Spatials

QuantumLattices.Spatials.heatmap — Constant

@recipe plot(reciprocalspace::BrillouinZone, data::AbstractMatrix{<:Number})
@recipe plot(reciprocalspace::ReciprocalZone, data::AbstractMatrix{<:Number})

Define the recipe for the heatmap visualization of data on a Brillouin/reciprocal zone.

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QuantumLattices.Spatials.line — Constant

@recipe plot(path::ReciprocalPath, data::AbstractMatrix{<:Number})

Define the recipe for the line visualization of data along a reciprocal path.

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QuantumLattices.Spatials.scatter — Constant

@recipe plot(path::ReciprocalPath, data::AbstractMatrix{<:Number}, weights::AbstractArray{<:Number, 3}; weightmultiplier=5.0, weightcolors=nothing, weightlabels=nothing)

Define the recipe for the scatter visualization of data along a reciprocal path with a series of weights.

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QuantumLattices.Spatials.AbstractLattice — Type

AbstractLattice{N, D<:Number, M}

Abstract type of a unitcell-described lattice.

It should have the following contents:

name::Symbol: the name of the lattice
coordinates::Matrix{D}: the coordinates of the lattice
vectors::SVector{M, SVector{N, D}}: the translation vectors of the lattice

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QuantumLattices.Spatials.Bond — Type

Bond{K, P<:Point} <: AbstractVector{P}

A generic bond, which could contains several points.

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QuantumLattices.Spatials.Bond — Method

Bond(point::Point)
Bond(kind, point₁::Point, point₂::Point, points::Point...)

Construct a bond.

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QuantumLattices.Spatials.BrillouinZone — Type

BrillouinZone{K, P, N, S<:SVector} <: FractionalReciprocalSpace{K, N, S}

Brillouin zone of a lattice.

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QuantumLattices.Spatials.BrillouinZone — Method

BrillouinZone(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, nk)
BrillouinZone{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, nk) where K
BrillouinZone{P}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}) where P
BrillouinZone{K, P}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}) where {K, P}

Construct a Brillouin zone.

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QuantumLattices.Spatials.FractionalReciprocalSpace — Type

FractionalReciprocalSpace{K, P<:SVector, N} <: ReciprocalSpace{K, P}

Abstract type of reciprocal spaces with fractional coordinates.

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QuantumLattices.Spatials.Lattice — Type

Lattice(lattice::AbstractLattice, ranges::OneAtLeast{Int}, boundaries::OneAtLeast{Union{Char, String, Symbol}}=ntuple(i->'O', Val(fieldcount(typeof(ranges)))); mode::Symbol=:nonnegative)
Lattice(lattice::AbstractLattice, ranges::OneAtLeast{UnitRange{Int}}, boundaries::OneAtLeast{Union{Char, String, Symbol}}=ntuple(i->'O', Val(fieldcount(typeof(ranges)))))

Construct a lattice from the translations of another.

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QuantumLattices.Spatials.Lattice — Type

Lattice{N, D<:Number, M} <: AbstractLattice{N, D, M}

Simplest lattice.

A simplest lattice can be constructed from its coordinates and translation vectors.

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QuantumLattices.Spatials.Lattice — Method

Lattice(coordinates::NTuple{N, Number}...; name::Symbol=:lattice, vectors::Union{AbstractVector{<:AbstractVector{<:Number}}, Nothing}=nothing) where N
Lattice(coordinates::AbstractVector{<:Number}...; name::Symbol=:lattice, vectors::Union{AbstractVector{<:AbstractVector{<:Number}}, Nothing}=nothing)
Lattice(coordinates::AbstractMatrix{<:Number}; name::Symbol=:lattice, vectors::Union{AbstractVector{<:AbstractVector{<:Number}}, Nothing}=nothing)

Construct a lattice.

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QuantumLattices.Spatials.Neighbors — Type

Neighbors{K, V<:Number} <: CompositeDict{K, V}

Neighbor vs. bond length maps.

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QuantumLattices.Spatials.Neighbors — Method

Neighbors(lattice::AbstractLattice, nneighbor::Integer; coordination::Integer=12)

Get the neighbor vs. bond length map of a lattice up to the nneighborth order.

