Skip to content
New issue

Have a question about this project? # for a free GitHub account to open an issue and contact its maintainers and the community.

#

By clicking “#”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? # to your account

Jump to bottom

Bug fix. #62

Merged
merged 2 commits into from
Nov 29, 2022
Merged

Bug fix. #62

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
36f8ee7
wip. fix bug for 3d polarmesh integrate
iintSjds Nov 23, 2022
2c888f2
wip
iintSjds Nov 25, 2022
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
173 changes: 42 additions & 131 deletions example/compositemesh.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -7,146 +7,57 @@ using BrillouinZoneMeshes.AbstractMeshes
using BrillouinZoneMeshes.LinearAlgebra
using BrillouinZoneMeshes.StaticArrays

using Test
lattice = Matrix([1 0; 0 1.0]')
atoms = [1]
positions = [zeros(2)]
br = BZMeshes.Cell(lattice=lattice, atoms=atoms, positions=positions)

_dispersion(k) = -sum(cos.(k)) + 0.1
# _dispersion(k) = dot(k, k) - π^2 / 4
T = 0.001

function dispersion(k)
# constrain to 1st bz
_k = [(abs(p) < π) ? p : π for p in k]
return _dispersion(_k)
end

function AbstractMeshes.interval(mesh::ProdMesh, I::Int)
inds = AbstractMeshes._ind2inds(size(mesh), I)
J = Base._sub2ind(size(mesh)[2:end], inds[2:end]...)
x1, x2 = AbstractMeshes.interval(mesh.grids[J], inds[1])
if length(inds) > 2
return [(x1, x2), AbstractMeshes.interval(mesh.mesh, J)...]
function integrand(k)
#if dot(k, k) <= π^2
if abs(k[1]) <= π && abs(k[2]) <= π
return 1 / (dispersion(k)^2 + T^2)
else
return [(x1, x2), AbstractMeshes.interval(mesh.mesh, J)]
return 0.0
end
end

struct CompositeMesh{T,PM,SM} <: AbstractMesh{T,1}
panelmesh::PM
submeshes::Vector{SM}
end

function CompositeMesh(panelmesh::PM, N) where {PM}
T = eltype(panelmesh)
submeshes = []
for (i, p) in enumerate(panelmesh)
intervals = AbstractMeshes.interval(panelmesh, i)
DIM = length(intervals)
origin = [intervals[j][1] for j in 1:DIM]
lattice = diagm(DIM, DIM, [intervals[j][2] - intervals[j][1] for j in 1:DIM])
cm = ChebMesh(origin, lattice, DIM, N)
push!(submeshes, cm)
function int_mesh(mesh)
data = zeros(Float64, size(mesh))
for i in 1:length(mesh)
data[i] = integrand(mesh[i])
end

SM = typeof(submeshes[1])
return CompositeMesh{T,PM,SM}(panelmesh, submeshes)
return integrate(data, mesh)
end

N = 8
bound = [-π, π]
theta = SimpleGrid.Uniform(bound, N; isperiodic=true)
# bzmesh = BZMeshes.PolarMesh(dispersion=dispersion, anglemesh=theta, cell=br,
# kmax=π, Nloggrid=5, Nbasegrid=4, minterval=0.001)
pm = BZMeshes.CompositePolarMesh(dispersion=dispersion,
anglemesh=theta, cell=br, basegridtype=:uniform,
kmax=π * sqrt(2.4), Nloggrid=8, Nbasegrid=3, minterval=0.1T, N=4)

@testset "CompositeMesh" begin
@testset "Constructor" begin
a, b = 0.8, 1.2

N, M = 3, 2
# theta grid dense around 0 and π
theta = CompositeGrid.LogDensedGrid(
:cheb,
[-π, π],
[-π, 0, π],
N,
0.1,
M
)
println(theta)
grids = [CompositeGrid.LogDensedGrid(:cheb, [0.0, 2.0], [sqrt(a * cos(θ)^2 + b * sin(θ)^2),], N, 0.1, M) for θ in theta]

pm = ProdMesh(theta, grids)
cm = CompositeMesh(pm, 3)
end

# @testset "2D" begin
# # given dispersion function accept a k in cartesian
# # goal is to find k_F at direction specified by angle
# dispersion(k) = dot(k, k) - 1.0

