MulticanonicalMCMCHandler.cpp

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#include <ostream>
#include <stdexcept>
#include "Fitters/MulticanonicalMCMCHandler.h"
#include "Parameters/ParameterHandlerBase.h"
#include "Samples/HistogramUtils.h"
 
 
M3::BiasFunction ParseBiasFunction(const std::string& biasFunctionName) {
  if (biasFunctionName == "gaussian") {
    return M3::BiasFunction::kGaussian;
  }
  if (biasFunctionName == "vonMises") {
    return M3::BiasFunction::kVonMises;
  }
  if (biasFunctionName == "generalisedGaussian") {
    return M3::BiasFunction::kGeneralisedGaussian;
  }
 
  throw MaCh3Exception(__FILE__, __LINE__, "Unknown multicanonical bias function: " + biasFunctionName);
}
 
MulticanonicalMCMCHandler::MulticanonicalMCMCHandler() {
  // Initialize member variables with defaults
  oscCovVar = -1;
  multicanonicalVar = -1;
  multicanonicalVar_dm23 = -1;
  multicanonicalSpline = false;
  multicanonicalBeta = 1.0;
  delta_cp_value = 0.0;
  delm23_value = 0.0;
  dcp_spline_IO = nullptr;
  dcp_spline_NO = nullptr;
  umbrellaMean = 0.0;
  umbrellaWidth = 1.0;
  umbrellaNumber = 5;
  umbrellaOverlapMode = false;
  umbrellaSigmaOverlap = 3.0;
  umbrellaAdjustStepScale = false;
  umbrellaStepScaleFactor = 1.0;
  flipWindow = false;
 
  vonMises_kappa = -1.0;
  vonMises_I0_kappa = -1.0;
  umbrellaBiasFunction = M3::BiasFunction::kGaussian;
  umbrellaBiasFunctionName = "gaussian";
}
 
MulticanonicalMCMCHandler::~MulticanonicalMCMCHandler() {
  // Destructor
}
 
#ifdef MACH3_DEBUG
void MulticanonicalMCMCHandler::setDebugStream(std::ostream* os, bool enabled) {
  debugStream = os;
  debugEnabled = enabled;
}
#endif
 
void MulticanonicalMCMCHandler::FindOscCovParams(const std::vector<ParameterHandlerBase*>& systematics) {
  bool foundDeltaCP = false;
  bool foundDelm23 = false;
 
  // Loop over the systematics and find the osc_cov systematic and the delta_cp parameter number
  MACH3LOG_INFO("Looping over systematics to find delta_cp parameter");
  MACH3LOG_INFO("Number of systematics: {}", systematics.size());
 
  for (size_t iCov = 0; iCov < systematics.size(); iCov++){
    auto* syst = systematics[static_cast<int>(iCov)];
    for (int i = 0; i < syst->GetNumParams(); i++) {
      if (syst->GetParName(i) == "delta_cp") {
        MACH3LOG_INFO("Found delta_cp parameter in systematic {} at index {}", syst->GetName(), i);
        oscCovVar = static_cast<int>(iCov);
        multicanonicalVar = i;
        foundDeltaCP = true;
      }
      if (syst->GetParName(i) == "delm2_23") {
        MACH3LOG_INFO("Found delm2_23 parameter in systematic {} at index {}", syst->GetName(), i);
        multicanonicalVar_dm23 = i;
        foundDelm23 = true;
      }
    }  
  }
 
  // if we didn't find both parameters we need to throw
  if (!foundDeltaCP) {
    MACH3LOG_ERROR("Could not find delta_cp parameter in osc_cov systematic");
    throw MaCh3Exception(__FILE__, __LINE__, "Could not find delta_cp parameter in osc_cov systematic");
  }
  if (!foundDelm23) {
    MACH3LOG_ERROR("Could not find delm2_23 parameter in osc_cov systematic");
    throw MaCh3Exception(__FILE__, __LINE__, "Could not find delm2_23 parameter in osc_cov systematic");
  }
}
 
void MulticanonicalMCMCHandler::InitializeMulticanonicalHandlerConfig(Manager* fitMan, std::vector<ParameterHandlerBase*>& systematics) {
  FindOscCovParams(systematics);
 
  const auto mcmcConfig = fitMan->raw()["General"]["MCMC"];
 
  // Get the multicanonical beta value from the configuration file
  // This acts as a global bias strength factor
  multicanonicalBeta = Get<double>(mcmcConfig["Multicanonical"]["Beta"],  __FILE__, __LINE__);
  MACH3LOG_INFO("Setting multicanonical beta to {}", multicanonicalBeta);
 
