GramCharlierComptonProfile.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 +
//------------------------------------------------------------------------------------------------
// Includes
//------------------------------------------------------------------------------------------------
#include "MantidCurveFitting/Functions/GramCharlierComptonProfile.h"
#include "MantidAPI/FunctionFactory.h"

#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_gamma.h> // for factorial
#include <gsl/gsl_spline.h>

#include <boost/math/special_functions/hermite.hpp>

#include <cmath>
#include <sstream>

namespace Mantid::CurveFitting::Functions {

using namespace CurveFitting;
// Register into factory
DECLARE_FUNCTION(GramCharlierComptonProfile)

namespace {
///@cond
const char *WIDTH_PARAM = "Width";
const char *HERMITE_PREFIX = "C_";
const char *KFSE_NAME = "FSECoeff";
const char *HERMITE_C_NAME = "HermiteCoeffs";
const int NFINE_Y = 1000;

/**
 * Computes the area under the curve given a set of [X,Y] points using
 * the trapezoidal method of integration
 * @param xv Vector of x values
 * @param yv Vector of y values
 * @returns The value of the area
 */
double trapzf(const std::vector<double> &xv, const std::vector<double> &yv) {
  const double stepsize = xv[1] - xv[0];
  const size_t endpoint = xv.size() - 1;
  double area(0.0);
  for (size_t i = 1; i < endpoint; i++) {
    area += yv[i];
  }
  area = stepsize / 2 * (yv[0] + 2 * area + yv[endpoint]); // final step
  return area;
}

// Cannot put these inside massProfile definition as you can't use local types
// as template
// arguments on some compilers

// massProfile needs to sort 1 vector but keep another in order. Use a struct of
// combined points
// and a custom comparator
struct Point {
  Point(double yvalue = 0.0, double qvalue = 0.0) : y(yvalue), q(qvalue) {}
  double y;
  double q;
};

struct InY {
  /// Sort by the y field
  bool operator()(Point const &a, Point const &b) { return a.y < b.y; }
};
///@endcond
} // namespace

GramCharlierComptonProfile::GramCharlierComptonProfile()
    : ComptonProfile(), m_hermite(), m_yfine(), m_qfine(), m_voigt(), m_voigtProfile(), m_userFixedFSE(false) {}

/**
 * @returns A string containing the name of the function
 */
std::string GramCharlierComptonProfile::name() const { return "GramCharlierComptonProfile"; }

void GramCharlierComptonProfile::declareParameters() {
  // Base class ones
  ComptonProfile::declareParameters();
  declareParameter(WIDTH_PARAM, 1.0, "Gaussian width parameter");
  declareParameter(KFSE_NAME, 1.0, "FSE coefficient k");
  // Other parameters depend on the Hermite attribute...
}

void GramCharlierComptonProfile::declareAttributes() {
  // Base class ones
  ComptonProfile::declareAttributes();
  declareAttribute(HERMITE_C_NAME,
                   IFunction::Attribute("")); // space-separated string 1/0
                                              // indicating which coefficients
                                              // are active
}

/**
 * @param name The name of the attribute
 * @param value The attribute's value
 */
void GramCharlierComptonProfile::setAttribute(const std::string &name, const Attribute &value) {
  if (name == HERMITE_C_NAME)
    setHermiteCoefficients(value.asString());
  ComptonProfile::setAttribute(name, value);
}

/**
 * Throws if the string is empty and contains something other than numbers
 * @param coeffs A string of space separated 1/0 values indicating which
 * polynomial coefficients to include in the fitting
 */
void GramCharlierComptonProfile::setHermiteCoefficients(const std::string &coeffs) {
  if (coeffs.empty()) {
    throw std::invalid_argument("GramCharlierComptonProfile - Hermite polynomial string is empty!");
  }
  m_hermite.clear();
  m_hermite.reserve(3); // Maximum guess
  std::istringstream is(coeffs);
  while (!is.eof()) {
    short value;
    is >> value;
    if (!is) {
      throw std::invalid_argument("NCSCountRate - Error reading int from hermite coefficient string: " + coeffs);
    }
    m_hermite.emplace_back(value);
  }
  declareGramCharlierParameters();
}

