settings["CredibleRegionColor"], {413, 406, 416}),
                                GetFromManager<bool>(Settings["CredibleInSigmas"], false));
  }
}
 
void DiagnoseCovarianceMatrix(MCMCProcessor* Processor, const std::string& inputFile)
{
  //Turn of plots from Processor
  Processor->SetPrintToPDF(false);
  // Open a TCanvas to write the posterior onto
  auto Canvas = std::make_unique<TCanvas>("Canvas", "Canvas", 0, 0, 1024, 1024);
  Canvas->SetGrid();
  gStyle->SetOptStat(0);
  gStyle->SetOptTitle(0);
  Canvas->SetTickx();
  Canvas->SetTicky();
  Canvas->SetBottomMargin(0.1f);
  Canvas->SetTopMargin(0.05f);
  Canvas->SetRightMargin(0.15f);
  Canvas->SetLeftMargin(0.10f);
  
  //KS: Fancy colours
  const int NRGBs = 10;
  TColor::InitializeColors();
  Double_t stops[NRGBs] = { 0.00, 0.10, 0.25, 0.35, 0.50, 0.60, 0.65, 0.75, 0.90, 1.00 };
  Double_t red[NRGBs]   = { 0.50, 1.00, 1.00, 0.25, 0.00, 0.10, 0.50, 1.00, 0.75, 0.55 };
  Double_t green[NRGBs] = { 0.00, 0.25, 1.00, 0.25, 0.00, 0.60, 0.90, 1.00, 0.75, 0.75 };
  Double_t blue[NRGBs]  = { 0.00, 0.25, 1.00, 1.00, 0.50, 0.60, 0.90, 1.00, 0.05, 0.05 };
  TColor::CreateGradientColorTable(NRGBs, stops, red, green, blue, 255);
  gStyle->SetNumberContours(255);
  
  std::string OutName = inputFile;
  OutName = OutName.substr(0, OutName.find(".root"));
  Canvas->Print(Form("Correlation_%s.pdf[", OutName.c_str()), "pdf");
  Canvas->Print(Form("Covariance_%s.pdf[", OutName.c_str()), "pdf");
  
  YAML::Node card_yaml = M3OpenConfig(config.c_str());
  YAML::Node Settings = card_yaml["ProcessMCMC"];
 
  const int entries = int(Processor->GetnSteps());
  const int NIntervals = GetFromManager<int>(Settings["NIntervals"], 5);
  const int IntervalsSize = entries/NIntervals;
  //We start with burn from 0 (no burn in at all)
  int BurnIn = 0;
  MACH3LOG_INFO("Diagnosing matrices with entries={}, NIntervals={} and IntervalsSize={}", entries, NIntervals, IntervalsSize);
 
  TMatrixDSym *Covariance = nullptr;
  TMatrixDSym *Correlation = nullptr;
  
  TH2D *CovariancePreviousHist = nullptr;
  TH2D *CorrelationPreviousHist = nullptr;
 
  TH2D *CovarianceHist = nullptr;
  TH2D *CorrelationHist = nullptr;
 
  //KS: Get first covariances, we need two for comparison...
  Processor->SetStepCut(BurnIn);
  Processor->GetCovariance(Covariance, Correlation);
  
  CovariancePreviousHist = TMatrixIntoTH2D(Covariance, "Covariance"); 
  CorrelationPreviousHist = TMatrixIntoTH2D(Correlation, "Correlation");
      
  delete Covariance;
  Covariance = nullptr;
  delete Correlation;
  Correlation = nullptr;
  
  //KS: Loop over all desired cuts
  for(int k = 1; k < NIntervals; ++k)
  {
    BurnIn = k*IntervalsSize;
    Processor->SetStepCut(BurnIn);
    Processor->GetCovariance(Covariance, Correlation);
    Processor->Reset2DPosteriors();
    
