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Tensor dynamical system for Z-eigenvector computation
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using LinearAlgebra | |
function tensor_apply(T::Array{Float64,3}, x::Vector{Float64}) | |
n = length(x) | |
y = zeros(Float64, n) | |
for k in 1:n; y += T[:, :, k] * x * x[k]; end | |
return y | |
end | |
function tensor_collapse(T::Array{Float64,3}, x::Vector{Float64}) | |
n = length(x) | |
Y = zeros(Float64, n, n) | |
for k in 1:n; Y += T[:, :, k] * x[k]; end | |
return Y | |
end | |
function dynsys_forward_euler(T::Array{Float64,3}, | |
h::Float64, niter::Int64=20) | |
function Λ(u::Vector{Float64}) # Derivative | |
F = eigen(tensor_collapse(T, u)) | |
ind = sortperm(abs.(real(F.values)))[1] | |
v = F.vectors[:, ind] | |
return sign(v[1]) * v # sign consistency | |
end | |
x = normalize(ones(Float64, size(T, 1)), 1) # starting point | |
λ_hist = [x' * tensor_apply(T, x)] | |
for _ = 1:niter | |
x += h * (Λ(x) - x) # forward Euler | |
push!(λ_hist, x' * tensor_apply(T, x)) # Rayleigh quotient | |
end | |
return (x, λ_hist) # guess at evec and history of evals | |
end |
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This code is now updated for Julia 1.0.