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QuantumLattices.Spatials.Point — Type

Point{N, D<:Number}

A point in a unitcell-described lattice.

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QuantumLattices.Spatials.Point — Method

Point(site::Integer, rcoordinate::SVector{N, D}, icoordinate::SVector{N, D}) where {N, D<:Number}
Point(site::Integer, rcoordinate::NTuple{N, <:Number}, icoordinate::NTuple{N, <:Number}=ntuple(i->0, Val(N))) where N
Point(site::Integer, rcoordinate::AbstractVector{<:Number}, icoordinate::AbstractVector{<:Number}=zero(SVector{length(rcoordinate), Int}))

Construct a labeled point.

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QuantumLattices.Spatials.ReciprocalCurve — Type

ReciprocalCurve{K, S<:SVector} <: ReciprocalSpace{K, S}

A curve in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalCurve — Method

ReciprocalCurve(reciprocalspace::ReciprocalSpace)

Construct a reciprocal curve from a reciprocal space.

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QuantumLattices.Spatials.ReciprocalCurve — Method

ReciprocalCurve(curve::AbstractVector{<:NTuple{N, Number}}) where N
ReciprocalCurve(curve::AbstractVector{<:AbstractVector{<:Number}})
ReciprocalCurve{K}(curve::AbstractVector{<:NTuple{N, Number}}) where {K, N}
ReciprocalCurve{K}(curve::AbstractVector{<:AbstractVector{<:Number}}) where K

Construct a curve in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalPath — Type

ReciprocalPath{K, S<:SVector, N, R} <: ReciprocalSpace{K, S}

A path in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalPath — Method

ReciprocalPath(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, contents::NamedTuple{(:points, :labels), <:Tuple{<:Tuple, <:Tuple}}; length=100, ends=nothing)
ReciprocalPath{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, contents::NamedTuple{(:points, :labels), <:Tuple{<:Tuple, <:Tuple}}; length=100, ends=nothing) where K

ReciprocalPath(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, points::OneOrMore{Number}...; labels=points, length=100, ends=nothing)
ReciprocalPath{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, points::OneOrMore{Number}...; labels=points, length=100, ends=nothing) where K

ReciprocalPath(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, segments::Pair{<:OneOrMore{Number}, <:OneOrMore{Number}}...; labels=segments, length=100, ends=nothing)
ReciprocalPath{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, segments::Pair{<:OneOrMore{Number}, <:OneOrMore{Number}}...; labels=segments, length=100, ends=nothing) where K

Construct a path in the reciprocal space.

Note

For connected segments,
- when length is an integer, it specifies the length of each segment except for the last whose length will be length+1;
- when ends is nothing, the start point will be included while the end point will be not for each segment except for the last both points of which will be included.
For disconnected segments, they can be partitioned into several connected parts, and the rules for connected segments apply for each of such connected parts.

With the above rules, all the points along the assigned path will be counted once and only once with the largest homogeneity.

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QuantumLattices.Spatials.ReciprocalScatter — Type

ReciprocalScatter{K, N, S<:SVector, V<:SVector{N}} <: FractionalReciprocalSpace{K, N, S}

A set of scatter points in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalScatter — Method

ReciprocalScatter(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, fractionals::AbstractVector{<:AbstractVector{<:Number}})
ReciprocalScatter{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, fractionals::AbstractVector{<:AbstractVector{<:Number}}) where K

Construct a set of reciprocal scatter points.

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QuantumLattices.Spatials.ReciprocalScatter — Method

ReciprocalScatter(reciprocalspace::FractionalReciprocalSpace)

Construct a set of reciprocal scatter points from a reciprocal space with fractional coordinates.

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QuantumLattices.Spatials.ReciprocalSpace — Type

ReciprocalSpace{K, P<:SVector} <: VectorSpace{P}

Abstract type of reciprocal spaces.