    CovarianceHist = TMatrixIntoTH2D(Covariance, "Covariance"); 
    CorrelationHist = TMatrixIntoTH2D(Correlation, "Correlation");
            
    TH2D *CovarianceDiff = static_cast<TH2D*>(CovarianceHist->Clone("Covariance_Ratio"));
    TH2D *CorrelationDiff = static_cast<TH2D*>(CorrelationHist->Clone("Correlation_Ratio"));
    
    //KS: Bit messy but quite often covariance is 0 is divided by 0 is problematic so
    #ifdef MULTITHREAD
    #pragma omp parallel for
    #endif
    for (int j = 1; j < CovarianceDiff->GetXaxis()->GetNbins()+1; ++j)
    {
      for (int i = 1; i < CovarianceDiff->GetYaxis()->GetNbins()+1; ++i)
      {
        if( std::fabs (CovarianceDiff->GetBinContent(j, i)) < 1.e-5 && std::fabs (CovariancePreviousHist->GetBinContent(j, i)) < 1.e-5)
        {
          CovarianceDiff->SetBinContent(j, i, M3::_BAD_DOUBLE_);
          CovariancePreviousHist->SetBinContent(j, i, M3::_BAD_DOUBLE_);
        }
        if( std::fabs (CorrelationDiff->GetBinContent(j, i)) < 1.e-5 && std::fabs (CorrelationPreviousHist->GetBinContent(j, i)) < 1.e-5)
        {
          CorrelationDiff->SetBinContent(j, i, M3::_BAD_DOUBLE_);
          CorrelationPreviousHist->SetBinContent(j, i, M3::_BAD_DOUBLE_);
        }
      }
    }
    //Divide matrices
    CovarianceDiff->Divide(CovariancePreviousHist);
    CorrelationDiff->Divide(CorrelationPreviousHist);
    
    //Now it is time for fancy names etc.
    for (int j = 0; j < CovarianceDiff->GetXaxis()->GetNbins(); ++j)
    {
      TString Title = "";
      double Prior = 1.0;
      double PriorError = 1.0;
  
      Processor->GetNthParameter(j, Prior, PriorError, Title);
      
      CovarianceDiff->GetXaxis()->SetBinLabel(j+1, Title);
      CovarianceDiff->GetYaxis()->SetBinLabel(j+1, Title);
      CorrelationDiff->GetXaxis()->SetBinLabel(j+1, Title);
      CorrelationDiff->GetYaxis()->SetBinLabel(j+1, Title);
    }
    CovarianceDiff->GetXaxis()->SetLabelSize(0.015f);
    CovarianceDiff->GetYaxis()->SetLabelSize(0.015f);
    CorrelationDiff->GetXaxis()->SetLabelSize(0.015f);
    CorrelationDiff->GetYaxis()->SetLabelSize(0.015f);
    
    std::stringstream ss;
    ss << "BCut_";
    ss << BurnIn;
    ss << "/";
    ss << "BCut_";
    ss << (k-1)*IntervalsSize;
    std::string str = ss.str();
    
    TString Title = "Cov " + str;
    CovarianceDiff->GetZaxis()->SetTitle( Title );
    Title = "Corr " + str;
    CorrelationDiff->GetZaxis()->SetTitle(Title);
    
    CovarianceDiff->SetMinimum(-2);
    CovarianceDiff->SetMaximum(2);
    CorrelationDiff->SetMinimum(-2);
    CorrelationDiff->SetMaximum(2);
 
    Canvas->cd();
    CovarianceDiff->Draw("colz");
    Canvas->Print(Form("Covariance_%s.pdf", OutName.c_str()), "pdf");
 
    CorrelationDiff->Draw("colz");
    Canvas->Print(Form("Correlation_%s.pdf", OutName.c_str()), "pdf");
        
