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.. highlight:: c
Meshes
#######
The linear meshes
==================
The mesh kind
--------------
This option is particularly important for the Matsubara Green functions in imaginary time.
Briefly, if we want to describe a function on an interval:
* ``full_bins`` includes both endpoints,
* ``half_bins`` includes none of the endpoints
* ``without_last`` includes only the first endpoint.
We then have to be careful for example when we fourier transform the function (to not take twice the same point).
The four basic meshes
=====================
Real time
----------
The domain is the set of real numbers.
By default, the mesh kind is ``full_bins``.
Be careful to the value of a function at a point in case of discontinuities: is its value equal to the limit from below ? To the limit from above ? By none of these limits ?
Real frequency
---------------
The domain is the set of real numbers.
By default, the mesh kind is ``full_bins``.
Matsubara time
---------------
The domain is (approximatively) the set of real numbers between 0 and :math:`\beta`.
In fact, other points are also in the domain, but the values at these points are given by the values on this restricted domain.
:math:`G(\tau+\beta)=-G(\tau)` for fermions, :math:`G(\tau+\beta)=G(\tau)` for bosons.
The limits from above or below at these both points can be different.
Depending on what one needs, we can choose ``full_bins``, ``half_bins`` or ``without_last``.
Matsubara frequency
--------------------
The domain is discrete. The Matsubara frequencies are :math:`\omega_n=\frac{(2n+1)\pi}{beta}` for fermions and :math:`\omega_n=\frac{2n\pi}{beta}` for bosons.