Moved files from fewbodyDVR
This commit is contained in:
ysyapa
parent
39cbcab8cf
commit
a082f140c1
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include("common.jl")
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using TensorOperations, KrylovKit, LinearAlgebra
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"A Hamiltonian that can be applied to a vector"
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struct HOperator{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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∂1::Matrix{Complex{T}}
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Vs::Array{T}
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function HOperator{T}(V_twobody::Function, d::Int, n::Int, N::Int, L::T, μ::T, n_image::Int) where {T<:Float}
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k = -N÷2:N÷2-1
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∂1 = ∂_1DOF.(L, N, k, k')
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Vs = calculate_Vs(V_twobody, d, n, N, L, n_image)
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return new{T}(d, n, N, L, μ, ∂1, Vs)
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end
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end
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Base.size(H::HOperator, i::Int)::Int = (i == 1 || i == 2) ? H.N^(H.d * (H.n - 1)) : throw(ArgumentError("HOperator only has 2 dimesions"))
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Base.size(H::HOperator)::Dims{2} = (size(H, 1), size(H, 2))
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"Dimensions of a vector to which H can be applied"
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vectorDims(H::HOperator)::Dims = tuple(fill(H.N, H.d * (H.n - 1))...)
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"Apply H on v and store the result in out"
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function LinearAlgebra.mul!(out::Array{Complex{T}}, H::HOperator{T}, v::Array{Complex{T}})::Array{Complex{T}} where {T<:Float}
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#LinearMaps.check_dim_mul(out,H,v) --- dimensions don't match
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# apply V operator
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@. out = H.Vs * v
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# apply K opereator
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coeff = -1 / (2 * H.μ)
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coords = H.n - 1
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nconList_v_template = -collect(1:H.d*(coords))
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for dim = 1:H.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.n, dim, coord1)
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i2 = which_index(H.n, 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.∂1, H.∂1, v), (nconList_1, nconList_2, nconList_v))
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out = axpy!(coeff, v_new, out)
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end
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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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"Apply H on v and return the result"
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function (H::HOperator{T})(v::Array{Complex{T}})::Array{Complex{T}} where {T<:Float}
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out = similar(v)
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return mul!(out, H, v)
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end
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tolerance = 1e-6
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"Wrapper for KrylovKit.eigsolve"
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function eig(H::HOperator{T}, levels::Int)::Tuple{Vector{T},Any,Any} where {T<:Float}
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x₀ = rand(Complex{T}, vectorDims(H))
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evals, evecs, info = eigsolve(H, x₀, levels, :SR; ishermitian = true, tol = tolerance)
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info.converged < levels && throw(error("Not enough convergence"))
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return real.(evals), evecs, info
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end
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@ -0,0 +1,106 @@
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include("common.jl")
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using KrylovKit, LinearAlgebra, CUDA, CUDA.CUTENSOR
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@assert CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu() "CUDA not available"
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"A Hamiltonian that can be applied to a vector"
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struct HOperator{T}
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d::Int
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n::Int
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N::Int
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K_diag::CuTensor{Complex{T}}
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K_mixed::CuTensor{Complex{T}}
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Vs::CuArray{T}
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function HOperator{T}(V_twobody::Function, d::Int, n::Int, N::Int, L::T, μ::T, n_image::Int) where {T<:Float}
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k = -N÷2:N÷2-1
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K_partial = (im / sqrt(2 * μ)) .* ∂_1DOF.(L, N, k, k')
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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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Vs = calculate_Vs(V_twobody, d, n, N, L, n_image)
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return new{T}(d, n, N, K_diag, K_mixed, Vs)
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end
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end
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Base.size(H::HOperator, i::Int)::Int = (i == 1 || i == 2) ? H.N^(H.d * (H.n - 1)) : throw(ArgumentError("HOperator only has 2 dimesions"))
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Base.size(H::HOperator)::Dims{2} = (size(H, 1), size(H, 2))
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"Dimensions of a vector to which H can be applied"
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vectorDims(H::HOperator)::Dims = tuple(fill(H.N, H.d * (H.n - 1))...)