  // delete the umbrella section, thats not ideal
  multicanonicalSpline = GetFromManager<bool>(mcmcConfig["Multicanonical"]["Spline"]["SplineMode"], false, __FILE__, __LINE__);
 
  const std::string biasFunctionName = GetFromManager<std::string>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaBiasFunction"], "", __FILE__, __LINE__);
  const bool hasBiasFunction = !biasFunctionName.empty();
 
  // Spline and umbrella modes are mutually exclusive
  if (multicanonicalSpline && hasBiasFunction) {
    MACH3LOG_ERROR("Cannot use multicanonical spline together with umbrella bias function selection.");
    throw MaCh3Exception(__FILE__, __LINE__, "Cannot use multicanonical spline together with umbrella bias function selection.");
  }
 
  // Umbrella mode requires an explicit bias function selection
  if (!multicanonicalSpline && !hasBiasFunction) {
    MACH3LOG_ERROR("Multicanonical umbrella mode requires UmbrellaBiasFunction to be set (gaussian, vonMises, or generalisedGaussian).");
    throw MaCh3Exception(__FILE__, __LINE__, "Multicanonical umbrella mode requires UmbrellaBiasFunction to be set.");
  }
 
  // Parse and set the umbrella bias function enum
  if (hasBiasFunction) {
    umbrellaBiasFunction = ParseBiasFunction(biasFunctionName);
    umbrellaBiasFunctionName = biasFunctionName;
    MACH3LOG_INFO("Using umbrella bias function {}", umbrellaBiasFunctionName);
  }
 
  // setup for spline bias mode
  if (multicanonicalSpline) {
    auto splineFileName = Get<std::string>(mcmcConfig["Multicanonical"]["Spline"]["SplineFile"], __FILE__, __LINE__);
    TFile* splineFile = M3::Open(splineFileName.c_str(), "READ",__FILE__, __LINE__);
 
    // grab the splines and do a quick check that they are evaluatable
    TSpline3* dcp_spline_IO_fromfile = static_cast<TSpline3*>(splineFile->Get("dcp_spline_IO"));
    dcp_spline_IO = static_cast<TSpline3*>(dcp_spline_IO_fromfile->Clone("dcp_spline_IO"));
    MACH3LOG_INFO("Using multicanonical spline from file {}", splineFileName);
    dcp_spline_IO->Eval(0.0); // check that the spline is valid
    MACH3LOG_INFO("Spline evaluated at 0.0 gives value: {}", dcp_spline_IO->Eval(0.0));
 
    TSpline3* dcp_spline_NO_fromfile = static_cast<TSpline3*>(splineFile->Get("dcp_spline_NO"));
    dcp_spline_NO = static_cast<TSpline3*>(dcp_spline_NO_fromfile->Clone("dcp_spline_NO"));
    MACH3LOG_INFO("Using multicanonical spline from file {}", splineFileName);
    dcp_spline_NO->Eval(0.0); // check that the spline is valid
    MACH3LOG_INFO("Spline evaluated at 0.0 gives value {}", dcp_spline_NO->Eval(0.0));
 
    splineFile->Close();
    splineFile = nullptr;
  } else {
    // Umbrella mode with explicit bias function selection
    MACH3LOG_INFO("Using umbrella multicanonical method with bias function {}", umbrellaBiasFunctionName);
    umbrellaMean = GetFromManager<double>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaMean"], 0, __FILE__, __LINE__);
    MACH3LOG_INFO("Setting multicanonical mean to {}", umbrellaMean);
 
    umbrellaNumber = GetFromManager<int>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaNumber"], 5, __FILE__, __LINE__);
 
    // dynamically adjust the width of the gaussians to ensure a certain level
    // of overlap? be careful, not enough windows here will lead to posterior
    // (rather than bias) dominated results
    umbrellaOverlapMode = GetFromManager<bool>(mcmcConfig["Multicanonical"]["Umbrella"]["AutoOverlapMode"], false, __FILE__, __LINE__);
 
    if (umbrellaOverlapMode) {
      MACH3LOG_INFO("Setting width based on # of sigma overlapping between umbrellas");
      umbrellaSigmaOverlap = GetFromManager<double>(mcmcConfig["Multicanonical"]["Umbrella"]["SigmaOverlap"], 3.0, __FILE__, __LINE__);
      MACH3LOG_INFO("Setting umbrella number to {}", umbrellaNumber);
      umbrellaWidth = TMath::Pi() / ((umbrellaNumber - 1) * (umbrellaSigmaOverlap));
    } else {
      // just grab the width directly from the config
      umbrellaWidth = GetFromManager<double>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaWidth"], (2 * TMath::Pi()) / umbrellaNumber, __FILE__, __LINE__);
      MACH3LOG_INFO("Setting width based on value in config {}", umbrellaWidth);
    }
 
