//----------------------------------------------------------------------------------------------
/// Set initial values to a function if it needs to.
/// @param function :: A fitting function.
/// @param fun :: A smooth approximation of the fitting data.
/// @param der1 :: The first derivative of the fitting data.
/// @param der2 :: The second derivative of the fitting data.
void setValues(API::IFunction &function, const SimpleChebfun &fun,
const SimpleChebfun &der1, const SimpleChebfun &der2) {
if (auto cf = dynamic_cast<const API::CompositeFunction *>(&function)) {
for (size_t i = 0; i < cf->nFunctions(); ++i) {
setValues(*cf->getFunction(i), fun, der1, der2);
}
return;
}
switch (whichFunction(function)) {
case Gaussian: {
double width = getPeakWidth(function.getParameter("PeakCentre"), der2);
function.setParameter("Sigma", width);
break;
}
case Lorentzian: {
double width = getPeakWidth(function.getParameter("PeakCentre"), der2);
function.setParameter("FWHM", width);
break;
}
case BackToBackExponential: {
setBackToBackExponential(function, fun, der1, der2);
break;
}
default:
break;
}
}
//----------------------------------------------------------------------------------------------
/// Set initial values to a BackToBackExponential.
/// @param function :: A fitting BackToBackExponential function.
/// @param fun :: A smooth approximation of the fitting data.
/// @param der1 :: The first derivative of the fitting data.
/// @param der2 :: The second derivative of the fitting data.
void setBackToBackExponential(API::IFunction &function,
const SimpleChebfun &fun,
const SimpleChebfun &der1,
const SimpleChebfun &der2) {
// Find the actual peak centre and gaussian component of the width
auto centre = getPeakCentre(function.getParameter("X0"), der1);
double sigma = getPeakWidth(centre, der2);
if (sigma == 0.0)
sigma = 1e-06;
function.setParameter("S", sigma);
g_log.debug() << "Estimating parameters of BackToBackExponential\n";
g_log.debug() << "centre= " << centre << '\n';
g_log.debug() << "sigma = " << sigma << '\n';
// Estimate the background level
auto xlr = getPeakLeftRightExtent(centre, der2);
g_log.debug() << "extent: " << xlr.first - centre << ' '
<< xlr.second - centre << '\n';
double yl = fun(xlr.first);
double yr = fun(xlr.second);
double slope = (yr - yl) / (xlr.second - xlr.first);
double background = yl + slope * (centre - xlr.first);
double height = fun(centre) - background;
g_log.debug() << "height= " << height << '\n';
g_log.debug() << "background= " << background << '\n';
g_log.debug() << "slope= " << slope << '\n';
// Remove the background as it affects A and B parameters.
LinearFunction bg(-yl + slope * xlr.first, -slope);
SimpleChebfun fun1(fun);
fun1 += bg;
// Find left and right "HWHM".
auto hwhm = getPeakHWHM(centre, height, fun1);
g_log.debug() << "HWHM: " << hwhm.first << ' ' << hwhm.second << '\n';
// Find the extent of the default fitting function (with new S set)
// to be able to make an approximation with a SimpleChebfun.
function.setParameter("I", 1.0);
double x0 = function.getParameter("X0");
double leftX = 1.0 / function.getParameter("A");
if (leftX < 3 * sigma) {
leftX = 3 * sigma;
}
leftX = x0 - leftX;
double rightX = 1.0 / function.getParameter("B");
if (rightX < 3 * sigma) {
rightX = 3 * sigma;
}
rightX = x0 + rightX;
// Find corrections to the default A and B parameters.
// A and B are responsible for differences in the widths.
{
SimpleChebfun b2b(fun.order(), function, leftX, rightX);
auto b2b_d1 = b2b.derivative();
auto centre1 = getPeakCentre(x0, b2b_d1);
double height1 = b2b(centre1);
auto hwhm1 = getPeakHWHM(centre1, height1, b2b);
g_log.debug() << "new HWHM: " << hwhm1.first << ' ' << hwhm1.second << '\n';
double denom = hwhm.first + sigma;
double aCorr = denom > 0 ? (hwhm1.first + sigma) / denom : 100.0;
if (aCorr < 0) {
aCorr = 100.0;
function.fix(2);
}
denom = hwhm.second - sigma;
double bCorr = denom > 0 ? (hwhm1.second - sigma) / denom : 100.0;
if (bCorr < 0) {
bCorr = 100.0;
function.fix(3);
}
g_log.debug() << "corrections: " << aCorr << ' ' << bCorr << '\n';
double a = function.getParameter("A") * aCorr;
double b = function.getParameter("B") * bCorr;
function.setParameter("A", a);
function.setParameter("B", b);
}
// After all shape parameters are set (S, A and B) shift X0
// and scale I.
{
SimpleChebfun b2b(fun.order(), function, leftX, rightX);
auto b2b_d1 = b2b.derivative();
double centre1 = getPeakCentre(x0, b2b_d1);
double height1 = b2b(centre1);
x0 += centre - centre1;
function.setParameter("X0", x0);
function.setParameter("I", height / height1);
}
g_log.debug() << "Parameters:\n";
g_log.debug() << "I " << function.getParameter("I") << '\n';
g_log.debug() << "X0 " << function.getParameter("X0") << '\n';
g_log.debug() << "A " << function.getParameter("A") << '\n';
g_log.debug() << "B " << function.getParameter("B") << '\n';
g_log.debug() << "S " << function.getParameter("S") << '\n';
}