LeBailFit.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 "MantidCurveFitting/Algorithms/LeBailFit.h"
#include "MantidAPI/FuncMinimizerFactory.h"
#include "MantidAPI/FunctionFactory.h"
#include "MantidAPI/TableRow.h"
#include "MantidAPI/TextAxis.h"
#include "MantidAPI/WorkspaceFactory.h"
#include "MantidCurveFitting/Algorithms/Fit.h"
#include "MantidCurveFitting/Functions/BackgroundFunction.h"
#include "MantidHistogramData/HistogramX.h"
#include "MantidHistogramData/HistogramY.h"
#include "MantidKernel/ArrayProperty.h"
#include "MantidKernel/ListValidator.h"
#include "MantidKernel/VisibleWhenProperty.h"
 
#include <boost/algorithm/string.hpp>
 
#include <cctype>
#include <fstream>
#include <iomanip>
 
const int OBSDATAINDEX(0);
const int CALDATAINDEX(1);
const int DATADIFFINDEX(2);
const int CALPUREPEAKINDEX(3);
// Output workspace background at ws index 4
const int CALBKGDINDEX(4);
// Input background
const int INPUTBKGDINDEX(6);
// Output workspace:  pure peak (data with background removed)
const int INPUTPUREPEAKINDEX(7);
 
const double NOBOUNDARYLIMIT(1.0E10);
const double EPSILON(1.0E-10);
 
using namespace Mantid;
using namespace Mantid::CurveFitting;
using namespace Mantid::DataObjects;
using namespace Mantid::API;
using namespace Mantid::Kernel;
using Mantid::HistogramData::HistogramX;
using Mantid::HistogramData::HistogramY;
 
using namespace std;
 
namespace Mantid::CurveFitting::Algorithms {
 
const Rfactor badR(DBL_MAX, DBL_MAX);
 
DECLARE_ALGORITHM(LeBailFit)
 
//----------------------------------------------------------------------------------------------
LeBailFit::LeBailFit()
    : m_lebailFunction(), m_dataWS(), m_outputWS(), parameterWS(), reflectionWS(), m_wsIndex(0), m_startX(DBL_MAX),
      m_endX(DBL_MIN), m_inputPeakInfoVec(), m_backgroundFunction(), m_funcParameters(), m_origFuncParameters(),
      m_peakType(), m_backgroundType(), m_backgroundParameters(), m_backgroundParameterNames(), m_bkgdorder(0),
      mPeakRadius(0), m_lebailFitChi2(0.), m_lebailCalChi2(0.), mMinimizer(), m_dampingFactor(0.),
      m_inputParameterPhysical(false), m_fitMode(), m_indicatePeakHeight(0.), m_MCGroups(), m_numMCGroups(0),
      m_bestRwp(0.), m_bestRp(0.), m_bestParameters(), m_bestBackgroundData(), m_bestMCStep(0), m_numMinimizeSteps(0),
      m_Temperature(DBL_MIN), m_useAnnealing(false), m_walkStyle(RANDOMWALK), m_minimumPeakHeight(DBL_MAX),
      m_tolerateInputDupHKL2Peaks(false), m_bkgdParameterNames(), m_numberBkgdParameters(0), m_bkgdParameterBuffer(),
      m_bestBkgdParams(), m_roundBkgd(0), m_bkgdParameterStepVec(), m_peakCentreTol(0.) {}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::init() {
  // --------------  Input and output Workspaces  -----------------
 
  // Input Data Workspace
  this->declareProperty(std::make_unique<WorkspaceProperty<MatrixWorkspace>>("InputWorkspace", "", Direction::Input),
                        "Input workspace containing the data to fit by LeBail algorithm.");
 
  // Output Result Data/Model Workspace
  this->declareProperty(std::make_unique<WorkspaceProperty<Workspace2D>>("OutputWorkspace", "", Direction::Output),
                        "Output workspace containing calculated pattern or "
                        "calculated background. ");
 
  // Instrument profile Parameters
  this->declareProperty(
      std::make_unique<WorkspaceProperty<TableWorkspace>>("InputParameterWorkspace", "", Direction::Input),
      "Input table workspace containing the parameters "
      "required by LeBail fit. ");
 
  // Output instrument profile parameters
  auto tablewsprop1 = std::make_unique<WorkspaceProperty<TableWorkspace>>(
      "OutputParameterWorkspace", "", Direction::Output, API::PropertyMode::Optional);
  this->declareProperty(std::move(tablewsprop1), "Input table workspace containing the "
                                                 "parameters required by LeBail fit. ");
 
  // Single peak: Reflection (HKL) Workspace, PeaksWorkspace
  this->declareProperty(std::make_unique<WorkspaceProperty<TableWorkspace>>("InputHKLWorkspace", "", Direction::Input),
                        "Input table workspace containing the list of reflections (HKL). ");
 
  // Bragg peaks profile parameter output table workspace
  auto tablewsprop2 = std::make_unique<WorkspaceProperty<TableWorkspace>>("OutputPeaksWorkspace", "", Direction::Output,
                                                                          API::PropertyMode::Optional);
  this->declareProperty(std::move(tablewsprop2), "Optional output table workspace "
                                                 "containing all peaks' peak "
                                                 "parameters. ");
 
  // WorkspaceIndex
  this->declareProperty("WorkspaceIndex", 0, "Workspace index of the spectrum to fit by LeBail.");
 
  // Interested region
  this->declareProperty(std::make_unique<Kernel::ArrayProperty<double>>("FitRegion"),
                        "Region of data (TOF) for LeBail fit.  Default is whole range. ");
 
  // Functionality: Fit/Calculation/Background
  std::vector<std::string> functions{"LeBailFit", "Calculation", "MonteCarlo", "RefineBackground"};
  auto validator = std::make_shared<Kernel::StringListValidator>(functions);
  this->declareProperty("Function", "LeBailFit", validator, "Functionality");
 
  // Peak type
  vector<string> peaktypes{"ThermalNeutronBk2BkExpConvPVoigt", "NeutronBk2BkExpConvPVoigt"};
  auto peaktypevalidator = std::make_shared<StringListValidator>(peaktypes);
  declareProperty("PeakType", "ThermalNeutronBk2BkExpConvPVoigt", peaktypevalidator, "Peak profile type.");
 
  /*------------------------  Background Related Properties
   * ---------------------------------*/
  // About background:  Background type, input (table workspace or array)
  std::vector<std::string> bkgdtype{"Polynomial", "Chebyshev", "FullprofPolynomial"};
  auto bkgdvalidator = std::make_shared<Kernel::StringListValidator>(bkgdtype);
  declareProperty("BackgroundType", "Polynomial", bkgdvalidator, "Background type");
 
  // Input background parameters (array)
  this->declareProperty(std::make_unique<Kernel::ArrayProperty<double>>("BackgroundParameters"),
                        "Optional: enter a comma-separated list of background order parameters "
                        "from order 0. ");
 
  // Input background parameters (tableworkspace)
  auto tablewsprop3 = std::make_unique<WorkspaceProperty<TableWorkspace>>(
      "BackgroundParametersWorkspace", "", Direction::InOut, API::PropertyMode::Optional);
  this->declareProperty(std::move(tablewsprop3), "Optional table workspace containing the fit result for background.");
 
  // Peak Radius
  this->declareProperty("PeakRadius", 5, "Range (multiplier relative to FWHM) for a full peak. ");
 
  /*------------------------  Properties for Calculation Mode
   * --------------------------------*/
  // Output option to plot each individual peak
  declareProperty("PlotIndividualPeaks", false, "Option to output each individual peak in mode Calculation.");
  setPropertySettings("PlotIndividualPeaks",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "Calculation"));
 
  // Make each reflection visible
  declareProperty("IndicationPeakHeight", 0.0,
                  "Heigh of peaks (reflections) if its calculated height is "
                  "smaller than user-defined minimum.");
  setPropertySettings("IndicationPeakHeight",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "Calculation"));
 
  // UseInputPeakHeights
  declareProperty("UseInputPeakHeights", true,
                  "For 'Calculation' mode only, use peak heights specified in "
                  "ReflectionWorkspace. "
                  "Otherwise, calcualte peaks' heights. ");
  setPropertySettings("UseInputPeakHeights",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "Calculation"));
 
  /*---------------------------  Properties for Fitting Mode
   * ---------------------------------*/
  // Minimizer
  std::vector<std::string> minimizerOptions = API::FuncMinimizerFactory::Instance().getKeys(); // :Instance().getKeys();
  declareProperty("Minimizer", "Levenberg-MarquardtMD",
                  Kernel::IValidator_sptr(new Kernel::ListValidator<std::string>(minimizerOptions)),
                  "The minimizer method applied to do the fit, default is "
                  "Levenberg-Marquardt",
                  Kernel::Direction::InOut);
  setPropertySettings("Minimizer", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "LeBailFit"));
 
  declareProperty("Damping", 1.0, "Damping factor if minimizer is 'Damped Gauss-Newton'");
  setPropertySettings("Damping", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "LeBailFit"));
  setPropertySettings("Damping", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("NumberMinimizeSteps", 100, "Number of Monte Carlo random walk steps.");
  setPropertySettings("NumberMinimizeSteps",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "LeBailFit"));
  setPropertySettings("NumberMinimizeSteps",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
  setPropertySettings("NumberMinimizeSteps",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "RefineBackground"));
 
  //-----------------  Parameters for Monte Carlo Simulated Annealing
  //--------------------------
  auto mcwsprop = std::make_unique<WorkspaceProperty<TableWorkspace>>("MCSetupWorkspace", "", Direction::Input,
                                                                      PropertyMode::Optional);
  declareProperty(std::move(mcwsprop), "Name of table workspace containing parameters' "
                                       "setup for Monte Carlo simualted annearling. ");
  setPropertySettings("MCSetupWorkspace", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("RandomSeed", 1, "Random number seed.");
  setPropertySettings("RandomSeed", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("AnnealingTemperature", 1.0,
                  "Temperature used Monte Carlo.  "
                  "Negative temperature is for simulated annealing. ");
  setPropertySettings("AnnealingTemperature",
                      std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("UseAnnealing", true, "Allow annealing temperature adjusted automatically.");
  setPropertySettings("UseAnnealing", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("DrunkenWalk", false,
                  "Flag to use drunken walk algorithm. "
                  "Otherwise, random walk algorithm is used. ");
  setPropertySettings("DrunkenWalk", std::make_unique<VisibleWhenProperty>("Function", IS_EQUAL_TO, "MonteCarlo"));
 
  declareProperty("MinimumPeakHeight", 0.01,
                  "Minimum height of a peak to be counted "
                  "during smoothing background by exponential smooth algorithm. ");
 
  // Flag to allow input hkl file containing degenerated peaks
  declareProperty("AllowDegeneratedPeaks", false,
                  "Flag to allow degenerated peaks in input .hkl file. "
                  "Otherwise, an exception will be thrown if this situation occurs.");
 
