DynamicKuboToyabe.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 "MantidCurveFitting/Functions/DynamicKuboToyabe.h"

#include "MantidAPI/FunctionFactory.h"
#include "MantidAPI/Jacobian.h"
#include "MantidAPI/MatrixWorkspace.h"
#include "MantidKernel/PhysicalConstants.h"

#include <iomanip>
#include <sstream>
#include <vector>

namespace Mantid::CurveFitting::Functions {

using namespace API;
using namespace CurveFitting;
using namespace Kernel;

DECLARE_FUNCTION(DynamicKuboToyabe)

void DynamicKuboToyabe::init() {
  declareAttribute("BinWidth", Attribute(m_eps));
  declareParameter("Asym", 0.2, "Amplitude at time 0");
  declareParameter("Delta", 0.2, "Local field");
  declareParameter("Field", 0.0, "External field");
  declareParameter("Nu", 0.0, "Hopping rate");
}

//--------------------------------------------------------------------------------------------------------------------------------------
// From Numerical Recipes

// Midpoint method
double midpnt(double func(const double, const double, const double), const double a, const double b, const int n,
              const double g, const double w0) {
  // quote & modified from numerical recipe 2nd edtion (page147)

  static double s;

  if (n == 1) {
    s = (b - a) * func(0.5 * (a + b), g, w0);
    return (s);
  } else {
    double x, tnm, sum, del, ddel;
    int it, j;
    for (it = 1, j = 1; j < n - 1; j++)
      it *= 3;
    tnm = it;
    del = (b - a) / (3 * tnm);
    ddel = del + del;
    x = a + 0.5 * del;
    sum = 0.0;
    for (j = 1; j <= it; j++) {
      sum += func(x, g, w0);
      x += ddel;
      sum += func(x, g, w0);
      x += del;
    }
    s = (s + (b - a) * sum / tnm) / 3.0;
    return s;
  }
}

// Polynomial interpolation
void polint(double xa[], const double ya[], int n, double x, double &y, double &dy) {
  int i, m, ns = 1;
  double dif;

  dif = fabs(x - xa[1]);
  std::vector<double> c(n + 1);
  std::vector<double> d(n + 1);
  for (i = 1; i <= n; i++) {
    double dift;
    if ((dift = fabs(x - xa[i])) < dif) {
      ns = i;
      dif = dift;
    }
    c[i] = ya[i];
    d[i] = ya[i];
  }
  y = ya[ns--];
  for (m = 1; m < n; m++) {
    for (i = 1; i <= n - m; i++) {
      double den, ho, hp, w;
      ho = xa[i] - x;
      hp = xa[i + m] - x;
      w = c[i + 1] - d[i];
      if ((den = ho - hp) == 0.0) { // error message!!!
        throw std::runtime_error("Error in routin polint");
      }
      den = w / den;
      d[i] = hp * den;
      c[i] = ho * den;
    }
    y += (dy = (2 * (ns) < (n - m) ? c[ns + 1] : d[ns--]));
  }
}

// Integration
double integral(double func(const double, const double, const double), const double a, const double b, const double g,
                const double w0) {

  const int JMAX = 14;
  const int JMAXP = JMAX + 1;
  const int K = 5;

  int j;
  double ss, dss;
  double h[JMAXP + 1], s[JMAXP];

  h[1] = 1.0;
  for (j = 1; j <= JMAX; j++) {
    s[j] = midpnt(func, a, b, j, g, w0);
    if (j >= K) {
      polint(&h[j - K], &s[j - K], K, 0.0, ss, dss);
      if (fabs(dss) <= fabs(ss))
        return ss;
    }
    h[j + 1] = h[j] / 9.0;
  }
  throw std::runtime_error("Too many steps in routine integrate");
}

// End of Numerical Recipes routines
//--------------------------------------------------------------------------------------------------------------------------------------

// f1: function to integrate
double f1(const double x, const double G, const double w0) {
  // G = Delta in doc
  // x = dummy time variable
  return (exp(-G * G * x * x / 2) * sin(w0 * x));
}

// Static Zero Field Kubo Toyabe relaxation function
// Also called Lorentzian Kubo-Toyabe
double ZFKT(const double x, const double G) {
  // q = Delta^2 t^2 in doc
  const double q = G * G * x * x;
  return (0.3333333333 + 0.6666666667 * exp(-0.5 * q) * (1 - q));
}

// Static non-zero field Kubo Toyabe relaxation function
double HKT(const double x, const double G, const double F) {
  // q = Delta^2 t^2 in doc
  const double q = G * G * x * x;
  // Muon gyromagnetic ratio * 2 * PI
  const double gm = 2 * M_PI * PhysicalConstants::MuonGyromagneticRatio;
  // w = omega_0 in doc
  double w;
  if (F > 2 * G) {
    // Use F
    w = gm * F;
  } else {
    // Use G
    w = gm * 2 * G;
  }
  // r = Delta^2/omega_0^2
  const double r = G * G / w / w;

  double ig;
  if (x > 0 && r > 0) {
    // Compute integral
    ig = integral(f1, 0.0, x, G, w);
  } else {
    // Integral is 0
    ig = 0;
  }

  const double ktb = (1 - 2 * r * (1 - exp(-q / 2) * cos(w * x)) + 2 * r * r * w * ig);

  if (F > 2 * G) {
    // longitudinal Gaussian field
    return ktb;
  } else {
    //
    const double kz = ZFKT(x, G);
    return kz + F / 2 / G * (ktb - kz);
  }
}