/**
 * Currently the first mass is assumed to be fitted with the Gram-Charlier
 * expansion.
 * The input string gives whether each even Hermite polnomial is active or not
 */
void GramCharlierComptonProfile::declareGramCharlierParameters() {
  // Gram-Chelier parameters are the even coefficents of the Hermite
  // polynomials, i.e
  // setting hermite coefficients to "1 0 1" uses coefficents C_0,C_4 and C_2 is
  // skipped.
  for (size_t i = 0; i < m_hermite.size(); ++i) {
    if (m_hermite[i] > 0) {
      std::ostringstream os;
      os << HERMITE_PREFIX << 2 * i;
      this->declareParameter(os.str(), 1.0, "Hermite polynomial coefficent");
    }
  }
}

std::vector<size_t> GramCharlierComptonProfile::intensityParameterIndices() const {
  assert(!m_hermite.empty());

  std::vector<size_t> indices;
  indices.reserve(m_hermite.size() + 1);
  for (size_t i = 0; i < m_hermite.size(); ++i) {
    if (m_hermite[i] > 0) {
      std::ostringstream os;
      os << HERMITE_PREFIX << 2 * i; // refactor to have method that produces the name
      indices.emplace_back(this->parameterIndex(os.str()));
    }
  }
  // Include Kfse if it is not fixed
  const size_t kIndex = this->parameterIndex(KFSE_NAME);
  if (isActive(kIndex)) {
    indices.emplace_back(kIndex);
  }

  return indices;
}

/**
 * Fills in a column for each active hermite polynomial, starting at the given
 * index
 * @param cmatrix InOut matrix whose columns should be set to the mass profile
 * for each active hermite polynomial
 * @param start Index of the column to start on
 * @param errors Data errors array
 * @returns The number of columns filled
 */
size_t GramCharlierComptonProfile::fillConstraintMatrix(Kernel::DblMatrix &cmatrix, const size_t start,
                                                        const HistogramData::HistogramE &errors) const {
  std::vector<double> profile(NFINE_Y, 0.0);
  const size_t nData(ySpace().size());
  std::vector<double> result(nData, 0.0);

  // If the FSE term is fixed by user then it's contribution is convoluted with
  // Voigt and summed with the first column
  // otherwise it gets a column of it's own at the end.
  // Either way it needs to be computed, so do this first

  std::vector<double> fse(NFINE_Y, 0.0);
  std::vector<double> convolvedFSE(nData, 0.0);
  addFSETerm(fse);
  convoluteVoigt(convolvedFSE.data(), nData, fse);

  size_t col(0);
  for (unsigned int i = 0; i < m_hermite.size(); ++i) {
    if (m_hermite[i] == 0)
      continue;

    const unsigned int npoly = 2 * i;
    addMassProfile(profile.data(), npoly);
    convoluteVoigt(result.data(), nData, profile);
    if (i == 0 && m_userFixedFSE) {
      std::transform(result.begin(), result.end(), convolvedFSE.begin(), result.begin(), std::plus<double>());
    }
    std::transform(result.begin(), result.end(), errors.begin(), result.begin(), std::divides<double>());
    cmatrix.setColumn(start + col, result);

    std::fill_n(profile.begin(), NFINE_Y, 0.0);
    std::fill_n(result.begin(), nData, 0.0);
    ++col;
  }

  if (!m_userFixedFSE) // Extra column for He3
  {
    std::transform(convolvedFSE.begin(), convolvedFSE.end(), errors.begin(), convolvedFSE.begin(),
                   std::divides<double>());
    cmatrix.setColumn(start + col, convolvedFSE);
    ++col;
  }
  return col;
}

/**
 * Uses a Gram-Charlier series approximation for the mass and convolutes it with
 * the Voigt
 * instrument resolution function. Also multiplies by the mass*e_i^0.1/q
 * @param result An pre-sized output array that should be filled with the
 * results
 * @param nData The length of the array
 */
void GramCharlierComptonProfile::massProfile(double *result, const size_t nData) const {
  UNUSED_ARG(nData);

  using namespace Mantid::Kernel;

