Migrate HO basis to SRC

ho_basis.jl

@@ -157,8 +157,8 @@ function get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxeva
     return V2
 end
 
-function get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μ1ω1, μ2ω2)
+function get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μ1ω1, μ2ω2; dtype=Float64)
-    mat = zeros(Float64, length(n1s), length(n1s))
+    mat = zeros(dtype, length(n1s), length(n1s))
     Threads.@threads for idx in CartesianIndices(mat)
         (i, j) = Tuple(idx)
         val = racahs_reduction_formula(n1s[i], l1s[i], n2s[i], l2s[i], n1s[j], l1s[j], n2s[j], l2s[j], Λ, μ1ω1, μ2ω2)
@@ -166,3 +166,37 @@ function get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μ1ω1, μ2ω2)
     end
     return sparse(mat)
 end
+
+function get_src_V_matrix(V_of_r, E_max, Λ, μω, 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')
+    mask2 = (n1s .== n1s') .&& (l1s .== l1s')
+    
+    V_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω, atol=atol, maxevals=maxevals)
+    V_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
+
+    V1 = get_sp_V_matrix(V_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_cache)
+    V2 = get_sp_V_matrix(V_elem, n2s, l2s; mask=mask2, dtype=ComplexF64, cache=V_cache)
+
+    V12 =  get_src_V12_matrix(V_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
+
+    return V1 + V2 + V12
+end
+
+function get_src_V12_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')
+    
+    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)
+    U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
+    V12 =  U' * V_relative * U
+
+    return V12
+end

ho_basis_3body_resonance.jl

@@ -8,11 +8,9 @@ V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 E_max = 30
 μω_global = 0.5 * exp(-2im * pi / 9)
 
-# due to Jacobi coordinates
+# due to simple relative coordinates
-μ1ω1 = μω_global * 1/2
+μω = μω_global * 2
-μ2ω2 = μω_global * 2
+μ = m/2
-μ1 = m * 1/2
-μ2 = m * 2/3
 
 println("No of threads = ", Threads.nthreads())
 
@@ -28,15 +26,16 @@ println("Basis size = ", length(Es))
 
 println("Constructing KE matrices")
 
-@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
+@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μω, μ=μ)
-@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
+@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μω, μ=μ)
+@time "T_cross" T_cross = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω; dtype=ComplexF64) ./ (2*μ)
 
 println("Constructing PE matrices")
 
-@time "V" V = get_jacobi_V_matrix(V_of_r, E_max, Λ, μ1ω1, μω_global)
+@time "V" V = get_src_V_matrix(V_of_r, E_max, Λ, μω, μω_global)
 
 println("Calculating spectrum")
-@time "H" H = T1 + T2 + V
+@time "H" H = T1 + T2 + T_cross + V
 @time "Eigenvalues" evals, _ = eigs(H, nev=5, ncv=50, which=:LI, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 
 display(evals)