[gf<imfreq>] Green function on Matsubara frequencies¶
This is a specialisation of gf for imaginary Matsubara frequencies.
Synopsis¶
gf<imfreq, Target, Opt>
The Target template parameter can take the following values:
| Target | Meaning |
|---|---|
| scalar_valued | The function is scalar valued (double, complex…). |
| matrix_valued [default] | The function is matrix valued. |
Domain & mesh¶
The domain is triqs::gfs::matsubara_domain.
The Matsubara frequencies are \(\omega_n=\frac{(2n+1)\pi}{\beta}\) for fermions and \(\omega_n=\frac{2n\pi}{\beta}\) for bosons.
The mesh is gf_mesh<imfreq>.
Evaluation method¶
- No interpolation.
- Return type:
- If Target==scalar_valued: a complex
- If Target==matrix_valued: an object modeling ImmutableMatrix concept.
- When the point is outside of the mesh, the high-frequency moments of the Green function are automatically determined using a least-square fitting procedure. They are then used to calculate the value of the Green function at the point.
Data storage¶
- If Target==scalar_valued :
- data_t: 1d array of complex<double>.
- g.data()(i) is the value of g for the i-th point of the mesh.
- If Target==matrix_valued :
- data_t: 3d array (C ordered) of complex<double>.
- g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
HDF5 storage convention¶
h5 tag: ImFreq
TODO: DECIDE if we have 2 tag, one for scalar, one for matrix….