epyr.lineshapes.lorentzian

epyr.lineshapes.lorentzian(x, center, width, derivative=0, phase=0.0, return_both=False)[source]

Area-normalized Lorentzian lineshape with derivatives and phase rotation.

The Lorentzian profile is fundamental in magnetic resonance, representing homogeneous broadening from finite lifetimes and collision processes.

Parameters:

xarray: Abscissa points
centerfloat: Peak center position
widthfloat: Full width at half maximum (FWHM)
derivativeint, default=0: Derivative order: - 0: Standard lineshape - 1: First derivative - 2: Second derivative - -1: Integral from -∞
phasefloat, default=0.0: Phase rotation in radians - 0: Pure absorption - π/2: Pure dispersion
return_bothbool, default=False: If True, return (absorption, dispersion) tuple

Returns:

array or tuple: Lorentzian values, optionally with dispersion component

Examples:

>>> x = np.linspace(-10, 10, 1000)
>>> # Standard absorption Lorentzian
>>> y = lorentzian(x, 0, 4)
>>> # First derivative
>>> dy = lorentzian(x, 0, 4, derivative=1)
>>> # Dispersion mode
>>> disp = lorentzian(x, 0, 4, phase=np.pi/2)
>>> # Both absorption and dispersion
>>> abs_part, disp_part = lorentzian(x, 0, 4, return_both=True)