Release 1.0

[OlivierHnt]

This PR aims to prepare the 1.0 release.

[dpsanders]

Very nice, thanks!

Whats the reason for removing @interval T a b?

[OlivierHnt]

SparseArrays seems to have a hook _iszero and _isnotzero to handle missing; we may be able to use this as well for intervals.

[OlivierHnt]

Whats the reason for removing @interval T a b?

Well that's just for consistency, since the method @interval a b is missing (I do not know how to implement it without conflicting with @interval T a)

[OlivierHnt]

Aqua tests are failing on Julia 1.10 due to method ambiguities with mul!.

[OlivierHnt]

I have removed the old functions which controlled the default behaviour for the flavor, matrix multiplication, the rounding, the power.
Now this is controlled by a configure(; rounding=:correct, flavor = :set_based, power = :fast, matmul = :fast) function.

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Attention: Patch coverage is 67.34694% with 16 lines in your changes missing coverage. Please review.

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Report is 26 commits behind head on master.

Files with missing lines	Patch %	Lines
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[OlivierHnt]

Note: maybe interval(1, 2) == interval(3, 4) can safely return false since there is no overlapping numbers (this means that == can only return true if the two intervals are identical singletons). Whatever is decided should also be applied to isapprox.

[lbenet]

The problem I see with the discussion around ==, <, >, iszero, etc, is that we are ending up defining methods by value, not by type; obviously, this touches type stability. The return type of these operators, if allowed, will be a Union{Bool, SomeError}, and while errors may be good and appreciated in certain cases, they also break the flow which may or may not be desired.

I think we could have them but within a submodule (e.g., Symbols). Then, we encourage the usage of isequal_interval, or if the submodule is loaded for these extensions, the user is concient of the subtleties, e.g. the returned union types. This proposal is to mimic the current usage of IntervalArithmetic.Symbols.

[Kolaru]

I think a reasonable philosophy for v1.0 is

• Interval act as much as a number as possible while keeping a guarantee of correctness. Which means that for them, we need to allow things like < and ==, but error when the operation is ill-defined as the pointwise extension of the function on number (e.g. (1..10) < (2..7) must be both true and false, and thus should error).
• BareInterval do not extend any properties of numbers. They are pure intervals, do not interface with numbers and, notably, do not support the pointwise extension of boolean functions.

It could be nice to have some in-between for specific applications. But I think it is reasonable for the time being to redirect users to use BareInterval if the extended functionalities are a concern.

[OlivierHnt]

Other things to do:

• check this PR against IntervalRootFinding.jl @Kolaru
• move det, eigvals, norm into a package extension

[OlivierHnt]

I have added the following definition in the ForwardDiff extension:

ForwardDiff.DiffRules._abs_deriv(x::Dual{T,<:Interval}) where {T} =
    Dual{T}(ForwardDiff.DiffRules._abs_deriv(value(x)), zero(partials(x)))

We now get the behaviour:

julia> using IntervalArithmetic, ForwardDiff

julia> g(x) = abs(x)^2
g (generic function with 1 method)

julia> a = ForwardDiff.hessian(v -> g(v[1]), [interval(0)])
1×1 Matrix{Interval{Float64}}:
 [0.0, 0.0]_trv_NG

julia> b = ForwardDiff.hessian(v -> g(v[1]), [interval(-1, 1)])
1×1 Matrix{Interval{Float64}}:
 [-2.0, 2.0]_trv_NG

julia> c = ForwardDiff.hessian(v -> g(v[1]), [interval(1)])
1×1 Matrix{Interval{Float64}}:
 [2.0, 2.0]_com_NG

julia> d = ForwardDiff.hessian(v -> g(v[1]), [interval(-1)])
1×1 Matrix{Interval{Float64}}:
 [2.0, 2.0]_com_NG

(it used to error before)

Obviously, the correct answer is $2$, and c and d are consistent.

• a is not correct due to us setting the derivative of abs at 0 to 0 (see the discussion Update abs diff rule to 0 at non-differentiable point JuliaDiff/DiffRules.jl#98 and our decision Derivative of abs(::Interval) #564).
• b is a bit peculiar and is probably due to a product operation similar to how interval(-1, 1) * interval(-1, 1) is different than interval(-1, 1)^2.

So a may be pretty bad; b is not ideal, but at least it contains the correct value $2$.
In both cases we have the trv decoration which indicates that the interval carries no meaningful information.

@Kolaru any thoughts? Could this break IntervalRootFinding.jl?
cc @agerlach

EDIT: now the derivative of abs at 0 returns $[-1, 1]$, see #703.

[OlivierHnt]

On this version of the 1.0 release, ==, < are defined and other functions such as in and issubset work.
Whenever we have non-thin intervals that are overlapping when calling == and <, an error is thrown.

julia> x = interval(1); y = interval(2); z = interval(2, 3)
[2.0, 3.0]_com

julia> x == y
false

julia> y == z
ERROR: ArgumentError: `==` is purposely not supported when the number is contained in the interval. See instead `isthin`

julia> z == z
ERROR: ArgumentError: `==` is purposely not supported when the intervals are overlapping. See instead `isequal_interval`

julia> x < y
true

julia> y < y
false

julia> z < z
ERROR: ArgumentError: `<` is purposely not supported when the intervals are overlapping. See instead `strictprecedes`

julia> y in z
ERROR: ArgumentError: `==` is purposely not supported when the number is contained in the interval. See instead `isthin`

julia> z in z
ERROR: ArgumentError: `==` is purposely not supported when the intervals are overlapping. See instead `isequal_interval`

julia> issubset(y, z)
ERROR: ArgumentError: `==` is purposely not supported when the number is contained in the interval. See instead `isthin`

julia> issubset(z, z)
ERROR: ArgumentError: `==` is purposely not supported when the intervals are overlapping. See instead `isequal_interval`

julia> interval(2) ≤ interval(2)
true

[OlivierHnt]

@Kolaru if you can double check the changes
We may still be missing some documentation, but we can add it in a separate PR.

[Kolaru]

@OlivierHnt I was a bit slow, but still double checked the last changes, and everything looks good to me.

It is really great we finally made it :D