IntegratePeaksMD.cpp

// 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 "MantidMDAlgorithms/IntegratePeaksMD.h"
#include "MantidAPI/AnalysisDataService.h"
#include "MantidAPI/Column.h"
#include "MantidAPI/FileProperty.h"
#include "MantidAPI/FunctionDomain1D.h"
#include "MantidAPI/FunctionFactory.h"
#include "MantidAPI/FunctionValues.h"
#include "MantidAPI/IMDEventWorkspace.h"
#include "MantidAPI/IPeakFunction.h"
#include "MantidAPI/Run.h"
#include "MantidAPI/TableRow.h"
#include "MantidAPI/TextAxis.h"
#include "MantidAPI/WorkspaceFactory.h"
#include "MantidDataObjects/CoordTransformDistance.h"
#include "MantidDataObjects/MDEventFactory.h"
#include "MantidDataObjects/PeakShapeSpherical.h"
#include "MantidDataObjects/PeaksWorkspace.h"
#include "MantidDataObjects/Workspace2D.h"
#include "MantidHistogramData/LinearGenerator.h"
#include "MantidKernel/ListValidator.h"
#include "MantidKernel/System.h"
#include "MantidKernel/Utils.h"
#include "MantidMDAlgorithms/GSLFunctions.h"

#include <algorithm>
#include <cmath>
#include <fstream>
#include <gsl/gsl_integration.h>

namespace Mantid {
namespace MDAlgorithms {

// Register the algorithm into the AlgorithmFactory
DECLARE_ALGORITHM(IntegratePeaksMD)

using namespace Mantid::Kernel;
using namespace Mantid::API;
using namespace Mantid::DataObjects;
using namespace Mantid::DataObjects;
using namespace Mantid::Geometry;
using namespace Mantid::HistogramData;

/** Initialize the algorithm's properties.
 */
void IntegratePeaksMD::init() {
  declareProperty(std::make_unique<WorkspaceProperty<IMDEventWorkspace>>("InputWorkspace", "", Direction::Input),
                  "An input MDEventWorkspace.");

  std::vector<std::string> propOptions{"Q (lab frame)", "Q (sample frame)", "HKL"};
  declareProperty("CoordinatesToUse", "Q (lab frame)", std::make_shared<StringListValidator>(propOptions),
                  "Ignored:  algorithm uses the InputWorkspace's coordinates.");

  declareProperty(std::make_unique<PropertyWithValue<double>>("PeakRadius", 1.0, Direction::Input),
                  "Fixed radius around each peak position in which to integrate (in the "
                  "same units as the workspace).");

  declareProperty(std::make_unique<PropertyWithValue<double>>("BackgroundInnerRadius", 0.0, Direction::Input),
                  "Inner radius to use to evaluate the background of the peak.\n"
                  "If smaller than PeakRadius, then we assume BackgroundInnerRadius = "
                  "PeakRadius.");

  declareProperty(std::make_unique<PropertyWithValue<double>>("BackgroundOuterRadius", 0.0, Direction::Input),
                  "Outer radius to use to evaluate the background of the peak.\n"
                  "The signal density around the peak (BackgroundInnerRadius < r < "
                  "BackgroundOuterRadius) is used to estimate the background under the "
                  "peak.\n"
                  "If smaller than PeakRadius, no background measurement is done.");

  declareProperty(std::make_unique<WorkspaceProperty<PeaksWorkspace>>("PeaksWorkspace", "", Direction::Input),
                  "A PeaksWorkspace containing the peaks to integrate.");

  declareProperty(std::make_unique<WorkspaceProperty<PeaksWorkspace>>("OutputWorkspace", "", Direction::Output),
                  "The output PeaksWorkspace will be a copy of the input PeaksWorkspace "
                  "with the peaks' integrated intensities.");

  declareProperty("ReplaceIntensity", true,
                  "Always replace intensity in PeaksWorkspacem (default).\n"
                  "If false, then do not replace intensity if calculated value "
                  "is 0 (used for SNSSingleCrystalReduction)");

  declareProperty("IntegrateIfOnEdge", true,
                  "Only warning if all of peak outer radius is not on detector (default).\n"
                  "If false, do not integrate if the outer radius is not on a detector.");

