Meshes

AbstractMesh

An abstract type representing the real axis. It is used to build the internal type system.

LinearMesh

Mutable struct. A linear and uniform mesh.

Members

• nmesh -> Number of mesh points.
• wmax -> Right boundary (maximum value).
• wmin -> Left boundary (minimum value).
• mesh -> Mesh itself.
• weight -> Precomputed integration weights (composite trapezoidal rule).

See also: TangentMesh.

TangentMesh

Mutable struct. A non-linear and non-uniform mesh. Note that it should be defined on both negative and positive half-axis.

Members

• nmesh -> Number of mesh points.
• wmax -> Right boundary (maximum value).
• wmin -> Left boundary (minimum value).
• mesh -> Mesh itself.
• weight -> Precomputed integration weights (composite trapezoidal rule).

See also: LinearMesh.

LorentzMesh

Mutable struct. A non-linear and non-uniform mesh. Note that it should be defined on both negative and positive half-axis.

Members

• nmesh -> Number of mesh points.
• wmax -> Right boundary (maximum value).
• wmin -> Left boundary (minimum value).
• mesh -> Mesh itself.
• weight -> Precomputed integration weights (composite trapezoidal rule).

See also: HalfLorentzMesh.

HalfLorentzMesh

Mutable struct. A non-linear and non-uniform mesh. Note that it should be defined on positive half-axis only.

Members

• nmesh -> Number of mesh points.
• wmax -> Right boundary (maximum value).
• wmin -> Left boundary (minimum value). It must be 0.0.
• mesh -> Mesh itself.
• weight -> Precomputed integration weights (composite trapezoidal rule).

See also: LorentzMesh.

DynamicMesh

Mutable struct. A mesh used internally in stochastic methods. It supports both uniform and non-uniform meshes. The mesh is usually generated by util/gmesh.jl, saved in fmesh.inp, and loaded dynamically during the initialization step. This mesh should not be used as a regular mesh for describing the spectral functions.

Note that only the StochAC and StochPX solvers support DynamicMesh. This is because δ-like peaks in the StochAC solver and poles in the StochPX solvers can distribute in a non-uniform mesh. While in the StochSK solver, the δ-like peaks must be distributed in an uniform mesh, so it doesn't support DynamicMesh. See sac.jl/calcfmesh() and spx.jl/calcfmesh() for more details.

Members

• nmesh -> Number of mesh points.
• wmax -> Right boundary (maximum value).
• wmin -> Left boundary (minimum value).
• mesh -> Mesh itself.
• weight -> Precomputed integration weights (composite trapezoidal rule).

See also: LinearMesh.

LinearMesh(nmesh::I64, wmin::T, wmax::T) where {T}

A constructor for the LinearMesh struct, which is announced in src/types.jl.

Arguments

• nmesh -> Number of mesh points.
• wmin -> Left boundary of the mesh.
• wmax -> Right boundary of the mesh.

Returns

• lm -> A LinearMesh struct.

See also: LinearMesh.

TangentMesh(nmesh::I64, wmin::T, wmax::T, 𝑝::T = 2.1) where {T}

A constructor for the TangentMesh struct, which is announced in src/types.jl.

Arguments

• nmesh -> Number of mesh points.
• wmin -> Left boundary of the mesh.
• wmax -> Right boundary of the mesh.
• 𝑝 -> A customized parameter.

Returns

• tm -> A TangentMesh struct.

See also: TangentMesh.

LorentzMesh(nmesh::I64, wmin::T, wmax::T, 𝑝::T = 0.01) where {T}

A constructor for the LorentzMesh struct, which is announced in src/types.jl. The algorithm for generating a lorentzian mesh is taken from:

• https://github.com/CQMP/Maxent.

Arguments

• nmesh -> Number of mesh points.
• wmin -> Left boundary of the mesh.
• wmax -> Right boundary of the mesh.
• 𝑝 -> A customized parameter.

Returns

• lm -> A LorentzMesh struct.

See also: LorentzMesh.

HalfLorentzMesh(nmesh::I64, wmax::T, 𝑝::T = 0.01) where {T}

A constructor for the HalfLorentzMesh struct, which is announced in src/types.jl. The algorithm for generating a half-lorentzian mesh is taken from:

• https://github.com/CQMP/Maxent.

Arguments

• nmesh -> Number of mesh points.
• wmax -> Right boundary of the mesh (wmin ≡ 0.0).
• 𝑝 -> A customized parameter.

Returns

• hm -> A HalfLorentzMesh struct.

See also: HalfLorentzMesh.

DynamicMesh(mesh::Vector{T}) where {T}

A constructor for the DynamicMesh struct, which is announced in src/types.jl. The δ peaks in stochastic analytic continuation methods or poles in stochastic pole expansion method could be placed in this mesh. This mesh should not be used to define the spectrum.

Arguments

• mesh -> Usually a mesh from file fmesh.inp. See util/gmesh.jl.

Returns

• dm -> A DynamicMesh struct.

See also: DynamicMesh.

Base.length(am::AbstractMesh)

Return number of mesh points in a Mesh-like struct.

Base.iterate(am::AbstractMesh)

Advance the iterator of a Mesh-like struct to obtain the next mesh point.

Base.iterate(am::AbstractMesh, i::I64)

This is the key method that allows a Mesh-like struct to be iterated, yielding a sequences of mesh points.

Base.eachindex(am::AbstractMesh)

Create an iterable object for visiting each index of a Mesh-like struct.

Base.firstindex(am::AbstractMesh)

Return the first index of a Mesh-like struct.

Base.lastindex(am::AbstractMesh)

Return the last index of a Mesh-like struct.

Base.getindex(am::AbstractMesh, ind::I64)

Retrieve the value(s) stored at the given key or index within a Mesh-like struct.

Base.getindex(am::AbstractMesh, I::UnitRange{I64})

Return a subset of a Mesh-like struct as specified by I.

nearest(am::AbstractMesh, r::F64)

Given a position r (0.0 ≤ r ≤ 1.0), and return the index of the nearest point in the mesh am.

Arguments

See above explanations.

Returns

See above explanations.

Examples

am = LinearMesh(1001, -10.0, 10.0)
pos = nearest(am, 0.2) # pos = 201
println(am[pos]) # -6.0

See also: AbstractMesh.