Integrals.jl
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A common interface for quadrature and numerical integration for the SciML scientific machine learning organization
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)