Integrals with incorrect dimensions for Unitful input

[Ickaser]

Describe the bug 🐞

An interpolator with Unitful input errors when integration is attempted.

Minimal Reproducible Example 👇

using Unitful
using DataInterpolations
A = ConstantInterpolation(rand(5)u"m", (1:5)u"s")
DataInterpolations.integral(A, 4u"s")

Error & Stacktrace ⚠️

ERROR: ArgumentError: zero(Quantity{Float64}) not defined.
Stacktrace:
 [1] zero(x::Type{Quantity{Float64}})
   @ Unitful C:\Users\iwheeler\.julia\packages\Unitful\nwwOk\src\quantities.jl:370
 [2] integral(A::ConstantInterpolation{…}, t1::Quantity{…}, t2::Quantity{…})
   @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\zmpkg\src\integrals.jl:21
 [3] integral(A::ConstantInterpolation{…}, t::Quantity{…})
   @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\zmpkg\src\integrals.jl:2
 [4] top-level scope
   @ REPL[19]:1
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

Occurs in DataInterpolations 7.1.0.

Suggested fix

DataInterpolations.jl/src/interpolation_utils.jl

Lines 192 to 200 in 1d10244

	function cumulative_integral(A, cache_parameters)
	if cache_parameters && hasmethod(_integral, Tuple{typeof(A), Number, Number, Number})
	integral_values = _integral.(
	Ref(A), 1:(length(A.t) - 1), A.t[1:(end - 1)], A.t[2:end])
	cumsum(integral_values)
	else
	promote_type(eltype(A.u), eltype(A.t))[]
	end
	end

promote_type(typeof(0.5u"m"), typeof(1u"s"))

yields a generic Quantity{Float64} without any units, since there is no way to decide what units the result type should have. A reasonable alternative to using promote_type might be

typeof(zero(eltype(A.u) * zero(eltype(A.t)))

which returns a concrete type with appropriate units for integration.