Update README.md

.gitignore

@@ -1,3 +1,9 @@
+# VSCode
+.vscode/
+
+# HPC scripts and logs
+hpc/
+
 # Calculation outputs
 *.dat
 *.csv

Hamiltonian.jl

@@ -9,9 +9,6 @@ struct Hamiltonian{T}
     K_partial::Matrix{Complex{T}}
     K_diag::Union{CuTensor{Complex{T}},Nothing}
     K_mixed::Union{CuTensor{Complex{T}},Nothing}
-    K_partial_1::Union{Tuple,Nothing}
-    K_partial_2::Union{Tuple,Nothing}
-    K_partial_c::Union{Tuple,Nothing}
     Vs::Union{Array{Complex{T}},CuArray{Complex{T}}}
     hermitian::Bool
     mode::Hamiltonian_backend
@@ -19,27 +16,25 @@ struct Hamiltonian{T}
     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 = -s.N÷2:s.N÷2-1
+        Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
         hermitian = ϕ == 0.0
         K_partial = (exp(-im * convert(T, ϕ)) * im / sqrt(2 * s.μ)) .* ∂_1DOF.(Ref(s), k, k')
-        K_partial_1, K_partial_2, K_partial_c = sym_reduce(s, K_partial)
-        Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
+        K_diag = nothing
+        K_mixed = nothing
         if mode == gpu_cutensor
             K_diag = CuTensor(CuArray(K_partial * K_partial), ['a', 'A'])
             K_mixed = CuTensor(CuArray(K_partial), ['a', 'A']) * CuTensor(CuArray(K_partial), ['b', 'B'])
             Vs = CuArray(Vs)
-        else
-            K_diag = nothing
-            K_mixed = nothing    
         end
-        return new{T}(s, K_partial, K_diag, K_mixed, K_partial_1, K_partial_2, K_partial_c, Vs, hermitian, mode)
+        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.s.N^(H.s.d * (H.s.n - 2)) * length(H.s.unique_i) : 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(length(H.s.unique_i), fill(H.s.N, H.s.d * (H.s.n - 2))...)
+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}
@@ -47,9 +42,10 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
     # apply V operator
     @. out = H.Vs * v
     # apply K opereator
-    nconList_v_template = -collect(1:(H.s.d * (H.s.n - 2) + 1))
+    coords = H.s.n - 1
+    nconList_v_template = -collect(1:H.s.d*(coords))
     for dim = 1:H.s.d
-        for coord1 = 1:(H.s.n - 1)
+        for coord1 = 1:coords
             for coord2 = 1:coord1
                 i1 = which_index(H.s, dim, coord1)
                 i2 = which_index(H.s, dim, coord2)
@@ -62,17 +58,7 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
                     nconList_v[i1] = 1
                 end
                 nconList_v[i2] = 2
-
-                if coord1 == 1 && coord2 == 1
-                    tensor1 = H.K_partial_1[dim]
-                    tensor2 = H.K_partial_2[dim]
-                else
-                    tensor1 = coord1 == 1 ? H.K_partial_c[dim] : H.K_partial
-                    tensor2 = coord2 == 1 ? H.K_partial_c[dim] : H.K_partial
-                end
-
-                v_new = @ncon((tensor1, tensor2, 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!(1, v_new, out)
             end
         end
@@ -82,8 +68,8 @@ end
 
 "cuTENSOR contraction and accumulation (C = A * B + C)"
 function contract_accumulate!(C::CuTensor, A::CuTensor, B::CuTensor)::CuTensor
-    CUTENSOR.contraction!(one(eltype(C)), A.data, A.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, CUTENSOR.CUTENSOR_OP_IDENTITY,
-                          one(eltype(C)), C.data, C.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, CUTENSOR.CUTENSOR_OP_IDENTITY)
+    cuTENSOR.contraction!(one(eltype(C)), A.data, A.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, cuTENSOR.CUTENSOR_OP_IDENTITY,
+                          one(eltype(C)), C.data, C.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, cuTENSOR.CUTENSOR_OP_IDENTITY)
     return C
 end
 
