Derivative with VEGAS: ERROR: AssertionError: prob.nout == 1

[KirillZubov]

using Quadrature, ForwardDiff, FiniteDiff, Zygote, Cuba

f(x,p) = sum(sin.(x .* p))
lb = ones(2)
ub = 3ones(2)
p = [1.5,2.0]
prob = QuadratureProblem(f,lb,ub,p)
solve(prob,VEGAS(),reltol=1e-6,abstol=1e-6,maxiters =1000)[1]

function testf(p)
    prob = QuadratureProblem(f,lb,ub,p)
    sin(solve(prob,VEGAS(),reltol=1e-6,abstol=1e-6,maxiters =1000)[1])
end
dp1 = Zygote.gradient(testf,p)
#julia> ERROR: AssertionError: prob.nout == 1
dp2 = FiniteDiff.finite_difference_gradient(testf,p)
dp3 = ForwardDiff.gradient(testf,p)
#julia> ERROR: AssertionError: prob.nout == 1

[lxvm]

@ChrisRackauckas I think this issue can be closed because it is upstream. The VEGAS implementation provided by MonteCarloIntegration.jl only supports integrating scalars, so the vector-valued gradient is not possible without doing a separate integral for each element of the gradient, which is not ideal.

However, if we change the implementation to the VEGAS routine in https://github.com/numericalEFT/MCIntegration.jl, it would allow vector-valued integrands.

If I update the MWE to this

using Integrals, ForwardDiff, FiniteDiff, Zygote, Cuba

f(x,p) = sum(sin.(x .* p))
lb = ones(2)
ub = 3ones(2)
p = [1.5,2.0]
prob = IntegralProblem(f,lb,ub,p)
solve(prob,VEGAS(),reltol=1e-6,abstol=1e-6,maxiters =1000)[1]

function testf(p)
    prob = IntegralProblem(f,lb,ub,p)
    sin(solve(prob,VEGAS(),reltol=1e-6,abstol=1e-6,maxiters =1000)[1])
end
dp1 = Zygote.gradient(testf,p)

The error message I get with Integrals@4 with MonteCarloIntegration@0.0.3 is now

ERROR: LoadError: AssertionError: VEGAS only supports Float64-valued scalar integrands

[ChrisRackauckas]

We should probably wrap MCIntegration.jl and not recommend MonteCarloIntegration. MonteCarloIntegration doesn't perform very well in practice.