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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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# https://docs.nvidia.com/cuda/cutensor/api/cutensor.html#cutensorcontraction
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compute_type = if eltype(C) == ComplexF32
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CUTENSOR.CUTENSOR_COMPUTE_TF32
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elseif eltype(C) == ComplexF64
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CUTENSOR.CUTENSOR_COMPUTE_64F
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else
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eltype(C)
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end
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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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compute_type=compute_type)
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return C
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end
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"Apply H on v and store the result in out"
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function LinearAlgebra.mul!(out::CuArray{Complex{T}}, H::HOperator{T}, v::CuArray{Complex{T}})::CuArray{Complex{T}} where {T<:Float}
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#LinearMaps.check_dim_mul(out,H,v) --- dimensions don't match
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ctx = context()
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# apply V operator
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NVTX.@range "V" @. out = H.Vs * v
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synchronize(ctx)
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# apply K opereator
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coords = H.n - 1
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inds_template = ('a' - 1) .+ collect(1:H.d*(coords))
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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.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.n, dim, coord1)
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i2 = which_index(H.n, 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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end
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end
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@assert out_t.inds == inds_template "out indices permuted"
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synchronize(ctx)
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return out_t.data
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end
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"Apply H on v and return the result"
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function (H::HOperator{T})(v::CuArray{Complex{T}})::CuArray{Complex{T}} where {T<:Float}
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out = similar(v)
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return mul!(out, H, v)
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end
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tolerance = 1e-6
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"Wrapper for KrylovKit.eigsolve"
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function eig(H::HOperator{T}, levels::Int)::Tuple{Vector{T},Any,Any} where {T<:Float}
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x₀ = CUDA.rand(Complex{T}, vectorDims(H)...) # ... added
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synchronize()
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evals, evecs, info = eigsolve(H, x₀, levels, :SR; ishermitian = true, tol = tolerance)
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info.converged < levels && throw(error("Not enough convergence"))
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return real.(evals), evecs, info
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end
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@ -0,0 +1,44 @@
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using CUDA
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GPU_mode = !("CPU" in ARGS) && CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu()
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println("Running with ",Threads.nthreads()," thread(s)")
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if GPU_mode
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include("GPU.jl")
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println("Available GPUs:")
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print(" ")
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println.(name.(devices()))
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else
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include("CPU.jl")
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end
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T=Float32
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function V_test(r2::T)::T
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return -4*exp(-r2/4)
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end
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function apply1000times(H,v)
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for i in 1:1000
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v=H(v);
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end
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end
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N=10
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n_image=1
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μ=0.5
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for L::T in 5.0:14.0
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println("Constructing H operator...")
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@time H=HOperator{T}(V_test,3,3,N,L,convert(T,μ),n_image)
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println("Applying H 1000 times...")
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if GPU_mode
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v=CUDA.rand(Complex{T},vectorDims(H)...)
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synchronize()
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CUDA.@profile CUDA.@time apply1000times(H,v)
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else
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v=rand(Complex{T},vectorDims(H)...)
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@time apply1000times(H,v)
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end
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end
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@ -0,0 +1,47 @@
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Float = Union{Float32,Float64}
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"Eq (46): Partial derivative matrix element for 1 degree of freedom"
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function ∂_1DOF(L::T, N::Int, k::Int, l::Int)::Complex{T} where {T<:Float}
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if k == l
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return -im * (π / L)
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else
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return (π / L) * (-1)^(k - l) * exp(-im * π * (k - l) / N) / sin(π * (k - l) / N)
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end
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end
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"Which index (dimension of the multidimensional array) corresponds to this dimension and coordinate?"
