Manipulation of Trees

.gitignore

@@ -1,2 +1,3 @@
+./samples/
 Manifest.toml
-samples/
+.DS_Store

Project.toml

@@ -4,19 +4,45 @@ authors = ["Ryo Watanabe <https://github.com/Ryo-wtnb11>"]
 version = "0.1.0"
 
 [deps]
+Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DataGraphs = "b5a273c3-7e6c-41f6-98bd-8d7f1525a36a"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+GraphTikZ = "cef0280d-a2bf-4776-a511-cf6253a7debc"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+ITensorNetworks = "2919e153-833c-4bdc-8836-1ea460a35fc7"
+ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
+NPZ = "15e1cf62-19b3-5cfa-8e77-841668bca605"
 NamedGraphs = "678767b0-92e7-4007-89e4-4527a8725b19"
+QuanticsGrids = "634c7f73-3e90-4749-a1bd-001b8efc642d"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 SimpleTensorNetworks = "3075f829-f72e-4896-a859-7fe0a9cabb9b"
+SparseIR = "4fe2279e-80f0-4adb-8463-ee114ff56b7d"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+T4ARegistrator = "52e3f0f8-52ab-4798-a033-7b9fb81451b4"
 TensorCrossInterpolation = "b261b2ec-6378-4871-b32e-9173bb050604"
 
 [compat]
+Combinatorics = "1.0.3"
 DataGraphs = "0.2.5"
+DataStructures = "0.18.22"
+Distributions = "0.25.120"
+Flux = "0.16.4"
+GraphTikZ = "0.1.0"
 Graphs = "1.12.0"
+ITensorNetworks = "0.14.1"
+ITensors = "0.9.11"
+NPZ = "0.4.3"
 NamedGraphs = "0.6.4"
+QuanticsGrids = "0.6.0"
 Random = "1.10"
+Revise = "3.9.0"
 SimpleTensorNetworks = "0.1.0"
+SparseIR = "1.1.4"
+Statistics = "1.11.1"
+T4ARegistrator = "0.2.1"
 TensorCrossInterpolation = "0.9.13"
 
 [extras]

samples/1d_tightbinding_model.jl

@@ -0,0 +1,65 @@
+using Random
+using LinearAlgebra
+using TreeTCI: crossinterpolate, crossinterpolate_with_structuralsearch, crossinterpolate_with_3site_swapping
+using NamedGraphs: NamedGraph, add_edge!, edges, src, dst
+using QuanticsGrids
+const QG = QuanticsGrids
+using SparseIR
+using ITensorNetworks
+using TreeTCI: ttnopt
+const ITN = ITensorNetworks
+using ITensors
+using NPZ
+include("utils.jl")
+include("graphs.jl")
+
+
+ε(k) = 2*cos(k) + cos(5*k) + 2*cos(20*k)
+
+gk(m::Int, kx::Float64; β::Float64=10.0) = begin
+    m = 2 * m + 1
+    ν = FermionicFreq(m)
+    iν = SparseIR.valueim(ν, β)
+    return 1 / (iν - ε(kx))
+end
+
+function gkb(b::Vector{Int}, n_m::Int, n_kx::Int; mu::Float64=0.0, β::Float64=10.0, layout::Symbol=:block)
+    @assert length(b) == n_m + n_kx
+    parts = split_bits(b; group_bits=[n_m, n_kx], layout=layout)
+    mb, kxb = parts
+    mbit = length(mb)
+    kxbit = length(kxb)
+    Nm = 2^mbit
+    Nkx = 2^kxbit
+    im = frombins(mb)
+    ikx = frombins(kxb)
+    @assert im ≤ Nm
+    @assert ikx ≤ Nkx
+    kx = 2π * (ikx - 1)/Nkx
+    m = (im - 1)
+    return gk(m, kx; mu=mu, β=β)
+end
+
+function main()
+    nkx_bit = 10
+    nm_bit = 10
+    localdims = fill(2, nkx_bit + nm_bit)
+    f(v) = gkb(v, nm_bit, nkx_bit; layout=:interleave)
+    g = graph_TT(nkx_bit + nm_bit)
+    maxbonddim = 200
+    kwargs = (maxbonddim = maxbonddim, maxiter = 100, tolerance = 1e-13)
+    center_vertex = (nkx_bit + nm_bit) ÷ 2
+    # center_vertex = 1
+
+    ttn, ranks, errors = crossinterpolate(ComplexF64, f, localdims, g; center_vertex = center_vertex, kwargs...)
+    @show last(ranks)
+
+
+    g_tmp, original_entanglements, entanglements = ttnopt(ttn; ortho_vertex = center_vertex, max_degree = 2)
+    ttn_, ranks, errors = crossinterpolate(ComplexF64, f, localdims, g_tmp; center_vertex = center_vertex, kwargs...)
+    @show last(ranks)
+
+    return 0
+end
+
+main()