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QuantumLattices.Spatials.ReciprocalZone — Type

ReciprocalZone{K, N, S<:SVector, V<:Number} <: FractionalReciprocalSpace{K, N, S}

A zone in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalZone — Method

ReciprocalZone(reciprocals::AbstractVector{<:AbstractVector{<:Number}}; length=100, ends=(true, false))
ReciprocalZone{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}; length=100, ends=(true, false)) where K

ReciprocalZone(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::Pair{<:Number, <:Number}...; length=100, ends=(true, false))
ReciprocalZone{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::Pair{<:Number, <:Number}...; length=100, ends=(true, false)) where K

ReciprocalZone(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::AbstractVector{<:Pair{<:Number, <:Number}}; length=100, ends=(true, false))
ReciprocalZone{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::AbstractVector{<:Pair{<:Number, <:Number}}; length=100, ends=(true, false)) where K

ReciprocalZone(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::OneAtLeast{Pair{<:Number, <:Number}}; length=100, ends=(true, false))
ReciprocalZone{K}(reciprocals::AbstractVector{<:AbstractVector{<:Number}}, bounds::OneAtLeast{Pair{<:Number, <:Number}}; length=100, ends=(true, false)) where K

Construct a rectangular zone in the reciprocal space.

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QuantumLattices.Spatials.ReciprocalZone — Method

ReciprocalZone(brillouinzone::BrillouinZone)

Construct a reciprocal zone from a Brillouin zone.

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QuantumLattices.Spatials.@hexagon_str — Macro

hexagon"P₁-P₂-P₃-..."
hexagon"P₁-P₂-P₃-..., 120°"
hexagon"P₁-P₂-P₃-..., 60°"

Construct a tuple of start-stop point pairs for the hexagonal reciprocal space.

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QuantumLattices.Spatials.@line_str — Macro

line"P₁-P₂-P₃-..."

Construct a tuple of start-stop point pairs for the one dimensional reciprocal space.

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QuantumLattices.Spatials.@rectangle_str — Macro

rectangle"P₁-P₂-P₃-..."

Construct a tuple of start-stop point pairs for the rectangular reciprocal space.

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Base.getindex — Method

getindex(lattice::AbstractLattice, i::Integer) -> SVector

Get the ith coordinate.

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Base.getindex — Method

getindex(bond::Bond, i::Integer) -> Point

Get the ith point contained in a generic bond.

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Base.hash — Method

hash(brillouinzone::BrillouinZone, h::UInt)

Hash a Brillouin zone.

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Base.length — Method

length(lattice::AbstractLattice) -> Int

Get the number of points contained in a lattice.

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Base.range — Method

range(brillouinzone::BrillouinZone, i::Integer) -> StepRangeLen{Float64}

Get the ith axis range of the fractional coordinates of a Brillouin zone.

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Base.range — Method

range(reciprocalzone::ReciprocalZone, i::Integer) -> StepRangeLen{Float64}

Get the ith axis range of the fractional coordinates of a reciprocal zone.

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Base.reverse — Method

reverse(bond::Bond) -> Bond

Get the reversed bond.

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Base.step — Method

step(path::ReciprocalPath, i::Integer) -> scalartype(path)

Get the step between the ith and the (i+1)th points in the path.

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LinearAlgebra.rank — Method

rank(reciprocalspace::FractionalReciprocalSpace) -> Int
rank(::Type{<:FractionalReciprocalSpace{K, N} where K}) where N -> Int

Get the rank, i.e., the number of reciprocal lattice vectors of a reciprocal space with fractional coordinates.

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QuantumLattices.QuantumOperators.matrix — Method

matrix(vs::AbstractVector{<:AbstractVector}) -> Matrix

Convert a vector of vector to a matrix.

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QuantumLattices.QuantumOperators.scalartype — Method

scalartype(::Type{<:AbstractLattice{N, D} where N}) where {D<:Number}

Get the data type of the coordinates of a lattice.

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QuantumLattices.QuantumOperators.scalartype — Method

scalartype(::Type{<:Point{N, D} where N}) where {D<:Number}

Get the data type of the coordinates of a point.

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QuantumLattices.QuantumOperators.scalartype — Method

scalartype(::Type{<:ReciprocalSpace{K, P} where K}) where {P<:SVector}

Get the data type of the coordinates of a reciprocal space.