    // set individual step scale for dcp, so that the ratio of the step scale to
    // the multicanonical sigma is stepscale/1sigmaerror = 1/2pi
    umbrellaAdjustStepScale = GetFromManager<bool>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaAdjustStepScale"], false, __FILE__, __LINE__);
    umbrellaStepScaleFactor = GetFromManager<double>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaStepScaleFactor"], 1.0, __FILE__, __LINE__);
 
    AdjustUmbrellaStepScale(systematics);
 
    // Set the flip window flag for the oscillation systematic DO NOT USE THIS
    // flipWindow =
    // GetFromManager<bool>(mcmcConfig["Multicanonical"]["Umbrella"]["FlipWindow"],
    // false, __FILE__, __LINE__); MACH3LOG_INFO("Flip Window: {}", flipWindow);
  }
 
  // initialize von Mises parameters
  if (umbrellaBiasFunction == M3::BiasFunction::kVonMises) {
    double temp_vonMises_sigma;
    temp_vonMises_sigma = GetFromManager<double>(mcmcConfig["Multicanonical"]["Umbrella"]["UmbrellaWidth"], umbrellaWidth, __FILE__, __LINE__);
    vonMises_kappa = 1.0 / (temp_vonMises_sigma * temp_vonMises_sigma);
    vonMises_I0_kappa = TMath::BesselI0(vonMises_kappa);
    MACH3LOG_INFO("Using von Mises distribution with kappa = {} and I0(kappa) = {}", vonMises_kappa, vonMises_I0_kappa);
  }
 
  if (umbrellaBiasFunction == M3::BiasFunction::kGeneralisedGaussian) {
    MACH3LOG_INFO("Using generalised Gaussian with mean {} and width {}", umbrellaMean, umbrellaWidth);
  }
}
 
void MulticanonicalMCMCHandler::AdjustUmbrellaStepScale(const std::vector<ParameterHandlerBase*>& systematics) {
  if (umbrellaAdjustStepScale) {
    MACH3LOG_INFO("Adjusting umbrella step scale to keep ratio of step scale to multicanonical sigma constant");
    MACH3LOG_INFO("Setting umbrella step scale factor to {}", umbrellaStepScaleFactor);
    double stepScale = (umbrellaWidth * umbrellaStepScaleFactor) / (2.0 * TMath::Pi());
    MACH3LOG_INFO("Setting individual step scale for multicanonical separate to {}", stepScale);
    systematics[oscCovVar]->SetIndivStepScale(multicanonicalVar, stepScale);
    MACH3LOG_INFO("Setting individual step scale for {} systematic to {}", multicanonicalVar, stepScale);
  } else {
    MACH3LOG_INFO("Not adjusting umbrella step scale, using value in OscCov config");
  }
}
 
void MulticanonicalMCMCHandler::InitializeMulticanonicalParams(std::vector<ParameterHandlerBase*>& systematics) {
  // Set starting point of chain to umbrella center for non-spline umbrella modes
  if (!multicanonicalSpline) {
    systematics[oscCovVar]->PrintPreFitCurrPropValues();
    systematics[oscCovVar]->SetParCurrProp(multicanonicalVar, umbrellaMean);
    MACH3LOG_INFO("Setting starting point of chain to mean value for multicanonical separate: {}", umbrellaMean);
    // pass the mean to the covarianceOsc object for parameter flipping DO NOT USE: UNTESTED
    // if (flipWindow) {
    //  auto* oscCov = dynamic_cast<covarianceOsc*>(syst);
    //  if (oscCov) {
    //    oscCov->setFlipWindow(flipWindow);
    //    oscCov->setMulticanonicalSeparateMean(umbrellaMean);
    //  }
    //}
    systematics[oscCovVar]->PrintPreFitCurrPropValues();
    MACH3LOG_INFO("Setting starting point of chain to umbrella center: {}", umbrellaMean);
  }
}
 
double MulticanonicalMCMCHandler::GetMulticanonicalWeightVonMises(double deltacp) {
  // calculate the Log form of the von Mises instead to avoid numerical issues
  // and return directly
  double log_vonMises = vonMises_kappa * std::cos(deltacp - umbrellaMean) - std::log(2 * TMath::Pi() * vonMises_I0_kappa);
  // return the log likelihood, ie the log of the normalised von Mises
  return -log_vonMises * (multicanonicalBeta);
}
 
