Fix adjoint for ChangeOfVariables (#246)

* better buffer docstring

* test for ChangeOfVariables rrule

* fix ChangeOfVariables rrule

* typo

* rephrase

* test an affine change of variables

* format

ext/IntegralsZygoteExt.jl

@@ -13,35 +13,20 @@ end
 ChainRulesCore.@non_differentiable Integrals.checkkwargs(kwargs...)
 ChainRulesCore.@non_differentiable Integrals.isinplace(f, args...)    # fixes #99
 ChainRulesCore.@non_differentiable Integrals.init_cacheval(alg, prob)
+ChainRulesCore.@non_differentiable Integrals.substitute_f(args...) # use ∂f/∂p instead
+ChainRulesCore.@non_differentiable Integrals.substitute_v(args...) # TODO for ∂f/∂u
+ChainRulesCore.@non_differentiable Integrals.substitute_bv(args...) # TODO for ∂f/∂u
 
-function ChainRulesCore.rrule(::typeof(Integrals.__solve), cache::Integrals.IntegralCache,
-        alg::Integrals.ChangeOfVariables, sensealg, udomain, p;
-        kwargs...)
-    _cache, vdomain = Integrals._change_variables(cache, alg, sensealg, udomain, p)
-    sol, back = Zygote.pullback((args...) -> Integrals.__solve(args...; kwargs...),
-        _cache, alg.alg, sensealg, vdomain, p)
-    function change_of_variables_pullback(Δ)
-        return (NoTangent(), back(Δ)...)
+# TODO move this adjoint to SciMLBase
+function ChainRulesCore.rrule(
+        ::typeof(SciMLBase.build_solution), prob::IntegralProblem, alg, u, resid; kwargs...)
+    function build_integral_solution_pullback(Δ)
+        return NoTangent(), NoTangent(), NoTangent(), Δ, NoTangent()
     end
-    prob = Integrals.build_problem(cache)
-    _sol = SciMLBase.build_solution(
-        prob, alg.alg, sol.u, sol.resid, chi = sol.chi, retcode = sol.retcode, stats = sol.stats)
-    return _sol, change_of_variables_pullback
+    return SciMLBase.build_solution(prob, alg, u, resid; kwargs...),
+    build_integral_solution_pullback
 end
 
-# we will need to implement the following adjoints when we compute ∂f/∂u
-function ChainRulesCore.rrule(::typeof(Integrals.substitute_v), args...)
-    function substitute_v_pullback(_)
-        return NoTangent(), ntuple(_ -> NoTangent(), length(args))...
-    end
-    return Integrals.substitute_v(args...), substitute_v_pullback
-end
-function ChainRulesCore.rrule(::typeof(Integrals.substitute_bv), args...)
-    function substitute_bv_pullback(_)
-        return NoTangent(), ntuple(_ -> NoTangent(), length(args))...
-    end
-    return Integrals.substitute_bv(args...), substitute_bv_pullback
-end
 function ChainRulesCore.rrule(::typeof(Integrals._evaluate!), f, y, u, p)
     out, back = Zygote.pullback(y, u, p) do y, u, p
         b = Zygote.Buffer(y)
@@ -51,6 +36,16 @@ function ChainRulesCore.rrule(::typeof(Integrals._evaluate!), f, y, u, p)
     out, Δ -> (NoTangent(), NoTangent(), back(Δ)...)
 end
 
+function ChainRulesCore.rrule(::typeof(Integrals.u2t), lb, ub)
+    tlb, tub = out = Integrals.u2t(lb, ub)
+    function u2t_pullback(Δ)
+        _, lbjac = Integrals.t2ujac(tlb, lb, ub)
+        _, ubjac = Integrals.t2ujac(tub, lb, ub)
+        return NoTangent(), Δ[1] / lbjac, Δ[2] / ubjac
+    end
+    return out, u2t_pullback
+end
+
 function ChainRulesCore.rrule(::typeof(Integrals.__solvebp), cache, alg, sensealg, domain,
         p;
         kwargs...)

