triqs.mesh.meshes.MeshReFreq

class triqs.mesh.meshes.MeshReFreq

Bases: object

Real frequency mesh type.

A real frequency mesh is defined by its size \(N \geq 0\) and a frequency interval \([\omega_{\mathrm{min}}, \omega_{\mathrm{max}}]\). It contains \(N\) equally spaced mesh points on the interval \([\omega_{\mathrm{min}}, \omega_{\mathrm{max}}]\) such that the distance between two consecutive mesh points (step size) is constant.

A real frequency mesh has the following properties:

• Each mesh point is identified by a unique index \(n \in \{0, 1, \ldots, N-1\}\).

• An index \(n\) is mapped to the corresponding data index \(d\) by the identity function \(d(n) = n\) and vice versa.

• An index \(n\) is mapped to the corresponding value \(\omega\) by the linear function \(\omega(n) = \omega_{\mathrm{min}} + n \cdot \Delta\) such that \(\omega(0) = \omega_{\mathrm{min}}\) and \(\omega(N - 1) = \omega_{\mathrm{max}}\). The step size of the mesh is \(\Delta = \frac{\omega_{\mathrm{max}} - \omega_{\mathrm{min}}}{N - 1}\) for \(N > 1\), otherwise it is undefined. For implementation purposes, we set \(\Delta = 0\) and \(\Delta^{-1} = 0\) for \(N = 0\) and \(\Delta = 0\) and \(\Delta^{-1} = \infty\) for \(N = 1\).

• An arbitrary value \(\omega \in [\omega_{\mathrm{min}}, \omega_{\mathrm{max}}]\) is mapped to the closest mesh point with index \(n\) by the function \(n(\omega) = \left\lfloor \frac{\omega - \omega_{\mathrm{min}}}{\Delta} + 0.5 \right\rfloor\).

Green’s function containers that are based on a real frequency mesh store the function values at the discrete frequency points \(\omega(n)\), i.e. \(f_n = f(\omega(n))\), and use linear interpolation to evaluate the function at an arbitrary frequency \(\omega \in [\omega_{\mathrm{min}}, \omega_{\mathrm{max}}]\).

---

Dispatched C++ constructor(s).

[1] (w_min: float = 0, w_max: float = 0, n_w: int = 0)

[2] (window: tuple[float, float], n_w: int)

Construct a real frequency mesh on the interval \([\omega_{\text{min}}, \omega_{\text{max}}]\) with \(N \geq 0\) equally spaced mesh points.

Parameters:

w_minfloat

Lower bound \(\omega_{\mathrm{min}}\) of the frequency interval.

w_maxfloat

Upper bound \(\omega_{\mathrm{max}}\) of the frequency interval.

n_wint, int

Size of the mesh.

windowtuple[float, float]

Pair containing the lower and upper bounds of the frequency interval.

Attributes

delta	Get the step size \(\Delta\) of the mesh, i.e. the distance between two consecutive mesh points.
delta_inv	Get the inverse of the step size of the mesh, i.e. \(1 / \Delta\).
first_index	Get the first index of the mesh, i.e. \(0\).
last_index	Get the last index of the mesh, i.e. \(N - 1\).
mesh_hash	Get the hash value of the mesh.
positive_only	Is the mesh restricted to positive frequencies?
w_max	Get the upper bound of the interval \(\omega_{\text{max}}\), i.e. the value of the last mesh point.
w_min	Get the lower bound of the interval \(\omega_{\text{min}}\), i.e. the value of the first mesh point.

Methods

__call__(*args, **kwargs)	Call self as a function.
copy	Get a copy of a mesh (for Python bindings).
copy_from	Copy one mesh into another (for Python bindings).
is_index_valid	Check if an index \(n\) is valid.
set_tail_fit_parameters	Set the pointer to a new tail-fitter object constructed with the given parameters.
to_data_index	Map an index \(n \in \{0, 1, \ldots, N-1\}\) to its corresponding data index \(d(n)\).
to_index	Map a data index \(d \in \{0, 1, \ldots, N-1\}\) to the corresponding index \(n(d)\).
to_value	Map an index \(n \in \{0, 1, \ldots, N-1\}\) to its corresponding value \(m(n)\).
values	Get the values of all mesh points in a mesh.