  // Tolerance of imported peak's position comparing to data range
  declareProperty("ToleranceToImportPeak", EMPTY_DBL(),
                  "Tolerance in TOF to import peak from Bragg "
                  "peaks list.  If it specified, all peaks within Xmin-Tol and "
                  "Xmax+Tol will be imported. "
                  "It is used in the case that the geometry parameters are "
                  "close to true values. ");
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::exec() {
  // Process input properties
  processInputProperties();
 
  // Import parameters from table workspace
  parseInstrumentParametersTable();
  parseBraggPeaksParametersTable();
 
  // Background function and calculation on it
  processInputBackground();
 
  // Create Le Bail function
  createLeBailFunction();
 
  // Create output workspace/workspace
  createOutputDataWorkspace();
 
  // 5. Adjust function mode according to input values
  if (m_lebailFunction->isParameterValid()) {
    // All peaks within range are physical and good to refine
    m_inputParameterPhysical = true;
  } else {
    // Some peaks within range have unphysical parameters.  Just calcualtion for
    // reference
    m_inputParameterPhysical = false;
    g_log.warning() << "Input instrument parameters values cause some peaks to have "
                       "unphysical profile parameters.\n";
    if (m_fitMode == FIT || m_fitMode == MONTECARLO) {
      g_log.warning() << "Function mode FIT is disabled.  Convert to Calculation mode.\n";
      m_fitMode = CALCULATION;
    }
  }
 
  // 7. Do calculation or fitting
  m_lebailFitChi2 = -1; // Initialize
  m_lebailCalChi2 = -1;
 
  switch (m_fitMode) {
  case CALCULATION:
    // Calculation
    g_log.notice() << "Function: Pattern Calculation.\n";
    execPatternCalculation();
    break;
 
  case FIT:
    // LeBail Fit
    g_log.notice() << "Function: Do LeBail Fit ==> Monte Carlo.\n";
  // fall through
  case MONTECARLO:
    // Monte carlo Le Bail refinement
    g_log.notice("Function: Do LeBail Fit By Monte Carlo Random Walk.");
    execRandomWalkMinimizer(m_numMinimizeSteps, m_funcParameters);
 
    break;
 
  case BACKGROUNDPROCESS:
    // Calculating background
    // FIXME : Determine later whether this functionality is kept or removed!
    g_log.notice() << "Function: Refine Background (Precisely).\n";
    execRefineBackground();
    break;
 
  default:
    // Impossible
    std::stringstream errmsg;
    errmsg << "FunctionMode = " << m_fitMode << " is not supported in exec().";
    g_log.error() << errmsg.str() << "\n";
    throw std::runtime_error(errmsg.str());
 
    break;
  }
 
  // 7. Output peak (table) and parameter workspace
  exportBraggPeakParameterToTable();
  exportInstrumentParameterToTable(m_funcParameters);
 
  setProperty("OutputWorkspace", m_outputWS);
 
  // 8. Final statistic
  Rfactor finalR = getRFactor(m_outputWS->y(0).rawData(), m_outputWS->y(1).rawData(), m_outputWS->e(0).rawData());
  g_log.notice() << "\nFinal R factor: Rwp = " << finalR.Rwp << ", Rp = " << finalR.Rp
                 << ", Data points = " << m_outputWS->y(1).size() << ", Range = " << m_outputWS->x(0)[0] << ", "
                 << m_outputWS->x(0).back() << "\n";
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::processInputBackground() {
  // FIXME - Need to think of FullprofPolynomial
  // Type
  m_backgroundType = getPropertyValue("BackgroundType");
 
  // Parameters
  m_backgroundParameters = getProperty("BackgroundParameters");
  TableWorkspace_sptr bkgdparamws = getProperty("BackgroundParametersWorkspace");
 
  // Determine where the background parameters are from
  if (!bkgdparamws) {
    // Set up parameter name
    m_backgroundParameterNames.clear();
    size_t i0 = 0;
    if (m_backgroundType == "FullprofPolynomial") {
      // TODO - Add this special case to Wiki
      m_backgroundParameterNames.emplace_back("Bkpos");
      if (m_backgroundParameters[0] < m_startX || m_backgroundParameters[0] > m_endX)
        g_log.warning("Bkpos is out side of data range.  It MIGHT NOT BE RIGHT. ");
      i0 = 1;
    }
 
    size_t numparams = m_backgroundParameters.size();
    for (size_t i = i0; i < numparams; ++i) {
      stringstream parss;
      parss << "A" << (i - i0);
      m_backgroundParameterNames.emplace_back(parss.str());
    }
 
    g_log.information() << "[Input] Use background specified with vector with "
                           "input vector sized "
                        << numparams << ".\n";
  } else {
    g_log.information() << "[Input] Use background specified by table workspace.\n";
    parseBackgroundTableWorkspace(bkgdparamws, m_backgroundParameterNames, m_backgroundParameters);
  }
 
  // Set up background order
  m_bkgdorder = static_cast<unsigned int>(m_backgroundParameterNames.size());
  if (m_backgroundType == "FullprofPolynomial") {
    // Consider 1 extra Bkpos
    if (m_bkgdorder == 0)
      throw runtime_error("FullprofPolynomial: Bkpos must be given! ");
    else if (m_bkgdorder <= 7)
      m_bkgdorder = 6;
    else if (m_bkgdorder <= 13)
      m_bkgdorder = 12;
    else
      throw runtime_error("There is something wrong to set up FullprofPolynomial. ");
  } else {
    // order n will have n+1 parameters
    if (m_bkgdorder == 0)
      throw runtime_error("Polynomial and Chebyshev at least be order 0 (1 parameter). ");
    --m_bkgdorder;
  }
}
 
//===================================  Pattern Calculation & Minimizing
//=======================
 
//----------------------------------------------------------------------------------------------
void LeBailFit::execPatternCalculation() {
  // Generate domain and values vectors
  const auto &vecX = m_dataWS->x(m_wsIndex).rawData();
  std::vector<double> vecY(m_outputWS->y(CALDATAINDEX).size(), 0);
 
  // Calculate diffraction pattern
  Rfactor rfactor(-DBL_MAX, -DBL_MAX);
  // FIXME - It should be a new ticket to turn on this option (use
  // user-specified peak height)
  bool useinputpeakheights = this->getProperty("UseInputPeakHeights");
  if (useinputpeakheights)
    g_log.warning("UseInputPeakHeights is temporarily turned off now. ");
 
  // Set the parameters to LeBailFunction
  map<string, double> profilemap = convertToDoubleMap(m_funcParameters);
  m_lebailFunction->setProfileParameterValues(profilemap);
 
  // Calculate peak intensities and diffraction pattern
  vector<double> emptyvec;
  bool resultphysical =
      calculateDiffractionPattern(m_dataWS->x(m_wsIndex), m_dataWS->y(m_wsIndex), true, true, emptyvec, vecY, rfactor);
  m_outputWS->mutableY(CALDATAINDEX) = vecY;
 
  // Calculate background
  m_outputWS->mutableY(INPUTBKGDINDEX) = m_lebailFunction->function(vecX, false, true);
 
  m_outputWS->mutableY(INPUTPUREPEAKINDEX) = m_outputWS->y(OBSDATAINDEX) - m_outputWS->y(INPUTBKGDINDEX);
 
  // Set up output workspaces
  m_outputWS->mutableY(DATADIFFINDEX) = m_outputWS->y(OBSDATAINDEX) - m_outputWS->y(CALDATAINDEX);
 
  // Calcualte individual peaks
  bool ploteachpeak = this->getProperty("PlotIndividualPeaks");
  g_log.information() << "Output individual peaks  = " << ploteachpeak << ".\n";
  if (ploteachpeak) {
    for (size_t ipk = 0; ipk < m_lebailFunction->getNumberOfPeaks(); ++ipk) {
      m_outputWS->mutableY(9 + ipk) = m_lebailFunction->calPeak(ipk, vecX, m_outputWS->y(9 + ipk).size());
    }
  }
 
  // Record for output
  Parameter par_rwp;
  par_rwp.name = "Rwp";
  par_rwp.curvalue = rfactor.Rwp;
  m_funcParameters["Rwp"] = par_rwp;
 
  g_log.notice() << "Rwp = " << rfactor.Rwp << ", Rp = " << rfactor.Rp << "\n";
 
  if (!resultphysical) {
    g_log.warning() << "Input parameters are unable to generate peaks that are physical."
                    << ".\n";
  }
}
 
//====================================  Refine background
//====================================
//----------------------------------------------------------------------------------------------
void LeBailFit::execRefineBackground() {
  // Set up class variables for background
  m_bkgdParameterNames = m_backgroundFunction->getParameterNames();
  m_numberBkgdParameters = m_bkgdParameterNames.size();
  m_bkgdParameterBuffer.resize(m_numberBkgdParameters);
  m_bestBkgdParams.resize(m_numberBkgdParameters);
  m_roundBkgd = 0;
  m_bkgdParameterStepVec.resize(m_numberBkgdParameters, 0.01);
  for (size_t i = 1; i < m_numberBkgdParameters; ++i) {
    m_bkgdParameterStepVec[i] = m_bkgdParameterStepVec[i - 1] * 0.0001;
  }
 
  // 1. Generate domain and value
  const auto &vecX = m_dataWS->x(m_wsIndex).rawData();
  const auto &vecY = m_dataWS->y(m_wsIndex);
  vector<double> valueVec(vecX.size(), 0);
  size_t numpts = vecX.size();
 
  API::FunctionDomain1DVector domain(vecX);
  API::FunctionValues values(domain);
 
  // 2. Calculate diffraction pattern
  Rfactor currR(DBL_MAX, DBL_MAX);
  m_backgroundFunction->function(domain, values);
  vector<double> backgroundvalues = values.toVector();
  for (size_t i = 0; i < numpts; ++i) {
    m_outputWS->mutableY(INPUTPUREPEAKINDEX)[i] = m_dataWS->y(m_wsIndex)[i] - values[i];
  }
  m_outputWS->setSharedE(INPUTPUREPEAKINDEX, m_dataWS->sharedE(m_wsIndex));
  map<string, double> parammap = convertToDoubleMap(m_funcParameters);
  m_lebailFunction->setProfileParameterValues(parammap);
  calculateDiffractionPattern(m_outputWS->x(INPUTPUREPEAKINDEX), m_outputWS->y(INPUTPUREPEAKINDEX), false, true,
                              backgroundvalues, valueVec, currR);
  Rfactor bestR = currR;
  storeBackgroundParameters(m_bestBkgdParams);
  stringstream bufss;
  bufss << "Starting background parameter ";
  for (size_t i = 0; i < m_bestBkgdParams.size(); ++i)
    bufss << "[" << i << "] = " << m_bestBkgdParams[i] << ", ";
  bufss << ".  Starting Rwp = " << currR.Rwp;
  g_log.notice(bufss.str());
 
  for (size_t istep = 0; istep < m_numMinimizeSteps; ++istep) {
    // a) Store current setup
    storeBackgroundParameters(m_bkgdParameterBuffer);
 