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QuantumLattices.Spatials.azimuth — Method

azimuth(v::AbstractVector{<:Number}) -> Number

Get the azimuth angle in radians of a vector.

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QuantumLattices.Spatials.azimuthd — Method

azimuthd(v::AbstractVector{<:Number}) -> Number

Get the azimuth angle in degrees of a vector.

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QuantumLattices.Spatials.bonds! — Method

bonds!(bonds::Vector, lattice::AbstractLattice, nneighbor::Integer; coordination::Integer=12) -> typeof(bonds)
bonds!(bonds::Vector, lattice::AbstractLattice, neighbors::Neighbors) -> typeof(bonds)

Get the required bonds of a lattice and append them to the input bonds.

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QuantumLattices.Spatials.bonds — Method

bonds(lattice::AbstractLattice, ::Colon) -> Matrix{Bond{Colon, Point{dimension(lattice), scalartype(lattice)}}}

Get the all-to-all bonds in a lattice.

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QuantumLattices.Spatials.bonds — Method

bonds(lattice::AbstractLattice, nneighbor::Integer; coordination::Integer=12) -> Vector{Bond{Int, Point{dimension(lattice), scalartype(lattice)}}}
bonds(lattice::AbstractLattice, neighbors::Neighbors) -> Vector{Bond{keytype(neighbors), Point{dimension(lattice), scalartype(lattice)}}}

Get the required bonds of a lattice.

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QuantumLattices.Spatials.direction — Method

direction(v::Char, args...) -> SVector{3, <:Number}
direction(v::Number, unit::Symbol) -> SVector{2, <:Number}
direction(v::Tuple{Number, Number}, unit::Symbol) -> SVector{3, <:Number}
direction(v::AbstractVector{<:Number}, args...) -> AbstractVector{<:Number}

Get the unit vector that specifies the direction of a vector.

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QuantumLattices.Spatials.distance — Method

distance(p₁::AbstractVector{<:Number}, p₂::AbstractVector{<:Number}) -> Number

Get the distance between two points.

Note

Compared to norm(p₁-p₂), this function avoids the memory allocation for p₁-p₂, thus is more efficient.

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QuantumLattices.Spatials.distance — Method

distance(path::ReciprocalPath) -> scalartype(path)
distance(path::ReciprocalPath, i::Integer) -> scalartype(path)
distance(path::ReciprocalPath, i::Integer, j::Integer) -> scalartype(path)

Get the distance

of the total path,
from the start point to the ith point in the path,
from the ith point to the jth point in the path (when i is greater than j, the value is negative).

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QuantumLattices.Spatials.dlmsave — Function

dlmsave(filename::AbstractString, x::AbstractVector{<:Number}, y::Union{AbstractVector{<:Number}, AbstractMatrix{<:Number}}, delim='	')
dlmsave(filename::AbstractString, x::AbstractVector{<:Number}, y::AbstractVector{<:Number}, z::Union{AbstractMatrix{<:Number}, AbstractArray{<:Number, 3}}, delim='	')
dlmsave(filename::AbstractString, reciprocalspace::Union{BrillouinZone, ReciprocalZone}, data::Union{AbstractMatrix{<:Number}, AbstractArray{<:Number, 3}}, delim='	'; fractional::Bool=true)
dlmsave(filename::AbstractString, reciprocalscatter::ReciprocalScatter, weights::AbstractMatrix{<:Number}, delim='	'; fractional::Bool=true)
dlmsave(filename::AbstractString, path::ReciprocalPath, data:AbstractMatrix{<:Number}, delim='	'; distance::Bool=true)
dlmsave(filename::AbstractString, path::ReciprocalPath, data::AbstractMatrix{<:Number}, weights::AbstractArray{<:Number, 3}, delim='	'; distance::Bool=true)
dlmsave(filename::AbstractString, path::ReciprocalPath, y::AbstractVector{<:Number}, data::Union{AbstractMatrix{<:Number}, AbstractArray{<:Number, 3}}, delim='	'; distance::Bool=true)

Save data to delimited files.