@@ -148,8 +134,7 @@ function eig(H::Hamiltonian{T}, levels::Int; resonances = !H.hermitian)::Tuple{V
         x₀ = CUDA.rand(Complex{T}, vectorDims(H)...)
         synchronize()
     end
-    KrylovKit_hermitian = H.hermitian && H.s.sym == all
-    evals, evecs, info = eigsolve(H, x₀, levels, resonances ? :LI : :SR; ishermitian = KrylovKit_hermitian, tol = tolerance, krylovdim = levels * 4)
+    evals, evecs, info = eigsolve(H, x₀, levels, resonances ? :LI : :SR; ishermitian = H.hermitian, tol = tolerance, krylovdim = levels * 8)
     info.converged < levels && throw(error("Not enough convergence"))
     if H.hermitian evals = real.(evals) end
     if H.mode == gpu_cutensor # to avoid possible GPU memory leak

LocalPreferences.toml

@@ -0,0 +1,2 @@
+[TensorOperations]
+precompile_workload = true

Project.toml

@@ -0,0 +1,7 @@
+[deps]
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+NVTX = "5da4648a-3479-48b8-97b9-01cb529c0a1f"
+Preferences = "21216c6a-2e73-6563-6e65-726566657250"
+TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
+cuTENSOR = "011b41b2-24ef-40a8-b3eb-fa098493e9e1"

README.md

@@ -0,0 +1,27 @@
+# DVR-jl
+
+Solves the quantum $n$-body problem in finite volume (lattice) with periodic boundary conditions. Uses discrete variable representation (DVR) with optional support for complex scaling to study resonances. All details can be found in [H. Yu, N. Yapa, and S. König, Complex scaling in finite volume, Phys. Rev. C 109, 014316 (2024)](https://doi.org/10.1103/PhysRevC.109.014316).
+
+Written in Julia with optional CUDA GPU acceleration (experimental).
+
+## Installation
+
+Make sure you have Julia installed. Required packages can be installed with a single command:
+```bash
+julia --project=. -e 'import Pkg; Pkg.instantiate()'
+```
+
+## Usage
+
+See `calculations/3b_bound.jl` for an example on a 3-body bound state.
+See `calculations/3b_res_from_paper.jl` for an example of a 3-body resonance via complex scaling.
+
+## Planned features
+
+- [ ] Spin and isospin degrees of freedom for nuclear calculations
+- [ ] Multi-node HPC support
+- [ ] Parity and cubic symmetries ($S_4$)
+
+## Acknowledgments
+
+The author gratefully acknowledges the guidance from Sebastian König.

calculations/3b_bound.jl

@@ -0,0 +1,19 @@
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32
+
+V_gauss(r2) = -2 * exp(-r2 / 4)
+
+d = 3
+n = 3
+N = 20
+L = 15
+n_imag = 1
+ϕ = 0
+
+s = system{T}(d, n, N, L)
+H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+@time evals, _, info = eig(H, 5)
+
+print(info.numops, " operations")
+display(evals)

calculations/3b_res_from_paper.jl

@@ -0,0 +1,36 @@
+# 10.1007/s00601-020-01550-8
+# Fig. 7
+# E_R = 4.18(8)
+
+#./En.run -d 3 -n 3 -N 16 -c pot=v_shifted_gauss,v0=2.0,r=1.5,a=3.0 -c n_eig=20 -c which=li -c tol=1e-6 -L 16 -c phi=0.3 -v
+
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+using Plots
+
+V_gauss(r2) =
+    2 * exp(-((sqrt(r2) - 3) / 1.5) ^ 2)
+
+d = 3
+n = 3
+N = 16
+L = 16
+n_imag = 0
+
+for ϕ::T in 0.2:0.05:0.4
+    s = system{T}(d, n, N, L)
+    H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+    @time evals, _, info = eig(H, 20)
+    
+    print(info.numops, " operations")
+    display(evals)
+
+    scatter(real.(evals), imag.(evals); legend=false)
+    xlabel!("Re E")
+    ylabel!("Im E")
+    xlims!(0, 6)
+    ylims!(-0.6, 0)
+    savefig("temp/phi$(Int(round(ϕ * 100))).png")
+end

calculations/ComplexScaling-FV-P-res.jl

@@ -0,0 +1,24 @@
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    -10 * exp(-(sqrt(r2)) ^ 2)
+
+d = 3
+n = 2
+N = 96
+ϕ = pi/6
+n_imag = 1
+
+open("ComplexScaling-FV-P-res.dat", "w") do f
+    for L = range(20, 35, length=16)
+        println("Calculating L=", L)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 40)
+
+        dataline = vcat([L], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/ComplexScaling-FV-S-bound-phi.jl

