FABADAMinimizer.cpp

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// Mantid Repository : https://github.com/mantidproject/mantid
//
// Copyright © 2018 ISIS Rutherford Appleton Laboratory UKRI,
//   NScD Oak Ridge National Laboratory, European Spallation Source,
//   Institut Laue - Langevin & CSNS, Institute of High Energy Physics, CAS
// SPDX - License - Identifier: GPL - 3.0 +
#include "MantidAPI/AlgorithmManager.h"
#include "MantidAPI/AnalysisDataService.h"
#include "MantidAPI/CostFunctionFactory.h"
#include "MantidAPI/FuncMinimizerFactory.h"
#include "MantidAPI/IFunction.h"
#include "MantidAPI/ITableWorkspace.h"
#include "MantidAPI/MatrixWorkspace.h"
#include "MantidAPI/ParameterTie.h"
#include "MantidAPI/TableRow.h"
#include "MantidAPI/WorkspaceFactory.h"
#include "MantidAPI/WorkspaceGroup.h"
#include "MantidAPI/WorkspaceProperty.h"
 
#include "MantidCurveFitting/Constraints/BoundaryConstraint.h"
#include "MantidCurveFitting/CostFunctions/CostFuncLeastSquares.h"
#include "MantidCurveFitting/FuncMinimizers/FABADAMinimizer.h"
 
#include "MantidHistogramData/LinearGenerator.h"
 
#include "MantidKernel/Logger.h"
#include "MantidKernel/MersenneTwister.h"
#include "MantidKernel/PseudoRandomNumberGenerator.h"
#include "MantidKernel/normal_distribution.h"
 
#include <boost/math/special_functions/fpclassify.hpp>
 
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <random>
 
namespace Mantid::CurveFitting::FuncMinimisers {
using namespace Mantid::API;
 
namespace {
 
std::string const DEFAULT_PDF_GROUP_NAME = "__PDF_Workspace";
 
// static logger object
Kernel::Logger g_log("FABADAMinimizer");
// number of iterations when convergence isn't expected
const size_t LOWER_CONVERGENCE_LIMIT = 350;
// jump checking rate
const size_t JUMP_CHECKING_RATE = 200;
// low jump limit
const double LOW_JUMP_LIMIT = 1e-25;
// random number generator
std::mt19937 rng;
 
API::MatrixWorkspace_sptr createWorkspace(std::vector<double> const &xValues, std::vector<double> const &yValues,
                                          int const numberOfSpectra,
                                          std::vector<std::string> const &verticalAxisNames) {
  auto createWorkspaceAlgorithm = AlgorithmManager::Instance().createUnmanaged("CreateWorkspace");
  createWorkspaceAlgorithm->initialize();
  createWorkspaceAlgorithm->setChild(true);
  createWorkspaceAlgorithm->setLogging(false);
  createWorkspaceAlgorithm->setProperty("DataX", xValues);
  createWorkspaceAlgorithm->setProperty("DataY", yValues);
  createWorkspaceAlgorithm->setProperty("NSpec", numberOfSpectra);
  createWorkspaceAlgorithm->setProperty("VerticalAxisUnit", "Text");
  createWorkspaceAlgorithm->setProperty("VerticalAxisValues", verticalAxisNames);
  createWorkspaceAlgorithm->setProperty("OutputWorkspace", "__PDF");
  createWorkspaceAlgorithm->execute();
  return createWorkspaceAlgorithm->getProperty("OutputWorkspace");
}
 
} // namespace
 
DECLARE_FUNCMINIMIZER(FABADAMinimizer, FABADA)
 
 
FABADAMinimizer::FABADAMinimizer()
    : m_counter(0), m_chainIterations(0), m_changes(), m_jump(), m_parameters(), m_chain(), m_chi2(0.),
      m_converged(false), m_convPoint(0), m_parConverged(), m_criteria(), m_maxIter(0), m_parChanged(),
      m_temperature(0.), m_counterGlobal(0), m_simAnnealingItStep(0), m_leftRefrPoints(0), m_tempStep(0.),
      m_overexploration(false), m_nParams(0), m_numInactiveRegenerations(), m_changesOld() {
  declareProperty("ChainLength", static_cast<size_t>(10000), "Length of the converged chain.");
  declareProperty("StepsBetweenValues", 10,
                  "Steps done between chain points to avoid correlation"
                  " between them.");
  declareProperty("ConvergenceCriteria", 0.01, "Variance in Cost Function for considering convergence reached.");
  declareProperty("InnactiveConvergenceCriterion", static_cast<size_t>(5),
                  "Number of Innactive Regenerations to consider"
                  " a certain parameter to be converged");
  declareProperty("JumpAcceptanceRate", 0.6666666, "Desired jumping acceptance rate");
  // Simulated Annealing properties
  declareProperty("SimAnnealingApplied", false,
                  "If minimization should be run with Simulated"
                  " Annealing or not");
  declareProperty("MaximumTemperature", 10.0, "Simulated Annealing maximum temperature");
  declareProperty("NumRefrigerationSteps", static_cast<size_t>(5), "Simulated Annealing number of temperature changes");
  declareProperty("SimAnnealingIterations", static_cast<size_t>(10000),
                  "Number of iterations for the Simulated Annealig");
  declareProperty("Overexploration", false,
                  "If Temperatures < 1 are desired for overexploration,"
                  " no error will jump for that (The temperature is"
                  " constant during the convergence period)."
                  " Useful to find the exact minimum.");
  // Output Properties
  declareProperty("PDF", DEFAULT_PDF_GROUP_NAME,
                  "Name for the output PDF workspace group. Default is " + DEFAULT_PDF_GROUP_NAME);
  declareProperty("NumberBinsPDF", 20, "Number of bins used for the output PDFs");
  declareProperty(std::make_unique<API::WorkspaceProperty<>>("Chains", "", Kernel::Direction::Output),
                  "The name to give the output workspace for the"
                  " complete chains.");
  declareProperty(std::make_unique<API::WorkspaceProperty<>>("ConvergedChain", "", Kernel::Direction::Output,
                                                             API::PropertyMode::Optional),
                  "The name to give the output workspace for just the"
                  "converged chain");
  declareProperty(std::make_unique<API::WorkspaceProperty<API::ITableWorkspace>>("CostFunctionTable", "",
                                                                                 Kernel::Direction::Output),
                  "The name to give the output workspace");
  declareProperty(
      std::make_unique<API::WorkspaceProperty<API::ITableWorkspace>>("Parameters", "", Kernel::Direction::Output),
      "The name to give the output workspace (Parameter values and errors)");
 