    //KS: Current hist become previous as we need it for further comparison
    delete CovariancePreviousHist;
    CovariancePreviousHist = static_cast<TH2D*>(CovarianceHist->Clone());
    delete CorrelationPreviousHist;
    CorrelationPreviousHist = static_cast<TH2D*>(CorrelationHist->Clone());
    
    delete CovarianceHist;
    CovarianceHist = nullptr;
    delete CorrelationHist;
    CorrelationHist = nullptr;
    
    delete CovarianceDiff;
    delete CorrelationDiff;
    delete Covariance;
    Covariance = nullptr;
    delete Correlation;
    Correlation = nullptr;
  }
  Canvas->cd();
  Canvas->Print(Form("Covariance_%s.pdf]", OutName.c_str()), "pdf");
  Canvas->Print(Form("Correlation_%s.pdf]", OutName.c_str()), "pdf");
  
  Processor->SetPrintToPDF(true);
  if(Covariance != nullptr)              delete Covariance;
  if(Correlation != nullptr)             delete Correlation;
  if(CovariancePreviousHist != nullptr)  delete CovariancePreviousHist;
  if(CorrelationPreviousHist != nullptr) delete CorrelationPreviousHist;
  if(CovarianceHist != nullptr)          delete CovarianceHist;
  if(CorrelationHist != nullptr)         delete CorrelationHist;
}
 
//KS: Convert TMatrix to TH2D, mostly useful for making fancy plots
TH2D* TMatrixIntoTH2D(TMatrixDSym* Matrix, const std::string& title)
{
  TH2D* hMatrix = new TH2D(title.c_str(), title.c_str(), Matrix->GetNrows(), 0.0, Matrix->GetNrows(), Matrix->GetNcols(), 0.0, Matrix->GetNcols());
  for(int i = 0; i < Matrix->GetNrows(); i++)
  {
    for(int j = 0; j < Matrix->GetNcols(); j++)
    {
      //KS: +1 because there is offset in histogram relative to TMatrix
      hMatrix->SetBinContent(i+1,j+1, (*Matrix)(i,j));
    }
  }
  return hMatrix;
}
 
// KS: Perform KS test to check if two posteriors for the same parameter came from the same distribution
void KolmogorovSmirnovTest(const std::vector<std::unique_ptr<MCMCProcessor>>& Processor,
                           const std::unique_ptr<TCanvas>& Posterior,
                           const TString& canvasname)
{
  constexpr Color_t CumulativeColor[] = {kBlue-1, kRed, kGreen+2};
  constexpr Style_t CumulativeStyle[] = {kSolid, kDashed, kDotted};
 
  for(int i = 0; i < Processor[0]->GetNParams(); ++i) 
  {
    // This holds the posterior density
    std::vector<std::unique_ptr<TH1D>> hpost(nFiles);
    std::vector<std::unique_ptr<TH1D>> CumulativeDistribution(nFiles);
       
    TString Title;
    double Prior = 1.0;
    double PriorError = 1.0;
 
    Processor[0]->GetNthParameter(i, Prior, PriorError, Title);
    bool Skip = false;
    for (int ik = 0 ; ik < nFiles;  ik++)
    {
      int Index = 0;
      if(ik == 0 ) Index = i;
      else
      {
        // KS: If somehow this chain doesn't given params we skip it
        Index = Processor[ik]->GetParamIndexFromName(hpost[0]->GetTitle());
        if(Index == M3::_BAD_INT_)
        {
          Skip = true;
          break;
        }
      }
      hpost[ik] = M3::Clone(Processor[ik]->GetHpost(Index));
      CumulativeDistribution[ik] = M3::Clone(Processor[ik]->GetHpost(Index));
      CumulativeDistribution[ik]->Fill(0., 0.);
      CumulativeDistribution[ik]->Reset();
      CumulativeDistribution[ik]->SetMaximum(1.);
      TString TempTitle = Title+" Kolmogorov Smirnov";
      CumulativeDistribution[ik]->SetTitle(TempTitle);
      