@@ -0,0 +1,24 @@
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    -10 * exp(-(sqrt(r2)) ^ 2)
+
+d = 3
+n = 2
+N = 30
+L = 6
+n_imag = 1
+
+open("ComplexScaling-FV-S-bound-phi.dat", "w") do f
+    for ϕ = range(0.0, 0.5, length=11)
+        println("Calculating ϕ=", ϕ)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 10, resonances = false)
+
+        dataline = vcat([ϕ], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/ComplexScaling-FV-S-res-phi.jl

@@ -0,0 +1,24 @@
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    2 * exp(- ((sqrt(r2)-3)/1.5) ^ 2)
+
+d = 3
+n = 2
+N = 96
+L = 30
+n_imag = 1
+
+open("ComplexScaling-FV-S-res-phi.dat", "w") do f
+    for ϕ = range(0.1, 0.6, length=26)
+        println("Calculating ϕ=", ϕ)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 40, resonances = true)
+
+        dataline = vcat([ϕ], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/EC-R2R-S.jl

@@ -0,0 +1,67 @@
+using Plots, Arpack
+
+include("../helper.jl")
+include("../Hamiltonian.jl")
+
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_r2(c) = r2 -> c * (-5 * exp(-r2/3) + 2 * exp(-r2/10))
+
+d = 3
+n = 2
+N = 48
+L = 30
+ϕ = pi/6
+n_imag = 1
+s = system{T}(d, n, N, L)
+
+train_cs = range(0.78, 0.45, length=5)
+train_ref = reverse([0.05387926313545913-0.008900278182520881im,
+    0.11254295298924327-0.020515067379548786im,
+    0.16060154707503538-0.03716539208626717im,
+    0.19741353362674618-0.05994519982799412im,
+    0.2219100763497223-0.08959449893439568im])
+
+extrapolate_cs = range(0.38, 0.22, length=5)
+extrapolate_ref = reverse([0.23165109150003316-0.12052751440975719im,
+    0.23190549514995962-0.1406687118589838im,
+    0.22763660218046278-0.1626190970863793im,
+    0.21807104244164865-0.18635600686249373im,
+    0.2020979906072586-0.21180157628258728im])
+
+training_E = ComplexF64[]
+training_vec = Array[]
+exact_E = ComplexF64[]
+extrapolated_E = ComplexF64[]
+
+for c in train_cs
+    println("Training c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, evecs, info = eig(H, 20, resonances = true)
+    i = nearestIndex(evals, pop!(train_ref))
+    push!(training_E, evals[i])
+    push!(training_vec, evecs[i])
+end
+
+N_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, training_vec)]
+
+for c in extrapolate_cs
+    println("Extrapolating c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, _, info = eig(H, 40, resonances = true)
+    nearestE = nearest(evals, pop!(extrapolate_ref))
+    push!(exact_E, nearestE)
+    
+    # EC extrapolation
+    H_training_vec = H.(training_vec)
+    H_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, H_training_vec)]
+
+    evals = eigvals(H_EC, N_EC)
+    push!(extrapolated_E, nearestE)
+end
+
+scatter(real.(training_E), imag.(training_E), label="training")
+scatter!(real.(exact_E), imag.(exact_E), label="exact")
+scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="extrapolated")
+savefig("temp/EC-R2R-S.pdf")

common.jl

@@ -1,7 +1,4 @@
-include("irrep.jl")
-
 Float = Union{Float32,Float64}
-@enum rep all A1
 
 "A few-body system defined by its physical parameters"
 struct system{T}
@@ -11,23 +8,7 @@ struct system{T}
     L::T
     μ::T
 
