First Jacobi implementation
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ysyapa
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@ -6,27 +6,23 @@ using TensorOperations, KrylovKit, LinearAlgebra, CUDA, cuTENSOR, NVTX
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"A Hamiltonian that can be applied to a vector"
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struct Hamiltonian{T}
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s::system{T}
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K_partial::Matrix{Complex{T}}
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K_diag::Union{CuTensor{Complex{T}},Nothing}
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K_mixed::Union{CuTensor{Complex{T}},Nothing}
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Vs::Union{Array{Complex{T}},CuArray{Complex{T}}}
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K::Union{CuTensor{Complex{T}}, Matrix{Complex{T}}}
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Vs::Union{Array{Complex{T}}, CuArray{Complex{T}}}
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hermitian::Bool
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mode::Hamiltonian_backend
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function Hamiltonian{T}(s::system{T}, V_twobody::Function, ϕ::Real, n_image::Int, mode::Hamiltonian_backend) where {T<:Float}
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@assert mode != gpu_cutensor || CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu() "CUDA not available"
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k = -s.N÷2:s.N÷2-1
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Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
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hermitian = ϕ == 0.0
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K_partial = (exp(-im * convert(T, ϕ)) * im / sqrt(2 * s.μ)) .* ∂_1DOF.(Ref(s), k, k')
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K_diag = nothing
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K_mixed = nothing
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Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
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k = -s.N÷2:s.N÷2-1
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∂ = ∂_1DOF.(Ref(s), k, k')
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K = exp(-2im * convert(T, ϕ)) .* (∂ * ∂) # TODO: Calculate K matrix elements directly
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if mode == gpu_cutensor
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K_diag = CuTensor(CuArray(K_partial * K_partial), ['a', 'A'])
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K_mixed = CuTensor(CuArray(K_partial), ['a', 'A']) * CuTensor(CuArray(K_partial), ['b', 'B'])
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K = CuTensor(K, ['a', 'A'])
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Vs = CuArray(Vs)
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end
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return new{T}(s, K_partial, K_diag, K_mixed, Vs, hermitian, mode)
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return new{T}(s, K, Vs, hermitian, mode)
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end
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end
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@ -45,31 +41,23 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
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coords = H.s.n - 1
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nconList_v_template = -collect(1:H.s.d*(coords))
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for dim = 1:H.s.d
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for coord1 = 1:coords
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for coord2 = 1:coord1
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i1 = which_index(H.s, dim, coord1)
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i2 = which_index(H.s, dim, coord2)
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nconList_1 = [-i1, 1]
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nconList_2 = [-i2, 2]
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nconList_v = copy(nconList_v_template)
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if i1 == i2
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nconList_2[1] = 1
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else
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nconList_v[i1] = 1
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end
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nconList_v[i2] = 2
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v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
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out = axpy!(1, v_new, out)
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end
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for coord = 1:coords
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i = which_index(H.s, dim, coord)
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nconList_K = [-i, 1]
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nconList_v = copy(nconList_v_template)
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nconList_v[i] = 1
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v_new = @ncon((H.K, v), (nconList_K, nconList_v))
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coeff = -1 / (2 * H.s.μs[coord])
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out = axpy!(coeff, v_new, out)
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end
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end
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return out
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end
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"cuTENSOR contraction and accumulation (C = A * B + C)"
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function contract_accumulate!(C::CuTensor, A::CuTensor, B::CuTensor)::CuTensor
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CUTENSOR.contraction!(one(eltype(C)), A.data, A.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, CUTENSOR.CUTENSOR_OP_IDENTITY,
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one(eltype(C)), C.data, C.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, CUTENSOR.CUTENSOR_OP_IDENTITY)
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function contract_accumulate!(alpha::Numer, C::CuTensor, A::CuTensor, B::CuTensor)::CuTensor
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cuTENSOR.contraction!(alpha, A.data, A.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, cuTENSOR.CUTENSOR_OP_IDENTITY,
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one(eltype(C)), C.data, C.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, cuTENSOR.CUTENSOR_OP_IDENTITY)
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return C
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end
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@ -86,31 +74,16 @@ function LinearAlgebra.mul!(out::CuArray{Complex{T}}, H::Hamiltonian{T}, v::CuAr
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v_t = CuTensor(v, copy(inds_template))
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out_t = CuTensor(out, copy(inds_template))
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for dim = 1:H.s.d
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for coord1 = 1:coords
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for coord2 = 1:coord1
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i1 = which_index(H.s, dim, coord1)
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i2 = which_index(H.s, dim, coord2)
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@assert v_t.inds == inds_template "v indices permuted"
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if i1 == i2
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@assert H.K_diag.inds[2] == 'A' "K_diag indices permuted"
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H.K_diag.inds[1] = 'a' - 1 + i1
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v_t.inds[i1] = 'A'
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#synchronize(ctx)
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NVTX.@range "K-diag" out_t = contract_accumulate!(out_t, H.K_diag, v_t)
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v_t.inds[i1] = 'a' - 1 + i1
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else
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@assert H.K_mixed.inds[2] == 'A' && H.K_mixed.inds[4] == 'B' "K_mixed indices permuted"
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H.K_mixed.inds[1] = 'a' - 1 + i1
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H.K_mixed.inds[3] = 'a' - 1 + i2
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# OPTIMIZE: A and B can be swapped