    // b) Propose new values and evalulate
    proposeNewBackgroundValues();
    Rfactor newR(DBL_MAX, DBL_MAX);
    m_backgroundFunction->function(domain, values);
    backgroundvalues = values.toVector();
    for (size_t i = 0; i < numpts; ++i) {
      m_outputWS->mutableY(INPUTPUREPEAKINDEX)[i] = m_dataWS->y(m_wsIndex)[i] - values[i];
    }
    parammap = convertToDoubleMap(m_funcParameters);
    m_lebailFunction->setProfileParameterValues(parammap);
    calculateDiffractionPattern(m_outputWS->x(INPUTPUREPEAKINDEX), m_outputWS->y(INPUTPUREPEAKINDEX), false, true,
                                backgroundvalues, valueVec, newR);
 
    g_log.information() << "[DBx800] New Rwp = " << newR.Rwp << ", Rp = " << newR.Rp << ".\n";
 
    bool accept = acceptOrDeny(currR, newR);
 
    // c) Process result
    if (!accept) {
      // Not accept.  Restore original
      recoverBackgroundParameters(m_bkgdParameterBuffer);
    } else {
      // Accept
      currR = newR;
      if (newR.Rwp < bestR.Rwp) {
        // Is it the best?
        bestR = newR;
        storeBackgroundParameters(m_bestBkgdParams);
 
        stringstream ss;
        ss << "Temp best background parameter ";
        for (size_t i = 0; i < m_bestBkgdParams.size(); ++i)
          ss << "[" << i << "] = " << m_bestBkgdParams[i] << ", ";
        g_log.information(ss.str());
      }
    }
 
    // d) Progress
    progress(static_cast<double>(istep) / static_cast<double>(m_numMinimizeSteps));
  }
 
  // 3. Recover the best
  recoverBackgroundParameters(m_bestBkgdParams);
 
  stringstream bufss1;
  bufss1 << "Best background parameter ";
  for (size_t i = 0; i < m_bkgdParameterStepVec.size(); ++i)
    bufss1 << "[" << i << "] = " << m_backgroundFunction->getParameter(i) << ", ";
  g_log.notice(bufss1.str());
 
  Rfactor outputR(-DBL_MAX, -DBL_MAX);
  m_backgroundFunction->function(domain, values);
  backgroundvalues = values.toVector();
  for (size_t i = 0; i < numpts; ++i) {
    m_outputWS->mutableY(INPUTPUREPEAKINDEX)[i] = m_dataWS->y(m_wsIndex)[i] - values[i];
  }
  parammap = convertToDoubleMap(m_funcParameters);
  m_lebailFunction->setProfileParameterValues(parammap);
  calculateDiffractionPattern(m_outputWS->x(INPUTPUREPEAKINDEX), m_outputWS->y(INPUTPUREPEAKINDEX), false, true,
                              backgroundvalues, valueVec, outputR);
 
  g_log.notice() << "[RefineBackground] Best Rwp = " << bestR.Rwp << ",  vs. recovered best Rwp = " << outputR.Rwp
                 << ".\n";
 
  // 4. Add data (0: experimental, 1: calcualted, 2: difference)
  auto &vecY1 = m_outputWS->mutableY(1);
  auto &vecY2 = m_outputWS->mutableY(2);
  for (size_t i = 0; i < numpts; ++i) {
    vecY1[i] = valueVec[i] + backgroundvalues[i];
    vecY2[i] = vecY[i] - (valueVec[i] + backgroundvalues[i]);
  }
 
  //   (3: peak without background, 4: input background)
  // m_backgroundFunction->function(domain, values);
  m_outputWS->mutableY(CALBKGDINDEX) = backgroundvalues;
  m_outputWS->mutableY(CALPUREPEAKINDEX) = valueVec;
 
  // 5. Output background to table workspace
  auto outtablews = std::make_shared<TableWorkspace>();
  outtablews->addColumn("str", "Name");
  outtablews->addColumn("double", "Value");
  outtablews->addColumn("double", "Error");
 
  for (const auto &parname : m_bkgdParameterNames) {
    double parvalue = m_backgroundFunction->getParameter(parname);
 
    TableRow newrow = outtablews->appendRow();
    newrow << parname << parvalue << 1.0;
  }
 
  setProperty("BackgroundParametersWorkspace", outtablews);
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::storeBackgroundParameters(vector<double> &bkgdparamvec) {
  for (size_t i = 0; i < m_numberBkgdParameters; ++i) {
    bkgdparamvec[i] = m_backgroundFunction->getParameter(i);
  }
}
 
void LeBailFit::recoverBackgroundParameters(const vector<double> &bkgdparamvec) {
  for (size_t i = 0; i < m_numberBkgdParameters; ++i) {
    m_backgroundFunction->setParameter(i, bkgdparamvec[i]);
  }
}
 
void LeBailFit::proposeNewBackgroundValues() {
  int iparam = m_roundBkgd % static_cast<int>(m_numberBkgdParameters);
 
  double currvalue = m_backgroundFunction->getParameter(static_cast<int>(iparam));
  double r = 2 * (static_cast<double>(rand()) / static_cast<double>(RAND_MAX) - 0.5);
  double newvalue = currvalue + r * m_bkgdParameterStepVec[iparam];
 
  g_log.information() << "[DBx804] Background " << iparam << " propose new value = " << newvalue << "  from "
                      << currvalue << ".\n";
 
  m_backgroundFunction->setParameter(static_cast<size_t>(iparam), newvalue);
 
  ++m_roundBkgd;
}
 
//===================================  Set up the Le Bail Fit
//================================
//----------------------------------------------------------------------------------------------
void LeBailFit::createLeBailFunction() {
  // Generate Le Bail function
  m_lebailFunction = std::make_shared<LeBailFunction>(LeBailFunction(m_peakType));
 
  // Set up profile parameters
  if (m_funcParameters.empty())
    throw runtime_error("Function parameters must be set up by this point.");
 
  map<string, double> pardblmap = convertToDoubleMap(m_funcParameters);
  m_lebailFunction->setProfileParameterValues(pardblmap);
 
  // Add peaks
  if (!isEmpty(m_peakCentreTol)) {
    const auto &vecx = m_dataWS->x(m_wsIndex);
    m_lebailFunction->setPeakCentreTolerance(m_peakCentreTol, vecx.front(), vecx.back());
  }
 
  vector<vector<int>> vecHKL;
  vector<pair<vector<int>, double>>::iterator piter;
  for (piter = m_inputPeakInfoVec.begin(); piter != m_inputPeakInfoVec.end(); ++piter)
    vecHKL.emplace_back(piter->first);
  m_lebailFunction->addPeaks(vecHKL);
 
  // Add background
  m_lebailFunction->addBackgroundFunction(m_backgroundType, m_bkgdorder, m_backgroundParameterNames,
                                          m_backgroundParameters, m_startX, m_endX);
}
 
//----------------------------------------------------------------------------------------------
API::MatrixWorkspace_sptr LeBailFit::cropWorkspace(const API::MatrixWorkspace_sptr &inpws, size_t wsindex) {
  // Process input property 'FitRegion' for range of data to fit/calculate
  std::vector<double> fitrange = this->getProperty("FitRegion");
 
  double tof_min, tof_max;
  if (fitrange.empty()) {
    tof_min = inpws->x(wsindex)[0];
    tof_max = inpws->x(wsindex).back();
  } else if (fitrange.size() == 2) {
    tof_min = fitrange[0];
    tof_max = fitrange[1];
  } else {
    g_log.warning() << "Input FitRegion has more than 2 entries.  Using "
                       "default in stread.\n";
 
    tof_min = inpws->x(wsindex)[0];
    tof_max = inpws->x(wsindex).back();
  }
 
  // Crop workspace
  auto cropalg = createChildAlgorithm("CropWorkspace", -1, -1, true);
  cropalg->initialize();
 
  cropalg->setProperty("InputWorkspace", inpws);
  cropalg->setPropertyValue("OutputWorkspace", "MyData");
  cropalg->setProperty("XMin", tof_min);
  cropalg->setProperty("XMax", tof_max);
 
  bool cropstatus = cropalg->execute();
  if (!cropstatus) {
    std::stringstream errmsg;
    errmsg << "DBx309 Cropping workspace unsuccessful.  Fatal Error. Quit!";
    g_log.error() << errmsg.str() << "\n";
    throw std::runtime_error(errmsg.str());
  }
 
  API::MatrixWorkspace_sptr cropws = cropalg->getProperty("OutputWorkspace");
  if (!cropws) {
    g_log.error("Unable to retrieve a Workspace2D object from ChildAlgorithm "
                "CropWorkspace");
    throw runtime_error("Unable to retrieve a Workspace2D object from "
                        "ChildAlgorithm CropWorkspace");
  } else {
    g_log.debug() << "DBx307: Cropped Workspace... Range From " << cropws->x(wsindex)[0] << " To "
                  << cropws->x(wsindex).back() << " of size " << cropws->x(wsindex).size() << "\n";
  }
 
  return cropws;
}
 
//================================= Import/Parse and Output
//===================================
//----------------------------------------------------------------------------------------------
void LeBailFit::processInputProperties() {
  // Peak type
  m_peakType = getPropertyValue("PeakType");
 
  // 1. Get input and perform some check
  // a) Import data workspace and related, do crop
  API::MatrixWorkspace_sptr inpWS = this->getProperty("InputWorkspace");
 
  int tempindex = this->getProperty("WorkspaceIndex");
  m_wsIndex = size_t(tempindex);
 
  if (m_wsIndex >= inpWS->getNumberHistograms()) {
    // throw if workspace index is not correct
    stringstream errss;
    errss << "Input WorkspaceIndex " << tempindex << " is out of boundary [0, " << inpWS->getNumberHistograms()
          << "). ";
    g_log.error(errss.str());
    throw runtime_error(errss.str());
  }
 
  m_dataWS = this->cropWorkspace(inpWS, m_wsIndex);
  m_startX = m_dataWS->x(0).front();
  m_endX = m_dataWS->x(0).back();
 
  // b) Minimizer
  std::string minim = getProperty("Minimizer");
  mMinimizer = minim;
 
  // c) Peak parameters and related.
  parameterWS = this->getProperty("InputParameterWorkspace");
  reflectionWS = this->getProperty("InputHKLWorkspace");
  mPeakRadius = this->getProperty("PeakRadius");
 