  declareProperty("AdaptiveQRadius", false,
                  "Default is false.   If true, all input radii are multiplied "
                  "by the magnitude of Q at the peak center so each peak has a "
                  "different integration radius.");

  declareProperty("Cylinder", false, "Default is sphere.  Use next five parameters for cylinder.");

  declareProperty(std::make_unique<PropertyWithValue<double>>("CylinderLength", 0.0, Direction::Input),
                  "Length of cylinder in which to integrate (in the same units as the "
                  "workspace).");

  declareProperty(std::make_unique<PropertyWithValue<double>>("PercentBackground", 0.0, Direction::Input),
                  "Percent of CylinderLength that is background (20 is 20%)");

  std::vector<std::string> peakNames = FunctionFactory::Instance().getFunctionNames<IPeakFunction>();
  peakNames.emplace_back("NoFit");
  declareProperty("ProfileFunction", "Gaussian", std::make_shared<StringListValidator>(peakNames),
                  "Fitting function for profile that is used only with "
                  "Cylinder integration.");

  std::vector<std::string> integrationOptions(2);
  integrationOptions[0] = "Sum";
  integrationOptions[1] = "GaussianQuadrature";
  auto integrationvalidator = std::make_shared<StringListValidator>(integrationOptions);
  declareProperty("IntegrationOption", "GaussianQuadrature", integrationvalidator,
                  "Integration method for calculating intensity "
                  "used only with Cylinder integration.");

  declareProperty(std::make_unique<FileProperty>("ProfilesFile", "", FileProperty::OptionalSave,
                                                 std::vector<std::string>(1, "profiles")),
                  "Save (Optionally) as Isaw peaks file with profiles included");
}

//----------------------------------------------------------------------------------------------
/** Integrate the peaks of the workspace using parameters saved in the algorithm
 * class
 * @param ws ::  MDEventWorkspace to integrate
 */
template <typename MDE, size_t nd> void IntegratePeaksMD::integrate(typename MDEventWorkspace<MDE, nd>::sptr ws) {
  if (nd != 3)
    throw std::invalid_argument("For now, we expect the input MDEventWorkspace "
                                "to have 3 dimensions only.");

  /// Peak workspace to integrate
  Mantid::DataObjects::PeaksWorkspace_sptr inPeakWS = getProperty("PeaksWorkspace");

  /// Output peaks workspace, create if needed
  Mantid::DataObjects::PeaksWorkspace_sptr peakWS = getProperty("OutputWorkspace");
  if (peakWS != inPeakWS)
    peakWS = inPeakWS->clone();

  /// Value of the CoordinatesToUse property.
  std::string CoordinatesToUseStr = getPropertyValue("CoordinatesToUse");
  Kernel::SpecialCoordinateSystem CoordinatesToUse = ws->getSpecialCoordinateSystem();
  g_log.warning() << " Warning" << CoordinatesToUse << '\n';
  if (CoordinatesToUse == Kernel::QLab && CoordinatesToUseStr != "Q (lab frame)")
    g_log.warning() << "Warning: used Q (lab frame) coordinates for MD "
                       "workspace, not CoordinatesToUse from input \n";
  else if (CoordinatesToUse == Kernel::QSample && CoordinatesToUseStr != "Q (sample frame)")
    g_log.warning() << "Warning: used Q (sample frame) coordinates for MD "
                       "workspace, not CoordinatesToUse from input \n";
  else if (CoordinatesToUse == Kernel::HKL && CoordinatesToUseStr != "HKL")
    g_log.warning() << "Warning: used HKL coordinates for MD workspace, not "
                       "CoordinatesToUse from input \n";