  // To be implemented in the future
  /*declareProperty(
      std::make_unique<API::WorkspaceProperty<>>(
          "Chi-squareLandscape", "", Kernel::Direction::Output),
      "The name to give the output workspace containing the chi-square"
      " landscape");*/
}
 
void FABADAMinimizer::initialize(API::ICostFunction_sptr function, size_t maxIterations) {
 
  m_leastSquares = std::dynamic_pointer_cast<CostFunctions::CostFuncLeastSquares>(function);
  if (!m_leastSquares) {
    throw std::invalid_argument("FABADA works only with least squares."
                                " Different function was given.");
  }
 
  m_fitFunction = m_leastSquares->getFittingFunction();
  m_counter = 0;
  m_counterGlobal = 0;
  m_converged = false;
  m_maxIter = maxIterations;
 
  // Initialize member variables related to fitting parameters, such as
  // m_chains, m_jump, etc
  initChainsAndParameters();
 
  // Initialize member variables related to simulated annealing, such as
  // m_temperature, m_overexploration, etc
  initSimulatedAnnealing();
 
  // Variable to calculate the total number of iterations required by the
  // SimulatedAnnealing and the posterior chain plus the burn in required
  // for the adaptation of the jump
  size_t totalRequiredIterations = 350 + m_chainIterations;
  if (!m_overexploration)
    totalRequiredIterations += m_simAnnealingItStep * m_leftRefrPoints;
 
  // Throw error if there are not enough iterations
  if (totalRequiredIterations >= maxIterations) {
    throw std::length_error("Too few iterations to perform the"
                            " Simulated Annealing and/or the posterior chain plus"
                            " 350 iterations for the burn-in period. Increase"
                            " MaxIterations property");
  }
}
 
bool FABADAMinimizer::iterate(size_t /*iteration*/) {
 
  if (!m_leastSquares) {
    throw std::runtime_error("Cost function isn't set up.");
  }
 
  size_t m = m_nParams;
 
  // Just for the last iteration. For doing exactly the indicated
  // number of iterations.
  if (m_converged && m_counter == m_chainIterations - 1) {
    size_t t = getProperty("ChainLength");
    m = t % m_nParams;
    if (m == 0)
      m = m_nParams;
  }
 
  // Do one iteration of FABADA's algorithm for each parameter.
  for (size_t i = 0; i < m; i++) {
 
    EigenVector newParameters = m_parameters;
 
    if (!m_fitFunction->isFixed(i)) {
      // Calculate the step from a Gaussian
      double step = gaussianStep(m_jump[i]);
 
      // Calculate the new value of the parameter
      double newValue = m_parameters.get(i) + step;
 
      // Checks if it is inside the boundary constrinctions.
      // If not, changes it.
      boundApplication(i, newValue, step);
      // Obs: As well as checking whether the ties are not contradictory is
      // too constly, if there are tied parameters that are bounded,
      // checking that the boundedness is fulfilled for all the parameters
      // is costly too (extremely costly if the relations get complex,
      // which is plausible). Therefore it is not yet implemented and
      // the user should be aware of that.
 
      // Set the new value in order to calculate the new Chi square value
      if (std::isnan(newValue))
        throw std::runtime_error("Parameter value is NaN.");
      newParameters.set(i, newValue);
 
      // Update the new value through the IFunction
      m_fitFunction->setParameter(i, newValue);
 
      // First, it fulfills the other ties, finally the current parameter tie
      // It notices m_leastSquares (the CostFuncLeastSquares) that we have
      // modified the parameters
      tieApplication(i, newParameters, newValue);
      m_fitFunction->applyTies();
    }
 
    // To track "unmovable" parameters (=> cannot converge)
    if (!m_parChanged[i] && newParameters.get(i) != m_parameters.get(i))
      m_parChanged[i] = true;
 
    // Calculate the new chi2 value
    double newChi2 = m_leastSquares->val();
    // Save the old one to check convergence later on
    double oldChi2 = m_chi2;
 
    // Given the new chi2, position, m_changes[parameterIndex] and chains are
    // updated
    algorithmDisplacement(i, newChi2, newParameters);
 