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which_index(n::Int, dim::Int, coord::Int)::Int = (dim - 1) * (n - 1) + coord
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"k value of the given degree of freedom at the corresponding index, with coord=0 always returning 0"
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get_k(n::Int, N::Int, i::CartesianIndex, dim::Int, coord::Int)::Int =
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coord == 0 ? 0 : i[which_index(n, dim, coord)] - N ÷ 2 - 1
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"k value of the DOF at the specified cubic image"
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get_shifted_k(n::Int, N::Int, i::CartesianIndex, dim::Int, coord::Int, image::Vector{Int})::Int =
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get_k(n, N, i, dim, coord) + N * image[dim]
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"Difference of k values between two particles"
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get_Δk(n::Int, N::Int, i::CartesianIndex, dim::Int, coord1::Int, coord2::Int, image::Vector{Int})::Int =
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get_k(n, N, i, dim, coord1) - get_shifted_k(n, N, i, dim, coord2, image)
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"Calculate diagonal elements of the V matrix"
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function calculate_Vs(V_twobody::Function, d::Int, n::Int, N::Int, L::T, n_image::Int)::Array{T} where {T<:Float}
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L²_over_N² = (L / N)^2
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coords = n - 1
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images = collect.(Iterators.product(fill(-n_image:n_image, d)...)) # TODO: Learn how to use tuples instead of vectors
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Vs = zeros(T, fill(N, d * coords)...)
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for image in images
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Threads.@threads for i in CartesianIndices(Vs)
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for coord1 in 1:coords
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for coord2 in 0:coord1-1
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Δk² = 0
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for dim in 1:d
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Δk² += get_Δk(n, N, i, dim, coord1, coord2, image)^2
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end
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Vs[i] += V_twobody(Δk² * L²_over_N²)
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end
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end
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end
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end
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return Vs
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end
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@ -0,0 +1,124 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" 2.748577 seconds (5.37 M allocations: 1.547 GiB, 2.72% gc time, 51.73% compilation time)\n",
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"318 operations : Float32[-6.121623, -4.333925, -4.3339176, -4.3331146, -4.333114, -4.2186065, -3.8715818, -3.87158, -3.5070298, -3.5068974]\n",
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" 0.831048 seconds (534.99 k allocations: 876.908 MiB, 3.50% gc time)\n",
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"210 operations : Float32[-5.682354, -3.9181006, -3.9180284, -3.9128082, -3.9127624, -3.2553062]\n",
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" 0.951621 seconds (619.15 k allocations: 1021.256 MiB, 3.53% gc time)\n",
