void BackToBackExponential::function1D(double* out, const double* xValues, const size_t nData)const
{
/*
const double& I = getParameter("I");
const double& a = getParameter("A");
const double& b = getParameter("B");
const double& x0 = getParameter("X0");
const double& s = getParameter("S");
*/
const double I = getParameter(0);
const double a = getParameter(1);
const double b = getParameter(2);
const double x0 = getParameter(3);
const double s = getParameter(4);
// find the reasonable extent of the peak ~100 fwhm
double extent = expWidth();
if ( s > extent ) extent = s;
extent *= 100;
double s2 = s*s;
double normFactor = a * b / (a + b) / 2;
//Needed for IntegratePeaksMD for cylinder profile fitted with b=0
if (normFactor == 0.0) normFactor = 1.0;
for (size_t i = 0; i < nData; i++) {
double diff=xValues[i]-x0;
if ( fabs(diff) < extent )
{
double val = 0.0;
double arg1 = a/2*(a*s2+2*diff);
val += exp( arg1 + gsl_sf_log_erfc((a*s2+diff)/sqrt(2*s2)) ); //prevent overflow
double arg2 = b/2*(b*s2-2*diff);
val += exp( arg2 + gsl_sf_log_erfc((b*s2-diff)/sqrt(2*s2)) ); //prevent overflow
out[i] = I*val*normFactor;
}
else
out[i] = 0.0;
}
}
void IkedaCarpenterPV::functionLocal(double *out, const double *xValues,
const size_t nData) const {
const double I = getParameter("I");
const double alpha0 = getParameter("Alpha0");
const double alpha1 = getParameter("Alpha1");
const double beta0 = getParameter("Beta0");
const double kappa = getParameter("Kappa");
const double voigtsigmaSquared = getParameter("SigmaSquared");
const double voigtgamma = getParameter("Gamma");
const double X0 = getParameter("X0");
// cal pseudo voigt sigmaSq and gamma and eta
double gamma = 1.0; // dummy initialization
double eta = 0.5; // dummy initialization
convertVoigtToPseudo(voigtsigmaSquared, voigtgamma, gamma, eta);
double sigmaSquared = gamma * gamma / (8.0 * M_LN2); // pseudo voigt sigma^2
const double beta = 1 / beta0;
// equations taken from Fullprof manual
const double k = 0.05;
// Not entirely sure what to do if sigmaSquared ever negative
// for now just post a warning
double someConst = std::numeric_limits<double>::max() / 100.0;
if (sigmaSquared > 0)
someConst = 1 / sqrt(2.0 * sigmaSquared);
else if (sigmaSquared < 0) {
g_log.warning() << "sigmaSquared negative in functionLocal.\n";
}
// update wavelength vector
calWavelengthAtEachDataPoint(xValues, nData);
for (size_t i = 0; i < nData; i++) {
double diff = xValues[i] - X0;
double R = exp(-81.799 / (m_waveLength[i] * m_waveLength[i] * kappa));
double alpha = 1.0 / (alpha0 + m_waveLength[i] * alpha1);
double a_minus = alpha * (1 - k);
double a_plus = alpha * (1 + k);
double x = a_minus - beta;
double y = alpha - beta;
double z = a_plus - beta;
double Nu = 1 - R * a_minus / x;
double Nv = 1 - R * a_plus / z;
double Ns = -2 * (1 - R * alpha / y);
double Nr = 2 * R * alpha * alpha * beta * k * k / (x * y * z);
double u = a_minus * (a_minus * sigmaSquared - 2 * diff) / 2.0;
double v = a_plus * (a_plus * sigmaSquared - 2 * diff) / 2.0;
double s = alpha * (alpha * sigmaSquared - 2 * diff) / 2.0;
double r = beta * (beta * sigmaSquared - 2 * diff) / 2.0;
double yu = (a_minus * sigmaSquared - diff) * someConst;
double yv = (a_plus * sigmaSquared - diff) * someConst;
double ys = (alpha * sigmaSquared - diff) * someConst;
double yr = (beta * sigmaSquared - diff) * someConst;
std::complex<double> zs =
std::complex<double>(-alpha * diff, 0.5 * alpha * gamma);
std::complex<double> zu = (1 - k) * zs;
std::complex<double> zv = (1 - k) * zs;
std::complex<double> zr =
std::complex<double>(-beta * diff, 0.5 * beta * gamma);
double N = 0.25 * alpha * (1 - k * k) / (k * k);
out[i] = I * N * ((1 - eta) * (Nu * exp(u + gsl_sf_log_erfc(yu)) +
Nv * exp(v + gsl_sf_log_erfc(yv)) +
Ns * exp(s + gsl_sf_log_erfc(ys)) +
Nr * exp(r + gsl_sf_log_erfc(yr))) -
eta * 2.0 / M_PI * (Nu * exponentialIntegral(zu).imag() +
Nv * exponentialIntegral(zv).imag() +
Ns * exponentialIntegral(zs).imag() +
Nr * exponentialIntegral(zr).imag()));
}
}
static VALUE Error_log_erfc(VALUE self, VALUE x) {
return rb_float_new(gsl_sf_log_erfc(NUM2DBL(x)));
}