  // d) Determine Functionality (function mode)
  std::string function = this->getProperty("Function");
  m_fitMode = FIT; // Default: LeBailFit
  if (function == "Calculation") {
    // peak calculation
    m_fitMode = CALCULATION;
  } else if (function == "CalculateBackground") {
    // automatic background points selection
    m_fitMode = BACKGROUNDPROCESS;
  } else if (function == "MonteCarlo") {
    // Monte Carlo random walk refinement
    m_fitMode = MONTECARLO;
  } else if (function == "LeBailFit") {
    // Le Bail Fit mode
    m_fitMode = FIT;
  } else if (function == "RefineBackground") {
    // Refine background mode
    m_fitMode = BACKGROUNDPROCESS;
  } else {
    stringstream errss;
    errss << "Function mode " << function << " is not supported by LeBailFit().";
    g_log.error(errss.str());
    throw invalid_argument(errss.str());
  }
 
  m_dampingFactor = getProperty("Damping");
 
  tempindex = getProperty("NumberMinimizeSteps");
  if (tempindex > 0)
    m_numMinimizeSteps = static_cast<size_t>(tempindex);
  else {
    m_numMinimizeSteps = 0;
    stringstream errss;
    errss << "Input number of random walk steps (" << m_numMinimizeSteps << ") cannot be less and equal to zero.";
    g_log.error(errss.str());
    throw invalid_argument(errss.str());
  }
 
  m_minimumPeakHeight = getProperty("MinimumPeakHeight");
  m_indicatePeakHeight = getProperty("IndicationPeakHeight");
 
  // Tolerate duplicated input peak or not?
  m_tolerateInputDupHKL2Peaks = getProperty("AllowDegeneratedPeaks");
 
  // Tolerance in peak positions to import peak
  m_peakCentreTol = getProperty("ToleranceToImportPeak");
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::parseInstrumentParametersTable() {
  // 1. Check column orders
  if (parameterWS->columnCount() < 3) {
    g_log.error() << "Input parameter table workspace does not have enough "
                     "number of columns. "
                  << " Number of columns (Input =" << parameterWS->columnCount() << ") >= 3 as required.\n";
    throw std::invalid_argument("Input parameter workspace is wrong. ");
  } else {
    g_log.information() << "[DB] Starting to parse instrument parameter table workspace " << parameterWS->getName()
                        << ".\n";
  }
 
  // 2. Import data to maps
  size_t numrows = parameterWS->rowCount();
  std::vector<std::string> colnames = parameterWS->getColumnNames();
  size_t numcols = colnames.size();
 
  std::map<std::string, double> tempdblmap;
  std::map<std::string, std::string> tempstrmap;
  std::map<std::string, double>::iterator dbliter;
  std::map<string, string>::iterator striter;
 
  std::string colname;
  double dblvalue;
  std::string strvalue;
 
  for (size_t ir = 0; ir < numrows; ++ir) {
    // a) Clear the map
    tempdblmap.clear();
    tempstrmap.clear();
 
    // b) Get the row
    API::TableRow trow = parameterWS->getRow(ir);
 
    // c) Parse each term
    for (size_t icol = 0; icol < numcols; ++icol) {
      colname = colnames[icol];
      if (colname != "FitOrTie" && colname != "Name") {
        // double data
        g_log.debug() << "Col-name = " << colname << ", ";
        trow >> dblvalue;
        g_log.debug() << "Value = " << dblvalue << ".\n";
        ;
        tempdblmap.emplace(colname, dblvalue);
      } else {
        // string data
        g_log.debug() << "Col-name = " << colname << ", ";
        trow >> strvalue;
        strvalue.erase(std::find_if(strvalue.rbegin(), strvalue.rend(), std::not_fn(::isspace)).base(), strvalue.end());
 
        g_log.debug() << "Value = " << strvalue << ".\n";
        tempstrmap.emplace(colname, strvalue);
      }
    }
 
    // d) Construct a Parameter instance
    Parameter newparameter;
    // i.   name
    striter = tempstrmap.find("Name");
    if (striter != tempstrmap.end()) {
      newparameter.name = striter->second;
    } else {
      std::stringstream errmsg;
      errmsg << "Parameter (table) workspace " << parameterWS->getName()
             << " does not contain column 'Name'.  It is not a valid input.  "
                "Quit ";
      g_log.error() << errmsg.str() << "\n";
      throw std::invalid_argument(errmsg.str());
    }
 
    // ii.  fit
    striter = tempstrmap.find("FitOrTie");
    if (striter != tempstrmap.end()) {
      std::string fitortie = striter->second;
      bool tofit = true;
      if (fitortie.length() > 0) {
        char fc = fitortie.c_str()[0];
        if (fc == 't' || fc == 'T') {
          tofit = false;
        }
      }
      newparameter.fit = tofit;
    } else {
      std::stringstream errmsg;
      errmsg << "Parameter (table) workspace " << parameterWS->getName()
             << " does not contain column 'FitOrTie'.  It is not a valid "
                "input.  Quit ";
      g_log.error() << errmsg.str() << "\n";
      throw std::invalid_argument(errmsg.str());
    }
 
    // iii. value
    dbliter = tempdblmap.find("Value");
    if (dbliter != tempdblmap.end()) {
      newparameter.curvalue = dbliter->second;
    } else {
      std::stringstream errmsg;
      errmsg << "Parameter (table) workspace " << parameterWS->getName()
             << " does not contain column 'Value'.  It is not a valid input.  "
                "Quit ";
      g_log.error() << errmsg.str() << "\n";
      throw std::invalid_argument(errmsg.str());
    }
 
    // iv.  min
    dbliter = tempdblmap.find("Min");
    if (dbliter != tempdblmap.end()) {
      newparameter.minvalue = dbliter->second;
    } else {
      newparameter.minvalue = -1.0E10;
    }
 
    // v.   max
    dbliter = tempdblmap.find("Max");
    if (dbliter != tempdblmap.end()) {
      newparameter.maxvalue = dbliter->second;
    } else {
      newparameter.maxvalue = 1.0E10;
    }
 
    // vi.  stepsize
    dbliter = tempdblmap.find("StepSize");
    if (dbliter != tempdblmap.end()) {
      newparameter.stepsize = dbliter->second;
    } else {
      newparameter.stepsize = 1.0;
    }
 
    // vii. error
    newparameter.fiterror = 1.0E10;
 
    // viii.  some historical records
    // FIXME : Consider to move parameter value's min/max to Monte Carlo table
    newparameter.minrecordvalue = newparameter.maxvalue + 1.0;
    newparameter.maxrecordvalue = newparameter.minvalue - 1.0;
 
    m_funcParameters.emplace(newparameter.name, newparameter);
    m_origFuncParameters.emplace(newparameter.name, newparameter.curvalue);
 
    g_log.information() << "Inserting Parameter " << newparameter.name << " = " << newparameter.curvalue << ".\n";
 
    if (newparameter.fit) {
      g_log.debug() << "[Input]: " << newparameter.name << ": value = " << newparameter.curvalue << " Range: ["
                    << newparameter.minvalue << ", " << newparameter.maxvalue
                    << "], MC Step = " << newparameter.stepsize << ", Fit? = " << newparameter.fit << "\n";
    }
  } // ENDFOR rows in Table
 
  g_log.information() << "[DB]: Successfully Imported Peak Parameters TableWorkspace " << parameterWS->getName()
                      << ". Imported " << m_funcParameters.size() << " parameters. "
                      << "\n";
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::parseBraggPeaksParametersTable() {
  // 1. Check column orders
  std::vector<std::string> colnames = reflectionWS->getColumnNames();
  if (colnames.size() < 3) {
    g_log.error() << "Input parameter table workspace does not have enough "
                     "number of columns. "
                  << " Number of columns = " << colnames.size() << " < 3 as required.\n";
    throw std::runtime_error("Input parameter workspace is wrong. ");
  }
  if (colnames[0] != "H" || colnames[1] != "K" || colnames[2] != "L") {
    stringstream errss;
    errss << "Input Bragg peak parameter TableWorkspace does not have the "
             "columns in order.  "
          << "It must be H, K, L. for the first 3 columns.";
    g_log.error(errss.str());
    throw std::runtime_error(errss.str());
  }
 
  // Has peak height?
  bool hasPeakHeight = false;
  if (colnames.size() >= 4 && colnames[3] == "PeakHeight") {
    // Has a column for peak height
    hasPeakHeight = true;
  }
 
  /* FIXME This section is disabled.  It should be a new ticket to turn on this
  option.
  bool userexcludepeaks = false;
  if (colnames.size() >= 5 && colnames[4] == "Include/Exclude")
  {
  userexcludepeaks = true;
  }
  */
 
  // 2. Import data to maps
  int h, k, l;
 
  size_t numrows = reflectionWS->rowCount();
  for (size_t ir = 0; ir < numrows; ++ir) {
    // 1. Get from table row
    API::TableRow trow = reflectionWS->getRow(ir);
    trow >> h >> k >> l;
 
    // 3. Insert related data structure
    std::vector<int> hkl;
    hkl.emplace_back(h);
    hkl.emplace_back(k);
    hkl.emplace_back(l);
 
    // optional peak height
    double peakheight = 1.0;
    if (hasPeakHeight) {
      trow >> peakheight;
    }
 
    m_inputPeakInfoVec.emplace_back(hkl, peakheight);
  } // ENDFOR row
 
  g_log.information() << "Imported HKL TableWorkspace.   Size of Rows = " << numrows << "\n";
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::parseBackgroundTableWorkspace(const TableWorkspace_sptr &bkgdparamws, vector<string> &bkgdparnames,
                                              vector<double> &bkgdorderparams) {
  g_log.debug() << "DB1105A Parsing background TableWorkspace.\n";
 
  // Clear (output) map
  bkgdorderparams.clear();
 
  // Check background parameter table workspace
  std::vector<std::string> colnames = bkgdparamws->getColumnNames();
  if (colnames.size() < 2) {
    stringstream errss;
    errss << "Input background parameter table workspace " << bkgdparamws->getName() << " has only " << colnames.size()
          << " columns, which is fewer than 2 columns as required. ";
    g_log.error(errss.str());
    throw runtime_error(errss.str());
  } else {
    if (!(colnames[0].starts_with("Name") && colnames[1].starts_with("Value"))) {
      // Column 0 and 1 must be Name and Value (at least started with)
      stringstream errss;
      errss << "Input parameter table workspace have wrong column definition. "
            << "Column 0 should be Name.  And column 1 should be Value. "
               "Current input is: \n";
      for (size_t i = 0; i < 2; ++i)
        errss << "Column " << i << ": " << colnames[0] << "\n";
      g_log.error(errss.str());
      throw runtime_error(errss.str());
    }
  }
 
