More beautiful display of :unknown

[Kolaru]

As discussed in the JuliaInterval call, this PR reintroduces showing more information for :unknown roots in vectors, with fancy connector to group the information.

However, this information is still hidden if the IOContext is :compact, like for matrices:

julia> f(x) = (x < 1) ? x : (x - 2)^2 * (x - 3)
f (generic function with 1 method)

julia> rts = roots(f, interval(-5, 5))
4-element Vector{Root{Interval{Float64}}}:
 Root([0.0, 0.0]_com, :unique)
 Root([1.0, 1.0]_com, :unknown)
 ├ Not converged: region size smaller than the tolerance
 ├ Warning: error encountered during computation (use showerror(root.error) to see the whole stacktrace)
 └ InconclusiveBooleanOperation: The operation `[1.0, 1.0]_com < [1.0, 1.0]_com_NG` cannot be determined unambiguously. See the documentation for more information. See also `strictprecedes`.
 Root([2.0, 2.0]_com_NG, :unknown)
 └ Not converged: region size smaller than the tolerance
 Root([3.0, 3.0]_com_NG, :unique)

julia> reshape(rts, 2, 2)
2×2 Matrix{Root{Interval{Float64}}}:
 Root([0.0, 0.0]_com, :unique)   Root([2.0, 2.0]_com_NG, :unknown)
 Root([1.0, 1.0]_com, :unknown)  Root([3.0, 3.0]_com_NG, :unique)

@dpsanders @OlivierHnt

[github-actions]

Benchmark Results

	master	0bcfd9b...	master / 0bcfd9b...
10 dimensional/IntervalRootFinding.Krawczyk	3.13 ± 0.041 s	3.13 ± 0.045 s	0.998 ± 0.019
10 dimensional/IntervalRootFinding.Newton	48 s	48.2 s	0.994
Dietmar-Ratz/Dietmar-Ratz 1/IntervalRootFinding.Krawczyk	3.58 ± 0.09 μs	3.63 ± 0.09 μs	0.986 ± 0.035
Dietmar-Ratz/Dietmar-Ratz 1/IntervalRootFinding.Newton	3.57 ± 0.08 μs	3.61 ± 0.091 μs	0.989 ± 0.033
Dietmar-Ratz/Dietmar-Ratz 2/IntervalRootFinding.Krawczyk	0.102 ± 0.0013 ms	0.102 ± 0.0011 ms	0.998 ± 0.017
Dietmar-Ratz/Dietmar-Ratz 2/IntervalRootFinding.Newton	0.238 ± 0.012 ms	0.239 ± 0.011 ms	0.996 ± 0.069
Dietmar-Ratz/Dietmar-Ratz 3/IntervalRootFinding.Krawczyk	0.252 ± 0.014 ms	0.252 ± 0.013 ms	1 ± 0.075
Dietmar-Ratz/Dietmar-Ratz 3/IntervalRootFinding.Newton	0.177 ± 0.012 ms	0.179 ± 0.011 ms	0.99 ± 0.09
Dietmar-Ratz/Dietmar-Ratz 4/IntervalRootFinding.Krawczyk	0.0518 ± 0.00076 ms	0.0506 ± 0.00061 ms	1.02 ± 0.019
Dietmar-Ratz/Dietmar-Ratz 4/IntervalRootFinding.Newton	0.0345 ± 0.0017 ms	0.0336 ± 0.001 ms	1.03 ± 0.059
Dietmar-Ratz/Dietmar-Ratz 5/IntervalRootFinding.Krawczyk	3.46 ± 0.11 μs	3.46 ± 0.12 μs	1 ± 0.047
Dietmar-Ratz/Dietmar-Ratz 5/IntervalRootFinding.Newton	3.47 ± 0.12 μs	3.43 ± 0.12 μs	1.01 ± 0.05
Dietmar-Ratz/Dietmar-Ratz 6/IntervalRootFinding.Krawczyk	13.2 ± 0.2 μs	13.1 ± 0.24 μs	1.01 ± 0.024
Dietmar-Ratz/Dietmar-Ratz 6/IntervalRootFinding.Newton	19.7 ± 0.34 μs	19.8 ± 0.39 μs	0.996 ± 0.026
Dietmar-Ratz/Dietmar-Ratz 7/IntervalRootFinding.Krawczyk	3.67 ± 0.099 μs	3.64 ± 0.08 μs	1.01 ± 0.035
Dietmar-Ratz/Dietmar-Ratz 7/IntervalRootFinding.Newton	3.67 ± 0.099 μs	3.64 ± 0.1 μs	1.01 ± 0.039
Dietmar-Ratz/Dietmar-Ratz 9/IntervalRootFinding.Krawczyk	3.98 ± 0.09 μs	3.96 ± 0.09 μs	1 ± 0.032
Dietmar-Ratz/Dietmar-Ratz 9/IntervalRootFinding.Newton	3.96 ± 0.1 μs	3.98 ± 0.091 μs	0.995 ± 0.034
Rastigrin stationary points/IntervalRootFinding.Krawczyk	0.147 ± 0.002 s	0.146 ± 0.0016 s	1 ± 0.018
Rastigrin stationary points/IntervalRootFinding.Newton	0.139 ± 0.0014 s	0.138 ± 0.00094 s	1 ± 0.012
Smiley/Smiley and Chun (2001), Example 2.2/IntervalRootFinding.Krawczyk	2.7 ± 0.051 ms	2.68 ± 0.053 ms	1.01 ± 0.027
Smiley/Smiley and Chun (2001), Example 2.2/IntervalRootFinding.Newton	2.16 ± 0.041 ms	2.1 ± 0.038 ms	1.03 ± 0.027
Smiley/Smiley and Chun (2001), Example 5.2/IntervalRootFinding.Krawczyk	0.037 ± 0.0034 s	0.0361 ± 0.0033 s	1.02 ± 0.13
Smiley/Smiley and Chun (2001), Example 5.2/IntervalRootFinding.Newton	0.0317 ± 0.0032 s	31.1 ± 3.2 ms	1.02 ± 0.15
Smiley/Smiley and Chun (2001), Example 5.4/IntervalRootFinding.Krawczyk	1.9 ± 0.032 ms	1.88 ± 0.03 ms	1.01 ± 0.023
Smiley/Smiley and Chun (2001), Example 5.4/IntervalRootFinding.Newton	1.8 ± 0.026 ms	1.76 ± 0.029 ms	1.02 ± 0.023
Smiley/Smiley and Chun (2001), Example 5.5/IntervalRootFinding.Krawczyk	5.5 s	5.48 s	1
Smiley/Smiley and Chun (2001), Example 5.5/IntervalRootFinding.Newton	5.04 s	5.01 s	1.01
time_to_load	0.397 ± 0.0064 s	0.401 ± 0.011 s	0.99 ± 0.031

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[OlivierHnt]

Really nice! There are only a few doctests to fix.

[Kolaru]

As discussed during the JuliaInterval call, this can be shipped :)