# # 2d
# N = 10
# bound = [-π, π]
# theta = SimpleGrid.Uniform(bound, N; isperiodic=true)

# k_F_previous = 0.0
# for θ in theta
# f(k) = dispersion(BZMeshes._polar2cart(Polar(k, θ)))
# k_F = find_zero(f, k_F_previous)
# @test k_F ≈ 1.0
# @test find_kFermi(dispersion, θ; kinit=k_F_previous) ≈ 1.0
# k_F_previous = k_F
# end

# # grids = kF_densed_kgrids(dispersion=dispersion, anglemesh=theta,
# # bound=[0.0, 2.0])
# # cm = CompositeMesh(theta, grids)
# DIM = 2
# lattice = Matrix([1.0 0; 0 1]')
# br = BZMeshes.Cell(lattice=lattice)

# pm = PolarMesh(dispersion=dispersion, anglemesh=theta, cell=br, kmax=2.0)
# @test AbstractMeshes.volume(pm) ≈ 4π

# end

# @testset "3D" begin
# dispersion(k) = dot(k, k) - 1.0

# N = 6
# bound = [-π, π]
# phi = SimpleGrid.Uniform(bound, N; isperiodic=true)

# N = 4
# bound = [-π / 2, π / 2]
# theta = SimpleGrid.Uniform(bound, N; isperiodic=true)

# am = CompositeMesh(phi, [theta for i in 1:length(phi)])

# k_F_previous = 0.0
# for ap in am
# f(k) = dispersion(BZMeshes._spherical2cart(Spherical(k, ap...)))
# k_F = find_zero(f, k_F_previous)
# @test k_F ≈ 1.0
# @test find_kFermi(dispersion, ap; kinit=k_F_previous) ≈ 1.0
# k_F_previous = k_F
# end

# DIM = 3
# lattice = Matrix([1.0 1.0 0; 1 0 1; 0 1 1]')
# br = BZMeshes.Cell(lattice=lattice)

# pm = PolarMesh(dispersion=dispersion, anglemesh=am, cell=br, kmax=2.0)
# @test AbstractMeshes.volume(pm) ≈ 32π / 3

# end

# @testset "Radial rescale" begin
# @testset "RescaledGrid" begin
# rmax = 2.0
# N = 10
# rgrid = SimpleG.Uniform([0.0, rmax^2], N; gpbound=[rmax^2 / 2N, rmax^2 * (1 - 1 / 2N)])
# rrg = radial_rescale(grid=rgrid, DIM=2)
# println(rrg.grid)
# bound = [-π, π]
# theta = SimpleGrid.Uniform(bound, N; gpbound=[π * (1 / N - 1), π * (1 - 1 / N)], isperiodic=true)
pm2 = BZMeshes.CompositePolarMesh(dispersion=dispersion,
anglemesh=theta, cell=br, basegridtype=:uniform,
kmax=π * sqrt(2.4), Nloggrid=10, Nbasegrid=6, minterval=0.01T, N=6)

# # for (i, p) in enumerate(theta)
# # println(volume(theta, i))
# # end

# DIM = 2
# lattice = Matrix([1.0 0; 0 1]')
# br = BZMeshes.Cell(lattice=lattice)
# bzmesh = PolarMesh(br, CompositeMesh(theta, [rrg for i in 1:length(theta)]))
# for (i, p) in enumerate(bzmesh)
# println(p, AbstractMeshes.volume(bzmesh, i))
# end
# end
println("N=$(length(pm)), ", int_mesh(pm))
println("N=$(length(pm2)), ", int_mesh(pm2))

# end
end
Nuni = 1000
um = BZMeshes.UniformBZMesh(cell=br, size=(Nuni, Nuni))
um2 = BZMeshes.UniformBZMesh(cell=br, size=(2Nuni, 2Nuni))
println("N=$(length(um)), ", int_mesh(um))
println("N=$(length(um2)), ", int_mesh(um2))
10 changes: 10 additions & 0 deletions src/BaseMesh.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -91,6 +91,16 @@ Here we assume periodic boundary condition so for all case it's the same.
AbstractMeshes.volume(mesh::AbstractUniformMesh) = cell_volume(mesh)
AbstractMeshes.volume(mesh::AbstractUniformMesh, i) = cell_volume(mesh) / length(mesh)