  // Hermite expansion (only even terms) + FSE term
  const size_t nhermite(m_hermite.size());

  // Sum over polynomials for each y
  std::vector<double> sumH(NFINE_Y);
  for (unsigned int i = 0; i < nhermite; ++i) {
    if (m_hermite[i] == 0)
      continue;
    const unsigned int npoly = 2 * i; // Only even ones
    addMassProfile(sumH.data(), npoly);
  }
  addFSETerm(sumH);
  convoluteVoigt(result, nData, sumH);
}

/**
 * Uses a Gram-Charlier series approximation for the mass and convolutes it with
 * the Voigt
 * instrument resolution function. Also multiplies by the mass*e_i^0.1/q. Sums
 * it with the given result
 * @param result An pre-sized output array that should be filled with the
 * results. Size is fixed at NFINE_Y
 * @param npoly An integer denoting the polynomial to calculate
 */
void GramCharlierComptonProfile::addMassProfile(double *result, const unsigned int npoly) const {

  using namespace Mantid::Kernel;

  const double amp(1.0), wg(getParameter(WIDTH_PARAM));
  const double ampNorm = amp / (std::sqrt(2.0 * M_PI) * wg);

  std::ostringstream os;
  os << HERMITE_PREFIX << npoly;
  const double hermiteCoeff = getParameter(os.str());
  const double factorial = gsl_sf_fact(npoly / 2);
  // Intel compiler doesn't overload pow for unsigned types
  const double denom = ((std::pow(2.0, static_cast<int>(npoly))) * factorial);

  for (int j = 0; j < NFINE_Y; ++j) {
    const double y = m_yfine[j] / M_SQRT2 / wg;
    const double hermiteI = boost::math::hermite(npoly, y);
    result[j] += ampNorm * std::exp(-y * y) * hermiteI * hermiteCoeff / denom;
  }
}

/**
 * Adds the FSE term to the result in the vector given
 * @param lhs Existing vector that the result should be added to
 */
void GramCharlierComptonProfile::addFSETerm(std::vector<double> &lhs) const {
  assert(static_cast<size_t>(NFINE_Y) == lhs.size());

  using namespace Mantid::Kernel;

  const double amp(1.0), wg(getParameter(WIDTH_PARAM));
  const double ampNorm = amp / (std::sqrt(2.0 * M_PI) * wg);

  double kfse(getParameter(KFSE_NAME));
  if (m_userFixedFSE)
    kfse *= getParameter("C_0");

  if (m_yfine.empty() || m_qfine.empty()) {
    throw std::runtime_error("The Y values or Q values have not been set");
  }

  for (int j = 0; j < NFINE_Y; ++j) {
    const double y = m_yfine[j] / M_SQRT2 / wg;
    const double he3 = boost::math::hermite(3, y);
    lhs[j] += ampNorm * std::exp(-y * y) * he3 * (kfse / m_qfine[j]);
  }
}

/**
 * Convolute with resolution and multiply by the final ei^0.1*mass/q prefactor
 * @param result Output array that holds the result of the convolution
 * @param nData The length of the array
 * @param profile The input mass profile
 */
void GramCharlierComptonProfile::convoluteVoigt(double *result, const size_t nData,
                                                const std::vector<double> &profile) const {
  const auto &modq = modQ();
  const auto &ei = e0();

  // Now convolute with the Voigt function (pre-calculated in setWorkspace as
  // its expensive)
  for (size_t i = 0; i < nData; ++i) {
    const std::vector<double> &voigt = m_voigt[i];
    // Multiply voigt with polynomial sum and put result in voigt to save using
    // another vector
    std::transform(voigt.begin(), voigt.end(), profile.begin(), m_voigtProfile.begin(), std::multiplies<double>());
    const double prefactor = std::pow(ei[i], 0.1) * mass() / modq[i];
    result[i] = prefactor * trapzf(m_yfine, m_voigtProfile);
  }
}

