Make unique and filter results from Newton

[dpsanders]

No description provided.

[coveralls]

Coverage increased (+0.1%) to 93.467% when pulling 37ca468 on merge_newton_results into 6b29087 on master.

[lbenet]

Nice! Does this work with multiple roots?

[codecov-io]

Current coverage is 93.84%

Merging #156 into master will increase coverage by 0.49%

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+ Hits            885        900    +15   
+ Misses           63         59     -4   
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Powered by Codecov. Last updated by 6b29087...7ab3101

[dpsanders]

Yes!:

julia> f(x) = (x-1) * (x^2 - 2)^3 * (x^3 - 2)^4
julia> newton(f, -5..5.1, maxlevel=100)
ValidatedNumerics.RootFinding.Root{Float64}(Interval(-1.4142135623730954, -1.414213562373095),:unknown)
 ValidatedNumerics.RootFinding.Root{Float64}(Interval(1.0, 1.0),:unique)
 ValidatedNumerics.RootFinding.Root{Float64}(Interval(1.259921049894873, 1.2599210498948734),:unknown)
 ValidatedNumerics.RootFinding.Root{Float64}(Interval(1.414213562373095, 1.4142135623730954),:unknown)

[coveralls]

Coverage increased (+0.2%) to 93.548% when pulling e5e52fa on merge_newton_results into 6b29087 on master.

[coveralls]

Coverage increased (+0.2%) to 93.548% when pulling e5e52fa on merge_newton_results into 6b29087 on master.

[lbenet]

Very nice!!

[lbenet]

I think you should merge this right away!

[coveralls]

Coverage increased (+0.2%) to 93.535% when pulling e3fb739 on merge_newton_results into 6b29087 on master.

[coveralls]

Coverage increased (+0.5%) to 93.848% when pulling 7ab3101 on merge_newton_results into 6b29087 on master.

[lbenet]

I recall that we deliberately decided to use nextfloat(m) to make sure that the two intervals considered were somehow separated. (Same comment for newton.jl.) Can you explain the reason behind the change?

[dpsanders]

I think that the idea of adding nextfloat was a mistake. Conceptually, it is incorrect since it misses out the interval between the two floats (compare unums). From a practical point of view, the current version is better since it allows to check for a non-empty intersection to see if the two intervals are neighbours.

[dpsanders]

Tests are failing on 0.5 due to some recent upstream breakage, apparently in base Julia.
We could merge anyway though?

[lbenet]

Tests pass in 0.4, and the problems seem to me to be related to FixedSizeArrays and appear in tests related to IntervalBox. If you think it will take a long time to solve this, I agree to merge it.

[dpsanders]

Since it's not clear how long that might take to fix, I'm going to merge.