Integrals.jl

Integrals.jl is an instantiation of the SciML common IntegralProblem interface for the common numerical integration packages of Julia, including both those based upon quadrature as well as Monte-Carlo approaches. By using Integrals.jl, you get a single predictable interface where many of the arguments are standardized throughout the various integrator libraries. This can be useful for benchmarking or for library implementations, since libraries which internally use a quadrature can easily accept a integration method as an argument.

Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Examples

For basic multidimensional quadrature we can construct and solve a IntegralProblem:

using Integrals
f(x, p) = sum(sin.(x))
prob = IntegralProblem(f, ones(2), 3ones(2))
sol = solve(prob, HCubatureJL(), reltol = 1e-3, abstol = 1e-3)

If we would like to parallelize the computation, we can use the batch interface to compute multiple points at once. For example, here we do allocation-free multithreading with Cubature.jl:

using Integrals, Cubature, Base.Threads
function f(dx, x, p)
    Threads.@threads for i in 1:size(x, 2)
        dx[i] = sum(sin.(@view(x[:, i])))
    end
end
prob = IntegralProblem(f, ones(2), 3ones(2), batch = 2)
sol = solve(prob, CubatureJLh(), reltol = 1e-3, abstol = 1e-3)

If we would like to compare the results against Cuba.jl's Cuhre method, then the change is a one-argument change:

using IntegralsCuba
sol = solve(prob, CubaCuhre(), reltol = 1e-3, abstol = 1e-3)