Merge branch 'master' into calculations

Hamiltonian.jl

@@ -5,39 +5,36 @@ using TensorOperations, KrylovKit, LinearAlgebra, CUDA, CUDA.CUTENSOR
 
 "A Hamiltonian that can be applied to a vector"
 struct Hamiltonian{T}
-    d::Int
+    s::system{T}
-    n::Int
+    K_partial::Matrix{Complex{T}}
-    N::Int
+    K_diag::Union{CuTensor{Complex{T}},Nothing}
-    L::T
+    K_mixed::Union{CuTensor{Complex{T}},Nothing}
-    μ::T
+    Vs::Union{Array{Complex{T}},CuArray{Complex{T}}}
-    ∂1 # Matrix{Complex{T}} or Nothing
-    K_diag # CuTensor{Complex{T}} or Nothing
-    K_mixed # CuTensor{Complex{T}} or Nothing
-    Vs # Array{Complex{T}} or CuArray{Complex{T}}
     hermitian::Bool
     mode::Hamiltonian_backend
-    function Hamiltonian{T}(V_twobody::Function, d::Int, n::Int, N::Int, L::T, ϕ::T, μ::T, n_image::Int, mode::Hamiltonian_backend) where {T<:Float}
+
+    function Hamiltonian{T}(s::system{T}, V_twobody::Function, ϕ::Real, n_image::Int, mode::Hamiltonian_backend) where {T<:Float}
         @assert mode != gpu_cutensor || CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu() "CUDA not available"
-        k = -N÷2:N÷2-1
+        k = -s.N÷2:s.N÷2-1
-        Vs = calculate_Vs(V_twobody, d, n, N, L, ϕ, n_image)
+        Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
         hermitian = ϕ == 0.0
-        if mode == cpu_tensor
+        K_partial = (exp(-im * convert(T, ϕ)) * im / sqrt(2 * s.μ)) .* ∂_1DOF.(Ref(s), k, k')
-            ∂1 = exp(-im * ϕ) .* ∂_1DOF.(L, N, k, k')
+        K_diag = nothing
-            return new{T}(d, n, N, L, μ, ∂1, nothing, nothing, Vs, hermitian, mode)                
+        K_mixed = nothing
-        elseif mode == gpu_cutensor
+        if mode == gpu_cutensor
-            K_partial = (exp(-im * ϕ) * im / sqrt(2 * μ)) .* ∂_1DOF.(L, N, k, k')
             K_diag = CuTensor(CuArray(K_partial * K_partial), ['a', 'A'])
             K_mixed = CuTensor(CuArray(K_partial), ['a', 'A']) * CuTensor(CuArray(K_partial), ['b', 'B'])
-            return new{T}(d, n, N, L, μ, nothing, K_diag, K_mixed, CuArray(Vs), hermitian, mode)
+            Vs = CuArray(Vs)
         end
+        return new{T}(s, K_partial, K_diag, K_mixed, Vs, hermitian, mode)
     end
 end
 
-Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.N^(H.d * (H.n - 1)) : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
+Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.s.N^(H.s.d * (H.s.n - 1)) : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
 Base.size(H::Hamiltonian)::Dims{2} = (size(H, 1), size(H, 2))
 
 "Dimensions of a vector to which 'H' can be applied"
-vectorDims(H::Hamiltonian)::Dims = tuple(fill(H.N, H.d * (H.n - 1))...)
+vectorDims(H::Hamiltonian)::Dims = tuple(fill(H.s.N, H.s.d * (H.s.n - 1))...)
 
