ForwardDiff directly on all non-C solvers

docs/src/basics/FAQ.md

@@ -6,7 +6,7 @@ The in-place interface allows evaluating vector-valued integrands without
 allocating an output array. This can be beneficial for reducing allocations when
 integrating many functions simultaneously or to make use of existing in-place
 code. However, note that not all algorithms use in-place operations under the
-hood, i.e. `HCubatureJL()`, and may still allocate.
+hood, i.e. [`HCubatureJL`](@ref), and may still allocate.
 
 You can construct an `IntegralFunction(f, prototype)`, where `f` is of the form
 `f(y, u, p)` where `prototype` is of the desired type and shape of `y`.
@@ -22,16 +22,17 @@ different points, which maximizes the parallelism for a given algorithm.
 You can construct an out-of-place `BatchIntegralFunction(bf)` where `bf` is of
 the form `bf(u, p) = stack(x -> f(x, p), eachslice(u; dims=ndims(u)))`, where
 `f` is the (unbatched) integrand.
+For interoperability with as many algorithms as possible, it is important that your out-of-place batch integrand accept an **empty** array of quadrature points and still return an output with a size and type consistent with the non-empty case.
 
 You can construct an in-place `BatchIntegralFunction(bf, prototype)`, where `bf`
 is of the form `bf(y, u, p) = foreach((y,x) -> f(y,x,p), eachslice(y, dims=ndims(y)), eachslice(x, dims=ndims(x)))`.
 
 Note that not all algorithms use in-place batched operations under the hood,
-i.e. `QuadGKJL()`.
+i.e. [`QuadGKJL`](@ref).
 
 ## What should I do if my solution is not converged?
 
-Certain algorithms, such as `QuadratureRule` used a fixed number of points to
+Certain algorithms, such as [`QuadratureRule`](@ref) used a fixed number of points to
 calculate an integral and cannot provide an error estimate. In this case, you
 have to increase the number of points and check the convergence yourself, which
 will depend on the accuracy of the rule you choose.
@@ -47,7 +48,7 @@ precision arithmetic may help.
 
 ## How can I integrate arbitrarily-spaced data?
 
-See `SampledIntegralProblem`.
+See [`SampledIntegralProblem`](@ref).
 
 ## How can I integrate on arbitrary geometries?
 
@@ -59,6 +60,13 @@ because that is what lower-level packages implement.
 Fixed quadrature rules from other packages can be used with `QuadratureRule`.
 Otherwise, feel free to open an issue or pull request.
 
+## My integrand works with algorithm X but fails on algorithm Y
+
+While bugs are not out of the question, certain algorithms, especially those implemented in C, are not compatible with arbitrary Julia types and have to return specific numeric types or arrays thereof.
+In some cases, such as [`ArblibJL`](@ref), it is also expected that the integrand work with a custom quadrature point type.
+Moreover, some algorithms, such as [`VEGAS`](@ref), only support scalar integrands.
+For more details see the [solver page](@ref solvers).
+
 ## Can I take derivatives with respect to the limits of integration?
 
 Currently this is not implemented.

ext/IntegralsForwardDiffExt.jl

@@ -3,27 +3,37 @@ using Integrals
 isdefined(Base, :get_extension) ? (using ForwardDiff) : (using ..ForwardDiff)
 ### Forward-Mode AD Intercepts
 
-#= Direct AD on solvers with QuadGK and HCubature
-# incompatible with iip since types must change
-function Integrals.__solvebp(cache, alg::QuadGKJL, sensealg, domain,
-        p::AbstractArray{<:ForwardDiff.Dual{T, V, P}, N};
-        kwargs...) where {T, V, P, N}
-    Integrals.__solvebp_call(cache, alg, sensealg, domain, p; kwargs...)
-end
+# Default to direct AD on solvers
+function Integrals.__solvebp(cache, alg, sensealg, domain,
+        p::Union{D,AbstractArray{<:D}};
+        kwargs...) where {T, V, P, D<:ForwardDiff.Dual{T, V, P}}
 
