MayersSampleCorrectionStrategy.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 +
//-----------------------------------------------------------------------------
// Includes
//-----------------------------------------------------------------------------
#include "MantidAlgorithms/SampleCorrections/MayersSampleCorrectionStrategy.h"
#include "MantidKernel/Math/ChebyshevPolyFit.h"
#include "MantidKernel/Math/Distributions/ChebyshevSeries.h"
#include "MantidKernel/MersenneTwister.h"
#include "MantidKernel/Statistics.h"
#include <cassert>
#include <cmath>
 
using Mantid::Kernel::ChebyshevPolyFit;
using Mantid::Kernel::ChebyshevSeries;
using Mantid::Kernel::getStatistics;
using Mantid::Kernel::MersenneTwister;
using Mantid::Kernel::StatOptions;
using std::pow;
 
namespace {
 
// The constants were set as default in the original fortran
size_t N_MUR_PTS = 21;
size_t N_RAD = 29;
size_t N_THETA = 29;
size_t N_POLY_ORDER = 4;
double TWOPI = 2.0 * M_PI;
 
// Avoid typing static_casts everywhere
template <typename R, typename T> inline R to(const T val) { return static_cast<R>(val); }
 
//-----------------------------------------------------------------------------
// Utility functions
//-----------------------------------------------------------------------------
 
double integrate(const std::vector<double> &y, const double dx) {
  assert(y.size() > 3);
  // strictly Simpson's rule says that n should be even but the old fortran
  // didn't...
  // sum even and odd terms excluding the front/back
  double sumEven(0.0), sumOdd(0.0);
  auto itend = y.end() - 1;
  for (auto it = y.begin() + 1; it != itend;) {
    sumOdd += *(it++);
    if (it == itend)
      break;
    sumEven += *(it++);
  }
  return dx * (y.front() + 4.0 * sumOdd + 2.0 * sumEven + y.back()) / 3.0;
}
} // namespace
 
namespace Mantid::Algorithms {
 
//-----------------------------------------------------------------------------
// Public methods
//-----------------------------------------------------------------------------
MayersSampleCorrectionStrategy::MayersSampleCorrectionStrategy(MayersSampleCorrectionStrategy::Parameters params,
                                                               HistogramData::Histogram inputHist)
    : m_pars(std::move(params)), m_histogram(std::move(inputHist)), m_tofVals(m_histogram.points()),
      m_histoYSize(m_histogram.size()), m_muRrange(calculateMuRange()), m_rng(std::make_unique<MersenneTwister>(1)) {
 
  const auto &xVals = m_histogram.x();
  if (!(xVals.front() < xVals.back())) {
    throw std::invalid_argument("TOF values are expected to be monotonically increasing");
  }
}
 
MayersSampleCorrectionStrategy::~MayersSampleCorrectionStrategy() = default;
 
Mantid::HistogramData::Histogram MayersSampleCorrectionStrategy::getCorrectedHisto() {
 
  // Temporary storage
  std::vector<double> xmur(N_MUR_PTS + 1, 0.0), yabs(N_MUR_PTS + 1, 1.0), // absorption signals
      wabs(N_MUR_PTS + 1, 1.0),                                           // absorption weights
      yms(0),                                                             // multiple scattering signals
      wms(0);                                                             // multiple scattering weights
  if (m_pars.mscat) {
    yms.resize(N_MUR_PTS + 1, 0.0);
    wms.resize(N_MUR_PTS + 1, 100.0);
  }
 
  // Main loop over mur. Limit is nrpts but vectors are nrpts+1. First value set
  // by initial values above
  const double dmuR = (muRmax() - muRmin()) / to<double>(N_MUR_PTS - 1);
  for (size_t i = 1; i < N_MUR_PTS + 1; ++i) {
    const double muRValue = muRmin() + to<double>(i - 1) * dmuR;
    xmur[i] = muRValue;
 
    auto attenuation = calculateSelfAttenuation(muRValue);
    const double absFactor = attenuation / (M_PI * muRValue * muRValue);
    // track these
    yabs[i] = 1. / absFactor;
    wabs[i] = absFactor;
    if (m_pars.mscat) {
      // ratio of second/first scatter
      auto mscat = calculateMS(i, muRValue, attenuation);
      yms[i] = mscat.first;
      wms[i] = mscat.second;
    }
  }
 
  // Fit polynomials to absorption values to interpolate to input data range
  ChebyshevPolyFit polyfit(N_POLY_ORDER);
  auto absCoeffs = polyfit(xmur, yabs, wabs);
  decltype(absCoeffs) msCoeffs(0);
  if (m_pars.mscat)
    msCoeffs = polyfit(xmur, yms, wms);
 
  // corrections to input
  const double muMin(xmur.front()), muMax(xmur.back()), flightPath(m_pars.l1 + m_pars.l2);
  ChebyshevSeries chebyPoly(N_POLY_ORDER);
 
  auto outputHistogram = m_histogram;
 
  auto &sigOut = outputHistogram.mutableY();
  auto &errOut = outputHistogram.mutableE();
 
  for (size_t i = 0; i < m_histoYSize; ++i) {
    const double yin(m_histogram.y()[i]), ein(m_histogram.e()[i]);
    if (yin == 0) {
      // Detector with 0 signal received - skip this bin
      continue;
    }
 
    const double sigt = sigmaTotal(flightPath, m_tofVals[i]);
    const double rmu = muR(sigt);
    // Varies between [-1,+1]
    const double xcap = ((rmu - muMin) - (muMax - rmu)) / (muMax - muMin);
    double corrfact = chebyPoly(absCoeffs, xcap);
    if (m_pars.mscat) {
      const double msVal = chebyPoly(msCoeffs, xcap);
      const double beta = m_pars.sigmaSc * msVal / sigt;
      corrfact *= (1.0 - beta);
    }
    // apply correction
 
    sigOut[i] = yin * corrfact;
    errOut[i] = sigOut[i] * ein / yin;
  }
  return outputHistogram;
}
 
double MayersSampleCorrectionStrategy::calculateSelfAttenuation(const double muR) {
  // Integrate over the cylindrical coordinates
  // Constants for calculation
  const double dyr = muR / to<double>(N_RAD - 1);
  const double dyth = TWOPI / to<double>(N_THETA - 1);
  const double muRSq = muR * muR;
  const double cosaz = cos(m_pars.azimuth);
 