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v_t.inds[i1] = 'A'
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v_t.inds[i2] = 'B'
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#synchronize(ctx)
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NVTX.@range "K-mixed" out_t = contract_accumulate!(out_t, H.K_mixed, v_t)
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v_t.inds[i1] = 'a' - 1 + i1
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v_t.inds[i2] = 'a' - 1 + i2
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end
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end
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for coord = 1:coords
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i = which_index(H.s, dim, coord)
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@assert v_t.inds == inds_template "v indices permuted"
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@assert H.K_diag.inds[2] == 'A' "K_diag indices permuted"
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H.K.inds[1] = 'a' - 1 + i
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v_t.inds[i] = 'A'
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#synchronize(ctx)
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coeff = -1 / (2 * H.s.μs[coord])
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NVTX.@range "K" out_t = contract_accumulate!(coeff, out_t, H.K, v_t)
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v_t.inds[i] = 'a' - 1 + i
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end
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end
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@assert out_t.inds == inds_template "out indices permuted"
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60
common.jl
60
common.jl
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@ -1,18 +1,33 @@
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Float = Union{Float32,Float64}
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norm_square(x) = sum(x .* x)
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reducedMass(m1::Float, m2::Float) = 1 / (1/m1 + 1/m2)
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"A few-body system defined by its physical parameters"
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struct system{T}
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d::Int
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n::Int
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N::Int
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L::T
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μ::T
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μs::Vector{T}
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invU::Matrix{T}
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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))
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function system{T}(d::Int, n::Int, N::Int, L::Real) where {T<:Float}
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μs = collect(1:n) ./ collect(2:(n + 1))
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U = zeros(T, n, n)
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for coord in 1:n
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U[coord, 1:coord] .= 1 / coord
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if coord != n
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U[coord, coord + 1] = -1
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end
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end
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invU = inv(U)[:, 1:(n - 1)]
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return new{T}(d, n, N, convert(T, L), μs, invU)
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end
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end
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norm_square(x::Array{Int})::Int = sum(x .* x)
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"Eq (46): Partial derivative matrix element for 1 degree of freedom"
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function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
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if k == l
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@ -22,19 +37,17 @@ function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
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end
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end
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"Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' and particle 'p'?"
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which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 1) + p
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"Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' of coordinate 'coord'?"
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which_index(s::system, dim::Int, coord::Int)::Int = (dim - 1) * (s.n - 1) + coord
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"Δk (distance in terms of lattice paramter) between two particles along the given dimension"
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function get_Δk(s::system, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
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if p1 == p2
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return 0
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elseif p1 == s.n
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return -(i[which_index(s, dim, p2)] - s.N ÷ 2 - 1)
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elseif p2 == s.n
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return i[which_index(s, dim, p1)] - s.N ÷ 2 - 1
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"Get the distance to the nearest image of the particle"
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function nearest(s, Δk)
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if Δk > s.N ÷ 2
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return Δk - s.N
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elseif Δk < -s.N ÷ 2
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return Δk + s.N
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else
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return i[which_index(s, dim, p1)] - i[which_index(s, dim, p2)]
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return Δk
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end
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end
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@ -44,21 +57,16 @@ function calculate_Vs(s::system{T}, V_twobody::Function, ϕ::T, n_image::Int)::A
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images = collect.(Iterators.product(fill(-n_image:n_image, s.d)...)) # TODO: Learn how to use tuples instead of vectors
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Vs = zeros(Complex{T}, fill(s.N, s.d * (s.n - 1))...)
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Threads.@threads for i in CartesianIndices(Vs)
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xs = reshape(collect(Tuple(i)), s.n - 1, s.d) .- (s.N ÷ 2 - 1)
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rs = s.invU * xs
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for p1 in 1:s.n
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for p2 in (p1 + 1):s.n
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min_Δk = Array{Int}(undef, s.d)
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for p2 in 1:(p1 - 1)
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Δk = Array{T}(undef, s.d)
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for dim in 1:s.d
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Δk = get_Δk(s, i, dim, p1, p2)
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if Δk > s.N ÷ 2
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min_Δk[dim] = Δk - s.N
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elseif Δk < -s.N ÷ 2
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min_Δk[dim] = Δk + s.N
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else
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min_Δk[dim] = Δk
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end
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Δk[dim] = nearest(s, rs[p1, dim] - rs[p2, dim])
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end
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for image in images
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Δk² = norm_square(min_Δk .- (s.N .* image))
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Δk² = norm_square(Δk .- (s.N .* image))
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Vs[i] += V_twobody(Δk² * coeff²)
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end
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end
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