gftool.basis.pole.PoleGf.from_tau

classmethod PoleGf.from_tau(gf_tau, n_pole, beta, moments=(), occ=False, width=1.0, weight=None)[source]

Generate instance fitting gf_tau.

Finds poles and weights for a pole Green’s function matching the given Green’s function gf_tau.

Note that for an odd number of moments, the central pole is at z = 0, so the causal Green’s function g(0) diverges.

Parameters:

gf_tau(…, N_tau) float np.ndarray: Imaginary times Green’s function which is fitted.
n_poleint: Number of poles to fit.
betafloat: The inverse temperature \(beta = 1/k_B T\).
moments(…, N) float array_like: Moments of the high-frequency expansion, where G(z) = moments / z**np.arange(N) for large z.
occfloat, optional: If given, fix occupation of pole Green’s function to occ (default: False).
widthfloat, optional: Distance of the largest pole to the origin (default: 1.0).
weight(…, N_tau) float np.ndarray, optional: Weight the values of gf_tau, can be provided to include uncertainty.

Returns:

PoleFct: Instance with (N) poles at the Chebyshev nodes for degree N and (…, N) residues such that the pole function fits gf_z.

Raises:

ValueError: If more moments are given than poles are fitted (len(moments) > n_pole).