/**
 * Used to cache some values when the workspace has been set
 * @param workspace A pointer to the workspace
 * @param wi A workspace index
 * @param startX Starting x-vaue (unused).
 * @param endX Ending x-vaue (unused).
 */
void GramCharlierComptonProfile::setMatrixWorkspace(std::shared_ptr<const API::MatrixWorkspace> workspace, size_t wi,
                                                    double startX, double endX) {
  ComptonProfile::setMatrixWorkspace(workspace, wi, startX,
                                     endX); // Do base-class calculation first
}

/**
 * @param tseconds A vector containing the time-of-flight values in seconds
 * @param detpar Structure containing detector parameters
 */
void GramCharlierComptonProfile::cacheYSpaceValues(const HistogramData::Points &tseconds,
                                                   const Algorithms::DetectorParams &detpar) {
  ComptonProfile::cacheYSpaceValues(tseconds,
                                    detpar); // base-class calculations

  // Is FSE fixed at the moment?
  // The ComptonScatteringCountRate fixes it but we still need to know if the
  // user wanted it fixed
  m_userFixedFSE = !this->isActive(this->parameterIndex(KFSE_NAME));

  const auto &yspace = ySpace();
  const auto &modq = modQ();

  // massProfile is calculated over a large range of Y, constructed by
  // interpolation
  // This is done over an interpolated range between ymin & ymax and y and hence
  // q must be sorted
  const size_t ncoarseY(yspace.size());
  std::vector<Point> points(ncoarseY);
  for (size_t i = 0; i < ncoarseY; ++i) {
    points[i] = Point(yspace[i], modq[i]);
  }
  std::sort(points.begin(), points.end(), InY());
  // Separate back into vectors as GSL requires them separate
  std::vector<double> sortedy(ncoarseY), sortedq(ncoarseY);
  for (size_t i = 0; i < ncoarseY; ++i) {
    const auto &p = points[i];
    sortedy[i] = p.y;
    sortedq[i] = p.q;
  }

  // Generate a more-finely grained y axis and interpolate Q values
  m_yfine.resize(NFINE_Y);
  m_qfine.resize(NFINE_Y);
  const double miny(sortedy.front()), maxy(sortedy.back());
  const double step = (maxy - miny) / static_cast<double>((NFINE_Y - 1));

  // Set up GSL interpolater
  gsl_interp_accel *acc = gsl_interp_accel_alloc();
  gsl_spline *spline = gsl_spline_alloc(gsl_interp_linear, ncoarseY); // Actually a linear interpolater
  gsl_spline_init(spline, sortedy.data(), sortedq.data(), ncoarseY);
  for (int i = 0; i < NFINE_Y - 1; ++i) {
    const double xi = miny + step * i;
    m_yfine[i] = xi;
    m_qfine[i] = gsl_spline_eval(spline, xi, acc);
  }
  // Final value to ensure it ends at maxy
  m_yfine.back() = maxy;
  m_qfine.back() = gsl_spline_eval(spline, maxy, acc);
  gsl_spline_free(spline);
  gsl_interp_accel_free(acc);

  // Cache voigt function over yfine
  std::vector<double> minusYFine(NFINE_Y);
  using std::placeholders::_1;
  std::transform(m_yfine.begin(), m_yfine.end(), minusYFine.begin(), std::bind(std::multiplies<double>(), _1, -1.0));
  std::vector<double> ym(NFINE_Y); // Holds result of (y[i] - yfine) for each original y
  m_voigt.resize(ncoarseY);

  for (size_t i = 0; i < ncoarseY; ++i) {
    std::vector<double> &voigt = m_voigt[i];
    voigt.resize(NFINE_Y);

    const double yi = yspace[i];
    std::transform(minusYFine.begin(), minusYFine.end(), ym.begin(),
                   std::bind(std::plus<double>(), _1, yi)); // yfine is actually -yfine
    m_resolutionFunction->voigtApprox(voigt, ym, 0, 1.0);
  }

  m_voigtProfile.resize(NFINE_Y); // Value holder for later to avoid repeated
                                  // memory allocations when creating a new
                                  // vector
}

} // namespace Mantid::CurveFitting::Functions