  /// Radius to use around peaks
  double PeakRadius = getProperty("PeakRadius");
  /// Background (end) radius
  double BackgroundOuterRadius = getProperty("BackgroundOuterRadius");
  /// Start radius of the background
  double BackgroundInnerRadius = getProperty("BackgroundInnerRadius");
  if (BackgroundInnerRadius < PeakRadius)
    BackgroundInnerRadius = PeakRadius;
  /// Cylinder Length to use around peaks for cylinder
  double cylinderLength = getProperty("CylinderLength");
  Workspace2D_sptr wsProfile2D, wsFit2D, wsDiff2D;
  size_t numSteps = 0;
  bool cylinderBool = getProperty("Cylinder");
  bool adaptiveQRadius = getProperty("AdaptiveQRadius");
  std::vector<double> PeakRadiusVector(peakWS->getNumberPeaks(), PeakRadius);
  std::vector<double> BackgroundInnerRadiusVector(peakWS->getNumberPeaks(), BackgroundInnerRadius);
  std::vector<double> BackgroundOuterRadiusVector(peakWS->getNumberPeaks(), BackgroundOuterRadius);
  if (cylinderBool) {
    numSteps = 100;
    size_t histogramNumber = peakWS->getNumberPeaks();
    Workspace_sptr wsProfile = WorkspaceFactory::Instance().create("Workspace2D", histogramNumber, numSteps, numSteps);
    wsProfile2D = std::dynamic_pointer_cast<Workspace2D>(wsProfile);
    AnalysisDataService::Instance().addOrReplace("ProfilesData", wsProfile2D);
    Workspace_sptr wsFit = WorkspaceFactory::Instance().create("Workspace2D", histogramNumber, numSteps, numSteps);
    wsFit2D = std::dynamic_pointer_cast<Workspace2D>(wsFit);
    AnalysisDataService::Instance().addOrReplace("ProfilesFit", wsFit2D);
    Workspace_sptr wsDiff = WorkspaceFactory::Instance().create("Workspace2D", histogramNumber, numSteps, numSteps);
    wsDiff2D = std::dynamic_pointer_cast<Workspace2D>(wsDiff);
    AnalysisDataService::Instance().addOrReplace("ProfilesFitDiff", wsDiff2D);
    auto newAxis1 = std::make_unique<TextAxis>(peakWS->getNumberPeaks());
    auto newAxis2 = std::make_unique<TextAxis>(peakWS->getNumberPeaks());
    auto newAxis3 = std::make_unique<TextAxis>(peakWS->getNumberPeaks());
    auto newAxis1Raw = newAxis1.get();
    auto newAxis2Raw = newAxis2.get();
    auto newAxis3Raw = newAxis3.get();
    wsProfile2D->replaceAxis(1, std::move(newAxis1));
    wsFit2D->replaceAxis(1, std::move(newAxis2));
    wsDiff2D->replaceAxis(1, std::move(newAxis3));
    for (int i = 0; i < peakWS->getNumberPeaks(); ++i) {
      // Get a direct ref to that peak.
      IPeak &p = peakWS->getPeak(i);
      std::ostringstream label;
      label << Utils::round(p.getH()) << "_" << Utils::round(p.getK()) << "_" << Utils::round(p.getL()) << "_"
            << p.getRunNumber();
      newAxis1Raw->setLabel(i, label.str());
      newAxis2Raw->setLabel(i, label.str());
      newAxis3Raw->setLabel(i, label.str());
    }
  }
  double percentBackground = getProperty("PercentBackground");
  size_t peakMin = 0;
  size_t peakMax = numSteps;
  double ratio = 0.0;
  if (cylinderBool) {
    peakMin = static_cast<size_t>(static_cast<double>(numSteps) * percentBackground / 100.);
    peakMax = numSteps - peakMin - 1;
    size_t numPeakCh = peakMax - peakMin + 1; // number of peak channels
    size_t numBkgCh = numSteps - numPeakCh;   // number of background channels
    ratio = static_cast<double>(numPeakCh) / static_cast<double>(numBkgCh);
  }
  /// Replace intensity with 0
  bool replaceIntensity = getProperty("ReplaceIntensity");
  bool integrateEdge = getProperty("IntegrateIfOnEdge");

  std::string profileFunction = getProperty("ProfileFunction");
  std::string integrationOption = getProperty("IntegrationOption");
  std::ofstream out;
  if (cylinderBool && profileFunction != "NoFit") {
    std::string outFile = getProperty("InputWorkspace");
    outFile.append(profileFunction);
    outFile.append(".dat");
    std::string save_path = ConfigService::Instance().getString("defaultsave.directory");
    outFile = save_path + outFile;
    out.open(outFile.c_str(), std::ofstream::out);
  }
  //
  // If the following OMP pragma is included, this algorithm seg faults
  // sporadically when processing multiple TOPAZ runs in a script, on
  // Scientific Linux 6.2.  Typically, it seg faults after 2 to 6 runs are
  // processed, though occasionally it will process all 8 requested in the
  // script without crashing.  Since the lower level codes already use OpenMP,
  // parallelizing at this level is only marginally useful, giving about a
  // 5-10% speedup.  Perhaps is should just be removed permanantly, but for
  // now it is commented out to avoid the seg faults.  Refs #5533
  // PRAGMA_OMP(parallel for schedule(dynamic, 10) )
  for (int i = 0; i < peakWS->getNumberPeaks(); ++i) {
    // Get a direct ref to that peak.
    IPeak &p = peakWS->getPeak(i);