    // Update the jump once each JUMP_CHECKING_RATE iterations
    if (m_counter % JUMP_CHECKING_RATE == 150) // JUMP CHECKING RATE IS 200, BUT
    // IS NOT CHECKED AT FIRST STEP, IT
    // IS AT 150
    {
      jumpUpdate(i);
    }
 
    // Check if the Chi square value has converged for parameter i.
    //(Obs: const int LOWER_CONVERGENCE_LIMIT = 350 := The iteration
    // since it starts to check if convergence is reached)
 
    // Take the unmovable parameters to be converged
    if (m_leftRefrPoints == 0 && !m_parChanged[i] && m_counter > LOWER_CONVERGENCE_LIMIT)
      m_parConverged[i] = true;
 
    if (m_leftRefrPoints == 0 && !m_parConverged[i] && m_counter > LOWER_CONVERGENCE_LIMIT) {
      if (oldChi2 != m_chi2) {
        double chi2Quotient = fabs(m_chi2 - oldChi2) / oldChi2;
        if (chi2Quotient < m_criteria[i]) {
          m_parConverged[i] = true;
        }
      }
    }
  } // for i
 
  // Update the counter, after finishing the iteration for each parameter
  m_counter += 1;
  m_counterGlobal += 1;
 
  // Check if Chi square has converged for all the parameters
  // if overexploring or Simulated Annealing completed
  convergenceCheck(); // updates m_converged
 
  // Check wheather it is refrigeration time or not (for Simulated Annealing)
  if (m_leftRefrPoints != 0 && m_counter == m_simAnnealingItStep) {
    simAnnealingRefrigeration();
  }
 
  // Evaluates if iterations should continue or not
  return iterationContinuation();
 
} // Iterate() end
 
double FABADAMinimizer::costFunctionVal() { return m_chi2; }
 
void FABADAMinimizer::finalize() {
 
  // Creating the reduced chain (considering only one each
  // "Steps between values" values)
  size_t chainLength = getProperty("ChainLength");
  int nSteps = getProperty("StepsBetweenValues");
  if (nSteps <= 0) {
    g_log.warning() << "StepsBetweenValues has a non valid value"
                       " (<= 0). Default one used"
                       " (StepsBetweenValues = 10).\n";
    nSteps = 10;
  }
  auto convLength = size_t(double(chainLength) / double(nSteps));
 
  // Reduced chain
  std::vector<std::vector<double>> reducedConvergedChain;
  // Declaring vectors for best values
  std::vector<double> bestParameters(m_nParams);
  std::vector<double> errorLeft(m_nParams);
  std::vector<double> errorRight(m_nParams);
 
  calculateConvChainAndBestParameters(convLength, nSteps, reducedConvergedChain, bestParameters, errorLeft, errorRight);
 
  if (!getPropertyValue("Parameters").empty()) {
    outputParameterTable(bestParameters, errorLeft, errorRight);
  }
 
  // Set the best parameter values
  // Again, we need to modify the CostFunction through the IFunction
 
  for (size_t j = 0; j < m_nParams; ++j) {
    m_fitFunction->setParameter(j, bestParameters[j]);
  }
  // Convert type to setDirty the cost function
  std::shared_ptr<MaleableCostFunction> leastSquaresMaleable =
      std::static_pointer_cast<MaleableCostFunction>(m_leastSquares);
  leastSquaresMaleable->setDirtyInherited();
  // Convert back to base class
  m_leastSquares = std::dynamic_pointer_cast<CostFunctions::CostFuncLeastSquares>(leastSquaresMaleable);
 
  // If required, output the complete chain
  if (!getPropertyValue("Chains").empty()) {
    outputChains();
  }
 
  double mostPchi2 = outputPDF(convLength, reducedConvergedChain);
 
  if (!getPropertyValue("ConvergedChain").empty()) {
    outputConvergedChains(convLength, nSteps);
  }
 
  if (!getPropertyValue("CostFunctionTable").empty()) {
    outputCostFunctionTable(convLength, mostPchi2);
  }
 
  // Set the best parameter values
  // Not used (needed if we want to return the most probable values too,
  // so saved as commented out)
  /*for (size_t j = 0; j < m_nParams; ++j) {
    m_leastSquares->setParameter(j, BestParameters[j]);
  }*/
}
 
double FABADAMinimizer::gaussianStep(const double &jump) {
  return Kernel::normal_distribution<double>(0.0, std::abs(jump))(rng);
}
 
void FABADAMinimizer::boundApplication(const size_t &parameterIndex, double &newValue, double &step) {
  API::IConstraint *iConstraint = m_fitFunction->getConstraint(parameterIndex);
  if (!iConstraint)
    return;
  auto const *bcon = dynamic_cast<Constraints::BoundaryConstraint *>(iConstraint);
  if (!bcon)
    return;
 
  double lower = bcon->lower();
  double upper = bcon->upper();
  double delta = upper - lower;
 