src/Integrals.jl

@@ -78,14 +78,6 @@ end
 
 function __solve(cache::IntegralCache, alg::ChangeOfVariables, sensealg, udomain, p;
         kwargs...)
-    _cache, vdomain = _change_variables(cache, alg, sensealg, udomain, p)
-    sol = __solve(_cache, alg.alg, sensealg, vdomain, p; kwargs...)
-    prob = build_problem(cache)
-    return SciMLBase.build_solution(
-        prob, alg.alg, sol.u, sol.resid, chi = sol.chi, retcode = sol.retcode, stats = sol.stats)
-end
-
-function _change_variables(cache, alg, sensealg, udomain, p)
     cacheval = cache.cacheval.alg
     g, vdomain = alg.fu2gv(cache.f, udomain)
     _cache = IntegralCache(Val(isinplace(g)),
@@ -97,7 +89,10 @@ function _change_variables(cache, alg, sensealg, udomain, p)
         sensealg,
         cache.kwargs,
         cacheval)
-    return _cache, vdomain
+    sol = __solve(_cache, alg.alg, sensealg, vdomain, p; kwargs...)
+    prob = build_problem(cache)
+    return SciMLBase.build_solution(
+        prob, alg.alg, sol.u, sol.resid, chi = sol.chi, retcode = sol.retcode, stats = sol.stats)
 end
 
 function get_prototype(prob::IntegralProblem)

src/algorithms.jl

@@ -5,8 +5,10 @@ One-dimensional Gauss-Kronrod integration from QuadGK.jl.
 This method also takes the optional arguments `order` and `norm`.
 Which are the order of the integration rule
 and the norm for calculating the error, respectively.
-Lastly, the `buffer` keyword, if set, will allocate a buffer to reuse
-for multiple integrals, which may require evaluating the integrand.
+Lastly, the `buffer` keyword, if set (e.g. `buffer=true`), will allocate a buffer to reuse
+for multiple integrals and may require evaluating the integrand unless an
+`integrand_prototype` is provided. Unlike the `segbuf` keyword to `quadgk`, you do not
+allocate the buffer as this is handled automatically.
 
 ## References
 
@@ -35,8 +37,10 @@ This method also takes the optional arguments `initdiv` and `norm`.
 Which are the initial number of segments
 each dimension of the integration domain is divided into,
 and the norm for calculating the error, respectively.
-Lastly, the `buffer` keyword, if set, will allocate a buffer to reuse
-for multiple integrals, which may require evaluating the integrand.
+Lastly, the `buffer` keyword, if set (e.g. `buffer=true`), will allocate a buffer to reuse
+for multiple integrals and may require evaluating the integrand unless an
+`integrand_prototype` is provided. Unlike the `buffer` keyword to `hcubature/hquadrature`,
+you do not allocate the buffer as this is handled automatically.
 
 ## References
 

src/infinity_handling.jl

@@ -29,7 +29,7 @@ function substitute_f(f::IntegralFunction{true}, v2ujac, lb, ub)
     vol = prod((ub - lb) / 2) # just to get the type of the jacobian determinant
     IntegralFunction{true}(prototype * vol) do y, v, p
         u, jac = substitute_v(v2ujac, v, lb, ub)
-        _y = _evaluate!(f, prototype, u, p)
+        _y = _evaluate!(_f, prototype, u, p)
         y .= _y .* jac
         return
     end

test/derivative_tests.jl

@@ -356,3 +356,30 @@ for (alg, req) in pairs(alg_req), (j, f) in enumerate(integrands),
     do_tests(; f = bfiip, scalarize, lb = ones(dim), ub = 3ones(dim),
         p = [2.0i for i in 1:nout], alg, abstol, reltol)
 end
+
+@testset "ChangeOfVariables rrule" begin
+    alg = QuadGKJL()
+    # test a simple u-substitution of x = 2.7u + 1.3
+    talg = Integrals.ChangeOfVariables(alg) do f, domain
+        if f isa IntegralFunction{false}
+            IntegralFunction((x, p) -> f((x - 1.3) / 2.7, p) / 2.7),
+            map(x -> 1.3 + 2.7x, domain)
+        else
+            error("not implemented")
+        end
+    end
+    testf = (f, lb, ub, p, alg) -> begin
+        prob = IntegralProblem(f, (lb, ub), p)
+        solve(prob, alg; abstol, reltol).u
+    end
+    _testf = (x, p) -> x^2 * p
+    lb, ub, p = 1.0, 5.0, 2.0
+    sol = Zygote.withgradient((args...) -> testf(_testf, args..., alg), lb, ub, p)
+    tsol = Zygote.withgradient((args...) -> testf(_testf, args..., talg), lb, ub, p)
+    @test sol.val ≈ tsol.val
+    # Fundamental theorem of Calculus part 1
+    @test sol.grad[1] ≈ tsol.grad[1] ≈ -_testf(lb, p)
+    @test sol.grad[2] ≈ tsol.grad[2] ≈ _testf(ub, p)
+    # This is to check ∂p
+    @test sol.grad[3] ≈ tsol.grad[3]
+end