    // Get the peak center as a position in the dimensions of the workspace
    V3D pos;
    if (CoordinatesToUse == Kernel::QLab) //"Q (lab frame)"
      pos = p.getQLabFrame();
    else if (CoordinatesToUse == Kernel::QSample) //"Q (sample frame)"
      pos = p.getQSampleFrame();
    else if (CoordinatesToUse == Kernel::HKL) //"HKL"
      pos = p.getHKL();

    // Get the instrument and its detectors
    inst = peakWS->getInstrument();
    // Do not integrate if sphere is off edge of detector
    if (BackgroundOuterRadius > PeakRadius) {
      if (!detectorQ(p.getQLabFrame(), BackgroundOuterRadius)) {
        g_log.warning() << "Warning: sphere/cylinder for integration is off "
                           "edge of detector for peak "
                        << i << '\n';
        if (!integrateEdge)
          continue;
      }
    } else {
      if (!detectorQ(p.getQLabFrame(), PeakRadius)) {
        g_log.warning() << "Warning: sphere/cylinder for integration is off "
                           "edge of detector for peak "
                        << i << '\n';
        if (!integrateEdge)
          continue;
      }
    }

    // Build the sphere transformation
    bool dimensionsUsed[nd];
    coord_t center[nd];
    for (size_t d = 0; d < nd; ++d) {
      dimensionsUsed[d] = true; // Use all dimensions
      center[d] = static_cast<coord_t>(pos[d]);
    }
    signal_t signal = 0;
    signal_t errorSquared = 0;
    signal_t bgSignal = 0;
    signal_t bgErrorSquared = 0;
    double background_total = 0.0;
    if (!cylinderBool) {
      // modulus of Q
      coord_t lenQpeak = 1.0;
      if (adaptiveQRadius) {
        lenQpeak = 0.0;
        for (size_t d = 0; d < nd; d++) {
          lenQpeak += center[d] * center[d];
        }
        lenQpeak = std::sqrt(lenQpeak);
      }
      PeakRadiusVector[i] = lenQpeak * PeakRadius;
      BackgroundInnerRadiusVector[i] = lenQpeak * BackgroundInnerRadius;
      BackgroundOuterRadiusVector[i] = lenQpeak * BackgroundOuterRadius;
      CoordTransformDistance sphere(nd, center, dimensionsUsed);

      if (auto *shapeablePeak = dynamic_cast<Peak *>(&p)) {

        PeakShape *sphereShape =
            new PeakShapeSpherical(PeakRadiusVector[i], BackgroundInnerRadiusVector[i], BackgroundOuterRadiusVector[i],
                                   CoordinatesToUse, this->name(), this->version());
        shapeablePeak->setPeakShape(sphereShape);
      }

      // Perform the integration into whatever box is contained within.
      ws->getBox()->integrateSphere(sphere, static_cast<coord_t>(lenQpeak * PeakRadius * lenQpeak * PeakRadius), signal,
                                    errorSquared);

      // Integrate around the background radius

      if (BackgroundOuterRadius > PeakRadius) {
        // Get the total signal inside "BackgroundOuterRadius"
        ws->getBox()->integrateSphere(
            sphere, static_cast<coord_t>(lenQpeak * BackgroundOuterRadius * lenQpeak * BackgroundOuterRadius), bgSignal,
            bgErrorSquared);

        // Evaluate the signal inside "BackgroundInnerRadius"
        signal_t interiorSignal = 0;
        signal_t interiorErrorSquared = 0;