  // Lower
  while (newValue < lower) {
    if (std::abs(step) > delta) {
      newValue = m_parameters.get(parameterIndex) + step / 10.0;
      step = step / 10;
      m_jump[parameterIndex] = m_jump[parameterIndex] / 10;
    } else {
      newValue = lower + std::abs(step) - (m_parameters.get(parameterIndex) - lower);
    }
  }
  // Upper
  while (newValue > upper) {
    if (std::abs(step) > delta) {
      newValue = m_parameters.get(parameterIndex) + step / 10.0;
      step = step / 10;
      m_jump[parameterIndex] = m_jump[parameterIndex] / 10;
    } else {
      newValue = upper - (std::abs(step) + m_parameters.get(parameterIndex) - upper);
    }
  }
}
 
void FABADAMinimizer::tieApplication(const size_t &parameterIndex, EigenVector &newParameters, double &newValue) {
  // Fulfill the ties of the other parameters
  for (size_t j = 0; j < m_nParams; ++j) {
    if (j != parameterIndex) {
      API::ParameterTie *tie = m_fitFunction->getTie(j);
      if (tie) {
        newValue = tie->eval();
        if (boost::math::isnan(newValue)) { // maybe not needed
          throw std::runtime_error("Parameter value is NaN.");
        }
        newParameters.set(j, newValue);
        m_fitFunction->setParameter(j, newValue);
      }
    }
  }
  // After all the other variables, the current one is updated to the ties
  API::ParameterTie *tie = m_fitFunction->getTie(parameterIndex);
  if (tie) {
    newValue = tie->eval();
    if (boost::math::isnan(newValue)) { // maybe not needed
      throw std::runtime_error("Parameter value is NaN.");
    }
    newParameters.set(parameterIndex, newValue);
    m_fitFunction->setParameter(parameterIndex, newValue);
  }
 
  // Convert type to setDirty the cost function
  //(to notify the CostFunction we have modified the IFunction)
  std::shared_ptr<MaleableCostFunction> leastSquaresMaleable =
      std::static_pointer_cast<MaleableCostFunction>(m_leastSquares);
 
  leastSquaresMaleable->setDirtyInherited();
 
  // Convert back to base class
  m_leastSquares = std::dynamic_pointer_cast<CostFunctions::CostFuncLeastSquares>(leastSquaresMaleable);
}
 
void FABADAMinimizer::algorithmDisplacement(const size_t &parameterIndex, const double &chi2New,
                                            const EigenVector &newParameters) {
 
  // If new Chi square value is lower, jumping directly to new parameter
  if (chi2New < m_chi2) {
    for (size_t j = 0; j < m_nParams; j++) {
      m_chain[j].emplace_back(newParameters.get(j));
    }
    m_chain[m_nParams].emplace_back(chi2New);
    m_parameters = newParameters;
    m_chi2 = chi2New;
    m_changes[parameterIndex] += 1;
  }
 
  // If new Chi square value is higher, it depends on the probability
  else {
    // Calculate probability of change
    double prob = exp((m_chi2 - chi2New) / (2.0 * m_temperature));
 
    // Decide if changing or not
    double p = std::uniform_real_distribution<double>(0.0, 1.0)(rng);
    if (p <= prob) {
      for (size_t j = 0; j < m_nParams; j++) {
        m_chain[j].emplace_back(newParameters.get(j));
      }
      m_chain[m_nParams].emplace_back(chi2New);
      m_parameters = newParameters;
      m_chi2 = chi2New;
      m_changes[parameterIndex] += 1;
    } else {
      for (size_t j = 0; j < m_nParams; j++) {
        m_chain[j].emplace_back(m_parameters.get(j));
      }
      m_chain[m_nParams].emplace_back(m_chi2);
      // Old parameters taken again
      for (size_t j = 0; j < m_nParams; ++j) {
        m_fitFunction->setParameter(j, m_parameters.get(j));
      }
      // Convert type to setDirty the cost function
      //(to notify the CostFunction we have modified the FittingFunction)
      std::shared_ptr<MaleableCostFunction> leastSquaresMaleable =
          std::static_pointer_cast<MaleableCostFunction>(m_leastSquares);
 
      leastSquaresMaleable->setDirtyInherited();
 
      // Convert back to base class
      m_leastSquares = std::dynamic_pointer_cast<CostFunctions::CostFuncLeastSquares>(leastSquaresMaleable);
    }
  }
}
 
void FABADAMinimizer::jumpUpdate(const size_t &parameterIndex) {
  const double jumpAR = getProperty("JumpAcceptanceRate");
  double newJump;
 
  if (m_leftRefrPoints == 0 && m_changes[parameterIndex] == m_changesOld[parameterIndex])
    ++m_numInactiveRegenerations[parameterIndex];
  else
    m_changesOld[parameterIndex] = m_changes[parameterIndex];
 
  if (m_changes[parameterIndex] == 0) {
    newJump = m_jump[parameterIndex] / JUMP_CHECKING_RATE;
    // JUST FOR THE CASE THERE HAS NOT BEEN ANY CHANGE
    //(treated as if only one acceptance).
  } else {
    m_numInactiveRegenerations[parameterIndex] = 0;
    double f = m_changes[parameterIndex] / double(m_counter);
 
    //*ALTERNATIVE CODE
    //*Current acceptance rate evaluated
    //*double f = m_changes[parameterIndex] / double(JUMP_CHECKING_RATE);
    //*Obs: should be quicker to explore, but less stable (maybe not ergodic)
 
    newJump = m_jump[parameterIndex] * f / jumpAR;
 
    //*ALTERNATIVE CODE
    //*Reset the m_changes value to get the information
    //*for the current jump, not the whole history (maybe not ergodic)
    //*m_changes[parameterIndex] = 0;
  }
 
  m_jump[parameterIndex] = newJump;
 
