A common interface for quadrature and numerical integration for the SciML scientific machine learning organization
MIT License
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.
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.
To perform one-dimensional quadrature, we can simply construct an IntegralProblem
. The code below evaluates $\int_{-2}^5 \sin(xp)~\mathrm{d}x$ with $p = 1.7$. This argument $p$ is passed
into the problem as the third argument of IntegralProblem
.
using Integrals
f(x, p) = sin(x * p)
p = 1.7
domain = (-2, 5) # (lb, ub)
prob = IntegralProblem(f, domain, p)
sol = solve(prob, QuadGKJL())
For basic multidimensional quadrature we can construct and solve a IntegralProblem
. Since we are using no arguments p
in this example, we omit the third argument of IntegralProblem
from above. The lower and upper bounds are now passed as vectors, with the i
th elements of
the bounds giving the interval of integration for x[i]
.
using Integrals
f(x, p) = sum(sin.(x))
domain = (ones(2), 3ones(2)) # (lb, ub)
prob = IntegralProblem(f, domain)
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
domain = (ones(2), 3ones(2)) # (lb, ub)
prob = IntegralProblem(BatchIntegralFunction(f, zeros(0)), domain)
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 Cuba
sol = solve(prob, CubaCuhre(), reltol = 1e-3, abstol = 1e-3)