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Branch ambiguity fixed

This commit is contained in:
Nuwan Yapa 2025-04-25 18:20:57 -04:00
parent bb7b9cb198
commit b01b6e5d6c
2 changed files with 5 additions and 8 deletions
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9
calculations/ACCC.jl
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@ -20,7 +20,7 @@ c0 = find_zero(quick_extrapolate, 0.85)
# Calculation of training and extrapolating E # Calculation of training and extrapolating E
training_c = range(1.2, 0.9, 9) # original: range(1.35, 0.9, 5) training_c = range(1.2, 0.9, 9) # original: range(1.35, 0.9, 5)
training_E = [quick_pole_E(V_system(c)) for c in training_c] training_E = [quick_pole_E(V_system(c)) for c in training_c]
training_k = new_sqrt.(2μ .* training_E) training_k = alt_sqrt.(2μ .* training_E)
extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8) extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c] exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c]
@ -28,7 +28,7 @@ exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c]
order::Int = ceil((length(training_c) - 1) / 2) # order of the Pade approximant order::Int = ceil((length(training_c) - 1) / 2) # order of the Pade approximant
# Solve coefficients as a linear system # Solve coefficients as a linear system
M_left_element(c, i) = complex(c - c0)^(i/2) M_left_element(c, i) = alt_sqrt(c - c0)^i
M_left = M_left_element.(training_c, (0:order)') M_left = M_left_element.(training_c, (0:order)')
M_right = -training_k .* M_left[:, 2:end] # remove the first column M_right = -training_k .* M_left[:, 2:end] # remove the first column
M = hcat(M_left, M_right) # M = [M_left | M_right] M = hcat(M_left, M_right) # M = [M_left | M_right]
@ -37,14 +37,11 @@ a = sol[1:order+1]
b = [1; sol[order+2:end]] b = [1; sol[order+2:end]]
# Pade approximant # Pade approximant
polynomial(a, c) = sum(i -> a[i+1] * complex(c - c0)^(i/2), 0:order) polynomial(a, c) = sum(i -> a[i+1] * alt_sqrt(c - c0)^i, 0:order)
pade_approx(c) = polynomial(a, c) / polynomial(b, c) pade_approx(c) = polynomial(a, c) / polynomial(b, c)
# Extrapolate # Extrapolate
extrapolated_k = pade_approx.([training_c; extrapolating_c]) extrapolated_k = pade_approx.([training_c; extrapolating_c])
if real.(extrapolated_k[end]) < 0 # flip if following anti-resonance
extrapolated_k = -conj.(extrapolated_k)
end
extrapolated_E = (extrapolated_k .^ 2) / (2μ) extrapolated_E = (extrapolated_k .^ 2) / (2μ)
# Plotting # Plotting

4
common.jl
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@ -2,8 +2,8 @@ using LinearAlgebra, DelimitedFiles, SparseArrays
@enum coordinate_system jacobi src @enum coordinate_system jacobi src
"Square root function with the branch cut along the postive real axis" "Square root function with the branch cut along the postive imaginary axis"
new_sqrt(x::Number)::ComplexF64 = im * sqrt(complex(-x)) alt_sqrt(x::Number)::ComplexF64 = sqrt(im * x) / sqrt(im)
"Sum over array while minimizing catastrophic cancellation as much as possible" "Sum over array while minimizing catastrophic cancellation as much as possible"
function better_sum(arr::Array{T}) where T<:Real function better_sum(arr::Array{T}) where T<:Real