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QuantumLattices.Spatials.fractionals — Method

fractionals(brillouinzone::BrillouinZone) -> AbstractVector{SVector{rank(brillouinzone), scalartype(brillouinzone)}}

Get the fractional coordinates of a Brillouin zone.

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QuantumLattices.Spatials.fractionals — Method

fractionals(reciprocalscatter::ReciprocalScatter) -> Vector{<:SVector}

Get the fractional coordinates of a reciprocal space.

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QuantumLattices.Spatials.fractionals — Method

fractionals(reciprocalzone::ReciprocalZone) -> AbstractVector{SVector{rank(reciprocalzone), scalartype(reciprocalzone)}}

Get the fractional coordinates of a reciprocal zone.

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QuantumLattices.Spatials.icoordinate — Method

icoordinate(bond::Bond) -> SVector

Get the icoordinate of the bond.

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QuantumLattices.Spatials.interlinks — Method

interlinks(cluster₁::AbstractMatrix{<:Number}, cluster₂::AbstractMatrix{<:Number}, neighbors::Neighbors) -> Vector{Tuple{Int, Int, Int}}

Use kdtree to get the intercluster nearest neighbors.

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QuantumLattices.Spatials.iscontinuous — Method

iscontinuous(brillouinzone::BrillouinZone) -> Bool
iscontinuous(::Type{<:BrillouinZone{K, P} where K}) where P -> Bool

Judge whether a Brillouin zone is continuous.

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QuantumLattices.Spatials.isdiscrete — Method

isdiscrete(brillouinzone::BrillouinZone) -> Bool
isdiscrete(::Type{<:BrillouinZone{K, P} where K}) where P -> Bool

Judge whether a Brillouin zone is discrete.

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QuantumLattices.Spatials.isintracell — Method

isintracell(bond::Bond) -> Bool

Judge whether a bond is intra the unit cell of a lattice.

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QuantumLattices.Spatials.isintracell — Method

isintracell(point::Point) -> Bool

Judge whether a point is intra the unitcell.

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QuantumLattices.Spatials.isintratriangle — Method

isintratriangle(
    p::AbstractVector{<:Number}, p₁::AbstractVector{<:Number}, p₂::AbstractVector{<:Number}, p₃::AbstractVector{<:Number};
    vertexes::NTuple{3, Bool}=(true, true, true), edges::NTuple{3, Bool}=(true, true, true), atol::Real=atol, rtol::Real=rtol
) -> Bool

Judge whether a point belongs to the interior of a triangle whose vertexes are p₁, 'p₂' and p₃ with the give tolerance. vertexes and edges define whether the interior should contain the vertexes or edges, respectively.

Note

The vertexes are in the order (p₁, p₂, p₃) and the edges are in the order (p₁p₂, p₂p₃, p₃p₁).
The edges do not contain the vertexes.

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QuantumLattices.Spatials.isonline — Method

isonline(
    p::AbstractVector{<:Number}, p₁::AbstractVector{<:Number}, p₂::AbstractVector{<:Number};
    ends::Tuple{Bool, Bool}=(true, true), atol::Real=atol, rtol::Real=rtol
) -> Bool

Judge whether a point is on a line segment whose end points are p₁ and p₂ with the given tolerance. ends defines whether the line segment should contain its ends.

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QuantumLattices.Spatials.isparallel — Method

isparallel(v₁::AbstractVector{<:Number}, v₂::AbstractVector{<:Number}; atol::Real=atol, rtol::Real=rtol) -> Int

Judge whether two vectors are parallel to each other with the given tolerance, 0 for not parallel, 1 for parallel and -1 for antiparallel.

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QuantumLattices.Spatials.issubordinate — Method

issubordinate(coordinate::AbstractVector{<:Number}, vectors::AbstractVector{<:AbstractVector{<:Number}}; atol::Real=atol, rtol::Real=rtol) -> Bool

Judge whether a coordinate belongs to a lattice defined by vectors with the given tolerance.

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QuantumLattices.Spatials.label — Method

label(reciprocalspace::ReciprocalSpace, i::Integer) -> String
label(::Type{<:ReciprocalSpace{K}}, i::Integer) where K -> String

Get the label of the ith axis of a reciprocal space.