        // Integrate this 3rd radius, if needed
        if (BackgroundInnerRadius != PeakRadius) {
          ws->getBox()->integrateSphere(
              sphere, static_cast<coord_t>(lenQpeak * BackgroundInnerRadius * lenQpeak * BackgroundInnerRadius),
              interiorSignal, interiorErrorSquared);
        } else {
          // PeakRadius == BackgroundInnerRadius, so use the previous value
          interiorSignal = signal;
          interiorErrorSquared = errorSquared;
        }
        // Subtract the peak part to get the intensity in the shell
        // (BackgroundInnerRadius < r < BackgroundOuterRadius)
        bgSignal -= interiorSignal;
        // We can subtract the error (instead of adding) because the two values
        // are 100% dependent; this is the same as integrating a shell.
        bgErrorSquared -= interiorErrorSquared;

        // Relative volume of peak vs the BackgroundOuterRadius sphere
        const double radiusRatio = (PeakRadius / BackgroundOuterRadius);
        const double peakVolume = radiusRatio * radiusRatio * radiusRatio;

        // Relative volume of the interior of the shell vs overall background
        const double interiorRatio = (BackgroundInnerRadius / BackgroundOuterRadius);
        // Volume of the bg shell, relative to the volume of the
        // BackgroundOuterRadius sphere
        const double bgVolume = 1.0 - interiorRatio * interiorRatio * interiorRatio;

        // Finally, you will multiply the bg intensity by this to get the
        // estimated background under the peak volume
        const double scaleFactor = peakVolume / bgVolume;
        bgSignal *= scaleFactor;
        bgErrorSquared *= scaleFactor * scaleFactor;
      }
    } else {
      CoordTransformDistance cylinder(nd, center, dimensionsUsed, 2);

      // Perform the integration into whatever box is contained within.
      Counts signal_fit(numSteps);
      signal_fit = 0;

      ws->getBox()->integrateCylinder(cylinder, static_cast<coord_t>(PeakRadius), static_cast<coord_t>(cylinderLength),
                                      signal, errorSquared, signal_fit.mutableRawData());

      Points points(signal_fit.size(), LinearGenerator(0, 1));
      wsProfile2D->setHistogram(i, points, signal_fit);

      // Integrate around the background radius
      if (BackgroundOuterRadius > PeakRadius) {
        // Get the total signal inside "BackgroundOuterRadius"
        signal_fit = 0;

        ws->getBox()->integrateCylinder(cylinder, static_cast<coord_t>(BackgroundOuterRadius),
                                        static_cast<coord_t>(cylinderLength), bgSignal, bgErrorSquared,
                                        signal_fit.mutableRawData());

        wsProfile2D->setHistogram(i, points, signal_fit);

        // Evaluate the signal inside "BackgroundInnerRadius"
        signal_t interiorSignal = 0;
        signal_t interiorErrorSquared = 0;

        // Integrate this 3rd radius, if needed
        if (BackgroundInnerRadius != PeakRadius) {
          ws->getBox()->integrateCylinder(cylinder, static_cast<coord_t>(BackgroundInnerRadius),
                                          static_cast<coord_t>(cylinderLength), interiorSignal, interiorErrorSquared,
                                          signal_fit.mutableRawData());
        } else {
          // PeakRadius == BackgroundInnerRadius, so use the previous value
          interiorSignal = signal;
          interiorErrorSquared = errorSquared;
        }
        // Subtract the peak part to get the intensity in the shell
        // (BackgroundInnerRadius < r < BackgroundOuterRadius)
        bgSignal -= interiorSignal;
        // We can subtract the error (instead of adding) because the two values
        // are 100% dependent; this is the same as integrating a shell.
        bgErrorSquared -= interiorErrorSquared;
        // Relative volume of peak vs the BackgroundOuterRadius cylinder
        const double radiusRatio = (PeakRadius / BackgroundOuterRadius);
        const double peakVolume = radiusRatio * radiusRatio * cylinderLength;

        // Relative volume of the interior of the shell vs overall background
        const double interiorRatio = (BackgroundInnerRadius / BackgroundOuterRadius);
        // Volume of the bg shell, relative to the volume of the
        // BackgroundOuterRadius cylinder
        const double bgVolume = 1.0 - interiorRatio * interiorRatio * cylinderLength;

