Uncertain.jl

Important

Handle uncertain values with ease and performance!

The most common case is numbers with measurement errors. Uncertain.jl only exports the ±ᵤ operator and the U module that contains other useful symbols:

julia> 1 ±ᵤ 0.1  # not `±` so that not to clash with the popular `IntervalSets.jl` package
1.0 ± 0.1

julia> typeof(1 ±ᵤ 0.1)
Uncertain.ValueReal{Float64, Float64}

julia> U.value(1 ±ᵤ 0.1)
1.0

julia> U.uncertainty(1 ±ᵤ 0.1)
0.1

The fundamental design difference of Uncertain.jl, compared to other Julia packages in this field like Measurements.jl and MonteCarloMeasurements.jl, is low overhead. It handles huge datasets of values with uncertainties. They occupy only 2x more memory than regular values, and have a performance overhead of only a factor of a few.

julia> n = 10^6
julia> x = rand(n)
julia> xu = x .±ᵤ 0.1

julia> Base.summarysize(x)
8000040

julia> Base.summarysize(xu)
16000040

julia> @b x .+ 1
482.584 μs (4 allocs: 7.629 MiB)

julia> @b xu .+ 1
1.201 ms (4 allocs: 15.259 MiB)

Other packages tend to have orders-of-magnitude overhead: Measurements.jl because they handle linear correlations, and MonteCarloMeasurements.jl because they use Monce-Carlo samples to represent uncertainties.

Uncertain.jl provides integrations with other parts of the Julia ecosystem:

• Conversions to and from IntervalSets.jl, Measurements.jl and MonteCarloMeasurements.jl objects
• Uncertain.Values with Unitful.jl quantities inside support the Unitful.jl interface
• Plotting works with Makie, you should be able to pass uncertain values to any recipe where it makes sense

The ultimate goal of Uncertain.jl is to support arbitrary uncertainty specifications, like asymmetric errors, intervals, or more complex distributions. All within a single uniform interface.

As said above, other packages have a much higher performance overhead, but they have other advantages over Uncertain.jl. In particular, here we only handle operations on independent uncertain values. All functions that involve only one uncertain number like exp(x::Uncertain.Value) or x::Uncertain.Value + y::Float64 are automatically correct as there are no dependencies possible. Computing multivariate functions like x::Uncertain.Value + y::Uncertain.Value correctly requires accounting for correlations in the general case; we do not do that here, and trying to evalue such an operation fails by default:

julia> x = 1 ±ᵤ 0.1
julia> y = 2 ±ᵤ 0.5

julia> x + y
ERROR: The `+` operation is only correct for independent `Uncertain.Value`s, and we have no way to prove the independence automatically.
Set `Uncertain.assume_independent() = true` to execute such functions.

As explained in the error message, there's a flag to enable the independence assumption for multivariate operations:

julia> Uncertain.assume_independent() = true

julia> x + y
3.0 ± 0.5099019513592785