-    sym::rep
-    unique_i::Array{Int}
-    unique_point::Array{Int}
-    multiplicity::Array{Int}
-    labels::Array{Int}
-
-    function system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5, sym::rep=all) where {T<:Float}
-        @assert d == 3 "Only supports 3D"
-        if sym == all
-            unique_i, unique_point, multiplicity, labels = calculate_all_data(N)
-        elseif sym == A1
-            unique_i, unique_point, multiplicity, labels = calculate_A1_data(N)
-        else
-            throw(ArgumentError("Symmetry not yet implemented"))
-        end
-        return new{T}(d, n, N, convert(T, L), convert(T, μ), sym, unique_i, unique_point, multiplicity, labels)
-    end
+    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)
@@ -42,27 +23,18 @@ function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
 end
 
 "Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' and particle 'p'?"
-which_index(s::system, dim::Int, p::Int)::Int = p == 1 ? 1 : (dim - 1) * (s.n - 2) + p
-
-"Δk (distance in terms of lattice paramter) between two particles along the given dimension"
-function get_k(s::system, i::CartesianIndex, dim::Int, p::Int)::Int
-    if p == 1
-        s.unique_point[i[1], dim]
-    else
-        return i[which_index(s, dim, p)] - s.N ÷ 2 - 1
-    end
-end
+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(s::system, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
     if p1 == p2
         return 0
     elseif p1 == s.n
-        return -get_k(s, i, dim, p2)
+        return -(i[which_index(s, dim, p2)] - s.N ÷ 2 - 1)
     elseif p2 == s.n
-        return get_k(s, i, dim, p1)
+        return i[which_index(s, dim, p1)] - s.N ÷ 2 - 1
     else
-        return get_k(s, i, dim, p1) - get_k(s, i, dim, p2)
+        return i[which_index(s, dim, p1)] - i[which_index(s, dim, p2)]
     end
 end
 
@@ -70,7 +42,7 @@ end
 function calculate_Vs(s::system{T}, V_twobody::Function, ϕ::T, n_image::Int)::Array{Complex{T}} where {T<:Float}
     coeff² = (exp(im * ϕ) * s.L / s.N)^2
     images = collect.(Iterators.product(fill(-n_image:n_image, s.d)...)) # TODO: Learn how to use tuples instead of vectors
-    Vs = zeros(Complex{T}, length(s.unique_i), fill(s.N, s.d * (s.n - 2))...)
+    Vs = zeros(Complex{T}, fill(s.N, s.d * (s.n - 1))...)
     Threads.@threads for i in CartesianIndices(Vs)
         for p1 in 1:s.n
             for p2 in (p1 + 1):s.n

helper.jl

@@ -0,0 +1,5 @@
+"Index of the nearest value in a list to a given reference point"
+nearestIndex(list::Array, ref) = argmin(norm.(list .- ref))
+
+"Nearest value in a list to a given reference point"
+nearest(list::Array, ref) = list[nearestIndex(list, ref)]

