gftool.basis.pole.PoleFct.from_z

classmethod PoleFct.from_z(z, gf_z, n_pole, moments=(), width=1.0, weight=None)[source]

Generate instance fitting gf_z.

This function is only meaningful away from the real axis. Finds poles and weights for a pole Green’s function matching the given Green’s function gf_z.

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:

z(…, N_z) complex np.ndarray: Frequencies at which gf_z is given. Mind that the fit is only meaningful away from the real axis.
gf_z(…, N_z) complex np.ndarray: Causal Green’s function which is fitted.
n_poleint: Number of poles to fit.
moments(…, N) float array_like: Moments of the high-frequency expansion, where G(z) = moments / z**np.arange(N) for large z.
widthfloat, optional: Distance of the largest pole to the origin (default: 1.0).
weight(…, N_z) float np.ndarray, optional: Weighting of the fit. If an error σ of the input gf_z is known, this should be weight=1/σ. If high-frequency moments should be fitted correctly, width=abs(z)**(N+1) is a good fit.

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).