gftool.polepade.asymptotic

gftool.polepade.asymptotic(z, fct_z, zeros, poles, weight=None)

Calculate large z asymptotic from roots and poles.

We assume f(z) = a * np.prod(z - zeros) / np.prod(z - poles), therefore The asymptotic for large abs(z) is f(z) ≈ a * z**(zeros.size - poles.size).

Parameters:

z, fct_z(N_z) complex np.ndarray

Variable where function is evaluated and function values.

zeros, poles(n), (m) complex np.ndarray

Position of the zeros and poles of the function.

weight(N_z) float np.ndarray, optional

Weighting of the data points, for a known error σ this should be weight = 1./σ.

Returns:

asym, stdfloat

Large z asymptotic and its standard deviation.