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koopman.jl
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koopman.jl
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struct KoopmanProblem{X,Y,U,C,PR,B,TR,TS,P,O}
x::X
y::Y
b::U
inds::C
prob::PR
basis::B
train::TR
test::TS
alg::P
options::O
eval_expression::Bool
end
struct KoopmanSolution{O,IN,S, E, F, A, P}
k::O
inds::IN
sets::S
error::E
folds::F
alg::A
options::P
end
select_by(::Val, sol::KoopmanSolution) = begin
@unpack k, error = sol
i = argmin(error)
return k[i], error[i]
end
select_by(::Val{:kfold}, sol::KoopmanSolution) = begin
@unpack k, folds, error = sol
size(k, 1) <= 1 && return select_by(1, sol)
i = argmin(mean(folds, dims = 1)[1,:])
return k[i], error[i]
end
## Apply the problem to get the operator
# DMD-Like
function CommonSolve.init(prob::AbstractDataDrivenProblem{N,C,P}, alg::AbstractKoopmanAlgorithm, args...; kwargs...) where {N,C,P}
# Build a basis
s_x = size(prob.X,1)
s_u = size(prob.U,1)
x = [Symbolics.variable(:x, i) for i in 1:s_x]
u = [Symbolics.variable(:u, i) for i in 1:s_u]
t = Symbolics.variable(:t)
b = Basis([x; u], x, controls = u, iv = t)
init(prob, b, alg, args...; kwargs...)
end
# All (g(E))DMD like
function CommonSolve.init(prob::AbstractDiscreteProb{N,C}, b::AbstractBasis, alg::A, args...; B = [], eval_expression = false, kwargs...) where {N,C, A <: AbstractKoopmanAlgorithm}
@is_applicable prob
@unpack X,p,t,U = prob
x = b(X[:,1:end-1], p, t[1:end-1], U[:,1:end-1])
y = b(X[:, 2:end], p, t[2:end], U[:, 2:end])
if !isempty(controls(b))
inds = .! is_dependent(map(eq->Num(eq.rhs),equations(b)), Num.(controls(b)))[1,:]
else
inds = ones(Bool, length(b))
end
options = DataDrivenCommonOptions(alg, N; kwargs...)
@unpack sampler = options
train, test = sampler(prob)
return KoopmanProblem(
x, y, B, inds, prob, b, train, test, alg, options, eval_expression
)
end
function CommonSolve.init(prob::AbstracContProb{N,C}, b::AbstractBasis, alg::A, args...; B = [], eval_expression = false, kwargs...) where {N,C, A <: AbstractKoopmanAlgorithm}
@is_applicable prob
@unpack DX,X,p,t,U = prob
x = b(prob)
y = similar(x)
J = jacobian(b)
if !isempty(U)
# Find the indexes of the control states
inds = .! is_dependent(map(eq->Num(eq.rhs),equations(b)), Num.(controls(b)))[1,:]
for i in 1:length(prob)
y[:, i] .= J(X[:, i], p, t[i], U[:, i])*DX[:, i]
end
else
inds = ones(Bool, length(b))
for i in 1:length(prob)
y[:, i] .= J(X[:, i], p, t[i])*DX[:, i]
end
end
options = DataDrivenCommonOptions(alg, N; kwargs...)
@unpack sampler = options
# Right now just ignore this
#train , test = nothing, nothing
train, test = sampler(prob)
return KoopmanProblem(
x, y, B, inds, prob, b, train, test, alg, options, eval_expression
)
end
function derive_operator(alg, x, y, b, z, inds)
if all(inds)
K, B = alg(x,y)
Q = y[inds, :]*x'
P = x*x'
C = z / y[inds, :]
elseif isempty(b)
K, B = alg(x[inds, :], y[inds, :], x[.! inds, :])
Q = y[inds, :]*x'
P = x*x'
C = z / y[inds, :]
else
K, B = alg(x[inds, :], y[inds, :], x[.! inds, :], b)
Q = y[inds, :]*x'
P = x*x'
C = z / y[inds, :]
end
return (K, B, C, P, Q,)
end
function operator_error(f, g)
(x,y,K,B,C,P,Q,inds) -> begin
k_ = Matrix(K)
isempty(B) && return g(f(k_*x, C, y))
return g(f(k_*x[inds, :]+B*x[.! inds, :], C, y))
end
end
function CommonSolve.solve!(k::KoopmanProblem)
@unpack x, y, b, inds, prob, basis, train, test, alg, options, eval_expression = k
@unpack normalize, denoise, sampler, maxiter, abstol, reltol, verbose, progress,f,g,digits,kwargs = options
z = get_target(prob)
xₜ = x[:, test]
zₜ = z[:, test]
trainerror = zeros(eltype(z), length(train), length(train))
testerror = zeros(eltype(z), length(train))
fg = operator_error(f, g)
ops = []
for (i,t) in enumerate(train)
op = derive_operator(alg, x[:, t], y[:, t], b, z[:, t], inds)
push!(ops, op)
testerror[i] = fg(xₜ, zₜ, op..., inds)
for (j, tt) in enumerate(train)
trainerror[i, j] = fg(x[:, tt], z[:, tt], op..., inds)
end
end
sol = KoopmanSolution(ops, inds, (train,test),testerror, trainerror, alg, options)
return DataDrivenSolution(prob, sol, basis, alg; eval_expression = eval_expression, digits = digits, kwargs...)
end