        // Finally, you will multiply the bg intensity by this to get the
        // estimated background under the peak volume
        const double scaleFactor = peakVolume / bgVolume;
        bgSignal *= scaleFactor;
        bgErrorSquared *= scaleFactor * scaleFactor;
      } else {
        wsProfile2D->setHistogram(i, points, signal_fit);
      }

      if (profileFunction == "NoFit") {
        auto &y = wsProfile2D->y(i);
        // sum signal between range
        signal = y.sum(peakMin, peakMax);
        // sum background outside of range
        background_total += y.sum(0, peakMin);
        background_total += y.sum(peakMax);
        errorSquared = std::abs(signal);
      } else {
        auto findpeaks = createChildAlgorithm("FindPeaks", -1, -1, false);
        findpeaks->setProperty("InputWorkspace", wsProfile2D);
        findpeaks->setProperty<int>("FWHM", 7);
        findpeaks->setProperty<int>("Tolerance", 4);
        // FindPeaks will do the checking on the validity of WorkspaceIndex
        findpeaks->setProperty("WorkspaceIndex", static_cast<int>(i));

        // Get the specified peak positions, which is optional
        findpeaks->setProperty<std::string>("PeakFunction", profileFunction);
        // FindPeaks will use linear or flat if they are better
        findpeaks->setProperty<std::string>("BackgroundType", "Quadratic");
        findpeaks->setProperty<bool>("HighBackground", true);
        findpeaks->setProperty<bool>("RawPeakParameters", true);
        std::vector<double> peakPosToFit;
        peakPosToFit.emplace_back(static_cast<double>(numSteps) / 2.0);
        findpeaks->setProperty("PeakPositions", peakPosToFit);
        findpeaks->setProperty<int>("MinGuessedPeakWidth", 4);
        findpeaks->setProperty<int>("MaxGuessedPeakWidth", 4);
        try {
          findpeaks->executeAsChildAlg();
        } catch (...) {
          g_log.error("Can't execute FindPeaks algorithm");
          continue;
        }

        API::ITableWorkspace_sptr paramws = findpeaks->getProperty("PeaksList");
        if (paramws->rowCount() < 1)
          continue;
        std::ostringstream fun_str;
        fun_str << "name=" << profileFunction;

        size_t numcols = paramws->columnCount();
        std::vector<std::string> paramsName = paramws->getColumnNames();
        std::vector<double> paramsValue;
        API::TableRow row = paramws->getRow(0);
        int spectrum;
        row >> spectrum;
        for (size_t j = 1; j < numcols; ++j) {
          double parvalue;
          row >> parvalue;
          if (j == numcols - 4)
            fun_str << ";name=Quadratic";
          // erase f0. or f1.
          // if (j > 0 && j < numcols-1) fun_str << "," <<
          // paramsName[j].erase(0,3) <<"="<<parvalue;
          if (j > 0 && j < numcols - 1)
            fun_str << "," << paramsName[j] << "=" << parvalue;
          paramsValue.emplace_back(parvalue);
        }
        if (i == 0) {
          for (size_t j = 0; j < numcols; ++j)
            out << std::setw(20) << paramsName[j] << " ";
          out << "\n";
        }
        out << std::setw(20) << i;
        for (size_t j = 0; j < numcols - 1; ++j)
          out << std::setw(20) << std::fixed << std::setprecision(10) << paramsValue[j] << " ";
        out << "\n";

        // Evaluate fit at points

        IFunction_sptr ifun = FunctionFactory::Instance().createInitialized(fun_str.str());
        std::shared_ptr<const CompositeFunction> fun = std::dynamic_pointer_cast<const CompositeFunction>(ifun);
        const auto &x = wsProfile2D->x(i);
        wsFit2D->setSharedX(i, wsProfile2D->sharedX(i));
        wsDiff2D->setSharedX(i, wsProfile2D->sharedX(i));

        FunctionDomain1DVector domain(x.rawData());
        FunctionValues yy(domain);
        fun->function(domain, yy);
        auto funcValues = yy.toVector();

        wsFit2D->mutableY(i) = std::move(funcValues);
        wsDiff2D->setSharedY(i, wsProfile2D->sharedY(i));
        wsDiff2D->mutableY(i) -= wsFit2D->y(i);