  // Check if the new jump is too small. It means that it has been a wrong
  // convergence.
  if (std::abs(m_jump[parameterIndex]) < LOW_JUMP_LIMIT) {
    g_log.warning() << "Wrong convergence might be reached for parameter " +
                           m_fitFunction->parameterName(parameterIndex) +
                           ". Try to set a proper initial value for this parameter\n";
  }
}
 
void FABADAMinimizer::convergenceCheck() {
  size_t innactConvCriterion = getProperty("InnactiveConvergenceCriterion");
 
  if (m_leftRefrPoints == 0 && m_counter > LOWER_CONVERGENCE_LIMIT && !m_converged) {
    size_t t = 0;
    bool ImmobilityConv = false;
    for (size_t i = 0; i < m_nParams; i++) {
      if (m_parConverged[i]) {
        t += 1;
      } else if (m_numInactiveRegenerations[i] >= innactConvCriterion) {
        ++t;
        ImmobilityConv = true;
      }
    }
    // If all parameters have converged (usually or through observed
    // immobility):
    // It sets up both the counter and the changes' vector to 0, in order to
    // consider only the data of the converged part of the chain, when updating
    // the jump.
    if (t == m_nParams) {
      m_converged = true;
 
      if (ImmobilityConv)
        g_log.warning() << "Convergence detected through immobility."
                           " It might be a bad convergence.\n";
 
      m_convPoint = m_counterGlobal * m_nParams + 1;
      m_counter = 0;
      for (size_t i = 0; i < m_nParams; ++i) {
        m_changes[i] = 0;
      }
 
      // If done with a different temperature, the error would be
      // wrongly obtained (because the temperature modifies the
      // chi-square landscape)
      // Although keeping ergodicity, more iterations will be needed
      // because a wrong step is initially used.
      m_temperature = 1.0;
    }
 
    // All parameters should converge at the same iteration
    else {
      // The not converged parameters can be identified at the last iteration
      if (m_counterGlobal < m_maxIter - m_chainIterations)
        for (size_t i = 0; i < m_nParams; ++i)
          m_parConverged[i] = false;
    }
  }
}
 
void FABADAMinimizer::simAnnealingRefrigeration() {
  // Update jump to separate different temperatures
  for (size_t i = 0; i < m_nParams; ++i)
    jumpUpdate(i);
 
  // Resetting variables for next temperature
  //(independent jump calculation for different temperatures)
  m_counter = 0;
  for (size_t j = 0; j < m_nParams; ++j) {
    m_changes[j] = 0;
  }
  // Simulated Annealing variables updated
  --m_leftRefrPoints;
  // To avoid numerical error accumulation
  if (m_leftRefrPoints == 0)
    m_temperature = 1.0;
  else
    m_temperature /= m_tempStep;
}
 
/* @return :: true if iteration must continue, false otherwise.
 *
 */
bool FABADAMinimizer::iterationContinuation() {
 
  // If still through Simulated Annealing
  if (m_leftRefrPoints != 0)
    return true;
 
  if (!m_converged) {
 
    // If there is not convergence continue the iterations.
    if (m_counterGlobal < m_maxIter - m_chainIterations) {
      return true;
    }
    // If there is not convergence, but it has been made
    // convergenceMaxIterations iterations, stop and throw the error.
    else {
      std::string failed = "";
      for (size_t i = 0; i < m_nParams; ++i) {
        if (!m_parConverged[i]) {
          failed = failed + m_fitFunction->parameterName(i) + ", ";
        }
      }
      failed.replace(failed.end() - 2, failed.end(), ".");
      throw std::runtime_error("Convegence NOT reached after " + std::to_string(m_maxIter - m_chainIterations) +
                               " iterations.\n   Try to set better initial values for parameters: " + failed +
                               " Or increase the maximum number of iterations "
                               "(MaxIterations property).");
    }
  } else {
    // If convergence has been reached, continue until we complete the chain
    // length. Otherwise, stop interations.
    return m_counter < m_chainIterations;
  }
  // can we even get here? -> Nope (we should not, so we do not want it to
  // continue)
  return false;
}
 
void FABADAMinimizer::outputChains() {
 
  size_t chainLength = m_chain[0].size();
  API::MatrixWorkspace_sptr wsC =
      API::WorkspaceFactory::Instance().create("Workspace2D", m_nParams + 1, chainLength, chainLength);
 
  // Do one iteration for each parameter plus one for Chi square.
  for (size_t j = 0; j < m_nParams + 1; ++j) {
    auto &X = wsC->mutableX(j);
    auto &Y = wsC->mutableY(j);
    for (size_t k = 0; k < chainLength; ++k) {
      X[k] = double(k);
      Y[k] = m_chain[j][k];
    }
  }
 
  // Set and name the workspace for the complete chain
  setProperty("Chains", wsC);
}
 
void FABADAMinimizer::outputConvergedChains(size_t convLength, int nSteps) {
 
  // Create the workspace for the converged part of the chain.
  API::MatrixWorkspace_sptr wsConv;
  if (convLength > 0) {
    wsConv = API::WorkspaceFactory::Instance().create("Workspace2D", m_nParams + 1, convLength, convLength);
  } else {
    g_log.warning() << "Empty converged chain, empty Workspace returned.";
    wsConv = API::WorkspaceFactory::Instance().create("Workspace2D", m_nParams + 1, 1, 1);
  }
 