AbstractMeshes.interp(data, mesh::AbstractUniformMesh, x) = data[locate(mesh, x)]

function AbstractMeshes.integrate(data, mesh::AbstractUniformMesh)
result = 0.0
for i in 1:length(mesh)
result += data[i] * volume(mesh, i)
end
return result
end

struct HasLattice <: AbstractMeshes.LatticeStyle end # has mesh.lattice and mesh.inv_lattice
AbstractMeshes.lattice_vector(::HasLattice, mesh) = mesh.lattice
AbstractMeshes.inv_lattice_vector(::HasLattice, mesh) = mesh.inv_lattice
Expand Down
4 changes: 1 addition & 3 deletions src/PolarMeshes.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -162,7 +162,7 @@ function AbstractMeshes.integrate(data, mesh::PolarMesh{T,3,MT}) where {T,MT}
weighteddata = similar(data)
for pi in 1:length(mesh)
r, θ, ϕ = _extract(mesh[AngularCoords, pi])
weighteddata[pi] = r^2 * sin(θ) * data[pi]
weighteddata[pi] = r^2 * cos(θ) * data[pi]
end
return integrate(weighteddata, mesh.mesh)
end
Expand Down Expand Up @@ -270,7 +270,6 @@ function PolarMesh(; dispersion, anglemesh, cell, kmax,

DIM = size(cell.lattice, 1)
bound = [0.0, kmax]
println(typeof(dispersion))
grids = kF_densed_kgrids(; dispersion=dispersion, anglemesh=anglemesh, bound=bound, DIM=DIM, kwargs...)
cm = ProdMesh(grids, anglemesh)
pm = PolarMesh(cell, cm)
Expand All @@ -282,7 +281,6 @@ function CompositePolarMesh(; dispersion, anglemesh, cell, kmax, N,

DIM = size(cell.lattice, 1)
bound = [0.0, kmax]
println(typeof(dispersion))
grids = kF_densed_kgrids(; dispersion=dispersion, anglemesh=anglemesh, bound=bound, DIM=DIM, kwargs...)
prm = ProdMesh(grids, anglemesh)
cm = CompositeMesh(prm, N)
Expand Down
38 changes: 38 additions & 0 deletions test/BZMeshes.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -231,6 +231,44 @@

end

@testset "3D CompositePolarMesh" begin
dispersion(k) = dot(k, k) - 1.0

N = 6
bound = [-π, π]
phi = SimpleGrid.Uniform(bound, N)

N = 4
bound = [-π / 2, π / 2]
theta = SimpleGrid.Uniform(bound, N)

am = ProdMesh([theta for i in 1:length(phi)], phi)

DIM = 3
lattice = Matrix([1.0 1.0 0; 1 0 1; 0 1 1]')
br = BZMeshes.Cell(lattice=lattice)

pm = CompositePolarMesh(dispersion=dispersion, anglemesh=am, cell=br, kmax=2.0, N=4)
@test AbstractMeshes.volume(pm) ≈ 32π / 3

data = zeros(size(pm))
for (pi, p) in enumerate(pm)
data[pi] = dispersion(p)
end

testN = 10
for i in 1:testN
r, ϕ, θ = rand(rng) * 2.0, (rand(rng) * 2 - 1) * π, (rand(rng) * 2 - 1) * π / 2
p = Spherical(r, θ, ϕ)
x = BZMeshes._cartesianize(p)
@test isapprox(AbstractMeshes.interp(data, pm, x), dispersion(x), rtol=1e-4)
@test isapprox(AbstractMeshes.interp(data, pm, p), dispersion(x), rtol=1e-4)
end

@test isapprox(AbstractMeshes.integrate(data, pm), 4π * 56 / 15, rtol=1e-4)

end

@testset "Radial rescale" begin
@testset "RescaledGrid" begin
rmax = 2.0
Expand Down