        // Calculate intensity
        signal = 0.0;
        if (integrationOption == "Sum") {

          for (size_t j = peakMin; j <= peakMax; j++)
            if (std::isfinite(yy[j]))
              signal += yy[j];
        } else {
          gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);

          double error;

          gsl_function F;
          F.function = &Mantid::MDAlgorithms::f_eval;
          F.params = &fun;

          gsl_integration_qags(&F, x[peakMin], x[peakMax], 0, 1e-7, 1000, w, &signal, &error);

          gsl_integration_workspace_free(w);
        }
        errorSquared = std::fabs(signal);
        // Get background counts
        for (size_t j = 0; j < numSteps; j++) {
          double background =
              paramsValue[numcols - 3] * x[j] * x[j] + paramsValue[numcols - 4] * x[j] + paramsValue[numcols - 5];
          if (j < peakMin || j > peakMax)
            background_total = background_total + background;
        }
      }
    }
    // Save it back in the peak object.
    if (signal != 0. || replaceIntensity) {
      p.setIntensity(signal - ratio * background_total - bgSignal);
      p.setSigmaIntensity(sqrt(errorSquared + ratio * ratio * std::fabs(background_total) + bgErrorSquared));
    }

    g_log.information() << "Peak " << i << " at " << pos << ": signal " << signal << " (sig^2 " << errorSquared
                        << "), with background " << bgSignal + ratio * background_total << " (sig^2 "
                        << bgErrorSquared + ratio * ratio * std::fabs(background_total) << ") subtracted.\n";
  }
  // This flag is used by the PeaksWorkspace to evaluate whether it has been
  // integrated.
  peakWS->mutableRun().addProperty("PeaksIntegrated", 1, true);
  // These flags are specific to the algorithm.
  peakWS->mutableRun().addProperty("PeakRadius", PeakRadiusVector, true);
  peakWS->mutableRun().addProperty("BackgroundInnerRadius", BackgroundInnerRadiusVector, true);
  peakWS->mutableRun().addProperty("BackgroundOuterRadius", BackgroundOuterRadiusVector, true);

  // save profiles in peaks file
  const std::string outfile = getProperty("ProfilesFile");
  if (outfile.length() > 0) {
    IAlgorithm_sptr alg;
    try {
      alg = createChildAlgorithm("SaveIsawPeaks", -1, -1, false);
    } catch (Exception::NotFoundError &) {
      g_log.error("Can't locate SaveIsawPeaks algorithm");
      throw;
    }
    alg->setProperty("InputWorkspace", peakWS);
    alg->setProperty("ProfileWorkspace", wsProfile2D);
    alg->setPropertyValue("Filename", outfile);
    alg->execute();
  }
  // Save the output
  setProperty("OutputWorkspace", peakWS);
}

/** Calculate if this Q is on a detector
 *
 * @param QLabFrame: The Peak center.
 * @param r: Peak radius.
 */
bool IntegratePeaksMD::detectorQ(Mantid::Kernel::V3D QLabFrame, double r) {
  bool in = true;
  const int nAngles = 8;
  double dAngles = static_cast<coord_t>(nAngles);
  // check 64 points in theta and phi at outer radius
  for (int i = 0; i < nAngles; ++i) {
    double theta = (2 * M_PI) / dAngles * i;
    for (int j = 0; j < nAngles; ++j) {
      double phi = (2 * M_PI) / dAngles * j;
      // Calculate an edge position at this point on the sphere surface.
      // Spherical coordinates to cartesian.
      V3D edge = V3D(QLabFrame.X() + r * std::cos(theta) * std::sin(phi),
                     QLabFrame.Y() + r * std::sin(theta) * std::sin(phi), QLabFrame.Z() + r * std::cos(phi));
      // Create the peak using the Q in the lab frame with all its info:
      try {
        Peak p(inst, edge);
        in = (in && p.findDetector());
        if (!in) {
          return false;
        }
      } catch (...) {
        return false;
      }
    }
  }
  return in;
}

//----------------------------------------------------------------------------------------------
/** Execute the algorithm.
 */
void IntegratePeaksMD::exec() {
  inWS = getProperty("InputWorkspace");

  CALL_MDEVENT_FUNCTION(this->integrate, inWS);
}

double f_eval(double x, void *params) {
  std::shared_ptr<const API::CompositeFunction> fun =
      *reinterpret_cast<std::shared_ptr<const API::CompositeFunction> *>(params);
  FunctionDomain1DVector domain(x);
  FunctionValues yval(domain);
  fun->function(domain, yval);
  return yval[0];
}

} // namespace MDAlgorithms
} // namespace Mantid