  // Parse input table workspace to a map.  Valid parameter names must start
  // with A.
  std::map<std::string, double> parmap;
  for (size_t ir = 0; ir < bkgdparamws->rowCount(); ++ir) {
    API::TableRow row = bkgdparamws->getRow(ir);
    std::string parname;
    double parvalue;
    row >> parname >> parvalue;
 
    // Remove extra white spaces
    boost::algorithm::trim(parname);
 
    if (!parname.empty() && (parname[0] == 'A' || parname == "Bkpos")) {
      // Insert parameter name starting with A or Bkpos (special case for
      // FullprofPolynomial)
      parmap.emplace(parname, parvalue);
    }
  }
 
  // Add pair to vector
  bkgdparnames.reserve(parmap.size());
  bkgdorderparams.reserve(parmap.size());
 
  std::map<std::string, double>::iterator mit;
  for (mit = parmap.begin(); mit != parmap.end(); ++mit) {
    std::string parname = mit->first;
    double parvalue = mit->second;
    bkgdparnames.emplace_back(parname);
    bkgdorderparams.emplace_back(parvalue);
  }
 
  // Debug output
  std::stringstream msg;
  msg << "Finished importing background TableWorkspace. "
      << "Background Order = " << bkgdorderparams.size() << ": ";
  for (size_t iod = 0; iod < bkgdorderparams.size(); ++iod) {
    msg << bkgdparnames[iod] << " = " << bkgdorderparams[iod] << "; ";
  }
  g_log.information(msg.str());
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::exportBraggPeakParameterToTable() {
  // Create peaks workspace
  DataObjects::TableWorkspace_sptr peakWS = DataObjects::TableWorkspace_sptr(new DataObjects::TableWorkspace);
 
  // Add columns to table/peak workspace
  peakWS->addColumn("int", "H");
  peakWS->addColumn("int", "K");
  peakWS->addColumn("int", "L");
  peakWS->addColumn("double", "Height");
  peakWS->addColumn("double", "TOF_h");
  peakWS->addColumn("double", "Alpha");
  peakWS->addColumn("double", "Beta");
  peakWS->addColumn("double", "Sigma2");
  peakWS->addColumn("double", "Gamma");
  peakWS->addColumn("double", "FWHM");
  peakWS->addColumn("int", "PeakGroup");
  peakWS->addColumn("double", "Chi^2");
  peakWS->addColumn("str", "FitStatus");
 
  // Add each peak in LeBailFunction to peak/table workspace
  for (size_t ipk = 0; ipk < m_lebailFunction->getNumberOfPeaks(); ++ipk) {
 
    // Miller index and peak parameters
    IPowderDiffPeakFunction_sptr peak = m_lebailFunction->getPeak(ipk);
 
    int h, k, l;
    peak->getMillerIndex(h, k, l);
    double tof_h = peak->centre();
    double height = peak->height();
    double alpha = peak->getPeakParameter("Alpha");
    double beta = peak->getPeakParameter("Beta");
    double sigma2 = peak->getPeakParameter("Sigma2");
    double gamma = peak->getPeakParameter("Gamma");
    double fwhm = peak->fwhm();
 
    // New row
    API::TableRow newrow = peakWS->appendRow();
    newrow << h << k << l << height << tof_h << alpha << beta << sigma2 << gamma << fwhm << -1 << -1.0 << "N/A";
 
    if (tof_h < 0) {
      stringstream errss;
      errss << "Peak (" << h << ", " << k << ", " << l << "): TOF_h (=" << tof_h << ") is NEGATIVE!";
      g_log.error(errss.str());
    }
  }
 
  // Set property
  this->setProperty("OutputPeaksWorkspace", peakWS);
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::exportInstrumentParameterToTable(const std::map<std::string, Parameter> &parammap) {
  // 1. Create table workspace
  DataObjects::TableWorkspace *tablews;
 
  tablews = new DataObjects::TableWorkspace();
  DataObjects::TableWorkspace_sptr parameterws(tablews);
 
  tablews->addColumn("str", "Name");
  tablews->addColumn("double", "Value");
  tablews->addColumn("str", "FitOrTie");
  tablews->addColumn("double", "chi^2");
  tablews->addColumn("double", "Min");
  tablews->addColumn("double", "Max");
  tablews->addColumn("double", "StepSize");
  tablews->addColumn("double", "StartValue");
  tablews->addColumn("double", "Diff");
 
  // 2. Add profile parameter value
  std::map<std::string, Parameter>::const_iterator paramiter;
  std::map<std::string, double>::iterator opiter;
  for (paramiter = parammap.begin(); paramiter != parammap.end(); ++paramiter) {
    std::string parname = paramiter->first;
    if (parname != "Height") {
      // Export every parameter except "Height"
 
      // a) current value
      double parvalue = paramiter->second.curvalue;
 
      // b) fit or tie?
      char fitortie = 't';
      if (paramiter->second.fit) {
        fitortie = 'f';
      }
      std::stringstream ss;
      ss << fitortie;
      std::string fit_tie = ss.str();
 
      // c) starting value
      opiter = m_origFuncParameters.find(parname);
      double origparvalue = -1.0E100;
      if (opiter != m_origFuncParameters.end()) {
        origparvalue = opiter->second;
      }
      double diff = origparvalue - parvalue;
 
      // d. (standard) error
      double paramerror = paramiter->second.fiterror;
 
      // e. create the row
      double min = paramiter->second.minvalue;
      double max = paramiter->second.maxvalue;
      double step = paramiter->second.stepsize;
 
      API::TableRow newparam = tablews->appendRow();
      newparam << parname << parvalue << fit_tie << paramerror << min << max << step << origparvalue << diff;
    } // ENDIF
  }
 
  // 3. Add chi^2
  if (m_fitMode == FIT && !m_inputParameterPhysical) {
    // Impossible mode
    throw runtime_error("Impossible to have this situation happen.  Flag 541.");
  } else if (!m_inputParameterPhysical) {
    // Input instrument profile parameters are not physical
    m_lebailCalChi2 = DBL_MAX;
    m_lebailFitChi2 = DBL_MAX;
  }
 
  if (m_fitMode == FIT) {
    // Do this for FIT mode only
    API::TableRow fitchi2row = tablews->appendRow();
    fitchi2row << "FitChi2" << m_lebailFitChi2 << "t" << 0.0 << 0.0 << 0.0 << 0.0 << 0.0 << 0.0;
    API::TableRow chi2row = tablews->appendRow();
    chi2row << "Chi2" << m_lebailCalChi2 << "t" << 0.0 << 0.0 << 0.0 << 0.0 << 0.0 << 0.0;
  }
 
  // 4. Add to output peroperty
  setProperty("OutputParameterWorkspace", parameterws);
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::createOutputDataWorkspace() {
  // 1. Determine number of output spectra
  size_t nspec = 9;
 
  if (m_fitMode == CALCULATION) {
    bool plotindpeak = this->getProperty("PlotIndividualPeaks");
    if (plotindpeak) {
      nspec += m_lebailFunction->getNumberOfPeaks();
      g_log.information() << "Number of peaks to add to output data = " << m_lebailFunction->getNumberOfPeaks()
                          << ".\n";
    }
  }
 
  // 2. Create workspace2D and set the data to spectrum 0 (common among all)
  size_t nbinx = m_dataWS->x(m_wsIndex).size();
  size_t nbiny = m_dataWS->y(m_wsIndex).size();
  m_outputWS = std::dynamic_pointer_cast<DataObjects::Workspace2D>(
      API::WorkspaceFactory::Instance().create("Workspace2D", nspec, nbinx, nbiny));
 
  // 3. Add values
  //    All X.
  for (size_t j = 0; j < m_outputWS->getNumberHistograms(); ++j)
    m_outputWS->setSharedX(j, m_dataWS->sharedX(m_wsIndex));
 
  //    Observation
  m_outputWS->setSharedY(OBSDATAINDEX, m_dataWS->sharedY(m_wsIndex));
  m_outputWS->setSharedE(OBSDATAINDEX, m_dataWS->sharedE(m_wsIndex));
 
  // 4. Set axis
  m_outputWS->getAxis(0)->setUnit("TOF");
 
  auto tAxis = std::make_unique<API::TextAxis>(nspec);
  tAxis->setLabel(0, "Data");
  tAxis->setLabel(1, "Calc");
  tAxis->setLabel(2, "Diff");
  tAxis->setLabel(3, "CalcNoBkgd");
  tAxis->setLabel(4, "OutBkgd");
  tAxis->setLabel(5, "InpCalc");
  tAxis->setLabel(6, "InBkgd");
  tAxis->setLabel(7, "DataNoBkgd");
  tAxis->setLabel(8, "SmoothedBkgd");
 
  if (m_fitMode == CALCULATION) {
    // Set the single peak labels
    for (size_t i = 0; i < (nspec - 9); ++i) {
      std::stringstream ss;
      ss << "Peak_" << i;
      tAxis->setLabel(9 + i, ss.str());
    }
  }
 
  m_outputWS->replaceAxis(1, std::move(tAxis));
}
 
// ====================================== Random Walk Suite
// ====================================
//----------------------------------------------------------------------------------------------
void LeBailFit::execRandomWalkMinimizer(size_t maxcycles, map<string, Parameter> &parammap) {
  // Set up random walk parameters
  const auto &vecX = m_dataWS->x(m_wsIndex);
  const auto &vecInY = m_dataWS->y(m_wsIndex);
 
  const auto &domain = m_dataWS->x(m_wsIndex).rawData();
  std::vector<double> vecCalPurePeaks(domain.size(), 0.0);
 
  //    Strategy and map
  TableWorkspace_sptr mctablews = getProperty("MCSetupWorkspace");
  if (mctablews) {
    setupRandomWalkStrategyFromTable(mctablews);
  } else {
    setupBuiltInRandomWalkStrategy();
  }
  //   Walking style/algorithm
  bool usedrunkenwalk = getProperty("DrunkenWalk");
  if (usedrunkenwalk)
    m_walkStyle = DRUNKENWALK;
  else
    m_walkStyle = RANDOMWALK;
  //    Annealing temperature
  m_Temperature = getProperty("AnnealingTemperature");
  if (m_Temperature < 0)
    m_Temperature = fabs(m_Temperature);
  m_useAnnealing = getProperty("UseAnnealing");
  //    Random seed
  int randomseed = getProperty("RandomSeed");
 
  //    R-factors used for MC procedure
  Rfactor startR(-DBL_MAX, -DBL_MAX);
 
  // Process background to make a pure peak spectrum in output workspace
  HistogramY vecBkgd = m_lebailFunction->function(vecX.rawData(), false, true);
  m_outputWS->mutableY(INPUTBKGDINDEX) = vecBkgd;
  m_outputWS->mutableY(INPUTPUREPEAKINDEX) = vecInY - vecBkgd;
 
