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Refactor 3-body V matrix

This commit is contained in:
Nuwan Yapa 2024-06-27 18:04:56 -04:00
parent edd63d8a31
commit 449c93817a
10 changed files with 54 additions and 46 deletions
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19
3body_resonance.jl
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@ -28,26 +28,15 @@ println("Basis size = ", length(Es))
println("Constructing KE matrices")
@time "T1" T1 = sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
println("Constructing PE matrices")
atol = 10^-6
maxevals = 10^5
V1_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μ1ω1, atol=atol, maxevals=maxevals)
V_relative_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω_global, atol=atol, maxevals=maxevals)
V1_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
V_relative_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
@time "V1" V1 = sp_V_matrix(V1_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V1_cache)
@time "V relative" V_relative = sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_relative_cache) + sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2, dtype=ComplexF64, cache=V_relative_cache)
@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
@time "V2" V2 = U' * V_relative * U
@time "V" V = get_jacobi_V_matrix(V_of_r, E_max, Λ, μ1ω1, μω_global)
println("Calculating spectrum")
@time "H" H = T1 + T2 + V1 + V2
@time "H" H = T1 + T2 + V
@time "Eigenvalues" evals, _ = eigs(H, nev=5, ncv=50, which=:LI, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
display(evals)

1
3body_resonance_EC.jl
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@ -7,7 +7,6 @@ training_c = 2.0 : -0.2 : 1.2
extrapolating_c = 1.05 .- [0.0 : 0.1 : 0.4; 0.45 : 0.05 : 0.60]
@time "H0" H0 = T1 + T2
@time "V" V = V1 + V2
# free memory
Es = n1s = l1s = n2s = l2s = mask1 = mask2 = T1 = T2 = V1_cache = V_relative_cache = V1 = V_relative = U = V2 = nothing

2
XZ_technique.jl
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@ -14,7 +14,7 @@ n_max = 15
ns = collect(0:n_max)
ls = fill(l, n_max + 1)
T = sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
n_EC = 8

4
berggren.jl
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@ -2,8 +2,8 @@ using SparseArrays
include("ho_basis.jl")
"Basis transformation from HO to momentum space"
function get_W_matrix(basis_p, basis_HO, μ1ω1, μ2ω2=μ1ω1; weights=true)
Es, n1s, l1s, n2s, l2s = basis_HO
function get_W_matrix(basis_p, E_max, Λ, μ1ω1, μ2ω2=μ1ω1; weights=true)
Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
W = zeros(ComplexF64, length(basis_p), length(Es))
Threads.@threads for idx in CartesianIndices(W)
(i1, i2) = Tuple(idx)

18
berggren_3body.jl
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@ -43,25 +43,13 @@ end
E_max = 30
μω_global = 0.5
μ1ω1 = μω_global * 1/2
μ2ω2 = μω_global * 2
basis_HO = get_2p_basis(E_max, Λ)
Es, n1s, l1s, n2s, l2s = basis_HO
l_max = max(maximum(l1s), maximum(l2s))
n_max = max(maximum(n1s), maximum(n2s))
mask1 = (n2s .== n2s') .&& (l2s .== l2s')
mask2 = (n1s .== n1s') .&& (l1s .== l1s')
@time "V2_HO" V2_HO = get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global)
V_relative_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω_global, atol=atol, maxevals=maxevals)
V_relative_cache = LRU{Tuple{UInt8, UInt8, UInt8}, Float64}(maxsize=(1+l_max)*(1+n_max)^2)
@time "V relative" V_relative = sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1, dtype=Float64, cache=V_relative_cache) + sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2, dtype=Float64, cache=V_relative_cache)
@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
@time "V2_HO" V2_HO = U' * V_relative * U
@time "W_right" W_right = get_W_matrix(basis, basis_HO, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, basis_HO, μ1ω1, μ2ω2; weights=false)
@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
@time "V2" V2 = W_left * V2_HO * transpose(W_right)
@time "H" H = T + V1 + V2

