110 lines
4.2 KiB
Julia
110 lines
4.2 KiB
Julia
using SparseArrays, LinearAlgebra, Arpack, Plots
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include("helper.jl")
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"EC model for a Hamiltonian family H(c) = H0 + c * H1"
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mutable struct affine_EC
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H0::SparseMatrixCSC{ComplexF64}
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H1::SparseMatrixCSC{ComplexF64}
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weights::Vector{ComplexF64}
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trained::Bool
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H0_EC
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H1_EC
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N_EC
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training_E::Vector{ComplexF64}
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exact_E::Vector{ComplexF64}
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extrapolated_E::Vector{ComplexF64}
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affine_EC(H0::SparseMatrixCSC{ComplexF64}, H1::SparseMatrixCSC{ComplexF64}, weights::Vector{ComplexF64}=ones(ComplexF64, size(H0, 1))) = new(H0, H1, weights, false, nothing, nothing, nothing, ComplexF64[], ComplexF64[], ComplexF64[])
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end
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"Train an EC model for a given range of c values.
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If a list is provided for ref_eval, they are used as reference values for picking the closest eigenvalues at each sampling point.
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If a single number is provided for ref_eval, it is used as a reference for the first point, and the previous eigenvalue is used as the reference for each successive point.
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Set orthonormalize_threshold=0 to skip Gram-Schmidt orthonormalization and use GEVP. Otherwise this value is used as the threshold for dropping redundant vectors."
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function train!(EC::affine_EC, c_vals; ref_eval=-10.0, orthonormalize_threshold=1e-5, CAEC=false, verbose=true, tol=1e-5)
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training_vecs = Vector{ComplexF64}[]
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for c in c_vals
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verbose && println("Training for c = $c")
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global current_E
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if ref_eval isa Number
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current_E = ref_eval
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ref_eval = nothing
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elseif !isnothing(ref_eval)
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current_E = popfirst!(ref_eval)
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end
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H = EC.H0 + c .* EC.H1
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evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=tol, ritzvec=true, check=1)
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current_E = nearest(evals, current_E)
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push!(EC.training_E, current_E)
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push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
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end
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CAEC && append!(training_vecs, conj.(training_vecs))
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if orthonormalize_threshold ≠ 0
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training_vecs = gram_schmidt!(training_vecs, EC.weights, orthonormalize_threshold; verbose=verbose)
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end
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EC_basis = hcat(training_vecs...)
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weights_mat = spdiagm(EC.weights)
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EC.H0_EC = transpose(EC_basis) * weights_mat * EC.H0 * EC_basis
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EC.H1_EC = transpose(EC_basis) * weights_mat * EC.H1 * EC_basis
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if orthonormalize_threshold == 0
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EC.N_EC = transpose(EC_basis) * weights_mat * EC_basis
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end
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EC.trained = true
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end
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"Extrapolate using a trained EC model for a given range of c values
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If a list is provided for ref_eval, they are used as reference values for picking the closest eigenvalues at each point.
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If a single number is provided for ref_eval, it is used as a reference for the first point, and the previous eigenvalue is used as the reference for each successive point."
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function extrapolate!(EC::affine_EC, c_vals; ref_eval=EC.training_E[end], verbose=true, tol=1e-5)
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@assert EC.trained "EC model must be trained using train() before extrapolation"
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for c in c_vals
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verbose && println("Extact solution for c = $c")
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global current_E
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if ref_eval isa Number
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current_E = ref_eval
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ref_eval = nothing
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elseif !isnothing(ref_eval)
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current_E = popfirst!(ref_eval)
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end
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H = EC.H0 + c .* EC.H1
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evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=tol, ritzvec=false, check=1)
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current_E = nearest(evals, current_E)
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push!(EC.exact_E, current_E)
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verbose && println("Extrapolating for c = $c")
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H_EC = EC.H0_EC + c .* EC.H1_EC
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evals = isnothing(EC.N_EC) ? eigvals(H_EC) : eigvals(H_EC, EC.N_EC)
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push!(EC.extrapolated_E, nearest(evals, current_E))
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end
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end
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"Export EC data as CSV file"
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exportCSV(EC::affine_EC, filename) = exportCSV(filename, (EC.training_E, EC.exact_E, EC.extrapolated_E), ("training", "exact", "extrapolated"))
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"Plot EC data and optionally save figure to a file"
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function plot(EC::affine_EC, save_fig_filename=nothing)
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scatter(real.(EC.training_E), imag.(EC.training_E), label="training")
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scatter!(real.(EC.exact_E), imag.(EC.exact_E), label="exact")
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scatter!(real.(EC.extrapolated_E), imag.(EC.extrapolated_E), label="extrapolated")
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isnothing(save_fig_filename) || savefig(save_fig_filename)
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end
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