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"243 operations : Float32[-5.6661367, -3.8267198, -3.826183, -3.8261826, -3.8142636, -3.813859, -3.813859, -2.9851913, -2.6131256]\n",
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" 0.521213 seconds (351.49 k allocations: 572.464 MiB, 3.02% gc time)\n",
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"138 operations : Float32[-5.7960987, -3.7636561, -3.7615638, -3.7473733, -3.7458477, -3.114099]\n",
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" 0.991049 seconds (499.35 k allocations: 820.918 MiB, 19.23% gc time)\n",
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"196 operations : Float32[-6.098429, -3.7029655, -3.6973379, -3.6973376, -3.6882992, -3.6845326, -3.6845293, -3.328601]\n",
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" 0.760867 seconds (496.83 k allocations: 821.141 MiB, 3.50% gc time)\n",
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"195 operations : Float32[-6.557852, -3.6505358, -3.639437, -3.6385512, -3.6385508, -3.6325362, -3.6325336, -3.464574, -3.0474584, -3.0474575, -2.8103795, -2.5698478, -2.566689]\n",
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" 0.475876 seconds (320.90 k allocations: 521.722 MiB, 3.28% gc time)\n",
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"126 operations : Float32[-7.090806, -3.6026099, -3.59206, -3.5818431, -3.5804336, -3.507454]\n",
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" 0.726440 seconds (435.62 k allocations: 713.962 MiB, 3.45% gc time)\n",
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"171 operations : Float32[-7.620871, -3.5517163, -3.5371916, -3.5240357, -3.524035]\n",
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" 0.429791 seconds (290.32 k allocations: 471.693 MiB, 3.72% gc time)\n",
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"114 operations : Float32[-8.108637, -3.4919598, -3.473435, -3.4578817, -3.443922, -3.4325478, -3.191059]\n",
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||||||
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" 0.702898 seconds (458.64 k allocations: 758.966 MiB, 3.41% gc time)\n",
|
||||||
|
"180 operations : Float32[-8.540969, -3.4251013, -3.4054415, -3.3879645, -3.3879626, -3.3685954, -3.3685944, -3.3663127, -3.167204, -3.1672013, -3.0144126]\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"# ./En.run -d 3 -n 3 -e 5 -c eps=0 -c pot=v_gauss,v0=-4,r=2 -N 6 -L 5:14 -c n_imag=1\n",
|
||||||
|
"\n",
|
||||||
|
"include(\"CPU.jl\")\n",
|
||||||
|
"\n",
|
||||||
|
"T=Float32\n",
|
||||||
|
"\n",
|
||||||
|
"function V_test(r2::T)::T\n",
|
||||||
|
" return -4*exp(-r2/4)\n",
|
||||||
|
"end\n",
|
||||||
|
"\n",
|
||||||
|
"N=6\n",
|
||||||
|
"for L::T in 5.0:14.0\n",
|
||||||
|
" H=HOperator{T}(V_test,3,3,N,L,0.5f0,1)\n",
|
||||||
|
" @time evals,evecs,info=eig(H,5)\n",
|
||||||
|
" print(info.numops,\" operations : \")\n",
|
||||||
|
" println(evals)\n",
|
||||||
|
"end"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 4,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
" 14.448286 seconds (50.73 M allocations: 3.915 GiB, 8.09% gc time, 88.73% compilation time)\n",
|
||||||
|
"537 operations : [-1.6584965779926615, 0.09641386689178666, 0.09723973976478092, 0.5328665170436317, 1.8025648869642366]\n",
|
||||||
|
" 1.604373 seconds (401.60 k allocations: 1.508 GiB, 3.30% gc time)\n",
|
||||||
|
"553 operations : [-1.5449615189600243, -0.09575302046477274, -0.03260724659630898, 0.4296397924712101, 1.2210175901367406]\n",
|
||||||
|
" 2.218717 seconds (511.34 k allocations: 1.925 GiB, 10.54% gc time)\n",
|
||||||
|
"704 operations : [-1.5104831395040967, -0.18248248011755844, -0.1824824801175365, -0.0513106144023292, 0.38929600143076387]\n",
|
||||||
|
" 1.405123 seconds (341.32 k allocations: 1.281 GiB, 3.24% gc time)\n",
|
||||||
|
"470 operations : [-1.5012367056346252, -0.22279714610399948, -0.04336905464703111, 0.3604715853445004, 0.6888462772294086]\n",