  // Do one iteration for each parameter plus one for Chi square.
  for (size_t j = 0; j < m_nParams + 1; ++j) {
    std::vector<double>::const_iterator first = m_chain[j].begin() + m_convPoint;
    std::vector<double>::const_iterator last = m_chain[j].end();
    std::vector<double> convChain(first, last);
    auto &X = wsConv->mutableX(j);
    auto &Y = wsConv->mutableY(j);
    for (size_t k = 0; k < convLength; ++k) {
      X[k] = double(k);
      Y[k] = convChain[nSteps * k];
    }
  }
 
  // Set and name the workspace for the converged part of the chain.
  setProperty("ConvergedChain", wsConv);
}
 
void FABADAMinimizer::outputCostFunctionTable(size_t convLength, double mostProbableChi2) {
  // Create the workspace for the Chi square values.
  API::ITableWorkspace_sptr wsChi2 = API::WorkspaceFactory::Instance().createTable("TableWorkspace");
  wsChi2->addColumn("double", "Chi2 Minimum");
  wsChi2->addColumn("double", "Most Probable Chi2");
  wsChi2->addColumn("double", "reduced Chi2 Minimum");
  wsChi2->addColumn("double", "Most Probable reduced Chi2");
 
  // Obtain the quantity of the initial data.
  API::FunctionDomain_sptr domain = m_leastSquares->getDomain();
  size_t dataSize = domain->size();
 
  // Calculate the value for the reduced Chi square.
  double minimumChi2Red = m_chi2 / (double(dataSize - m_nParams)); // For de minimum value.
  double mostProbableChi2Red;
  if (convLength > 0)
    mostProbableChi2Red = mostProbableChi2 / (double(dataSize - m_nParams));
  else {
    g_log.warning() << "Most probable chi square not calculated. -1 is returned.\n"
                    << "Most probable reduced chi square not calculated. -1 is "
                       "returned.\n";
    mostProbableChi2Red = -1;
  }
 
  // Add the information to the workspace and name it.
  API::TableRow row = wsChi2->appendRow();
  row << m_chi2 << mostProbableChi2 << minimumChi2Red << mostProbableChi2Red;
  setProperty("CostFunctionTable", wsChi2);
}
 
double FABADAMinimizer::outputPDF(std::size_t const &convLength, std::vector<std::vector<double>> &reducedChain) {
 
  // To store the most probable chi square value
  double mostPchi2;
 
  // Create the workspace for the Probability Density Functions
  int pdfLength = getProperty("NumberBinsPDF"); // histogram length for the PDF output workspace
  if (pdfLength <= 0) {
    g_log.warning() << "Non valid Number of bins for the PDF (<= 0)."
                       " Default value (20 bins) taken\n";
    pdfLength = 20;
  }
 
  // Calculate the cost function Probability Density Function
  if (convLength > 0) {
    std::sort(reducedChain[m_nParams].begin(), reducedChain[m_nParams].end());
    std::vector<double> xValues((m_nParams + 1) * (pdfLength + 1));
    std::vector<double> yValues((m_nParams + 1) * pdfLength);
    std::vector<double> PDFYAxis(pdfLength, 0);
    double const start = reducedChain[m_nParams][0];
    double const bin = (reducedChain[m_nParams][convLength - 1] - start) / double(pdfLength);
 
    mostPchi2 = getMostProbableChiSquared(convLength, reducedChain, pdfLength, xValues, yValues, PDFYAxis, start, bin);
 
    outputPDF(xValues, yValues, reducedChain, convLength, pdfLength);
 
  } // if convLength > 0
  else {
    g_log.warning() << "No points to create PDF. Empty Workspace returned.\n";
    mostPchi2 = -1;
  }
 
  return mostPchi2;
}
 
void FABADAMinimizer::outputPDF(std::vector<double> &xValues, std::vector<double> &yValues,
                                std::vector<std::vector<double>> const &reducedChain, std::size_t const &convLength,
                                int const &pdfLength) {
  setParameterXAndYValuesForPDF(xValues, yValues, reducedChain, convLength, pdfLength);
  auto parameterNames = m_fitFunction->getParameterNames();
  parameterNames.emplace_back("Chi Squared");
  auto const workspace = createWorkspace(xValues, yValues, int(m_nParams) + 1, parameterNames);
 
  const auto pdfName = getPropertyValue("PDF");
  if (AnalysisDataService::Instance().doesExist(pdfName)) {
    auto groupPDF = AnalysisDataService::Instance().retrieveWS<WorkspaceGroup>(pdfName);
    groupPDF->addWorkspace(workspace);
    AnalysisDataService::Instance().addOrReplace(pdfName, groupPDF);
  } else {
    auto groupPDF = std::make_shared<WorkspaceGroup>();
    groupPDF->addWorkspace(workspace);
    AnalysisDataService::Instance().addOrReplace(pdfName, groupPDF);
  }
}
 
double FABADAMinimizer::getMostProbableChiSquared(std::size_t const &convLength,
                                                  std::vector<std::vector<double>> const &reducedChain,
                                                  int const &pdfLength, std::vector<double> &xValues,
                                                  std::vector<double> &yValues, std::vector<double> &PDFYAxis,
                                                  double const &start, double const &bin) {
  std::size_t step = 0;
  std::size_t const chiXStartPos = m_nParams * (pdfLength + 1);
  std::size_t const chiYStartPos = m_nParams * pdfLength;
 