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QuantumLattices.Spatials.label — Method

label(reciprocalspace::ReciprocalSpace) -> Symbol
label(::Type{<:ReciprocalSpace{K}}) where K -> Symbol

Get the label of a reciprocal space.

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QuantumLattices.Spatials.minimumlengths — Function

minimumlengths(cluster::AbstractVector{<:Number}, vectors::AbstractVector{<:AbstractVector{<:Number}}, nneighbor::Integer=1; coordination::Integer=12) -> Vector{Float}
minimumlengths(cluster::AbstractMatrix{<:Number}, vectors::AbstractVector{<:AbstractVector{<:Number}}, nneighbor::Integer=1; coordination::Integer=12) -> Vector{Float}

Use kdtree to search the lowest several minimum bond lengths within a lattice translated by a cluster.

When the translation vectors are not empty, the lattice will be considered periodic in the corresponding directions. Otherwise the lattice will be open in all directions. To search for the bonds across the periodic boundaries, the cluster will be pre-translated to become a supercluster, which has open boundaries but is large enough to contain all the nearest neighbors within the required order. The coordination parameter sets the average number of each order of nearest neighbors. If it is to small, larger bond lengths may not be searched, and the result will contain Inf. This is a sign that you may need a larger coordination. Another situation that Inf appears in the result occurs when the minimum lengths are searched in open lattices. Indeed, the cluster may be too small so that the required order just goes beyond it. In this case the warning message can be safely ignored.

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QuantumLattices.Spatials.period — Method

period(brillouinzone::BrillouinZone, i::Integer) -> Integer/Inf
period(::Type{<:BrillouinZone{K, P} where K}, i::Integer) where P -> Integer/Inf

Get the ith period of a brillouin zone.

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QuantumLattices.Spatials.periods — Method

periods(brillouinzone::BrillouinZone) -> Tuple
periods(::Type{<:BrillouinZone{K, P} where K}) -> P

Get the periods of a brillouin zone.

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QuantumLattices.Spatials.polar — Method

polar(v::AbstractVector{<:Number}) -> Number

Get the polar angle in radians of a vector.

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QuantumLattices.Spatials.polard — Method

polard(v::AbstractVector{<:Number}) -> Number

Get the polar angle in degrees of a vector.

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QuantumLattices.Spatials.rcoordinate — Method

rcoordinate(bond::Bond) -> SVector

Get the rcoordinate of the bond.

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QuantumLattices.Spatials.reciprocals — Method

reciprocals(lattice::AbstractLattice) -> Vector{<:SVector}

Get the reciprocal translation vectors of the dual lattice.

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QuantumLattices.Spatials.reciprocals — Method

reciprocals(vectors::AbstractVector{AbstractVector{<:Number}}) -> AbstractVector{<:AbstractVector{<:Number}}

Get the reciprocals dual to the input vectors.

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QuantumLattices.Spatials.reciprocals — Method

reciprocals(reciprocalspace::FractionalReciprocalSpace) -> AbstractVector{<:AbstractVector{<:Number}}

Get the reciprocal lattice vectors of a reciprocal space with fractional coordinates.

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QuantumLattices.Spatials.rotate — Method

rotate(vector::AbstractVector{<:Number}, angle::Number; axis::Tuple{Union{AbstractVector{<:Number}, Nothing}, Tuple{<:Number, <:Number}}=(nothing, (0, 0))) -> AbstractVector{<:Number}
rotate(cluster::AbstractMatrix{<:Number}, angle::Number; axis::Tuple{Union{AbstractVector{<:Number}, Nothing}, Tuple{<:Number, <:Number}}=(nothing, (0, 0))) -> AbstractMatrix{<:Number}

Get a rotated vector/cluster of the original one by a certain angle around an axis.

The axis is determined by a point it gets through (nothing can be used to denote the origin), and its polar as well as azimuth angles in radians. The default axis is the z axis.

Note

The result is given by the Rodrigues' rotation formula.
Only 2 and 3 dimensional vectors can be rotated.
When the input vectors are 2 dimensional, both the polar and azimuth of the axis must be 0.