-function Integrals.__solvebp(cache, alg::HCubatureJL, sensealg, domain,
-        p::AbstractArray{<:ForwardDiff.Dual{T, V, P}, N};
-        kwargs...) where {T, V, P, N}
-    Integrals.__solvebp_call(cache, alg, sensealg, domain, p; kwargs...)
+    if isinplace(cache.f)
+        prototype = cache.f.integrand_prototype
+        elt = eltype(prototype)
+        ForwardDiff.can_dual(elt) || throw(ArgumentError("ForwardDiff of in-place integrands only supports prototypes with real elements"))
+        dprototype = similar(prototype, replace_dualvaltype(D, elt))
+        df = if cache.f isa BatchIntegralFunction
+            BatchIntegralFunction{true}(cache.f.f, dprototype)
+        else
+            IntegralFunction{true}(cache.f.f, dprototype)
+        end
+        prob = Integrals.build_problem(cache)
+        dprob = remake(prob, f = df)
+        dcache = init(dprob, alg; sensealg = sensealg, do_inf_transformation=Val(false), kwargs...)
+        Integrals.__solvebp_call(dcache, alg, sensealg, domain, p; kwargs...)
+    else
+        Integrals.__solvebp_call(cache, alg, sensealg, domain, p; kwargs...)
+    end
 end
-=#
+
 
 # TODO: add the pushforward for derivative w.r.t lb, and ub (and then combinations?)
 
 # Manually split for the pushforward
-function Integrals.__solvebp(cache, alg, sensealg, domain,
-        p::Union{D, AbstractArray{<:D}};
-        kwargs...) where {T, V, P, D <: ForwardDiff.Dual{T, V, P}}
+function Integrals.__solvebp(cache, alg::Integrals.AbstractIntegralCExtensionAlgorithm, sensealg, domain,
+        p::Union{D,AbstractArray{<:D}};
+        kwargs...) where {T, V, P, D<:ForwardDiff.Dual{T, V, P}}
 
     # we need the output type to avoid perturbation confusion while unwrapping nested duals
     # We compute a vector-valued integral of the primal and dual simultaneously
@@ -73,6 +83,7 @@ function Integrals.__solvebp(cache, alg, sensealg, domain,
         end
     end
 
+    DT <: Real || throw(ArgumentError("differentiating algorithms in C"))
     ForwardDiff.can_dual(elt) || ForwardDiff.throw_cannot_dual(elt)
     rawp = p isa D ? reinterpret(V, [p]) : copy(reinterpret(V, vec(p)))
 

src/algorithms_extension.jl

@@ -1,8 +1,9 @@
 ## Extension Algorithms
 
 abstract type AbstractIntegralExtensionAlgorithm <: SciMLBase.AbstractIntegralAlgorithm end
+abstract type AbstractIntegralCExtensionAlgorithm <: AbstractIntegralExtensionAlgorithm end
 
-abstract type AbstractCubaAlgorithm <: AbstractIntegralExtensionAlgorithm end
+abstract type AbstractCubaAlgorithm <: AbstractIntegralCExtensionAlgorithm end
 
 """
     CubaVegas()
@@ -152,7 +153,7 @@ function CubaCuhre(; flags = 0, minevals = 0, key = 0)
     return CubaCuhre(flags, minevals, key)
 end
 
-abstract type AbstractCubatureJLAlgorithm <: AbstractIntegralExtensionAlgorithm end
+abstract type AbstractCubatureJLAlgorithm <: AbstractIntegralCExtensionAlgorithm end
 
 """
     CubatureJLh(; error_norm=Cubature.INDIVIDUAL)
@@ -219,7 +220,7 @@ documentation for additional details the algorithm arguments and on implementing
 high-precision integrands. Additionally, the error estimate is included in the return value
 of the integral, representing a ball.
 """
-struct ArblibJL{O} <: AbstractIntegralExtensionAlgorithm
+struct ArblibJL{O} <: AbstractIntegralCExtensionAlgorithm
     check_analytic::Bool
     take_prec::Bool
     warn_on_no_convergence::Bool