  xValues[chiXStartPos] = start;
  for (std::size_t i = 1; i < static_cast<std::size_t>(pdfLength) + 1; i++) {
    double binEnd = start + double(i) * bin;
    xValues[chiXStartPos + i] = binEnd;
    while (step < convLength && reducedChain[m_nParams][step] <= binEnd) {
      PDFYAxis[i - 1] += 1;
      ++step;
    }
    // Divided by convLength * bin to normalize
    yValues[chiYStartPos + i - 1] = PDFYAxis[i - 1] / (double(convLength) * bin);
  }
 
  auto indexMostProbableChi2 = std::max_element(PDFYAxis.begin(), PDFYAxis.end());
 
  return xValues[indexMostProbableChi2 - PDFYAxis.begin()] + (bin / 2.0);
}
 
void FABADAMinimizer::setParameterXAndYValuesForPDF(std::vector<double> &xValues, std::vector<double> &yValues,
                                                    std::vector<std::vector<double>> const &reducedChain,
                                                    std::size_t const &convLength, int const &pdfLength) {
  for (std::size_t j = 0; j < m_nParams; ++j) {
 
    // Calculate the Probability Density Function
    std::vector<double> PDFYAxis(pdfLength, 0);
    double start = reducedChain[j][0];
    double bin = (reducedChain[j][convLength - 1] - start) / double(pdfLength);
    std::size_t step = 0;
    std::size_t const startXPos = j * (pdfLength + 1);
    std::size_t const startYPos = j * pdfLength;
 
    xValues[startXPos] = start;
    for (std::size_t i = 1; i < static_cast<std::size_t>(pdfLength) + 1; i++) {
      double binEnd = start + double(i) * bin;
      xValues[startXPos + i] = binEnd;
      while (step < convLength && reducedChain[j][step] <= binEnd) {
        PDFYAxis[i - 1] += 1;
        ++step;
      }
      yValues[startYPos + i - 1] = PDFYAxis[i - 1] / (double(convLength) * bin);
    }
  }
}
 
void FABADAMinimizer::outputParameterTable(const std::vector<double> &bestParameters,
                                           const std::vector<double> &errorLeft,
                                           const std::vector<double> &errorRight) {
 
  // Create the workspace for the parameters' value and errors.
  API::ITableWorkspace_sptr wsPdfE = API::WorkspaceFactory::Instance().createTable("TableWorkspace");
  wsPdfE->addColumn("str", "Name");
  wsPdfE->addColumn("double", "Value");
  wsPdfE->addColumn("double", "Left's error");
  wsPdfE->addColumn("double", "Right's error");
 
  for (size_t j = 0; j < m_nParams; ++j) {
    API::TableRow row = wsPdfE->appendRow();
    row << m_fitFunction->parameterName(j) << bestParameters[j] << errorLeft[j] << errorRight[j];
  }
  // Set and name the Parameter Errors workspace.
  setProperty("Parameters", wsPdfE);
}
 
void FABADAMinimizer::calculateConvChainAndBestParameters(size_t convLength, int nSteps,
                                                          std::vector<std::vector<double>> &reducedChain,
                                                          std::vector<double> &bestParameters,
                                                          std::vector<double> &errorLeft,
                                                          std::vector<double> &errorRight) {
 
  // In case of reduced chain
  if (convLength > 0) {
    // Write first element of the reduced chain
    for (size_t e = 0; e <= m_nParams; ++e) {
      std::vector<double> v;
      v.emplace_back(m_chain[e][m_convPoint]);
      reducedChain.emplace_back(std::move(v));
    }
 
    // Calculate the reducedConvergedChain for the cost fuction.
    for (size_t k = 1; k < convLength; ++k) {
      reducedChain[m_nParams].emplace_back(m_chain[m_nParams][nSteps * k + m_convPoint]);
    }
 
    // Calculate the position of the minimum Chi square value
    auto positionMinChi2 = std::min_element(reducedChain[m_nParams].begin(), reducedChain[m_nParams].end());
    m_chi2 = *positionMinChi2;
 
    // Calculate the parameter value and the errors
    for (size_t j = 0; j < m_nParams; ++j) {
      // Obs: Starts at 1 (0 already added)
      for (size_t k = 1; k < convLength; ++k) {
        reducedChain[j].emplace_back(m_chain[j][m_convPoint + nSteps * k]);
      }
      // best fit parameters taken
      bestParameters[j] = reducedChain[j][positionMinChi2 - reducedChain[m_nParams].begin()];
      std::sort(reducedChain[j].begin(), reducedChain[j].end());
      auto posBestPar = std::find(reducedChain[j].begin(), reducedChain[j].end(), bestParameters[j]);
      double varLeft = 0, varRight = 0;
      for (auto k = reducedChain[j].begin(); k < reducedChain[j].end(); k += 2) {
        if (k < posBestPar)
          varLeft += (*k - bestParameters[j]) * (*k - bestParameters[j]);
        else if (k > posBestPar)
          varRight += (*k - bestParameters[j]) * (*k - bestParameters[j]);
      }
      if (posBestPar != reducedChain[j].begin())
        varLeft /= double(posBestPar - reducedChain[j].begin());
      if (posBestPar != reducedChain[j].end() - 1)
        varRight /= double(reducedChain[j].end() - posBestPar - 1);
 
      errorLeft[j] = -sqrt(varLeft);
      errorRight[j] = sqrt(varRight);
    }
  } // End if there is converged chain
 