 "Apply 'H' on 'v' and store the result in 'out' using the 'cpu_tensor' backend"
 function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{Complex{T}})::Array{Complex{T}} where {T<:Float}
@@ -45,14 +42,13 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
     # apply V operator
     @. out = H.Vs * v
     # apply K opereator
-    coeff = -1 / (2 * H.μ)
+    coords = H.s.n - 1
-    coords = H.n - 1
+    nconList_v_template = -collect(1:H.s.d*(coords))
-    nconList_v_template = -collect(1:H.d*(coords))
+    for dim = 1:H.s.d
-    for dim = 1:H.d
         for coord1 = 1:coords
             for coord2 = 1:coord1
-                i1 = which_index(H.n, dim, coord1)
+                i1 = which_index(H.s, dim, coord1)
-                i2 = which_index(H.n, dim, coord2)
+                i2 = which_index(H.s, dim, coord2)
                 nconList_1 = [-i1, 1]
                 nconList_2 = [-i2, 2]
                 nconList_v = copy(nconList_v_template)
@@ -62,8 +58,8 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
                     nconList_v[i1] = 1
                 end
                 nconList_v[i2] = 2
-                v_new = @ncon((H.∂1, H.∂1, v), (nconList_1, nconList_2, nconList_v))
+                v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
-                out = axpy!(coeff, v_new, out)
+                out = axpy!(1, v_new, out)
             end
         end
     end
@@ -85,15 +81,15 @@ function LinearAlgebra.mul!(out::CuArray{Complex{T}}, H::Hamiltonian{T}, v::CuAr
     NVTX.@range "V" @. out = H.Vs * v
     synchronize(ctx)
     # apply K opereator
-    coords = H.n - 1
+    coords = H.s.n - 1
-    inds_template = ('a' - 1) .+ collect(1:H.d*(coords))
+    inds_template = ('a' - 1) .+ collect(1:H.s.d*(coords))
     v_t = CuTensor(v, copy(inds_template))
     out_t = CuTensor(out, copy(inds_template))
-    for dim = 1:H.d
+    for dim = 1:H.s.d
         for coord1 = 1:coords
             for coord2 = 1:coord1
-                i1 = which_index(H.n, dim, coord1)
+                i1 = which_index(H.s, dim, coord1)
-                i2 = which_index(H.n, dim, coord2)
+                i2 = which_index(H.s, dim, coord2)
                 @assert v_t.inds == inds_template "v indices permuted"
                 if i1 == i2
                     @assert H.K_diag.inds[2] == 'A' "K_diag indices permuted"

benchmark.jl

@@ -27,11 +27,11 @@ end
 
 N=10
 n_image=1
-μ=0.5
 
-for L::T in 5.0:14.0
+for L in 5.0:14.0
     println("Constructing H operator...")
-    @time H=Hamiltonian{T}(V_test,3,3,N,L,convert(T,0),convert(T,μ),n_image,mode)
+    s=system{T}(3,3,N,L)
+    @time H=Hamiltonian{T}(s,V_test,0,n_image,mode)
     println("Applying H 1000 times...")
     if GPU_mode
         v=CUDA.rand(Complex{T},vectorDims(H)...)

common.jl

@@ -1,53 +1,64 @@
 Float = Union{Float32,Float64}
 
+"A few-body system defined by its physical parameters"
+struct system{T}
+    d::Int
+    n::Int
+    N::Int
+    L::T
+    μ::T
+
+    system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5) where {T<:Float} = new{T}(d, n, N, convert(T, L), convert(T, μ))
+end
+
 norm_square(x::Array{Int})::Int = sum(x .* x)
 
 "Eq (46): Partial derivative matrix element for 1 degree of freedom"
-function ∂_1DOF(L::T, N::Int, k::Int, l::Int)::Complex{T} where {T<:Float}
+function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
     if k == l
-        return -im * (π / L)
+        return -im * (π / s.L)
     else
-        return (π / L) * (-1)^(k - l) * exp(-im * π * (k - l) / N) / sin(π * (k - l) / N)
+        return (π / s.L) * (-1)^(k - l) * exp(-im * π * (k - l) / s.N) / sin(π * (k - l) / s.N)
     end
 end
 
 "Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' and particle 'p'?"
-which_index(n::Int, dim::Int, p::Int)::Int = (dim - 1) * (n - 1) + p
+which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 1) + p
 
 "Δk (distance in terms of lattice paramter) between two particles along the given dimension"
-function get_Δk(n::Int, N::Int, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
+function get_Δk(s::system, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
     if p1 == p2
         return 0
-    elseif p1 == n
+    elseif p1 == s.n
-        return -(i[which_index(n, dim, p2)] - N ÷ 2 - 1)
+        return -(i[which_index(s, dim, p2)] - s.N ÷ 2 - 1)
-    elseif p2 == n
+    elseif p2 == s.n
-        return i[which_index(n, dim, p1)] - N ÷ 2 - 1
+        return i[which_index(s, dim, p1)] - s.N ÷ 2 - 1
     else
-        return i[which_index(n, dim, p1)] - i[which_index(n, dim, p2)]
+        return i[which_index(s, dim, p1)] - i[which_index(s, dim, p2)]
     end
 end
 
