Numerically Solving Integrals

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])))
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)