d"), (1., 1., "dashdot")] >>> for params in parameters_list: ... sigma, gamma, linestyle = params ... voigt = voigt_profile(x, sigma, gamma) ... ax.plot(x, voigt, label=rf"$\sigma={sigma},\, \gamma={gamma}$", ... ls=linestyle) >>> ax.legend() >>> plt.show() Verify visually that the Voigt profile indeed arises as the convolution of a normal and a Cauchy distribution. >>> from scipy.signal import convolve >>> x, dx = np.linspace(-10, 10, 500, retstep=True) >>> def gaussian(x, sigma): ... return np.exp(-0.5 * x**2/sigma**2)/(sigma * np.sqrt(2*np.pi)) >>> def cauchy(x, gamma): ... return gamma/(np.pi * (np.square(x)+gamma**2)) >>> sigma = 2 >>> gamma = 1 >>> gauss_profile = gaussian(x, sigma) >>> cauchy_profile = cauchy(x, gamma) >>> convolved = dx * convolve(cauchy_profile, gauss_profile, mode="same") >>> voigt = voigt_profile(x, sigma, gamma) >>> fig, ax = plt.subplots(figsize=(8, 8)) >>> ax.plot(x, gauss_profile, label="Gauss: $G$", c='b') >>> ax.plot(x, cauchy_profile, label="Cauchy: $C$", c='y', ls="dashed") >>> xx = 0.5*(x[1:] + x[:-1]) # midpoints >>> ax.plot(xx, convolved[1:], label="Convolution: $G * C$", ls='dashdot', ... c='k') >>> ax.plot(x, voigt, label="Voigt", ls='dotted', c='r') >>> ax.legend() >>> plt.show() Ú