Unified operator interface for SciML.ai and beyond
SciMLOperators is a package for managing linear, nonlinear,
time-dependent, and parameter dependent operators acting on vectors,
(or column-vectors of matrices). We provide wrappers for matrix-free
operators, fast tensor-product evaluations, pre-cached mutating
evaluations, as well as Zygote-compatible non-mutating evaluations.
The lazily implemented operator algebra allows the user to update the
operator state by passing in an update function that accepts arbitrary
parameter objects. Further, our operators behave like AbstractMatrix types
thanks to overloads defined for methods in Base, and LinearAlgebra.
Therefore, an AbstractSciMLOperator can be passed to LinearSolve.jl,
or NonlinearSolve.jl as a linear/nonlinear operator, or to
OrdinaryDiffEq.jl as an ODEFunction. Examples of usage within the
SciML ecosystem are provided in the documentation.
SciMLOperators.jl is a registered package and can be installed via
julia> import Pkg
julia> Pkg.add("SciMLOperators")
Let M, D, F be matrix-based, diagonal-matrix-based, and function-based
SciMLOperators respectively.
N = 4
f(u, p, t) = u .* u
f(v, u, p, t) = v .= u .* u
M = MatrixOperator(rand(N, N))
D = DiagonalOperator(rand(N))
F = FunctionOperator(f, zeros(N), zeros(N))Then, the following codes just work.
L1 = 2M + 3F + LinearAlgebra.I + rand(N, N)
L2 = D * F * M'
L3 = kron(M, D, F)
L4 = M \ D
L5 = [M; D]' * [M F; F D] * [F; D]Each L# can be applied to AbstractVectors of appropriate sizes:
p = nothing # parameter struct
t = 0.0 # time
u = rand(N)
v = L1(u, p, t) # == L1 * u
u_kron = rand(N^3)
v_kron = L3(u_kron, p, t) # == L3 * u_kronFor mutating operator evaluations, call cache_operator to generate
in-place cache so the operation is nonallocating.
α, β = rand(2)
# allocate cache
L2 = cache_operator(L2, u)
L4 = cache_operator(L4, u)
# allocation-free evaluation
L2(v, u, p, t) # == mul!(v, L2, u)
L4(v, u, p, t, α, β) # == mul!(v, L4, u, α, β)