  // Store values at each point
  std::vector<double> yr(N_RAD), yth(N_THETA);
  for (size_t i = 0; i < N_RAD; ++i) {
    const double r0 = to<double>(i) * dyr;
 
    for (size_t j = 0; j < N_THETA; ++j) {
      const double theta = to<double>(j) * dyth;
      // distance to vertical axis
      double fact1 = muRSq - std::pow(r0 * sin(theta), 2);
      if (fact1 < 0.0)
        fact1 = 0.0;
      // + final distance to scatter point
      const double mul1 = sqrt(fact1) + r0 * cos(theta);
      // exit distance after scatter
      double fact2 = muRSq - std::pow(r0 * sin(m_pars.twoTheta - theta), 2);
      if (fact2 < 0.0)
        fact2 = 0.0;
      const double mul2 = (sqrt(fact2) - r0 * cos(m_pars.twoTheta - theta)) / cosaz;
      yth[j] = exp(-mul1 - mul2);
    }
 
    yr[i] = r0 * integrate(yth, dyth);
  }
  return integrate(yr, dyr);
}
 
std::pair<double, double> MayersSampleCorrectionStrategy::calculateMS(const size_t irp, const double muR,
                                                                      const double abs) {
  // Radial coordinate raised to power 1/3 to ensure uniform density of points
  // across circle following discussion with W.G.Marshall (ISIS)
  const double radDistPower = 1. / 3.;
  const double muH = muR * (m_pars.cylHeight / m_pars.cylRadius);
  const double cosaz = cos(m_pars.azimuth);
  seedRNG(irp);
 
  // Take an average over a number of sets of second scatters
  std::vector<double> deltas(m_pars.msNRuns, 0.0);
  for (size_t j = 0; j < m_pars.msNRuns; ++j) {
    double sum = 0.0;
    for (size_t i = 0; i < m_pars.msNEvents; ++i) {
      // Random (r,theta,z)
      const double r1 = pow(m_rng->nextValue(), radDistPower) * muR;
      const double r2 = pow(m_rng->nextValue(), radDistPower) * muR;
      const double z1 = m_rng->nextValue() * muH;
      const double z2 = m_rng->nextValue() * muH;
      const double th1 = m_rng->nextValue() * TWOPI;
      const double th2 = m_rng->nextValue() * TWOPI;
      double fact1 = pow(muR, 2) - std::pow(r1 * sin(th1), 2);
      if (fact1 < 0.0)
        fact1 = 0.0;
      // Path into first point
      const double mul1 = sqrt(fact1) + r1 * cos(th1);
      double fact2 = pow(muR, 2) - pow(r2 * sin(m_pars.twoTheta - th2), 2);
      if (fact2 < 0.0)
        fact2 = 0.0;
      // Path out from final point
      const double mul2 = (sqrt(fact2) - r2 * cos(m_pars.twoTheta - th2)) / cosaz;
      // Path between point 1 & 2
      const double mul12 =
          sqrt(pow(r1 * cos(th1) - r2 * cos(th2), 2) + pow(r1 * sin(th1) - r2 * sin(th2), 2) + pow(z1 - z2, 2));
      if (mul12 < 0.01)
        continue;
      sum += exp(-(mul1 + mul2 + mul12)) / pow(mul12, 2);
    }
    const double beta = pow(M_PI * muR * muR * muH, 2) * sum / to<double>(m_pars.msNEvents);
    const double delta = 0.25 * beta / (M_PI * abs * muH);
    deltas[j] = delta;
  }
  auto stats = getStatistics(deltas, StatOptions::Mean | StatOptions::CorrectedStdDev);
  return std::make_pair(stats.mean, stats.mean / stats.standard_deviation);
}
 
//-----------------------------------------------------------------------------
// Private methods
//-----------------------------------------------------------------------------
std::pair<double, double> MayersSampleCorrectionStrategy::calculateMuRange() const {
  const double flightPath(m_pars.l1 + m_pars.l2);
  const double tmin(m_tofVals[0]), tmax(m_tofVals[m_histoYSize - 1]);
  return std::make_pair(muR(flightPath, tmin), muR(flightPath, tmax));
}
 
double MayersSampleCorrectionStrategy::muR(const double flightPath, const double tof) const {
  return muR(sigmaTotal(flightPath, tof));
}
 
double MayersSampleCorrectionStrategy::muR(const double sigt) const {
  // Dimensionless number - rho in (1/Angtroms^3), sigt in barns
  // (1/Angstrom = 1e8/cm) * (barn = 1e-24cm) --> factors cancel out
  return m_pars.rho * sigt * (m_pars.cylRadius * 1e2);
}
 
double MayersSampleCorrectionStrategy::sigmaTotal(const double flightPath, const double tof) const {
  // sigabs = sigabs(@2200(m/s)^-1)*2200 * velocity;
  const double sigabs = m_pars.sigmaAbs * 2200.0 * tof * 1e-6 / flightPath;
  return sigabs + m_pars.sigmaSc;
}
 
void MayersSampleCorrectionStrategy::seedRNG(const size_t seed) { m_rng->setSeed(seed); }
 
} // namespace Mantid::Algorithms