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QuantumLattices.Spatials.selectpath — Method

selectpath(brillouinzone::BrillouinZone, contents::NamedTuple{(:points, :labels), <:Tuple{<:Tuple, <:Tuple}}; ends=nothing, atol::Real=atol, rtol::Real=rtol) -> Tuple(ReciprocalPath, Vector{Int})
selectpath(brillouinzone::BrillouinZone, points::OneOrMore{Number}...; labels=points, ends=nothing, atol::Real=atol, rtol::Real=rtol) -> Tuple(ReciprocalPath, Vector{Int})
selectpath(brillouinzone::BrillouinZone, segments::Pair{<:OneOrMore{Number}, <:OneOrMore{Number}}...; labels=segments, ends=nothing, atol::Real=atol, rtol::Real=rtol) -> Tuple(ReciprocalPath, Vector{Int})

Select a path from a BrillouinZone. Return a ReciprocalPath and the positions of the equivalent points in the BrillouinZone.

Note

For connected segments, the start point will be included while the stop point will be not for each segment except for the last both points of which will be included if ends is nothing.
For disconnected segments, they can be partitioned into several connected parts, and the rule for connected segments applies for each of such connected parts.

With the above rules, all the points along the assigned path will be counted once and only once.

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QuantumLattices.Spatials.setup — Method

@recipe plot(reciprocalspace::BrillouinZone, data::AbstractArray{<:Number, 3}; subtitles=nothing, subtitlefontsize=8, nrow=nothing, ncol=nothing, clims=nothing)
@recipe plot(reciprocalspace::ReciprocalZone, data::AbstractArray{<:Number, 3}; subtitles=nothing, subtitlefontsize=8, nrow=nothing, ncol=nothing, clims=nothing)
@recipe plot(path::ReciprocalPath, y::AbstractVector{<:Number}, data::AbstractArray{<:Number, 3}; subtitles=nothing, subtitlefontsize=8, nrow=nothing, ncol=nothing, clims=nothing)

Define the recipe for the heatmap visualization of a series of data on

a Brillouin zone,
a reciprocal zone,
the x-y plain with the x axis being a reciprocal path.

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QuantumLattices.Spatials.shrink — Method

shrink(reciprocalzone::ReciprocalZone, ranges::OrdinalRange{<:Integer}...) -> ReciprocalZone

Shrink a reciprocal zone.

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QuantumLattices.Spatials.ticks — Method

ticks(path::ReciprocalPath) -> Tuple{Vector{scalartype(path)}, Vector{String}}

Get the position-label pairs of the ticks of a path.

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QuantumLattices.Spatials.tile — Method

tile(cluster::AbstractVector{<:Number}, vectors::AbstractVector{<:AbstractVector{<:Number}}, translations) -> AbstractMatrix{<:Number}
tile(cluster::AbstractMatrix{<:Number}, vectors::AbstractVector{<:AbstractVector{<:Number}}, translations) -> AbstractMatrix{<:Number}

Tile a supercluster by translations of the input cluster.

Basically, the final supercluster is composed of several parts, each of which is a translation of the original cluster, with the translation vectors specified by vectors and each set of the translation indices contained in translations. When translation vectors are empty, a copy of the original cluster will be returned.

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QuantumLattices.Spatials.translate — Method

translate(cluster::AbstractVector{<:Number}, vector::AbstractVector{<:Number}) -> AbstractVector{<:Number}
translate(cluster::AbstractMatrix{<:Number}, vector::AbstractVector{<:Number}) -> AbstractMatrix{<:Number}

Get the translated cluster of the original one by a vector.

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QuantumLattices.Spatials.volume — Method

volume(vectors::AbstractVector{<:AbstractVector{<:Number}}) -> Number
volume(v::AbstractVector{<:Number}) -> Number
volume(v₁::AbstractVector{<:Number}, v₂::AbstractVector{<:Number}) -> Number
volume(v₁::AbstractVector{<:Number}, v₂::AbstractVector{<:Number}, v₃::AbstractVector{<:Number}) -> Number

Get the volume spanned by the input vectors.