irrep.jl

@@ -1,77 +0,0 @@
-using DelimitedFiles, LinearAlgebra
-
-function calculate_all_data(N::Int)
-    ks = -N÷2:N÷2-1
-    lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
-    labels = reshape(collect(1:N^3), (N, N, N))
-
-    unique_i = collect(1:N^3)
-    multiplicity = fill(1, length(unique_i))
-    unique_point = transpose(lattice)
-
-    return unique_i, unique_point, multiplicity, labels
-end
-
-function calculate_A1_data(N::Int)
-    rotations = readdlm("rotations.mat", ',', Int, '\n')
-    rotations = reshape(rotations, (24, 3, 3))
-    
-    ks = -N÷2:N÷2-1
-    lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
-    labels = reshape(collect(1:N^3), (N, N, N))
-    
-    for r in 1:24
-        rotated_lattice = Matrix(rotations[r, :, :]) * lattice
-        for index in 1:N^3
-            rotated_lattice_point = rotated_lattice[:, index]
-            (i, j, k) = mod1.(rotated_lattice_point .+ (N÷2 + 1), N)
-            old_label = max(labels[index], labels[i, j, k])
-            new_label = min(labels[index], labels[i, j, k])
-            if old_label != new_label
-                for o in findall(isequal(old_label), labels)
-                    labels[o] = new_label
-                end
-            end
-        end
-    end
-
-    unique_i = unique(labels)
-    multiplicity = [count(labels.==i) for i in unique_i]
-    unique_point = transpose(lattice[:, unique_i])
-
-    return unique_i, unique_point, multiplicity, labels
-end
-
-function sym_reduce(s, K_partial)
-    I = one(K_partial)
-
-    K_partial_x1 = kron(kron(K_partial, I), I)
-    K_partial_y1 = kron(kron(I, K_partial), I)
-    K_partial_z1 = kron(kron(I, I), K_partial)
-
-    K_partial_x1 = K_partial_x1[s.unique_i, :]
-    K_partial_y1 = K_partial_y1[s.unique_i, :]
-    K_partial_z1 = K_partial_z1[s.unique_i, :]
-
-    K_partial_x2 = kron(kron(K_partial, I), I)
-    K_partial_y2 = kron(kron(I, K_partial), I)
-    K_partial_z2 = kron(kron(I, I), K_partial)
-
-    for (i, label) in enumerate(s.labels)
-        if i != label
-            K_partial_x2[:, label] .+= K_partial_x2[:, i]
-            K_partial_y2[:, label] .+= K_partial_y2[:, i]
-            K_partial_z2[:, label] .+= K_partial_z2[:, i]
-        end
-    end
-
-    K_partial_x2 = K_partial_x2[:, s.unique_i]
-    K_partial_y2 = K_partial_y2[:, s.unique_i]
-    K_partial_z2 = K_partial_z2[:, s.unique_i]
-
-    K_partial_xc = K_partial_x2[s.unique_i, :]
-    K_partial_yc = K_partial_y2[s.unique_i, :]
-    K_partial_zc = K_partial_z2[s.unique_i, :]
-
-    return (K_partial_x1, K_partial_y1, K_partial_z1), (K_partial_x2, K_partial_y2, K_partial_z2), (K_partial_xc, K_partial_yc, K_partial_zc)
-end

rotations.mat

@@ -1,24 +0,0 @@
-1,0,0,0,1,0,0,0,1
-1,0,0,0,0,-1,0,1,0
-0,0,1,0,1,0,-1,0,0
-0,-1,0,1,0,0,0,0,1
-1,0,0,0,-1,0,0,0,-1
--1,0,0,0,1,0,0,0,-1
--1,0,0,0,-1,0,0,0,1
-1,0,0,0,0,1,0,-1,0
-0,0,-1,0,1,0,1,0,0
-0,1,0,-1,0,0,0,0,1
-0,0,-1,1,0,0,0,-1,0
-0,0,1,-1,0,0,0,-1,0
-0,0,-1,-1,0,0,0,1,0
-0,0,1,1,0,0,0,1,0
-0,1,0,0,0,-1,-1,0,0
-0,-1,0,0,0,-1,1,0,0
-0,-1,0,0,0,1,-1,0,0
-0,1,0,0,0,1,1,0,0
-0,1,0,1,0,0,0,0,-1
-0,-1,0,-1,0,0,0,0,-1
-0,0,1,0,-1,0,1,0,0
-0,0,-1,0,-1,0,-1,0,0
--1,0,0,0,0,1,0,1,0
--1,0,0,0,0,-1,0,-1,0

testing.jl

@@ -1,23 +0,0 @@
-include("Hamiltonian.jl")
-
-println("Running with ",Threads.nthreads()," thread(s)")
-
-T=Float32
-
-function V_test(r2)
-    return -4*exp(-r2/4)
-end
-
-n = 3
-N = 8
-println("\n$n-body system with N=$N")
-
-for L::T in [16]
-    println("L=$L")
-    println("Constructing Hamiltonian")
-    s=system{T}(3,n,N,L,0.5,A1)
-    @time H=Hamiltonian{T}(s,V_test,0,0,cpu_tensor)
-    println("Solving eigenvalues")
-    @time evals,_,_ = eig(H,5)
-    println(evals)
-end