gftool.fourier.tt2z_simps

gftool.fourier.tt2z_simps(tt, gf_t, z)

Laplace transform of the real-time Green’s function gf_t.

Approximate the Laplace integral using the Simpson rule.

Parameters:

tt(Nt) float np.ndarray

The equidistant points for which the Green’s function gf_t is given.

gf_t(…, Nt) complex np.ndarray

Green’s function at time points tt.

z(…, Nz) complex np.ndarray

Frequency points for which the Laplace transformed Green’s function should be evaluated.

Returns:

(…, Nz) complex np.ndarray

Laplace transformed Green’s function for complex frequencies z.

See also

tt2z_trapz

Plain implementation using trapezoidal rule.

tt2z_lin

Laplace integration using Filon’s method.

Notes

If numexpr is available, it is used for the significant speed up it provides for transcendental equations. Internally the sum is evaluated as a matrix product to leverage the speed-up of BLAS.