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QuantumLattices.Spatials.volume — Method

volume(brillouinzone::BrillouinZone) -> Number

Get the volume of a Brillouin zone.

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QuantumLattices.Spatials.volume — Method

volume(reciprocalzone::ReciprocalZone) -> Number

Get the volume of a reciprocal zone.

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QuantumLattices.decompose — Method

decompose(m::AbstractMatrix{<:Number}, m₀::AbstractMatrix{<:Number}) -> Number
decompose(m::AbstractMatrix{<:Number}, ms::ZeroAtLeast{AbstractMatrix{<:Number}}) -> ZeroAtLeast{Number}
decompose(m::AbstractMatrix{<:Number}, ms::AbstractVector{<:AbstractMatrix{<:Number}}) -> Vector{<:Number}

Decompose a matrix.

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QuantumLattices.decompose — Method

decompose(v₀::AbstractVector{<:Number}, v₁::AbstractVector{<:Number}) -> Number
decompose(v₀::AbstractVector{<:Number}, v₁::AbstractVector{<:Number}, v₂::AbstractVector{<:Number}) -> Tuple{Number, Number}
decompose(v₀::AbstractVector{<:Number}, v₁::AbstractVector{<:Number}, v₂::AbstractVector{<:Number}, v₃::AbstractVector{<:Number}) -> Tuple{Number, Number, Number}
decompose(v₀::AbstractVector{<:Number}, vs::AbstractVector{<:AbstractVector{<:Number}}) -> Vector{<:Number}

Decompose a vector with respect to input basis vectors.

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QuantumLattices.dimension — Method

dimension(lattice::AbstractLattice) -> Int
dimension(::Type{<:AbstractLattice{N}}) where N -> Int

Get the space dimension of the lattice.

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QuantumLattices.dimension — Method

dimension(bond::Bond) -> Int
dimension(::Type{<:Bond{K, P} where K}) where {P<:Point} -> Int

Get the space dimension of a concrete bond.

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QuantumLattices.dimension — Method

dimension(point::Point) -> Int
dimension(::Type{<:Point{N}}) where N -> Int

Get the spatial dimension of a point.

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QuantumLattices.dimension — Method

dimension(reciprocalspace::ReciprocalSpace) -> Int
dimension(::Type{<:ReciprocalSpace{K, P} where K}) where {P<:SVector} -> Int

Get the spatial dimension of a reciprocal space.

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QuantumLattices.expand — Method

expand(reciprocalspace::FractionalReciprocalSpace, fractional::AbstractVector{<:Number}) -> AbstractVector{<:AbstractVector{<:Number}}

Expand the fractional coordinate in a reciprocal space to the Cartesian coordinate.

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RecipesBase.apply_recipe — Function

@recipe plot(lattice::AbstractLattice, neighbors::Union{Int, Neighbors}, filter::Function=bond->true; siteon=false)

Define the recipe for the visualization of a lattice.

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RecipesBase.apply_recipe — Method

@recipe plot(reciprocalspace::FractionalReciprocalSpace; fractional=false, autolims=true)

Define the recipe for the visualization of a reciprocal space with fractional coordinates.

When fractional is true, the fractional coordinates will be plotted. Otherwise the Cartesian coordinates will be plotted.

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RecipesBase.apply_recipe — Method

@recipe plot(curve::ReciprocalCurve)

Define the recipe for the visualization of a reciprocal curve.

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RecipesBase.apply_recipe — Method

@recipe plot(path::ReciprocalPath, y::AbstractVector{<:Number}, data::AbstractMatrix{<:Number})

Define the recipe for the heatmap visualization of data on the x-y plain with the x axis being a reciprocal path.

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RecipesBase.apply_recipe — Method

@recipe plot(path::ReciprocalPath)

Define the recipe for the visualization of a reciprocal path.

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RecipesBase.apply_recipe — Method

@recipe plot(reciprocalscatter::ReciprocalScatter, weights::AbstractMatrix{<:Number}; fractional=true, weightmultiplier=1.0, weightcolors=nothing, weightlabels=nothing)

Define the recipe for the scatter visualization of reciprocal points with a series of weights.

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