      TempTitle = Title+" Value";
      CumulativeDistribution[ik]->GetXaxis()->SetTitle(TempTitle);
      CumulativeDistribution[ik]->GetYaxis()->SetTitle("Cumulative Probability");
      
      CumulativeDistribution[ik]->SetLineWidth(2);
      CumulativeDistribution[ik]->SetLineColor(CumulativeColor[ik]);
      CumulativeDistribution[ik]->SetLineStyle(CumulativeStyle[ik]);
    }
 
    // Don't plot if this is a fixed histogram (i.e. the peak is the whole integral)
    if(hpost[0]->GetMaximum() == hpost[0]->Integral()*1.5 || Skip) {
      continue;
    }
    
    for (int ik = 0 ; ik < nFiles;  ik++)
    {
      const int NumberOfBins = hpost[ik]->GetXaxis()->GetNbins();
      double Cumulative = 0;
      const double Integral = hpost[ik]->Integral();
      for (int j = 1; j < NumberOfBins+1; ++j)
      {
        Cumulative += hpost[ik]->GetBinContent(j)/Integral;
        CumulativeDistribution[ik]->SetBinContent(j, Cumulative);
      }
      //KS: Set overflow to 1 just in case
      CumulativeDistribution[ik]->SetBinContent(NumberOfBins+1, 1.);
    }
    
    std::vector<int> TestStatBin(nFiles, 0);
    std::vector<double> TestStatD(nFiles, -999);
    std::vector<std::unique_ptr<TLine>> LineD(nFiles);
    //Find KS statistic
    for (int ik = 1 ; ik < nFiles;  ik++)
    {
      const int NumberOfBins = CumulativeDistribution[0]->GetXaxis()->GetNbins();
      for (int j = 1; j < NumberOfBins+1; ++j)
      {
        const double BinValue = CumulativeDistribution[0]->GetBinCenter(j);
        const int BinNumber = CumulativeDistribution[ik]->FindBin(BinValue);
        //KS: Calculate D statistic for this bin, only save it if it's bigger than previously found value
        double TempDstat = std::fabs(CumulativeDistribution[0]->GetBinContent(j) - CumulativeDistribution[ik]->GetBinContent(BinNumber));
        if(TempDstat > TestStatD[ik])
        {
          TestStatD[ik] = TempDstat;
          TestStatBin[ik] = j;
        }
      }
    }
 
    for (int ik = 0 ; ik < nFiles;  ik++)
    {
      LineD[ik] = std::make_unique<TLine>(CumulativeDistribution[0]->GetBinCenter(TestStatBin[ik]), 0, CumulativeDistribution[0]->GetBinCenter(TestStatBin[ik]), CumulativeDistribution[0]->GetBinContent(TestStatBin[ik]));
      LineD[ik]->SetLineColor(CumulativeColor[ik]);
      LineD[ik]->SetLineWidth(2.0);
    }
    CumulativeDistribution[0]->Draw();
    for (int ik = 0 ; ik < nFiles;  ik++)
      CumulativeDistribution[ik]->Draw("SAME");
    
    auto leg = std::make_unique<TLegend>(0.15, 0.7, 0.5, 0.90);
    leg->SetTextSize(0.04f);
    for (int ik = 0; ik < nFiles;  ik++)
      leg->AddEntry(CumulativeDistribution[ik].get(), TitleNames[ik].c_str(), "l");
    for (int ik = 1; ik < nFiles;  ik++)
      leg->AddEntry(LineD[ik].get(), Form("#Delta D = %.4f", TestStatD[ik]), "l");
    
    leg->SetLineColor(0);
    leg->SetLineStyle(0);
    leg->SetFillColor(0);
    leg->SetFillStyle(0);
    leg->Draw("SAME");
 
    for (int ik = 1; ik < nFiles;  ik++)
      LineD[ik]->Draw("sam");
      
    Posterior->cd();
    Posterior->Print(canvasname);
  } //End loop over parameter
}