Thompson-cox-hastings Pseudo-voigt Function Direct

[ \eta = 1.36603 \left( \frac\Gamma_L\Gamma_V \right) - 0.47719 \left( \frac\Gamma_L\Gamma_V \right)^2 + 0.11116 \left( \frac\Gamma_L\Gamma_V \right)^3 ]

# Normalized Gaussian & Lorentzian with FWHM = G_V sigma = G_V / (2*sqrt(2*log(2))) # Gaussian sigma gamma = G_V / 2 # Lorentzian half-width at half-max t = (x - x0) thompson-cox-hastings pseudo-voigt function

G = (1/(sigma*sqrt(2*pi))) * exp(-0.5*(t/sigma)**2) L = (gamma/pi) / (t**2 + gamma**2) [ \eta = 1

The is:

[ V_\textTCH(x) = \eta , L(x) + (1-\eta) , G(x) ] L(x) + (1-\eta)