MatsubaraGrid

A MatsubaraGrid{PT} is a sorted (symmetric) set of MatsubaraFrequency{PT} objects and can be constructed by

T  = 1.0
N  = 128
g1 = MatsubaraGrid(T, N, Fermion) # total no. frequencies is 2N 
g2 = MatsubaraGrid(T, N, Boson)   # total no. frequencies is 2N - 1

where $N$ is the number of non-negative frequencies defined as follows:

Particle type	Fermion	Boson
total no. frequencies	2N	2N-1
range of Matsubara index	-N: N-1	-N+1:N-1
definition	(2n+1)πT	2nπT

MatsubaraGrid{PT} instances are iterable

T = 1.0
N = 128
g = MatsubaraGrid(T, N, Fermion)

for v in g
  println(value(v)) 
  println(index(v))
end

and can be evaluated using either a MatsubaraFrequency{PT}, MatsubaraIndex{PT} or Float64. As long as the input argument is in bounds, this will return the corresponding linear index of the grid in the two former cases and the linear index of the closest frequency in the latter case

T   = 1.0
N   = 128
g   = MatsubaraGrid(T, N, Fermion)
idx = rand(eachindex(g))
@assert g(g[idx]) == idx 
@assert g(value(g[idx])) == idx

MatsubaraGrid{PT} objects can be saved in HDF5 file format as

using MatsubaraFunctions 
using HDF5

file = h5open("test.h5", "w")
T    = 1.0
N    = 128
g    = MatsubaraGrid(T, N, Fermion)

save_matsubara_grid!(file, "grid", g) 
gp = load_matsubara_grid(file, "grid")
close(file)

Types

MatsubaraFunctions.AbstractMatsubaraGrid — Type

abstract type AbstractMatsubaraGrid

MatsubaraFunctions.MatsubaraGrid — Type

struct MatsubaraGrid{PT <: AbstractParticle} <: AbstractMatsubaraGrid

MatsubaraGrid type with fields:

T :: Float64 : temperature
data :: OffsetVector{MatsubaraFrequency{PT}, Vector{MatsubaraFrequency{PT}}} : list of MatsubaraFrequency objects

Functions

Base.firstindex — Function

function firstindex(
    grid :: AbstractMatsubaraGrid
    )    :: Int64

Returns the index of the first Matsubara frequency in grid

Base.lastindex — Function

function lastindex(
    grid :: AbstractMatsubaraGrid
    )    :: Int64

Returns the index of the last Matsubara frequency in grid

Base.axes — Function

function axes(grid :: AbstractMatsubaraGrid)

Returns range of valid indices for Matsubara grid

function axes(f :: MatsubaraFunction)

Returns a tuple of valid index ranges for f.data

function axes(f :: MatsubaraFunction, idx :: Int64)

Returns the range of valid indices along dimension idx of f.data

MatsubaraFunctions.is_inbounds — Function

function is_inbounds(
    w    :: MatsubaraFrequency{PT},
    grid :: MatsubaraGrid{PT}
    )    :: Bool where {PT <: AbstractParticle}

Checks if w is contained in grid

function is_inbounds(
    x    :: MatsubaraIndex{PT},
    grid :: MatsubaraGrid{PT}
    )    :: Bool where {PT <: AbstractParticle}

Checks if x is contained in grid

function is_inbounds(
    w    :: Float64,
    grid :: AbstractMatsubaraGrid
    )    :: Bool

Checks if w lies within grid bounds

MatsubaraFunctions.N — Function

function N(
    grid :: AbstractMatsubaraGrid
    )    :: Int64

Returns that value N used to construct the grid

MatsubaraFunctions.firstvalue — Function

function firstvalue(
    grid :: AbstractMatsubaraGrid
    )    :: Float64

Returns the value of the first Matsubara frequency in grid

MatsubaraFunctions.lastvalue — Function

function lastvalue(
    grid :: AbstractMatsubaraGrid
    )    :: Float64

Returns the value of the last Matsubara frequency in grid

MatsubaraFunctions.indices — Function

function indices(grid :: AbstractMatsubaraGrid)

Returns list of indices for Matsubara frequencies in grid

Base.values — Function

Base.:values(grid :: AbstractMatsubaraGrid)

Returns list of values for Matsubara frequencies in grid

MatsubaraFunctions.info — Function

function info(
    grid :: MatsubaraGrid{PT}
    )    :: Nothing where {PT <: AbstractParticle}

Prints summary of grid properties

function info(
    f :: MatsubaraFunction{GD, SD, DD, Q}
    ) :: Nothing where {GD, SD, DD, Q <: Number}

Prints summary of function properties

MatsubaraFunctions.save_matsubara_grid! — Function

function save_matsubara_grid!(
    h :: HDF5.File,
    l :: String,
    g :: AbstractMatsubaraGrid
    ) :: Nothing

Save MatsubaraGrid g with label l to file h

MatsubaraFunctions.load_matsubara_grid — Function

function load_matsubara_grid(
    h :: HDF5.File,
    l :: String
    ) :: AbstractMatsubaraGrid

Load MatsubaraGrid with label l from file h