// Dynamic Kubo-Toyabe
double DynamicKuboToyabe::getDKT(double t, double G, double F, double v, double eps) const {

  const auto tsmax = static_cast<int>(std::ceil(32.768 / eps));

  static double oldG = -1., oldV = -1., oldF = -1., oldEps = -1.;

  const auto maxTsmax = static_cast<int>(std::ceil(32.768 / m_minEps));
  static std::vector<double> gStat(maxTsmax), gDyn(maxTsmax);

  if ((G != oldG) || (v != oldV) || (F != oldF) || (eps != oldEps)) {

    // If G or v or F or eps have changed with respect to the
    // previous call, we need to re-do the computations

    if (G != oldG || (F != oldF)) {

      // But we only need to
      // re-compute gStat if G or F have changed

      // Generate static Kubo-Toyabe
      if (F == 0) {
        for (int k = 0; k < tsmax; k++) {
          gStat[k] = ZFKT(k * eps, G);
        }
      } else {
        for (int k = 0; k < tsmax; k++) {
          gStat[k] = HKT(k * eps, G, F);
        }
      }
      // Store new G value
      oldG = G;
      // Store new F value
      oldF = F;
    }

    // Store new v value
    oldV = v;
    // Store new eps value
    oldEps = eps;

    double hop = v * eps;

    // Generate dynamic Kubo Toyabe
    for (int k = 0; k < tsmax; k++) {
      double y = gStat[k];
      // do integration
      for (int j = k - 1; j > 0; j--) {
        y = y * (1 - hop) + hop * gDyn[k - j] * gStat[j];
      }
      gDyn[k] = y;
    }
  }

  // Interpolate table
  // If beyond end, extrapolate
  auto x = int(fabs(t) / eps);
  if (x > tsmax - 2)
    x = tsmax - 2;
  double xe = (fabs(t) / eps) - x;
  return gDyn[x] * (1 - xe) + xe * gDyn[x + 1];
}

// Dynamic Kubo Toyabe function
void DynamicKuboToyabe::function1D(double *out, const double *xValues, const size_t nData) const {
  const double &A = getParameter("Asym");
  const double &G = fabs(getParameter("Delta"));
  const double &F = fabs(getParameter("Field"));
  const double &v = fabs(getParameter("Nu"));

  // Zero hopping rate
  if (v == 0.0) {

    // Zero external field
    if (F == 0.0) {
      for (size_t i = 0; i < nData; i++) {
        out[i] = A * ZFKT(xValues[i], G);
      }
    }
    // Non-zero external field
    else {
      for (size_t i = 0; i < nData; i++) {
        out[i] = A * HKT(xValues[i], G, F);
      }
    }
  }

  // Non-zero hopping rate
  else {

    for (size_t i = 0; i < nData; i++) {
      out[i] = A * getDKT(xValues[i], G, F, v, m_eps);
    }
  }
}

//----------------------------------------------------------------------------------------------
/** Constructor
 */
DynamicKuboToyabe::DynamicKuboToyabe() : m_eps(0.05), m_minEps(0.001), m_maxEps(0.1) {}

//----------------------------------------------------------------------------------------------
/** Function to calculate derivative numerically
 */
void DynamicKuboToyabe::functionDeriv(const API::FunctionDomain &domain, API::Jacobian &jacobian) {
  calNumericalDeriv(domain, jacobian);
}

//----------------------------------------------------------------------------------------------
/** Function to calculate derivative analytically
 */
void DynamicKuboToyabe::functionDeriv1D(API::Jacobian * /*jacobian*/, const double * /*xValues*/,
                                        const size_t /*nData*/) {
  throw Mantid::Kernel::Exception::NotImplementedError("functionDeriv1D is not implemented for DynamicKuboToyabe.");
}

//----------------------------------------------------------------------------------------------
/** Set new value of the i-th parameter
 * @param i :: parameter index
 * @param value :: new value
 */
void DynamicKuboToyabe::setActiveParameter(size_t i, double value) { setParameter(i, fabs(value), false); }

//----------------------------------------------------------------------------------------------
/** Set Attribute
 * @param attName :: The attribute name. If it is not "eps" exception is thrown.
 * @param att :: A double attribute containing a new positive value.
 */
void DynamicKuboToyabe::setAttribute(const std::string &attName, const API::IFunction::Attribute &att) {
  if (attName == "BinWidth") {

    double newVal = att.asDouble();

    if (newVal < 0) {
      clearAllParameters();
      throw std::invalid_argument("DKT: Attribute BinWidth cannot be negative.");

    } else if (newVal < m_minEps) {
      clearAllParameters();
      std::stringstream ss;
      ss << "DKT: Attribute BinWidth too small (BinWidth < " << std::setprecision(3) << m_minEps << ")";
      throw std::invalid_argument(ss.str());

    } else if (newVal > m_maxEps) {
      clearAllParameters();
      std::stringstream ss;
      ss << "DKT: Attribute BinWidth too large (BinWidth > " << std::setprecision(3) << m_maxEps << ")";
      throw std::invalid_argument(ss.str());
    }

    if (!nParams()) {
      init();
    }
    m_eps = newVal;
    IFunction::setAttribute(attName, Attribute(m_eps));

  } else {
    throw std::invalid_argument("DynamicKuboToyabe: Unknown attribute " + attName);
  }
}

} // namespace Mantid::CurveFitting::Functions