samples/2d_model.jl

@@ -0,0 +1,92 @@
+using Random
+using LinearAlgebra
+using TreeTCI: crossinterpolate, crossinterpolate_with_structuralsearch, crossinterpolate_with_3site_swapping
+using NamedGraphs: NamedGraph, add_edge!, edges, src, dst
+using QuanticsGrids
+const QG = QuanticsGrids
+using SparseIR
+using ITensorNetworks
+using TreeTCI: ttnopt
+const ITN = ITensorNetworks
+using ITensors
+using NPZ
+include("utils.jl")
+include("graphs.jl")
+
+
+ε(kx, ky) = -2*cos(kx) - 2*cos(ky)
+
+gk(kx::Float64, ky::Float64; mu::Float64=0.0, β::Float64=10.0) = begin
+    m = 1
+    ν = FermionicFreq(m)
+    iν = SparseIR.valueim(ν, β)
+    return 1 / (iν - ε(kx, ky) + mu)
+end
+
+function gkb(b::Vector{Int}, n_kx::Int, n_ky; mu::Float64=0.0, β::Float64=10.0, layout::Symbol=:block)
+    @assert length(b) == n_kx + n_ky
+    parts = split_bits(b; group_bits=[n_kx, n_ky], layout=layout)
+    kxb, kyb = parts
+    kxbit = length(kxb)
+    kybit = length(kyb)
+    Nkx = 2^kxbit
+    Nky = 2^kybit
+    iky = frombins(kyb)
+    ikx = frombins(kxb)
+    @assert ikx ≤ Nkx
+    @assert iky ≤ Nky
+    kx = 2π * (ikx - 1)/Nkx
+    ky = 2π * (iky - 1)/Nky
+    return gk(kx, ky; mu=mu, β=β)
+end
+
+
+function calculate_entanglements(entanglements)
+    ee = 0.0
+    edges = []
+    edge_vals = []
+    for (key, value) in entanglements
+        ee += value
+        push!(edges, key)
+        push!(edge_vals, value)
+    end
+    @show ee / length(edges)
+    @show edges
+    @show edge_vals
+end
+
+function main()
+    nkx_bit = 10
+    nky_bit = 10
+    localdims = fill(2, nkx_bit + nky_bit)
+    f(v) = gkb(v, nky_bit, nkx_bit; layout=:interleave, mu=-1.0, β=10.0)
+    g = graph_TT(nkx_bit + nky_bit)
+    maxbonddim = 200
+    kwargs = (maxbonddim = maxbonddim, maxiter = 100, tolerance = 1e-13)
+    center_vertex = (nkx_bit + nky_bit) ÷ 2
+
+    ttn, ranks, errors = crossinterpolate(ComplexF64, f, localdims, g; center_vertex = center_vertex, kwargs...)
+
+    g_tmp, original_entanglements, entanglements = ttnopt(ttn; ortho_vertex = center_vertex, max_degree = 1)
+    ttn_, ranks, errors = crossinterpolate(ComplexF64, f, localdims, g_tmp; center_vertex = center_vertex, kwargs...)
+    println("original_entanglements")
+    calculate_entanglements(original_entanglements)
+    @show last(ranks)
+
+    println("--------------------------------")
+    println("ΔG = 2")
+    calculate_entanglements(entanglements)
+    @show last(ranks)
+
+    g_tmp, original_entanglements, entanglements = ttnopt(ttn; ortho_vertex = center_vertex, max_degree = 2)
+    ttn_, ranks, errors = crossinterpolate(ComplexF64, f, localdims, g_tmp; center_vertex = center_vertex, kwargs...)
+
+    println("--------------------------------")
+    println("ΔG = 3")
+    calculate_entanglements(entanglements)
+    @show last(ranks)
+
+    return 0
+end
+
+main()

