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Piecewise functions #655

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dpsanders opened this issue May 26, 2024 · 5 comments · May be fixed by #689
Open

Piecewise functions #655

dpsanders opened this issue May 26, 2024 · 5 comments · May be fixed by #689

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@dpsanders
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dpsanders commented May 26, 2024 •
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Here's a possible implementation for piecewise functions:

using IntervalArithmetic
using IntervalArithmetic.Symbols # to use the constructor `..`

# represents a piecewise 1D function
struct Piecewise{T <: Tuple}
    pieces::T 
end

Piecewise(pairs...) = Piecewise(pairs)

function (piecewise::Piecewise)(X::Interval)
    return reduce(hull, f(intersect_interval(X, region)) for (region, f) ∈ piecewise.pieces)
end

f = Piecewise(
        0..3 => x -> x + interval(1),
        3..6 => identity,
        6..Inf => x -> x + interval(2)
)

f(2..5)

Then Heaviside should be definable with

H = Piecewise(-Inf..0 => zero, 0..Inf => one)

but that is not working for me right now 🤔 E.g. it gives

julia> H(1..1)
[0.0, 1.0]_trv

whereas it should give [1, 1].
@dpsanders
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Ah that's because

julia> zero(emptyinterval())
[0.0, 0.0]_com

I have an idea for how to make a default 0 value.

@dpsanders
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dpsanders commented May 26, 2024 •
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This version works:

function (piecewise::Piecewise)(X::Interval)
    return reduce(hull, begin
                            val = intersect_interval(X, region)
                            isempty_interval(val) ? val : f(val)
                        end
                    for (region, f) ∈ piecewise.pieces)
end

H = Piecewise(-Inf..0 => zero, 0..Inf => one)

@dpsanders
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It would probably be worth having a PiecewiseConstant too.

@dpsanders
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We also need to add the decoration of course.

@OlivierHnt
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OlivierHnt commented May 26, 2024 •
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This issue seems to supersede #653 and #654 no?

Also, with such a feature, implementing the Heaviside function would be even simpler than it already is so I am not sure it would warrant being defined inside the library.

This was referenced May 26, 2024
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This was referenced Nov 6, 2024
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@Kolaru Kolaru linked a pull request Nov 28, 2024 that will close this issue
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@OlivierHnt OlivierHnt linked a pull request Dec 12, 2024 that will close this issue
Implement piecewise function #689
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Implement piecewise function Kolaru/IntervalArithmetic.jl
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@dpsanders @OlivierHnt