  // Calcualte starting Rwp and etc
  const auto &vecPurePeak = m_outputWS->y(INPUTPUREPEAKINDEX);
 
  map<string, double> pardblmap = convertToDoubleMap(parammap);
  m_lebailFunction->setProfileParameterValues(pardblmap);
  bool startvaluevalid = calculateDiffractionPattern(vecX, vecPurePeak, false, false, vecBkgd, vecCalPurePeaks, startR);
  if (!startvaluevalid) {
    // Throw exception if starting values are not valid for all
    throw runtime_error("Starting value of instrument profile parameters can "
                        "generate peaks with"
                        " unphyiscal parameters values.");
  }
 
  doMarkovChain(parammap, vecX, vecPurePeak, vecBkgd.rawData(), maxcycles, startR, randomseed);
 
  // 5. Sum up: retrieve the best result from class variable: m_bestParameters
  Rfactor finalR(-DBL_MAX, -DBL_MAX);
  map<string, double> bestparams = convertToDoubleMap(m_bestParameters);
  m_lebailFunction->setProfileParameterValues(bestparams);
  calculateDiffractionPattern(vecX, vecPurePeak, false, false, vecBkgd, vecCalPurePeaks, finalR);
 
  auto &vecCalY = m_outputWS->mutableY(CALDATAINDEX);
  auto &vecDiff = m_outputWS->mutableY(DATADIFFINDEX);
  auto &vecCalPurePeak = m_outputWS->mutableY(CALPUREPEAKINDEX);
  auto &vecCalBkgd = m_outputWS->mutableY(CALBKGDINDEX);
  // Calculated (refined) data
  vecCalY = vecCalPurePeaks;
  vecCalY += vecBkgd;
  // Diff
  vecDiff = vecInY - vecCalY;
  // Calcualted without background (pure peaks)
  vecCalPurePeak = vecCalPurePeaks;
  // Different between calculated peaks and raw data
  vecCalBkgd = vecInY - vecCalPurePeaks;
 
  // c) Apply the best parameters to param
  applyParameterValues(m_bestParameters, parammap);
  Parameter par_rwp;
  par_rwp.name = "Rwp";
  par_rwp.curvalue = m_bestRwp;
  parammap["Rwp"] = par_rwp;
} // Main Exec MC
 
//----------------------------------------------------------------------------------------------
void LeBailFit::doMarkovChain(const map<string, Parameter> &parammap, const Mantid::HistogramData::HistogramX &vecX,
                              const Mantid::HistogramData::HistogramY &vecPurePeak, const vector<double> &vecBkgd,
                              size_t maxcycles, const Rfactor &startR, int randomseed) {
 
  // Rfactors in loop
  Rfactor currR(-DBL_MAX, -DBL_MAX), newR(-DBL_MAX, -DBL_MAX);
  // parameter map for newly proposed values
  map<string, Parameter> mapCurrParameter = parammap;
  map<string, Parameter> newparammap = mapCurrParameter;
  // Output vector from
  std::vector<double> veccalpurepeaks(vecX.size(), 0.0);
 
  // Set starting parameters
  currR = startR;
  m_bestRwp = currR.Rwp + EPSILON;
  m_bestRp = currR.Rp + EPSILON;
  bookKeepBestMCResult(mapCurrParameter, vecBkgd, currR, 0);
 
  g_log.notice() << "[MC-Start] Random-walk Starting Rwp = " << currR.Rwp << ", Rp = " << currR.Rp << "\n";
 
  // Random walk loops
  // generate some MC trace structure
  vector<double> vecIndex(maxcycles + 1);
  vector<Rfactor> vecR(maxcycles + 1);
  size_t numinvalidmoves = 0;
  size_t numacceptance = 0;
  bool prevcyclebetterR = true;
 
  // Annealing record
  int numRecentAcceptance = 0;
  int numRecentSteps = 0;
  int numConsecutiveInvalid = 0;
 
  // FIXME - It seems that annealing cannot work together with reset invalid if
  // in the region of invalid.
  //         Need to write down the procedure to think it over.
  int numMaxConsecutiveInvalid = 5;
  int m_numStepsCheckTemperature = 10;
 
  // Loop start
  srand(randomseed);
 
  for (size_t icycle = 1; icycle <= maxcycles; ++icycle) {
    // Refine parameters (for all parameters in turn) to data with background
    // removed
    for (const auto &MCGroup : m_MCGroups) {
      // Propose new value for ONE AND ONLY ONE Monte Carlo parameter group
      /*
      int igroup = giter->first; // group id
      g_log.debug() << "BigTrouble: Group " << igroup << "\n";
      */
      bool hasnewvalues = proposeNewValues(MCGroup.second, currR, mapCurrParameter, newparammap, prevcyclebetterR);
 
      if (!hasnewvalues) {
        // No parameter to have value updated in this MC group.  Skip evaluation
        // of LeBail function.
        continue;
      }
 
      // Evaluate LeBail function
      map<string, double> newpardblmap = convertToDoubleMap(newparammap);
      m_lebailFunction->setProfileParameterValues(newpardblmap);
      bool validparams = calculateDiffractionPattern(vecX, vecPurePeak, false, false, vecBkgd, veccalpurepeaks, newR);
      g_log.debug() << "[Calculation] Rwp = " << newR.Rwp << ", Rp = " << newR.Rp << ".\n";
 
      // Determine whether to take the change or not
      bool acceptchange;
      if (!validparams) {
        ++numinvalidmoves;
        acceptchange = false;
        prevcyclebetterR = false;
        ++numConsecutiveInvalid;
      } else {
        acceptchange = acceptOrDeny(currR, newR);
 
        prevcyclebetterR = newR.Rwp < currR.Rwp;
      }
 
      g_log.debug() << "[DBx317] Step " << icycle << ": New Rwp = " << setprecision(10) << newR.Rwp
                    << ", Rp = " << setprecision(5) << newR.Rp << "; Accepted = " << acceptchange
                    << "; Proposed parameters valid =" << validparams << "\n";
 
      // Apply change and book keeping
      if (acceptchange) {
        // Apply the change to current
        applyParameterValues(newparammap, mapCurrParameter);
        currR = newR;
 
        // All tim ebest
        // FIXME - [RPRWP] Use Rp now
        if (currR.Rwp < m_bestRwp) {
          // Book keep the best
          bookKeepBestMCResult(mapCurrParameter, vecBkgd, currR, icycle);
        }
        // FIXME - After determining to use Rp or Rwp, this should be got into
        // bookKeepBestMCResult
        if (currR.Rp < m_bestRp)
          m_bestRp = currR.Rp;
        if (currR.Rwp < m_bestRwp)
          m_bestRwp = currR.Rwp;
 
        // Statistic
        ++numacceptance;
        ++numRecentAcceptance;
      }
      ++numRecentSteps;
 
      // Annealing or start over
      if (numConsecutiveInvalid >= numMaxConsecutiveInvalid) {
        // Exceeds the limit of consecutive invalid proposed new values.  Start
        // over
        mapCurrParameter = m_bestParameters;
 
        // Reset counters
        numConsecutiveInvalid = 0;
        numRecentAcceptance = 0;
        numRecentSteps = 0;
 
      } else if (m_useAnnealing) {
        // Annealing: change temperature to tune the acceptance rate
        // FIXME : Here are some magic numbers
        if (numRecentSteps == m_numStepsCheckTemperature) {
          // i. Change temperature
          if (numRecentAcceptance <= 2) {
            m_Temperature *= 2.0;
          } else if (numRecentAcceptance >= 8) {
            m_Temperature /= 2.0;
          }
          // ii  Reset counters
          numRecentAcceptance = 0;
          numRecentSteps = 0;
        }
      }
 
      // e) Debug output?
 
    } // END FOR Group
 
    // v. Improve the background
    // FIXME - [RPRWP] Use Rp now
    if (currR.Rwp < m_bestRwp) {
      // FIXME - Fit background is disabled at this moment
      // fitBackground(m_wsIndex, domainB, valuesB, background);
    }
 
    // vi. Record some information
    vecIndex[icycle] = static_cast<double>(icycle);
    if (currR.Rwp < 1.0E5)
      vecR[icycle] = currR;
    else {
      Rfactor dum(-1, -1);
      vecR[icycle] = dum;
    }
 
    // vii. progress
    if (icycle % 10 == 0)
      progress(double(icycle) / double(maxcycles));
 
  } // ENDFOR MC Cycles
 
  progress(1.0);
 
  // a) Summary output
  g_log.notice() << "[SUMMARY] Random-walk R-factor:  Best step @ " << m_bestMCStep
                 << ", Acceptance ratio = " << double(numacceptance) / double(maxcycles * m_numMCGroups) << ".\n"
                 << "Rwp: Starting = " << startR.Rwp << ", Best = " << m_bestRwp << ", Ending = " << currR.Rwp << "\n"
                 << "Rp : Starting = " << startR.Rp << ", Best = " << m_bestRp << ", Ending = " << currR.Rp << "\n";
 
  map<string, Parameter>::iterator mapiter;
  for (mapiter = mapCurrParameter.begin(); mapiter != mapCurrParameter.end(); ++mapiter) {
    const Parameter &param = mapiter->second;
    if (param.fit) {
      g_log.notice() << setw(10) << param.name << "\t: Average Stepsize = " << setw(10) << setprecision(5)
                     << param.sumstepsize / double(maxcycles) << ", Max Step Size = " << setw(10) << setprecision(5)
                     << param.maxabsstepsize << ", Number of Positive Move = " << setw(4) << param.numpositivemove
                     << ", Number of Negative Move = " << setw(4) << param.numnegativemove
                     << ", Number of No Move = " << setw(4) << param.numnomove << ", Minimum tried value = " << setw(4)
                     << param.minrecordvalue << ", Maximum tried value = " << setw(4) << param.maxrecordvalue << "\n";
    }
  }
  g_log.notice() << "Number of invalid proposed moves = " << numinvalidmoves << "\n";
 
  // b) Export trace of R
  stringstream filenamess;
  filenamess << "r_trace_" << vecR.size() << ".dat";
  writeRfactorsToFile(vecIndex, vecR, filenamess.str());
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::setupRandomWalkStrategyFromTable(const DataObjects::TableWorkspace_sptr &tablews) {
  g_log.information("Set up random walk strategy from table.");
 
  // Scan the table
  size_t numrows = tablews->rowCount();
  for (size_t i = 0; i < numrows; ++i) {
    // 1. Get a row and pass out
    TableRow temprow = tablews->getRow(i);
    string parname;
    double a0, a1;
    int nonnegative, group;
 
    temprow >> parname >> a0 >> a1 >> nonnegative >> group;
 
    // 2. MC group
    map<int, vector<string>>::iterator giter;
    giter = m_MCGroups.find(group);
    if (giter != m_MCGroups.end()) {
      giter->second.emplace_back(parname);
    } else {
      // First instance in the new group.
      m_MCGroups.emplace(group, std::initializer_list<std::string>{parname});
    }
 