|
||||||
|
" 1.210149 seconds (316.61 k allocations: 1.186 GiB, 2.94% gc time)\n",
|
||||||
|
"436 operations : [-1.4988400995145905, -0.24196385384291874, -0.032981565737151275, 0.33103969539525147, 0.5259297115623096]\n",
|
||||||
|
" 1.332379 seconds (315.88 k allocations: 1.185 GiB, 9.01% gc time)\n",
|
||||||
|
"435 operations : [-1.4982182159585573, -0.2512983034534455, -0.02487547395190237, 0.29998450185680947, 0.4122309417963048]\n",
|
||||||
|
" 1.195907 seconds (314.47 k allocations: 1.182 GiB, 3.37% gc time)\n",
|
||||||
|
"433 operations : [-1.4980550726371076, -0.25596036323828786, -0.019096799768268946, 0.26880364248084865, 0.3307745735815646]\n",
|
||||||
|
" 1.715641 seconds (424.90 k allocations: 1.603 GiB, 2.77% gc time)\n",
|
||||||
|
"585 operations : [-1.49801176610691, -0.25834484110826805, -0.2583448411082359, -0.014990294007072302, 0.23909670164137475, 0.2709248751032005, 0.3173198198351823, 0.4388941435702842]\n",
|
||||||
|
" 1.627872 seconds (391.47 k allocations: 1.476 GiB, 7.94% gc time)\n",
|
||||||
|
"539 operations : [-1.4980001524634678, -0.2595900399451015, -0.2595900399450435, -0.012010461572629527, 0.21193520997052917, 0.22589198387830156, 0.2668519716084061, 0.39403726730136146]\n",
|
||||||
|
" 1.503319 seconds (383.48 k allocations: 1.443 GiB, 3.06% gc time)\n",
|
||||||
|
"528 operations : [-1.4979970118272345, -0.2602517135112987, -0.26025171351127213, -0.009793271721286467, 0.1877986939216265, 0.19126207990343963, 0.22720822569865662]\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"# ./En.run -d 3 -n 2 -e 5 -c eps=0 -c pot=v_gauss,v0=-4,r=2 -N 32 -L 5:14 -c n_imag=0\n",
|
||||||
|
"\n",
|
||||||
|
"include(\"CPU.jl\")\n",
|
||||||
|
"\n",
|
||||||
|
"T=Float64\n",
|
||||||
|
"\n",
|
||||||
|
"function V_test(r2::T)::T\n",
|
||||||
|
" return -4*exp(-r2/4)\n",
|
||||||
|
"end\n",
|
||||||
|
"\n",
|
||||||
|
"N=32\n",
|
||||||
|
"for L::T in 5.0:14.0\n",
|
||||||
|
" H=HOperator{T}(V_test,3,2,N,L)\n",
|
||||||
|
" @time evals,evecs,info=eig(H,5)\n",
|
||||||
|
" print(info.numops,\" operations : \")\n",
|
||||||
|
" println(evals)\n",
|
||||||
|
"end"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"metadata": {
|
||||||
|
"kernelspec": {
|
||||||
|
"display_name": "Julia 1.7.1",
|
||||||
|
"language": "julia",
|
||||||
|
"name": "julia-1.7"
|
||||||
|
},
|
||||||
|
"language_info": {
|
||||||
|
"file_extension": ".jl",
|
||||||
|
"mimetype": "application/julia",
|
||||||
|
"name": "julia",
|
||||||
|
"version": "1.7.1"
|
||||||
|
},
|
||||||
|
"orig_nbformat": 4
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 2
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,41 @@
|
||||||
|
using CUDA
|
||||||
|
|
||||||
|
GPU_mode = !("CPU" in ARGS) && CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu()
|
||||||
|
|
||||||
|
println("Running with ",Threads.nthreads()," thread(s)")
|
||||||
|
|
||||||
|
if GPU_mode
|
||||||
|
include("GPU.jl")
|
||||||
|
println("Available GPUs:")
|
||||||
|
print(" ")
|
||||||
|
println.(name.(devices()))
|
||||||
|
else
|
||||||
|
include("CPU.jl")
|
||||||
|
end
|
||||||
|
|
||||||
|
T=Float32
|
||||||
|
|
||||||
|
function V_zero(r2::T)::T
|
||||||
|
return 0.0
|
||||||
|
end
|
||||||
|
|
||||||
|
function V_test(r2::T)::T
|
||||||
|
return -4*exp(-r2/4)
|
||||||
|
end
|
||||||
|
|
||||||
|
N=6
|
||||||
|
n_image=1
|
||||||
|
μ=0.5
|
||||||
|
|
||||||
|
levels=5
|
||||||
|
|
||||||
|
for L::T in 5.0:14.0
|
||||||
|
H=HOperator{T}(V_test,3,3,N,L,convert(T,μ),n_image)
|
||||||
|
if GPU_mode
|
||||||
|
CUDA.@time evals,evecs,info=eig(H,levels)
|
||||||
|
else
|
||||||
|
@time evals,evecs,info=eig(H,levels)
|
||||||
|
end
|
||||||
|
print(info.numops," operations : ")
|
||||||
|
println(evals)
|
||||||
|
end
|
||||||
Loading…
Reference in New Issue