  // If the converged chain is empty
  else {
    g_log.warning() << "There is no converged chain."
                       " Thus the parameters' errors are not"
                       " computed.\n";
    for (size_t k = 0; k < m_nParams; ++k) {
      bestParameters[k] = *(m_chain[k].end() - 1);
    }
  }
}
 
void FABADAMinimizer::initChainsAndParameters() {
  // The "real" parametersare got (not the active ones)
  m_nParams = m_fitFunction->nParams();
  if (m_nParams == 0) {
    throw std::invalid_argument("Function has 0 fitting parameters.");
  }
  // The initial parameters are saved
  if (m_parameters.size() != m_nParams) {
    m_parameters.resize(m_nParams);
  }
 
  size_t n = getProperty("ChainLength");
  m_chainIterations = size_t(ceil(double(n) / double(m_nParams)));
 
  // Save parameter constraints
  for (size_t i = 0; i < m_nParams; ++i) {
 
    double param = m_fitFunction->getParameter(i);
    m_parameters.set(i, param);
 
    API::IConstraint *iConstraint = m_fitFunction->getConstraint(i);
    if (iConstraint) {
      auto const *bcon = dynamic_cast<Constraints::BoundaryConstraint *>(iConstraint);
      if (bcon) {
        if (bcon->hasLower()) {
          if (param < bcon->lower())
            m_parameters.set(i, bcon->lower());
        }
        if (bcon->hasUpper()) {
          if (param > bcon->upper())
            m_parameters.set(i, bcon->upper());
        }
      }
    }
 
    // Initialize chains
    m_chain.emplace_back(std::vector<double>(1, param));
    // Initilize jump parameters
    m_jump.emplace_back(param != 0.0 ? std::abs(param / 10) : 0.01);
  }
  m_chi2 = m_leastSquares->val();
  m_chain.emplace_back(std::vector<double>(1, m_chi2));
  m_parChanged = std::vector<bool>(m_nParams, false);
  m_changes = std::vector<int>(m_nParams, 0);
  m_changesOld = m_changes;
  m_numInactiveRegenerations = std::vector<size_t>(m_nParams, 0);
  m_parConverged = std::vector<bool>(m_nParams, false);
  m_criteria = std::vector<double>(m_nParams, getProperty("ConvergenceCriteria"));
}
 
void FABADAMinimizer::initSimulatedAnnealing() {
 
  // Obs: Simulated Annealing with maximum temperature = 1.0, 1step,
  // could be used to increase the "burn-in" period before beginning to
  // check for convergence (Not the ideal way -> Think something)
  if (getProperty("SimAnnealingApplied")) {
 
    m_temperature = getProperty("MaximumTemperature");
    if (m_temperature == 0.0) {
      g_log.warning() << "MaximumTemperature not a valid temperature"
                         " (T = 0). Default (T = 10.0) taken.\n";
      m_temperature = 10.0;
    }
    if (m_temperature < 0) {
      g_log.warning() << "MaximumTemperature not a temperature"
                         " (< 0), absolute value taken\n";
      m_temperature = -m_temperature;
    }
    m_overexploration = getProperty("Overexploration");
    if (!m_overexploration && m_temperature < 1) {
      m_temperature = 1 / m_temperature;
      g_log.warning() << "MaximumTemperature reduces proper"
                         " exploration (0 < T < 1), product inverse taken ("
                      << m_temperature << ")\n";
    }
    if (m_overexploration && m_temperature > 1) {
      m_overexploration = false;
      g_log.warning() << "Overexploration wrong temperature. Not"
                         " overexploring. Applying usual Simulated Annealing.\n";
    }
    // Obs: The result is truncated to not have more iterations than
    // the chosen by the user and for all temperatures have the same
    // number of iterations
    m_leftRefrPoints = getProperty("NumRefrigerationSteps");
    if (m_leftRefrPoints == 0) {
      g_log.warning() << "Wrong value for the number of refrigeration"
                         " points (== 0). Therefore, default value (5 points) taken.\n";
      m_leftRefrPoints = 5;
    }
 
    m_simAnnealingItStep = getProperty("SimAnnealingIterations");
    m_simAnnealingItStep /= m_leftRefrPoints;
 
    m_tempStep = pow(m_temperature, 1.0 / double(m_leftRefrPoints));
 
    // m_simAnnealingItStep stores the number of iterations per step
    // 50 for pseudo-continuous temperature decrease
    // without hindering the fitting algorithm itself
    if (m_simAnnealingItStep < 50 && !m_overexploration) {
      g_log.warning() << "SimAnnealingIterations/NumRefrigerationSteps too small"
                         " (< 50 it). Simulated Annealing not applied\n";
      m_leftRefrPoints = 0;
      m_temperature = 1.0;
    }
 
    // During Overexploration, the temperature will not be changed
    if (m_overexploration)
      m_leftRefrPoints = 0;
  } else {
    m_temperature = 1.0;
    m_leftRefrPoints = 0;
  }
}
 
} // namespace Mantid::CurveFitting::FuncMinimisers