    // 3. Set up MC parameters, A0, A1, non-negative
    auto piter = m_funcParameters.find(parname);
    if (piter != m_funcParameters.end()) {
      piter->second.mcA0 = a0;
      piter->second.mcA1 = a1;
      piter->second.nonnegative = (nonnegative != 0);
    }
  }
 
  m_numMCGroups = m_MCGroups.size();
 
  // 4. Reset
  map<string, Parameter>::iterator mapiter;
  for (mapiter = m_funcParameters.begin(); mapiter != m_funcParameters.end(); ++mapiter) {
    mapiter->second.movedirection = 1;
    mapiter->second.sumstepsize = 0.0;
    mapiter->second.numpositivemove = 0;
    mapiter->second.numnegativemove = 0;
    mapiter->second.numnomove = 0;
    mapiter->second.maxabsstepsize = -0.0;
  }
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::setupBuiltInRandomWalkStrategy() {
  g_log.information("Set up random walk strategy from build-in. ");
 
  stringstream dboutss;
  dboutss << "Monte Carlo minimizer refines: ";
 
  // 1. Monte Carlo groups
  // a. Instrument gemetry
  vector<string> geomparams;
  addParameterToMCMinimize(geomparams, "Dtt1");
  addParameterToMCMinimize(geomparams, "Dtt1t");
  addParameterToMCMinimize(geomparams, "Dtt2t");
  addParameterToMCMinimize(geomparams, "Zero");
  addParameterToMCMinimize(geomparams, "Zerot");
  addParameterToMCMinimize(geomparams, "Width");
  addParameterToMCMinimize(geomparams, "Tcross");
  m_MCGroups.emplace(0, geomparams);
 
  dboutss << "Geometry parameters: ";
  for (const auto &geomparam : geomparams)
    dboutss << geomparam << "\t\t";
  dboutss << "\n";
 
  // b. Alphas
  vector<string> alphs;
  addParameterToMCMinimize(alphs, "Alph0");
  addParameterToMCMinimize(alphs, "Alph1");
  addParameterToMCMinimize(alphs, "Alph0t");
  addParameterToMCMinimize(alphs, "Alph1t");
  m_MCGroups.emplace(1, alphs);
 
  dboutss << "Alpha parameters";
  for (const auto &alph : alphs)
    dboutss << alph << "\t\t";
  dboutss << "\n";
 
  // c. Beta
  vector<string> betas;
  addParameterToMCMinimize(betas, "Beta0");
  addParameterToMCMinimize(betas, "Beta1");
  addParameterToMCMinimize(betas, "Beta0t");
  addParameterToMCMinimize(betas, "Beta1t");
  m_MCGroups.emplace(2, betas);
 
  dboutss << "Beta parameters";
  for (const auto &beta : betas)
    dboutss << beta << "\t\t";
  dboutss << "\n";
 
  // d. Sig
  vector<string> sigs;
  addParameterToMCMinimize(sigs, "Sig0");
  addParameterToMCMinimize(sigs, "Sig1");
  addParameterToMCMinimize(sigs, "Sig2");
  m_MCGroups.emplace(3, sigs);
 
  dboutss << "Sig parameters";
  for (const auto &sig : sigs)
    dboutss << sig << "\t\t";
  dboutss << "\n";
 
  g_log.notice(dboutss.str());
 
  m_numMCGroups = m_MCGroups.size();
 
  // 2. Dictionary for each parameter for non-negative, mcX0, mcX1
  // a) Sig0, Sig1, Sig2
  for (const auto &parname : sigs) {
    m_funcParameters[parname].mcA0 = 2.0;
    m_funcParameters[parname].mcA1 = 1.0;
    m_funcParameters[parname].nonnegative = true;
  }
 
  // b) Alpha
  for (const auto &parname : alphs) {
    m_funcParameters[parname].mcA1 = 1.0;
    m_funcParameters[parname].nonnegative = false;
  }
  m_funcParameters["Alph0"].mcA0 = 0.05;
  m_funcParameters["Alph1"].mcA0 = 0.02;
  m_funcParameters["Alph0t"].mcA0 = 0.1;
  m_funcParameters["Alph1t"].mcA0 = 0.05;
 
  // c) Beta
  for (const auto &parname : betas) {
    m_funcParameters[parname].mcA1 = 1.0;
    m_funcParameters[parname].nonnegative = false;
  }
  m_funcParameters["Beta0"].mcA0 = 0.5;
  m_funcParameters["Beta1"].mcA0 = 0.05;
  m_funcParameters["Beta0t"].mcA0 = 0.5;
  m_funcParameters["Beta1t"].mcA0 = 0.05;
 
  // d) Geometry might be more complicated
  m_funcParameters["Width"].mcA0 = 0.0;
  m_funcParameters["Width"].mcA1 = 0.1;
  m_funcParameters["Width"].nonnegative = true;
 
  m_funcParameters["Tcross"].mcA0 = 0.0;
  m_funcParameters["Tcross"].mcA1 = 1.0;
  m_funcParameters["Tcross"].nonnegative = true;
 
  m_funcParameters["Zero"].mcA0 = 5.0; // 5.0
  m_funcParameters["Zero"].mcA1 = 0.0;
  m_funcParameters["Zero"].nonnegative = false;
 
  m_funcParameters["Zerot"].mcA0 = 5.0; // 5.0
  m_funcParameters["Zerot"].mcA1 = 0.0;
  m_funcParameters["Zerot"].nonnegative = false;
 
  m_funcParameters["Dtt1"].mcA0 = 5.0; // 20.0
  m_funcParameters["Dtt1"].mcA1 = 0.0;
  m_funcParameters["Dtt1"].nonnegative = true;
 
  m_funcParameters["Dtt1t"].mcA0 = 5.0; // 20.0
  m_funcParameters["Dtt1t"].mcA1 = 0.0;
  m_funcParameters["Dtt1t"].nonnegative = true;
 
  m_funcParameters["Dtt2t"].mcA0 = 0.1;
  m_funcParameters["Dtt2t"].mcA1 = 1.0;
  m_funcParameters["Dtt2t"].nonnegative = false;
 
  // 4. Reset
  map<string, Parameter>::iterator mapiter;
  for (mapiter = m_funcParameters.begin(); mapiter != m_funcParameters.end(); ++mapiter) {
    mapiter->second.movedirection = 1;
    mapiter->second.sumstepsize = 0.0;
    mapiter->second.numpositivemove = 0;
    mapiter->second.numnegativemove = 0;
    mapiter->second.numnomove = 0;
    mapiter->second.maxabsstepsize = -0.0;
  }
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::addParameterToMCMinimize(vector<string> &parnamesforMC, const string &parname) {
  map<string, Parameter>::iterator pariter;
  pariter = m_funcParameters.find(parname);
  if (pariter == m_funcParameters.end()) {
    stringstream errss;
    errss << "Parameter " << parname << " does not exisit Le Bail function parameters. ";
    g_log.error(errss.str());
    throw runtime_error(errss.str());
  }
 
  if (pariter->second.fit)
    parnamesforMC.emplace_back(parname);
}
 
//----------------------------------------------------------------------------------------------
bool LeBailFit::calculateDiffractionPattern(const HistogramX &vecX, const HistogramY &vecY, bool inputraw,
                                            bool outputwithbkgd, const HistogramY &vecBkgd, std::vector<double> &values,
                                            Rfactor &rfactor) {
  HistogramY veccalbkgd(vecX.size());
  bool veccalbkgdIsEmpty = true;
 
  // Examine whether all peaks are valid
  double maxfwhm = vecX.back() - vecX.front();
  bool peaksvalid = m_lebailFunction->isParameterValid(maxfwhm);
 
  // If not valid, then return error message
  if (!peaksvalid) {
    g_log.information() << "Proposed new instrument profile values cause peak(s) to have "
                        << "unphysical parameter values.\n";
    rfactor = badR;
    return false;
  }
 
  // Calculate peaks' height
  if (inputraw) {
    // Remove background
    vector<double> vecPureY(vecY.size(), 0.);
    if (vecBkgd.size() == vecY.size()) {
      // Use input background
      g_log.information() << "Calculate diffraction pattern from raw and input "
                             "background vector. "
                          << ".\n";
      ::transform(vecY.begin(), vecY.end(), vecBkgd.begin(), vecPureY.begin(), ::minus<double>());
    } else {
      // Calculate background
      g_log.information() << "Calculate diffraction pattern from input data "
                             "and newly calculated background. "
                          << ".\n";
      veccalbkgd = m_lebailFunction->function(vecX.rawData(), false, true);
      ::transform(vecY.begin(), vecY.end(), veccalbkgd.begin(), vecPureY.begin(), ::minus<double>());
      veccalbkgdIsEmpty = false;
    }
 
    // Calculate peak intensity
    peaksvalid = m_lebailFunction->calculatePeaksIntensities(vecX.rawData(), vecPureY, values);
  } // [input is raw]
  else {
    // Calculate peaks intensities
    g_log.debug() << "Calculate diffraction pattern from input data with "
                     "background removed. "
                  << ".\n";
    peaksvalid = m_lebailFunction->calculatePeaksIntensities(vecX.rawData(), vecY.rawData(), values);
  }
 
  // Calculate Le Bail function
  if (values.size() != vecY.size()) {
    g_log.error() << "Input/output vector 'values' has a wrong size = " << values.size() << ".  Resize it to "
                  << vecY.size() << ".\n";
    throw runtime_error("Impossible...");
  }
 
  // Integrated with background if required
  if (outputwithbkgd) {
    if (vecBkgd.size() == vecY.size()) {
      ::transform(values.begin(), values.end(), vecBkgd.begin(), values.begin(), ::plus<double>());
    } else {
      if (veccalbkgdIsEmpty)
        throw runtime_error("Programming logic error.");
      ::transform(values.begin(), values.end(), veccalbkgd.begin(), values.begin(), ::plus<double>());
    }
    rfactor = getRFactor(m_dataWS->y(m_wsIndex).rawData(), values, m_dataWS->e(m_wsIndex).rawData());
  } else {
    vector<double> caldata(values.size(), 0.0);
    if (vecBkgd.size() == vecY.size()) {
      // Use input background vector
      std::transform(values.begin(), values.end(), vecBkgd.begin(), caldata.begin(), std::plus<double>());
    } else {
      // Re-calculate background
      if (veccalbkgdIsEmpty)
        throw runtime_error("Programming logic error (2). ");
      std::transform(values.begin(), values.end(), veccalbkgd.begin(), caldata.begin(), std::plus<double>());
    }
    rfactor = getRFactor(m_dataWS->y(m_wsIndex).rawData(), caldata, m_dataWS->e(m_wsIndex).rawData());
  }
 
  if (!peaksvalid) {
    g_log.information("LeBailFit: Some peaks have unphysical peak value. ");
    rfactor = badR;
    return false;
  }
 
  return true;
}
 
//----------------------------------------------------------------------------------------------
bool LeBailFit::proposeNewValues(const vector<string> &mcgroup, Rfactor r, map<string, Parameter> &curparammap,
                                 map<string, Parameter> &newparammap, bool prevBetterRwp) {
  // TODO: Study the possibility to merge curparammap and newparammap
 