samples/graphs.jl

@@ -0,0 +1,9 @@
+using NamedGraphs: NamedGraph, add_edge!
+
+function graph_TT(R::Int)
+    g = NamedGraph(R)
+    for i in 1:R-1
+        add_edge!(g, i, i+1)
+    end
+    return g
+end

samples/sample_strucuralsearch.jl

@@ -0,0 +1,49 @@
+using Random
+using LinearAlgebra
+using TreeTCI: crossinterpolate_with_3site_swapping
+using Statistics
+using Distributions
+using NamedGraphs: NamedGraph, add_edge!, edges
+using QuanticsGrids
+const QG = QuanticsGrids
+
+
+function build_problem()
+    Random.seed!(1234)
+    R = 4
+    μ = zeros(3)
+    Σ = rand(LKJ(3, 50.0))
+    dist = MvNormal(μ, Hermitian(Σ))
+    f(x,y,z) = pdf(dist, [x,y,z])
+
+    grid = QG.DiscretizedGrid{3}(R, (-5,-5,-5), (5,5,5); unfoldingscheme=:interleaved)
+    fq = QG.quanticsfunction(Float64, grid, f)
+
+    nsites = 3R
+    g = NamedGraph(nsites)
+    for i in 1:(nsites-1)
+        add_edge!(g, i, i+1)
+    end
+    localdims = fill(grid.base, nsites)
+
+    return fq, localdims, g
+end
+
+function main()
+
+    fq, localdims, g = build_problem()
+
+    kwargs = (
+            maxbonddim = 10,
+            tolerance = 1e-10,
+            maxiter = 100,
+        )
+
+    tci = crossinterpolate_with_3site_swapping(Float64, fq, localdims, g; kwargs...)
+
+    ttn = TreeTensorNetwork(tci.g, tci.sitetensors)
+
+    return tci
+end
+
+main()

samples/sample_treetci.jl

@@ -0,0 +1,27 @@
+using Test
+using TreeTCI
+import NamedGraphs: NamedGraph, NamedEdge, add_edge!, vertices, edges, has_edge
+
+function main()
+    # make graph
+    g = NamedGraph(10)
+    add_edge!(g, 1, 3)
+    add_edge!(g, 2, 3)
+    add_edge!(g, 3, 5)
+
+    add_edge!(g, 4, 5)
+    add_edge!(g, 5, 7)
+    add_edge!(g, 6, 7)
+    add_edge!(g, 7, 8)
+    add_edge!(g, 8, 9)
+    add_edge!(g, 8, 10)
+
+    localdims = fill(2, length(vertices(g)))
+    f(v) = 1 / (1 + v' * v)
+    kwargs = (maxbonddim = 20, maxiter = 10)
+    ttn, ranks, errors = TreeTCI.crossinterpolate(Float64, f, localdims, g; kwargs...)
+    @show ttn([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), f([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
+    @show ttn([1, 2, 1, 2, 1, 2, 1, 2, 1, 2]), f([1, 2, 1, 2, 1, 2, 1, 2, 1, 2])
+end
+
+main()

samples/sample_treetci2.jl

@@ -0,0 +1,32 @@
+using Test
+using TreeTCI
+import NamedGraphs: NamedGraph, NamedEdge, add_edge!, vertices, edges, has_edge
+
+function f_pairwise(v::Vector{Int})
+    s = 0.0
+    for i in 1:2:length(v)-1
+        s += v[i] * v[i+1]
+    end
+    return 1 / (1+s)
+end
+
+
+function main()
+    # make graph
+    g = NamedGraph(8)
+    add_edge!(g, 1, 2)
+    add_edge!(g, 2, 3)
+    add_edge!(g, 3, 4)
+    add_edge!(g, 4, 5)
+    add_edge!(g, 5, 6)
+    add_edge!(g, 6, 7)
+    add_edge!(g, 7, 8)
+
+    localdims = fill(8, length(vertices(g)))
+    f(v) = f_pairwise(v)
+    kwargs = (maxbonddim = 64, maxiter = 10)
+    ttn, ranks, errors = TreeTCI.crossinterpolate(Float64, f, localdims, g; kwargs...)
+
+end
+
+main()