36
ho_basis.jl
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@ -56,7 +56,7 @@ function get_2p_basis(E_max, Λ=-1)
return (Es, n1s, l1s, n2s, l2s)
end
function sp_T_matrix(ns, ls; mask=trues(length(ns),length(ns)), μω_gen=1.0, μ=1.0)
function get_sp_T_matrix(ns, ls; mask=trues(length(ns),length(ns)), μω_gen=1.0, μ=1.0)
mat = spzeros(length(ns), length(ns))
for idx in CartesianIndices(mat)
if !mask[idx]; continue; end
@ -73,7 +73,7 @@ function sp_T_matrix(ns, ls; mask=trues(length(ns),length(ns)), μω_gen=1.0, μ
return (μω_gen / μ) .* mat
end
function sp_V_matrix(V_l, ns, ls; mask=trues(length(ns),length(ns)), dtype=Float64, cache=LRU{Tuple{UInt8, UInt8, UInt8}, dtype}(maxsize=(1+maximum(ns))^2))
function get_sp_V_matrix(V_l, ns, ls; mask=trues(length(ns),length(ns)), dtype=Float64, cache=LRU{Tuple{UInt8, UInt8, UInt8}, dtype}(maxsize=(1+maximum(ns))^2))
mat = zeros(dtype, length(ns), length(ns))
Threads.@threads for idx in CartesianIndices(mat)
if !mask[idx]; continue; end
@ -137,3 +137,35 @@ function V_numerical(V_of_r, l, n1, n2; μω_gen=1.0, atol=0, maxevals=10^7)
(integral, _) = quadgk(integrand, 0, Inf; atol=atol, maxevals=maxevals)
return integral
end
function get_jacobi_V_matrix(V_of_r, E_max, Λ, μ1ω1, μω_global; atol=10^-6, maxevals=10^5)
_, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
l_max = max(maximum(l1s), maximum(l2s))
n_max = max(maximum(n1s), maximum(n2s))
mask1 = (n2s .== n2s') .&& (l2s .== l2s')
V1_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μ1ω1, atol=atol, maxevals=maxevals)
V1_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
V1 = get_sp_V_matrix(V1_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V1_cache)
V2 = get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
return V1 + V2
end
function get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxevals=10^5)
Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
l_max = max(maximum(l1s), maximum(l2s))
n_max = max(maximum(n1s), maximum(n2s))
mask1 = (n2s .== n2s') .&& (l2s .== l2s')
mask2 = (n1s .== n1s') .&& (l1s .== l1s')
V_relative_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω_global, atol=atol, maxevals=maxevals)
V_relative_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_relative_cache) + get_sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2, dtype=ComplexF64, cache=V_relative_cache)
U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
V2 = U' * V_relative * U
return V2
end

4
ho_basis_2body.jl
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@ -17,11 +17,11 @@ Es, n1s, l1s = get_sp_basis(E_max)
println("Basis size = ", length(Es))
println("Constructing KE matrices")
@time "T1" T1 = sp_T_matrix(n1s, l1s; μω_gen=μω_gen, μ=μ1)
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; μω_gen=μω_gen, μ=μ1)
println("Constructing PE matrices")
V1_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω_gen)
@time "V1" V1 = sp_V_matrix(V1_elem, n1s, l1s)
@time "V1" V1 = get_sp_V_matrix(V1_elem, n1s, l1s)
println("Calculating spectrum")
@time "H" H = T1 + V1

8
ho_basis_3body.jl
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@ -26,14 +26,14 @@ end
println("Basis size = ", length(Es))
println("Constructing KE matrices")
@time "T1" T1 = sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
println("Constructing PE matrices")
V1_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μ1ω1)
V_relative_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω_global)
@time "V1" V1 = sp_V_matrix(V1_elem, n1s, l1s; mask=mask1)
@time "V relative" V_relative = sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1) + sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2)
@time "V1" V1 = get_sp_V_matrix(V1_elem, n1s, l1s; mask=mask1)
@time "V relative" V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1) + get_sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2)
@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
@time "V2" V2 = U' * V_relative * U

4
ho_basis_benchmark.jl
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@ -14,10 +14,10 @@ n_max = 15
ns = collect(0:n_max)
ls = fill(l, n_max + 1)
T = sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
V_l(l, n1, n2) = V1 * V_Gaussian(R1, l, n1, n2; μω_gen=μω_gen) + V2 * V_Gaussian(R2, l, n1, n2; μω_gen=μω_gen)
V = sp_V_matrix(V_l, ns, ls; dtype=ComplexF64)
V = get_sp_V_matrix(V_l, ns, ls; dtype=ComplexF64)
cs = range(1.25, 0.25, 10)

4
ho_basis_test.jl
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@ -9,10 +9,10 @@ n_max = 20
ns = collect(0:n_max)
ls = fill(l, n_max + 1)
T = sp_T_matrix(ns, ls)
T = get_sp_T_matrix(ns, ls)
V_l(l, n1, n2) = V0 * V_Gaussian(R, l, n1, n2)
V = sp_V_matrix(V_l, ns, ls)
V = get_sp_V_matrix(V_l, ns, ls)
H = T + V