SciML / Integrals.jl

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization
https://docs.sciml.ai/Integrals/stable/
MIT License
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Integrating a vector valued out-of-place integrand returns a scalar #249

Open Sleort opened 5 months ago

Sleort commented 5 months ago

Describe the bug 🐞

A 1D integral of a vector valued out-of-place function returns a scalar, even when a vector valued integrand prototype is provided. The equivalent in-place problem works as expected.

Expected behavior

When a vector valued integrand prototype is provided, the solution should be the same for out-of-place and in-place integrands.

Minimal Reproducible Example πŸ‘‡

This works as expected:

using Integrals

integrand_prototype = zeros(2)

#In-place integrand
f!(y,u,p) = @. y = exp(-u^2)
test! = IntegralFunction(f!, integrand_prototype)
solve(IntegralProblem(test!, -Inf, Inf), QuadGKJL()).u #Vector return value, as expected

while this doesn't:

#Out-of-place integrand
f(u,p) = @. exp(-u^2)
test = IntegralFunction(f, integrand_prototype)
solve(IntegralProblem(test, -Inf, Inf), QuadGKJL()).u #Scalar return value!?

Environment

Status `/tmp/jl_pPHahC/Project.toml`
  [de52edbc] Integrals v4.4.1
Status `/tmp/jl_pPHahC/Manifest.toml`
  [47edcb42] ADTypes v1.2.1
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [4fba245c] ArrayInterface v7.10.0
  [49dc2e85] Calculus v0.5.1
  [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.4
  [34da2185] Compat v4.15.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.5
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [31c24e10] Distributions v0.25.108
  [ffbed154] DocStringExtensions v0.9.3
  [fa6b7ba4] DualNumbers v0.6.8
  [4e289a0a] EnumX v1.0.4
  [e2ba6199] ExprTools v0.1.10
  [1a297f60] FillArrays v1.11.0
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.1.6
  [19dc6840] HCubature v1.6.0
  [34004b35] HypergeometricFunctions v0.3.23
  [18e54dd8] IntegerMathUtils v0.1.2
  [de52edbc] Integrals v4.4.1
  [3587e190] InverseFunctions v0.1.14
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [73f95e8e] LatticeRules v0.0.1
  [2ab3a3ac] LogExpFunctions v0.3.27
  [1914dd2f] MacroTools v0.5.13
  [e1d29d7a] Missings v1.2.0
  [4886b29c] MonteCarloIntegration v0.2.0
  [77ba4419] NaNMath v1.0.2
  [bac558e1] OrderedCollections v1.6.3
  [90014a1f] PDMats v0.11.31
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [27ebfcd6] Primes v0.5.6
  [43287f4e] PtrArrays v1.2.0
  [1fd47b50] QuadGK v2.9.4
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  [ae029012] Requires v1.3.0
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  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
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  [82ae8749] StatsAPI v1.7.0
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Julia Version 1.10.3
Commit 0b4590a5507 (2024-04-30 10:59 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 Γ— Intel(R) Core(TM) i7-10875H CPU @ 2.30GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
lxvm commented 5 months ago

Hi,

To me it looks like your integrand is behaving as expected because QuadGK.jl gives your integrand a scalar, u, and so your broadcasting function f will also return a scalar because there is nothing to give it a shape, unlike f! which gets its shape from y. Does this help?

Sleort commented 5 months ago

Hmm...Yeah... I guess I just misunderstood the documentation saying that

If integrand_prototype is present for either in-place or out-of-place integrands it is used to infer the return type of the integrand.

In other words, I imagined integrand_prototype would provide the shape...

Maybe cases like this one, i.e. when typeof(solution(...).u) != typeof(integrand_prototype), should error instead?

lxvm commented 5 months ago

Yes, we use integrand_prototype to determine the type and shape of the integrand in some cases, in particular for C libraries or to pre-allocate workspaces with correct types for algorithms. Also, we currently assume the output of the user's function is consistent with the prototype, but we don't assert it because the type of the solution may depend on the library used. Any pr to check for correctness would be welcome as long as the type assertions don't incur runtime overhead for type-stable use-cases.