 "Calculate diagonal elements of the V matrix"
-function calculate_Vs(V_twobody::Function, d::Int, n::Int, N::Int, L::T, ϕ::T, n_image::Int)::Array{Complex{T}} where {T<:Float}
+function calculate_Vs(s::system{T}, V_twobody::Function, ϕ::T, n_image::Int)::Array{Complex{T}} where {T<:Float}
-    coeff² = (exp(im * ϕ) * L / N)^2
+    coeff² = (exp(im * ϕ) * s.L / s.N)^2
-    images = collect.(Iterators.product(fill(-n_image:n_image, d)...)) # TODO: Learn how to use tuples instead of vectors
+    images = collect.(Iterators.product(fill(-n_image:n_image, s.d)...)) # TODO: Learn how to use tuples instead of vectors
-    Vs = zeros(Complex{T}, fill(N, d * (n - 1))...)
+    Vs = zeros(Complex{T}, fill(s.N, s.d * (s.n - 1))...)
     Threads.@threads for i in CartesianIndices(Vs)
-        for p1 in 1:n
+        for p1 in 1:s.n
-            for p2 in (p1 + 1):n
+            for p2 in (p1 + 1):s.n
-                min_Δk = Array{Int}(undef, d)
+                min_Δk = Array{Int}(undef, s.d)
-                for dim in 1:d
+                for dim in 1:s.d
-                    Δk = get_Δk(n, N, i, dim, p1, p2)
+                    Δk = get_Δk(s, i, dim, p1, p2)
-                    if Δk > N ÷ 2
+                    if Δk > s.N ÷ 2
-                        min_Δk[dim] = Δk - N
+                        min_Δk[dim] = Δk - s.N
-                    elseif Δk < -N ÷ 2
+                    elseif Δk < -s.N ÷ 2
-                        min_Δk[dim] = Δk + N
+                        min_Δk[dim] = Δk + s.N
                     else
                         min_Δk[dim] = Δk
                     end
                 end
                 for image in images
-                    Δk² = norm_square(min_Δk .- (N .* image))
+                    Δk² = norm_square(min_Δk .- (s.N .* image))
                     Vs[i] += V_twobody(Δk² * coeff²)
                 end
             end

example.ipynb

@@ -24,12 +24,12 @@
     "d = 3\n",
     "n = 3\n",
     "N = 6\n",
-    "L::T = 12\n",
+    "L = 12\n",
-    "ϕ::T = 0.0\n",
+    "ϕ = 0.0\n",
-    "μ::T = 0.5\n",
     "n_imag = 1\n",
     "\n",
-    "H = Hamiltonian{T}(V_gauss, d, n, N, L, ϕ, μ, n_imag, mode)\n",
+    "s = system{T}(d, n, N, L)\n",
+    "H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)\n",
     "@time evals, evecs, info = eig(H, 5)\n",
     "print(info.numops, \" operations : \")\n",
     "println(evals)"
@@ -49,12 +49,12 @@
     "d = 3\n",
     "n = 2\n",
     "N = 32\n",
-    "L::T = 16\n",
+    "L = 16\n",
-    "ϕ::T = 0.5\n",
+    "ϕ = 0.5\n",
-    "μ::T = 0.5\n",
     "n_imag = 0\n",
     "\n",
-    "H = Hamiltonian{T}(V_gauss, d, n, N, L, ϕ, μ, n_imag, mode)\n",
+    "s = system{T}(d, n, N, L)\n",
+    "H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)\n",
     "@time evals, evecs, info = eig(H, 20)\n",
     "print(info.numops, \" operations : \")\n",
     "print(evals)\n",

testing.ipynb

@@ -0,0 +1,71 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "include(\"Hamiltonian.jl\")\n",
+    "\n",
+    "println(\"Running with \",Threads.nthreads(),\" thread(s)\")\n",
+    "println(\"Available GPUs:\")\n",
+    "println.(name.(devices()))\n",
+    "\n",
+    "T=Float32\n",
+    "\n",
+    "function V_test(r2)\n",
+    "    return -4*exp(-r2/4)\n",
+    "end\n",
+    "\n",
+    "function test(mode)\n",
+    "    for (n,N) in [(2,16),(3,8)]\n",
+    "        println(\"\\n$n-body system with N=$N\")\n",
+    "        n_image=0\n",
+    "        for L::T in 5.0:9.0\n",
+    "            print(\"L=$L\")\n",
+    "            s=system{T}(3,n,N,L)\n",
+    "            H=Hamiltonian{T}(s,V_test,0.0,n_image,mode)\n",
+    "            evals,_,_ = eig(H,5)\n",
+    "            println(real.(evals))\n",
+    "        end\n",
+    "    end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "test(cpu_tensor)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "test(gpu_cutensor)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.8.5",
+   "language": "julia",
+   "name": "julia-1.8"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.8.5"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}