  // Initialize some flags
  bool anyparamtorefine = false;
 
  // Find out parameters to refine in this step/MC group
  g_log.debug() << "Parameter Number In Group = " << mcgroup.size() << "\n";
  for (const auto &paramname : mcgroup) {
    // Find out the i-th parameter to be refined or not
    auto mapiter = curparammap.find(paramname);
    if (mapiter == curparammap.end()) {
      stringstream errmsg;
      errmsg << "Parameter to update (" << paramname << ") is not in the pool of parameters to get updated. "
             << ".\n"
             << "Number of parameters to update in this group = " << curparammap.size() << ".  They are ";
      for (mapiter = curparammap.begin(); mapiter != curparammap.end(); ++mapiter) {
        errmsg << mapiter->first << ", ";
      }
      g_log.error(errmsg.str());
      throw runtime_error(errmsg.str());
    }
    Parameter &param = mapiter->second;
 
    if (param.fit)
      anyparamtorefine = true;
    else
      continue;
 
    // Pick a random number between -1 and 1 and calculate step size
    double randomnumber = 2 * static_cast<double>(rand()) / static_cast<double>(RAND_MAX) - 1.0;
 
    // FIXME - [RPRWP] Try using Rp this time.
    double weight = r.Rwp;
    if (weight > 1.0)
      weight = 1.0;
    double stepsize = m_dampingFactor * weight * (param.curvalue * param.mcA1 + param.mcA0) * randomnumber;
    if (fabs(stepsize) > 0.5 * (param.maxvalue - param.minvalue))
      stepsize = fabs(stepsize) / stepsize * 0.5 * (param.maxvalue - param.minvalue);
 
    // Direction of new value: drunk walk or random walk
    double newvalue;
    if (m_walkStyle == RANDOMWALK) {
      // Random walk.  No preference on direction
      newvalue = param.curvalue + stepsize;
    } else if (m_walkStyle == DRUNKENWALK) {
      // Drunken walk.  Prefer to previous successful move direction
      int prevRightDirection;
      if (prevBetterRwp)
        prevRightDirection = 1;
      else
        prevRightDirection = -1;
 
      double randirint = static_cast<double>(rand()) / static_cast<double>(RAND_MAX);
      g_log.debug() << "[TestRandom] random = " << randirint << "\n";
 
      // FIXME Here are some MAGIC numbers
      if (randirint < 0.1) {
        // Negative direction to previous direction
        stepsize = -1.0 * fabs(stepsize) * static_cast<double>(param.movedirection * prevRightDirection);
      } else if (randirint < 0.4) {
        // No preferance and thus do nothing
      } else {
        // Positive direction to previous direction
        stepsize = fabs(stepsize) * static_cast<double>(param.movedirection * prevRightDirection);
      }
 
      newvalue = param.curvalue + stepsize;
    } else {
      throw runtime_error("Unrecoganized walk style. ");
    }
 
    // Restriction on the new value: non-negative
    if (param.nonnegative && newvalue < 0) {
      // If not allowed to be negative
      newvalue = fabs(newvalue);
    }
 
    // Restriction on the new value: keep the new value in the boundary
    if (newvalue < param.minvalue) {
      int toss = rand() % 2;
      double direction = -1.0;
      newvalue = limitProposedValueInBound(param, newvalue, direction, toss);
    } else if (newvalue > param.maxvalue) {
      int toss = rand() % 2;
      double direction = 1.0;
      newvalue = limitProposedValueInBound(param, newvalue, direction, toss);
    }
 
    // Apply to new parameter map
    auto newmiter = newparammap.find(paramname);
    if (newmiter == newparammap.end())
      throw runtime_error("New parameter map does not contain parameter that is updated.");
    newmiter->second.curvalue = newvalue;
    g_log.debug() << "[ProposeNewValue] " << paramname << " --> " << newvalue << "; random number = " << randomnumber
                  << "\n";
 
    // g) record some trace
    Parameter &p = param;
    if (stepsize > 0) {
      p.movedirection = 1;
      ++p.numpositivemove;
    } else if (stepsize < 0) {
      p.movedirection = -1;
      ++p.numnegativemove;
    } else {
      p.movedirection = -1;
      ++p.numnomove;
    }
    p.sumstepsize += fabs(stepsize);
    if (fabs(stepsize) > p.maxabsstepsize)
      p.maxabsstepsize = fabs(stepsize);
 
    if (newvalue > p.maxrecordvalue)
      p.maxrecordvalue = newvalue;
    else if (newvalue < p.minrecordvalue)
      p.minrecordvalue = newvalue;
 
    g_log.debug() << "[DBx257] " << paramname << "\t"
                  << "Proposed value = " << setw(15) << newvalue << " (orig = " << param.curvalue
                  << ",  step = " << stepsize << "), totRwp = " << r.Rwp << "\n";
  } // ENDFOR (i): Each parameter in this MC group/step
 
  return anyparamtorefine;
}
 
//-----------------------------------------------------------------------------------------------
double LeBailFit::limitProposedValueInBound(const Parameter &param, double newvalue, double direction, int choice) {
  if (choice == 0) {
    // Half distance
    if (direction > 0) {
      newvalue = (param.maxvalue - param.curvalue) * 0.5 + param.curvalue;
    } else {
      newvalue = param.minvalue + 0.5 * (param.curvalue - param.minvalue);
    }
  } else {
    double deltaX = param.maxvalue - param.minvalue;
 
    if (deltaX < NOBOUNDARYLIMIT) {
      choice = 1; // periodic
    } else {
      choice = 2; // reflection
    }
 
    if (choice == 1) {
      // Periodic boundary
      if (direction > 0) {
        // newvalue = param.minvalue + (newvalue - param.maxvalue) % deltaX;
        double dval = (newvalue - param.maxvalue) / deltaX;
        newvalue = param.minvalue + deltaX * (dval - floor(dval));
      } else {
        // newvalue = param.maxvalue - (param.minvalue - newvalue) % deltaX;
        double dval = (param.minvalue - newvalue) / deltaX;
        newvalue = param.maxvalue - deltaX * (dval - floor(dval));
      }
    } else {
      // Reflective boundary
      if (direction > 0) {
        newvalue = param.maxvalue - (newvalue - param.maxvalue);
      } else {
        newvalue = param.minvalue + (param.maxvalue - newvalue);
      }
    }
  }
 
  return newvalue;
}
 
//-----------------------------------------------------------------------------------------------
bool LeBailFit::acceptOrDeny(Rfactor currR, Rfactor newR) {
  bool accept;
 
  // FIXME - [RPRWP] Using Rp for peak fitting
  double new_goodness = newR.Rwp;
  double cur_goodness = currR.Rwp;
 
  if (new_goodness < cur_goodness) {
    // Lower Rwp.  Take the change
    accept = true;
  } else if (new_goodness > 1.0 - 1.0E-9) {
    // Too high
    g_log.debug() << "Goodness > " << 1.0 - 1.0E-9 << ".  Reject!"
                  << ".\n";
    accept = false;
  } else {
    // Higher Rwp/Rp. Take a chance to accept
    double dice = static_cast<double>(rand()) / static_cast<double>(RAND_MAX);
    g_log.debug() << "[TestRandom] dice " << dice << "\n";
    double bar = exp(-(new_goodness - cur_goodness) / (cur_goodness * m_Temperature));
 
    accept = dice < bar;
  }
 
  return accept;
}
 
//----------------------------------------------------------------------------------------------
void LeBailFit::bookKeepBestMCResult(const map<string, Parameter> &parammap, const vector<double> &bkgddata,
                                     Rfactor rfactor, size_t istep) {
  // TODO : [RPRWP] Here is a metric of goodness of it.
  double goodness = rfactor.Rwp;
  bool better = goodness < m_bestRwp;
 
  if (better) {
    // In case obtain the best solution so far
 
    // a) Record goodness and step
    m_bestRwp = rfactor.Rwp;
    m_bestRp = rfactor.Rp;
    m_bestMCStep = istep;
 
    // b) Record parameters
    if (m_bestParameters.empty()) {
      // If not be initialized, initialize it!
      m_bestParameters = parammap;
    } else {
      // in case initialized, copy the value over
      applyParameterValues(parammap, m_bestParameters);
    }
 
    // c) Background
    m_bestBackgroundData = bkgddata;
  } else {
    // In code calling this function, it should be better always.
    g_log.warning("[Book keep best MC result] Shouldn't be here as it is found "
                  "that it is not the best solution ");
  }
}
 
//------------------------------------------------------------------------------------------------
void LeBailFit::applyParameterValues(const map<string, Parameter> &srcparammap, map<string, Parameter> &tgtparammap) {
  map<string, Parameter>::const_iterator srcmapiter;
  map<string, Parameter>::iterator tgtmapiter;
  for (srcmapiter = srcparammap.begin(); srcmapiter != srcparammap.end(); ++srcmapiter) {
    string parname = srcmapiter->first;
    Parameter srcparam = srcmapiter->second;
 
    tgtmapiter = tgtparammap.find(parname);
    if (tgtmapiter == tgtparammap.end()) {
      stringstream errss;
      errss << "Parameter " << parname << " cannot be found in target Parameter map containing " << tgtparammap.size()
            << " entries. ";
      g_log.error(errss.str());
      throw runtime_error("Programming or memory error!  This situation cannot happen!");
    }
 
    tgtmapiter->second.curvalue = srcparam.curvalue;
  }
}
 
std::map<std::string, double> LeBailFit::convertToDoubleMap(std::map<std::string, Parameter> &inmap) {
  std::map<std::string, double> outmap;
  std::map<std::string, Parameter>::iterator miter;
  for (miter = inmap.begin(); miter != inmap.end(); ++miter) {
    outmap.emplace(miter->first, miter->second.curvalue);
  }
 
  return outmap;
}
 
// ============================ External Auxiliary Functions
// =================================
 
void writeRfactorsToFile(const vector<double> &vecX, const vector<Rfactor> &vecR, const string &filename) {
  ofstream ofile;
  ofile.open(filename.c_str());
 
  for (size_t i = 0; i < vecX.size(); ++i)
    ofile << setw(15) << setprecision(5) << vecX[i] << setw(15) << setprecision(5) << vecR[i].Rwp << setw(15)
          << setprecision(5) << vecR[i].Rp << "\n";
 
  ofile.close();
}
 
} // namespace Mantid::CurveFitting::Algorithms