// this now sorts through the available bias functions in a single function
double MulticanonicalMCMCHandler::GetMulticanonicalWeight(double deltacp, double delm23) {
  if (multicanonicalSpline) {
    return GetMulticanonicalWeightSpline(deltacp, delm23);
  }
 
  switch (umbrellaBiasFunction) {
  case M3::BiasFunction::kGaussian:
    return GetMulticanonicalWeightGaussian(deltacp);
  case M3::BiasFunction::kVonMises:
    return GetMulticanonicalWeightVonMises(deltacp);
  case M3::BiasFunction::kGeneralisedGaussian:
    return GetMulticanonicalWeightGenGaussian(deltacp);
  }
 
  return GetMulticanonicalWeightGaussian(deltacp);
}
 
double MulticanonicalMCMCHandler::GetMulticanonicalWeightSpline(double deltacp, double delm23) {
  double dcp_spline_val;
 
  if (delm23 < 0) {
    dcp_spline_val = dcp_spline_IO->Eval(deltacp);
    return -(-std::log(dcp_spline_val) + std::log(dcp_spline_IO->Eval(-TMath::Pi() / 2))) * (multicanonicalBeta); // do I want this offset?? does it matter?
  } else {
    dcp_spline_val = dcp_spline_NO->Eval(deltacp);
    return -(-std::log(dcp_spline_val) + std::log(dcp_spline_NO->Eval(-TMath::Pi() / 2))) * (multicanonicalBeta);
  }
  // std::cout << "Evaluating spline at delta_cp = " << deltacp << " gives value
  // " << dcp_spline_val << "with -log lh of :" << -log(dcp_spline_val) <<
  // std::endl;
}
 
double MulticanonicalMCMCHandler::GetMulticanonicalWeightGaussian(double deltacp) {
  const double inv_sqrt_2pi = 1 / std::sqrt(2 * TMath::Pi());
  const double neg_half_sigma_sq = -1 / (2 * umbrellaWidth * umbrellaWidth);
  // return the log likelihood, ie the log of the normalised gaussian
  return (-std::log(inv_sqrt_2pi * (1 / umbrellaWidth) * std::exp(neg_half_sigma_sq * (deltacp - umbrellaMean) * (deltacp - umbrellaMean)))) * (multicanonicalBeta);
}
 
double MulticanonicalMCMCHandler::generalisedGaussian2(double x, double mean, double width) {
  constexpr int n = 2; // this controls the tightness of the gaussian fixed at 2 for now due to normalisation
  // 1/4 * Gamma(1/4) = 0.906402477055 (this factor from 2n/Gamma(1/2n) for n=2)
  const double normFactor = 1 / ((M3::UmbrellaGaussianNormFactor) * 2 * std::sqrt(2) * width); // the normalisation is a little ugly (uses gamma functions), im just going to hardcode them for now
  double likelihood = normFactor * std::exp(-std::pow((std::pow(x - mean, 2) / (2 * std::pow(width, 2))), n));
  return likelihood;
}
 
double MulticanonicalMCMCHandler::circularDistance(double x, double mean) { return std::atan2(std::sin(x - mean), std::cos(x - mean)); }
 
double MulticanonicalMCMCHandler::GetMulticanonicalWeightGenGaussian(double deltacp) {
  // implemenetation of the generalised gaussian as a bias function
  // for now with a fixed n = 2 for simplicity
  double g0 = generalisedGaussian2(deltacp, umbrellaMean, umbrellaWidth); // these two repeats are required for wrapping the gaussian around -pi and pi
  double g1 = generalisedGaussian2(deltacp, umbrellaMean - 2 * TMath::Pi(), umbrellaWidth);
  double g2 = generalisedGaussian2(deltacp, umbrellaMean + 2 * TMath::Pi(), umbrellaWidth);
#ifdef MACH3_DEBUG
  if (debugStream && debugEnabled) (*debugStream) << " g0: " << g0 << " g1: " << g1 << " g2: " << g2 << std::endl;
#endif
  return -std::log(g0 + g1 + g2) * (multicanonicalBeta);
}
 
double MulticanonicalMCMCHandler::GetMulticanonicalWeightTripleGaussian(double deltacp) { // pretty much deprecated at this point, just here for testing
  // precalculated constants
  constexpr double inv_sqrt_2pi = 0.3989422804014337;
  double sigma = umbrellaWidth;
  const double neg_half_sigma_sq = -1 / (2 * sigma * sigma);
  // three gaussians centered at -pi, 0, pi with sigma pre-defined above
  double exp1 = std::exp(neg_half_sigma_sq * (deltacp - TMath::Pi()) * (deltacp - TMath::Pi()));
  double exp2 = std::exp(neg_half_sigma_sq * (deltacp) * (deltacp));
  double exp3 = std::exp(neg_half_sigma_sq * (deltacp + TMath::Pi()) * (deltacp + TMath::Pi()));
 
  // return the log likelihood, ie the log of the normalised sum of the
  // gaussians
  return -std::log(inv_sqrt_2pi * (1 / sigma) * (exp1 + exp2 + exp3)) * (multicanonicalBeta);
}